The Effect of Pressure Oscillations on Respiratory Performance

Transcription

1 The Effect of Pressure Oscllatos o Respratory Performace Praska Iderjeeth Reddy A thess submtted to Aucklad Uversty of Techology fulflmet of the degree of Doctor of Phlosophy Aucklad, New Zealad by Praska I. Reddy

2 DELARATIONS I hereby declare that I am the sole author of ths thess. I authorze the Aucklad Uversty of Techology to led ths thess to other sttutos or dvduals for the sole purpose of scholarly research Praska I. Reddy I further authorze the Aucklad Uversty of Techology to reproduce ths thess by photocopyg or by other meas, total or part, at the request of other sttutos or dvduals for the sole purpose of scholarly research. Praska I. Reddy

3 BORROWERS PAGE The Aucklad Uversty of Techology requres the sgatures of all people usg or photocopyg ths thess. Accordgly, all borrowers are requred to fll out ths page. Date Name Address Sgature

4 To my parets, Ider ad Prema Malal v

5 AKNOWLEDGEMENTS There are may people I would lke to formally thak for ther cotrbuto to ths thess. The frst ad most sgfcat beg my academc supervsor, Professor Ahmed Al-Jumaly, for hs dedcato, kowledge ad attetve supervso at every stage of ths research ad for the most credble support ad ecouragemet he has gve ot just to me but to all hs studets. I also owe a great deal to my dustral supervsor, Dr. Geoff Bold who made sure that I had the best avalable resources, trag ad specalzed support through hm ad other colleagues the feld. Your aalytcal approach ad humlty towards research, ad the world geeral, wll stay wth me always. I lke to ackowledge the Tertary Educato ommsso ad Fsher & Paykel Healthcare Ltd. for geerously fudg ths research. My thaks to Assocate Prof. Jae Pllow for provdg the -vvo data that served as the valdato for ths work ad to her, Prof. Ala Jobe ad ther team Perth for sharg ther clcal kowledge, gudace ad resources durg the amal trals. Also, I thak hrs Butcher ad hrsta Savlle for ther assstace durg ths tme. I m grateful to Davd Whte, Phl Lacey, Dr. Max Ramos, Ross Rechardt, Bradley Scott, hrs Whyburd ad Ya Wag from the School of Egeerg for the techcal expertse ad prorty that you attached to the project despte your busy schedules. Thak you to my fellow studets, Drs. Alex Du ad Robert Paxto, Gjs Ijpma, Joe El- Aklouk, Ha La ad Ashs Mookerj for your academc, techcal ad brotherly help throughout the years ad makg IBTE a all roud great place to be. O a persoal ote, Thak you to my relatves ad freds for always supportg ad ecouragg me to do my best. Thak you Arz, for beg a excellet proof reader. To my husbad ad sprato, Mural, who has had to share my burdes ad has bee costatly at my sde, a smple Thak you wll ot suffce. It s wth you that I share ths work. To Mum ad Dad, I hope that ths some small way makes up for the all the sacrfces you ve had to make for my educato ad happess. Fally, a quet thak you to God, for all the grace ad stregth you have gve me. I offer ths work to you. v

6 ABSTRAT Ths thess s amed at uderstadg the effectve operato of the Bubble PAP System whe treatg eoates wth respratory dstress sydrome (RDS). It s also amed at determg the effect that pressure oscllatos have o respratory performace terms of the work of breath (WOB) ad surfactat dyamcs. The prcple objectves were to: reate a orgal mult-compartmetal model of the eoatal lug that cludes compartmet-specfc ertace ad vscoelastcty for 8 day (premature) ad 4 day (ear-term) gestato lambs. Valdate the model wth expermetal data obtaed from clcal trals. Use the model to determe the effect of pressure oscllatos as produced by the Bubble PAP System o respratory performace. Determe the frequeces of oscllato that provde the optmal respratory support. Buld a surface teso model that smulates surface teso dyamcs a alveolus exposed to pressure oscllato frequeces the rage typcally produced by the Bubble PAP System. Valdate the surface teso model wth expermets coducted o a custom-bult pulsatg bubble surfactometer (PBS). To fulfll the frst four objectves, a mathematcal model of the eoatal ove lug was developed Smulk wth the Matlab evromet. Mechacal ad physcal parameters that were requred for the model were ether emprcally determed from measuremets o preterm lamb lugs or derved from the lterature. Smulatos were the performed to determe the effectveess of Bubble PAP ad the use of optmal frequeces eoatal resprato. To study the surface teso dyamcs, a PBS was costructed to study the effect of frequeces o a surfactat bubble whch smulated a alveolus. Modulated frequeces (0-70 Hz) were supermposed o the breath cycle at 3 dfferet ampltudes expressed as a percetage of the tdal volume (TV) excurso (5%TV,.5%TV ad 30%TV). A umercal model was also bult Matlab to characterze the surfactat behavour ad help determe the mechasms resposble for ay observed chages surface teso. v

7 The expermetal results ad computer smulatos resulted the followg coclusos: The model s able to accurately predct the respratory parameters at the arway opeg durg PAP ad Bubble PAP operato. The model shows the ablty to predct the ueve vetlato profles the eoatal lug. Both model predctos ad expermetal measuremets show the tred that the mechacal WOB s greater (mproved) durg vetlato uder Bubble PAP whe compared to PAP. Pressure oscllato frequeces whch show mproved WOB measures the 8 day gestato lamb lug were detfed as 9, 3, 8, 33, 44, 49, 54, 8, 88, 99, ad 3 Hz. Model predctos showed that the mprovemet WOB (due to mechacal effects) relatve to PAP-oly treatmet was -% whe troducg sgle frequeces at the geerator, but creased to 4-6% whe troducg mxed frequeces at the geerator ad 4-0% whe troducg mxed frequeces at the patet terface. It was show that the Bubble PAP System delvers frequeces smlar to the detfed optmal frequeces of the 8 day gestato lug (7 ad 3 Hz) whch cotrbute to the otced mprovemet WOB. The average treds of all the expermets o a PBS ad results from the umercal model revealed that the mmum ad maxmum surface teso a alveolus decreases wth creasg frequecy ad creasg ampltude. The mechasm of mprovemet of surface teso the alveolus wth frequecy ad ampltude s due to the creased dffuso ad adsorpto of surfactat molecules to the ar-lqud terface, creasg the terfacal surface cocetrato ad decreasg the surface teso. v

8 TABLE OF ONTENTS DELARATIONS.... BORROWERS PAGE. AKNOWLEDGEMENTS..v ABSTRAT.....v TABLE OF ONTENTS...v LIST OF FIGURES xv LIST OF TABLES xv LIST OF NOTATIONS......xx ABBREVIATIONS.... xxv HAPTER.... Itroducto..... Backgroud..... Respratory Dstress Sydrome Surfactat Therapy Tradtoal Vetlato Treatmets The Bubble PAP System MR90 Humdfcato hamber Sgle-Heated Breathg rcut Pressure Mafold PAP Geerator Nasal Tubg, Nasal Progs ad Ifat Boet Respratory System Structure ad Fucto Aatomy Isprato, Exprato ad the Respratory Muscles Respratory Volumes ad apactes Mechacs of Resprato Arway Resstace... 6 v

9 .5.. omplace Impedace Alveolar Surface Teso Work of Breath losure... 3 HAPTER Lterature Revew Itroducto Vetlato Techques usg Pressure Oscllatos Hgh Frequecy Vetlato otuous Postve Arway Pressure (PAP) wth Pressure Oscllatos Bologcally Varable Vetlato The Role of Vbrato Overvew Modellg Respratory System Dyamcs Morphometrcs Models Mechacal Models Overvew Modellg Surfactat Dyamcs Research Pla ad Objectves losure HAPTER Respratory System Model Itroducto Model Formulato Model Assumptos x

10 3... Model Developmet Mass Flow Rate Expressos Lobe Dyamcs Assumptos ad Justfcatos Lobe Dyamcs Developmet The Pleural ompartmet ad hest Wall Emprcally Measured Model Parameters Lug asts Pressure-Volume urves Lug ad Lobe Masses Lterature Derved Model Parameters Volumes ad Surface Areas Pressure-Volume ad Elastace-Volume urves Lobe Resstaces Pleural Volume Dampg coeffcets Tdal Volumes ad Respratory Rates Smulk Model losure HAPTER Model Valdato ad Results Itroducto ollato of Expermetal Data omparso of Model ad Expermetal Results omparso of Model Predctos wth PAP measuremets omparso of Model Predctos wth Bubble PAP measuremets Model Predctos of Pressure Oscllato Effects x

11 4.4.. alculatg the WOB WOB omparso of premature ad ear-term lugs Addg pressure oscllatos at the PAP geerator Addg pressure oscllatos at the patet terface losure... 0 HAPTER Surface Teso Model Itroducto omputatoal Model Formulato ovecto-dffuso Equato Ital ad Boudary odtos Regmes of Mass Trasport Mass trasport equatos for each regme Isotherm Numercal Soluto Dscretzato of Tme Dscretzato of Space Dscretzato of Bubble Dmesos Dscretzato of ross-sectoal Area Dscretzato of the Dffuso Equato Defg the Volume Flow Rate The Dmesoless Dffuso oeffcet Dscretzato of Relatve Veloctes Dscretzato of the Boudary odtos Dscretzato of the equatos descrbg the three regmes Soluto of the Tr-dagoal Matrx Model Valdato x

12 5.5. Expermets o urosurf usg Modulated Frequeces Expermetal Equpmet ad Setup Expermetal Methodology Expermetal Results Model ad Expermetal Results omparso losure HAPTER Overall Dscusso Itroducto Ove Mechacal Model ad Expermets Model Predcto of Expermetal Results durg PAP Model Predcto of Expermetal Results durg Bubble-PAP alculatg the WOB of premature ad ear-term lugs Effect of Addg Pressure Oscllatos at the Geerator Effect of Addg Pressure Oscllatos at the Patet Iterface Effect of Pressure Oscllatos o the Lug - Summary Pulsatg Bubble Surfactometer Expermet ad Numercal Model Mmum ad Maxmum Surface Teso Results omparso of Expermetal ad Model Results Effect of Modulated Frequeces o Surface Teso - Summary... 8 HAPTER oclusos ad Future Work Itroducto oclusos Future Work x

13 HAPTER Refereces.86 APPENDIES..96 Appedx A 96 Appedx B 09 Appedx 0 Appedx D Appedx E 6 Appedx F 9 Appedx G 3 Appedx H....5 x

14 LIST OF FIGURES Fgure. Huma lug developmet wth gestato... Fgure. Ital Bubble PAP as used by olumba Presbytera Medcal etre [3] Fgure.3 Bubble PAP System ompoets Fgure.4 Respratory System Orgas [5]... 9 Fgure.5 Brachg of coductg arways the lug [6]... 0 Fgure.6 Respratory zoe of the lug [6].... Fgure.7 ells the alveol [6].... Fgure.8 Isprato process durg quet breathg [6]... 3 Fgure.9 Exprato process durg quet breathg [6] Fgure.0 The pleural cavty [6] Fgure. Respratory volumes ad capactes Fgure. Neoatal lug ad chest wall complace Fgure.3 Pressure-volume curves of ar-flled ad sale-flled lugs Fgure.4 Mammala surfactat composto... 0 Fgure.5 Phospholpd molecule.... Fgure.6 Phospholpd molecules at the ar-lqud terface... Fgure. Pedelluft pheomeo showg fllg ad emptyg of uts Fgure. Velocty profles durg covectve gas trasport Fgure.3 Facltated dffuso durg HFV... 7 Fgure.4 The effect of pressure oscllatos of dfferet elemets of resprato... 3 Fgure.5 Lug models to model respratory system mechacs [68] Fgure.6 Vscoelastc model as used by Athaasades et al. [70] Fgure 3. The elemets of the ove respratory system model Fgure 3. Schematc dagram of the lumped respratory system (showg secto umberg) Fgure 3.3 Geeral schematc for a lobe sprg mass damper system Fgure 3.4 Schematc of Pleural ompartmet ad hest Wall Fgure 3.5 Lug casts before (a) ad after (b) macerato by KOH Fgure 3.6 Subject supe posto wth ope chest exposg lug Fgure 3.7 Measurg P-V curves wth syrge ad maometer setup xv

15 Fgure 3.8 Average P-V curves for 8 day gestato whole, rght ad left lugs Fgure 3.9 Average P-V curves for 4 day gestato whole, rght ad left lugs Fgure 3.0 Average P-V curves as a percetage of maxmum volume for 8 day gestato whole, rght ad left lugs Fgure 3. Average P-V curves as a percetage of maxmum volume for 4 day gestato whole, rght ad left lugs Fgure 3. Dstrbuto of arway resstace across each Webel geerato humas Fgure 3.3 Elemets of the Smulk Model Fgure 3.4 Geeral form of the block dagram for equatos (3.0) to (3.5) ad (3.37) to (3.60) Fgure 3.5 Geeral form for the block dagram for equatos (3.6) to (3.3) ad (3.6) to (3.69) Fgure 3.6 Geeral form for the block dagram for equatos (3.73) to (3.87) Fgure 3.7 Block dagram for equato (3.88) Fgure 3.8 Block dagram for equato (3.9) Fgure 4. Amal prepared for trals o fat warmer wth occlusve wrap Fgure 4. Model-expermet tdal volume calbrato of a 8 day gestato lamb... 9 Fgure 4.3 Model-expermet comparso of arway opeg pressure for a 8 day gestato lamb recevg PAP... 9 Fgure 4.4 Model-expermet comparso of arway opeg flow rate for a 8 day gestato lamb recevg PAP... 9 Fgure 4.5 Model predctos for lobe pressures, flows ad volumes a 8 day gestato lamb recevg PAP Fgure 4.6 Model-expermet comparso for arway opeg pressure a 8 day gestato lamb recevg Bubble PAP Fgure 4.7 Model-expermet comparso for arway opeg flow rate a 8 day gestato lamb recevg Bubble PAP Fgure 4.8 Model-expermet comparso for tdal volume a 8 day gestato lamb recevg Bubble PAP Fgure 4.9 Pressures left lobes of a 8 day gestato lamb recevg Bubble PAP xv

16 Fgure 4.0 Pressures rght lobes of a 8 day gestato lamb recevg Bubble PAP Fgure 4. Flow left lobes of a 8 day gestato lamb recevg Bubble PAP Fgure 4. Flow rght lobes of a 8 day gestato lamb recevg Bubble PAP.. 99 Fgure 4.3 Volume left lobes of a 8 day gestato lamb recevg Bubble PAP Fgure 4.4 Volume rght lobes of a 8 day gestato lamb recevg Bubble PAP Fgure 4.5 Normalzed values of WOB of 8 day ad 4 day gestato lambs recevg 6.75 cm H O PAP... 0 Fgure 4.6 Power spectrum of the stataeous work at the arway opeg of a 8 day gestato lamb recevg PAP ad whte ose Fgure 4.7 WOB (relatve to PAP-oly treatmet) at specfed locatos for a varety of oscllatory treatmets o a 8 day gestato lamb Fgure 4.8 Average WOB (relatve to PAP-oly treatmet) at the patet terface calculated from expermetal data Fgure 4.9 Power spectrum of the stataeous work at the arway opeg of a 8 day gestato lamb recevg Bubble PAP Fgure 4.0 Power spectrum of the stataeous work at the arway opeg of a 8 day gestato lamb recevg PAP ad whte ose at the terface Fgure 4. WOB (relatve to PAP-oly treatmet) at the upper trachea for a varety of oscllatory treatmets o a 8 day gestato lamb Fgure 4. WOB (relatve to PAP-oly treatmet) at the rght lobes for a varety of oscllatory treatmets o a 8 day gestato lamb Fgure 4.3 WOB (relatve to PAP-oly treatmet) at the left lobes for a varety of oscllatory treatmets o a 8 day gestato lamb... 0 Fgure 5. Schematc of a bubble a bulk lqud cotag surfactat... Fgure 5. Vsual represetato of the terfacal cocetrato Γ (t)... 8 Fgure 5.3 The locatos of the three regmes o the γ A loop [78, 80] Fgure 5.4 Isotherm relatg surface teso ( γ ) to surface cocetrato ( Γ surfactat.... Fgure 5.5 Dscretzato of tme Fgure 5.6 Dscretzato of space xv max Γ * ) of

17 Fgure 5.7 Dscretzato of bubble dmesos... 7 Fgure 5.8 Dscretzato of the cross sectoal area Fgure 5.9 A three grd-pot cluster for a oe dmesoal cotrol volume approach. 30 Fgure 5.0. Notatos used to dscretze relatve veloctes Fgure 5. Dscretzato at the terface Fgure 5. omparso of γ A loops at steady state for (A) expermetal data from Schurch et al.[8], (B) match of Schurch data usg computatoal model Fgure 5.3 Schematc dagram of expermetal setup Fgure 5.4 Photograph of expermetal setup Fgure 5.5 Bubble chamber Fgure 5.6 Permaet maget shaker Fgure 5.7 Photro hgh speed dgtal camera ad log dstace mcroscope Fgure 5.8 Mmum surface teso measuremets Fgure 5.9 Maxmum surface teso measuremets Fgure 5.0 Treds mmum surface teso Fgure 5. Treds maxmum surface teso Fgure 5. Match of maxmum ad mmum surface teso a breath cycle Fgure 5.3 Match of mmum surface teso for 5%TV oscllato Fgure 5.4 Match of mmum surface teso for.5%tv oscllato Fgure 5.5 Match of mmum surface teso for 30%TV oscllato Fgure 5.6 Match of maxmum surface teso for 5%TV oscllato Fgure 5.7 Match of maxmum surface teso for.5%tv oscllato Fgure 5.8 Match of maxmum surface teso for 30%TV oscllato xv

18 LIST OF TABLES Table 3. The 7 elemets of the ove respratory system model Table 3. Scalg factors Reyolds-Lee equato [83]... 5 Table 3.3 Descrpto of lambs used lug casts Table 3.4 Average arway legths per ut brthweght for 8 day ad 4 day gestato lambs Table 3.5 Average arway dameters per ut brthweght for 8 day ad 4 day gestato lambs Table 3.6 Descrpto of the amals used pressure-volume curves Table 3.7 Pressure-volume data for 8 day ad 4 day gestato lugs Table 3.8 Descrpto of amals used to measure lug, lobe ad chest wall masses Table 3.9 Masses of lugs, lobes ad chest wall of 8 day ad 4 day gestato lambs Table 3.0 Weght, volume ad surface area dstrbuto ewbor lambs Table 3. Surface areas per ut brthweght for dvdual lobes for 8 day ad 4 gestato lugs Table 3. Maxmum lobe volume per ut brthweght for dvdual 8 day ad 4 gestato lobes Table 3.3 Scaled pressure-volume data for each lobe 8 day ad 4 day gestato lugs Table 3.4 Fttg parameters ad best-ft coeffcet for dvdual lobe deflato curves for 8 day ad 4 day gestato lugs Table 3.5 oductace of dvdual lobes both 8 day ad 4 day gestato lugs Table 4. Detals of amals ad vetlato strateges used expermets Table 4. Detals of selected amal from group Table 4.3 Percetage dfferece of pressure ad flow betwee model ad expermet. 9 Table 4.4 Detals of selected amal from group Table 4.5 Percetage crease WOB total at each locato... 0 Table 4.6 Normalzed power of sgfcat frequeces at dfferet locatos o addto of whte ose at the PAP geerator xv

19 Table 4.7 Sgfcat frequeces detfed PSD aalyss of expermetal data. (Key: Stem uts=0 Hz, Leaf uts= Hz) Table 5. Model parameters used by Morrs [79] to match expermetal data of Schurch et al [8] Table 5. Expermetal detals Table 5.3 Surface teso measuremets Table 5.4 Model parameters to predct surface teso for a breath cycle wthout frequecy modulato Table 5.5 Idetfed rages for D ad k values Table 5.6 D ad k values that best ft expermetal data xx

20 α a A * A LIST OF NOTATIONS Dmesoless dffuso coeffcet Scalg coeffcet Tme varyg area of a bubble Iterfacal area correspodg to equlbrum surface teso A γ m Iterfacal area correspodg to mmum surface teso A lobe Alveolar surface area of a lobe A L card Alveolar surface area of left cardac lobe A L daph Alveolar surface area of left daphragmatc lobe A pleural Surface area of pleural surface A R ap Alveolar surface area of rght apcal lobe A R card Alveolar surface area of rght cardac lobe A R daph Alveolar surface area of rght daphragmatc lobe b Scalg coeffcet B pleural Effectve bulk modulus of pleural flud c Scalg coeffcet c damp Dampg coeffcet ocetrato bot ocetrato at the mdpot of the upwd ode bulk Bulk lqud cocetrato W hest wall complace L Lug complace L card lobe oductace the left cardac lobe L daph lobe oductace the left daphragmatc lobe lobe oductace a lobe R ap lobe oductace the rght apcal lobe R card lobe oductace the rght cardac lobe R daph lobe oductace the rght daphragmatc lobe xx

21 T Total respratory system complace top ocetrato at the mdpot of the dowwd lobe P arway Pressure dfferece across a arway P total Total statc pressure loss a arway segmet P poseulle Poseulle pressure loss a arway segmet d D Scalg coeffcet Dffuso coeffcet D L card Dameter of left cardac brochus D L ma Dameter of left ma brochus D L majdaph Dameter of left major daphragmatc brochus D low trachea Dameter of lower trachea D L post daph Dameter of left posteror daphragmatc brochus D R at daph Dameter of rght ateror daphragmatc brochus D R ap Dameter of rght apcal brochus D R card Dameter of rght cardac brochus D R ma Dameter of rght ma brochus D R majdaph Dameter of rght major daphragmatc brochus D R post daph Dameter of rght posteror daphragmatc brochus D sec to Dameter of a arway secto D up trachea Dameter of upper trachea E L Lug elastace f L card ostat vscous resstace left cardac lobe f L daph ostat vscous resstace left daphragmatc lobe f lobe ostat vscous resstace a lobe f R ap ostat vscous resstace rght apcal lobe f R card ostat vscous resstace rght cardac lobe f R daph ostat vscous resstace rght daphragmatc lobe xx

22 f pleural Vscous resstace of pleural compartmet ad chest wall F th Thoracc Force Γ * Γ Iterfacal cocetrato Equlbrum terfacal cocetrato Γ max Maxmum terfacal cocetrato γ Surface Teso * γ Equlbrum surface teso γ m Mmum surface teso γ 0 Surface teso of water J κ k k Dffusve flux Surface dlatoal vscosty Adsorpto coeffcet Desorpto coeffcet k L card Varable sprg stffess of left cardac lobe k L daph Varable sprg stffess of left daphragmatc lobe k lobe Varable sprg stffess a lobe k R ap Varable sprg stffess of rght apcal lobe k R card Varable sprg stffess of rght cardac lobe k R daph Varable sprg stffess of rght daphragmatc lobe k pleural Varable sprg stffess of pleural compartmet ad chest wall l D l A L Dffusve legth Adsorptve legth Depth of bulk lqud L L card Legth of left cardac brochus L L ma Legth of left ma brochus L L majdaph Legth of left major daphragmatc brochus L low trachea Legth of lower trachea L L post daph Legth of left posteror daphragmatc brochus xx

23 L R at daph Legth of rght ateror daphragmatc brochus L R ap Legth of rght apcal brochus L R card Legth of rght cardac brochus L R ma Legth of rght ma brochus L R majdaph Legth of rght major daphragmatc brochus L R post daph Legth of rght posteror daphragmatc brochus L secto Legth of a arway secto L up trachea Legth of upper trachea µ dyamc vscosty m Slope of sotherm regme m Slope of sotherm regme m Mass that eters a secto/lobe m lobe Mass of ar a lobe m out Mass that leaves a secto/lobe m sec to Mass of ar a secto M Mass of surfactat at the terface M L card Mass of left cardac lobe M L daph Mass of left daphragmatc lobe M lobe Mass of a lobe M pleural Mass of pleural compartmet ad chest wall M R ap Mass of rght apcal lobe M R card Mass of rght cardac lobe M R daph Mass of rght daphragmatc lobe m L broch The sum of m L post daph, m L majdaph ad m L card m L card Mass flow rate to the left cardac brochus m Mass flow rate to left cardac lobe L card lobe m Mass flow rate due to left cardac lobe wall movemet L card wall m L daph lobe Mass flow rate to left daphragmatc lobe xx

24 m L daph wall Mass flow rate due to left daphragmatc lobe wall movemet m L ma Mass flow rate to the left ma brochus m L majdaph Mass flow rate to the left major daphragmatc brochus m L majdaph lobe Mass flow rate leavg left major daphragmatc brochus m md trachea Mass flow rate to the md trachea m lobe wall Mass flow rate due to lobe wall movemet m low trachea Mass flow rate to the lower trachea m L post daph Mass flow rate to the rght posteror daphragmatc brochus m L post daph lobe Mass flow rate leavg left posteror daphragmatc brochus m R at daph Mass flow rate to the rght ateror daphragmatc brochus m R at daph lobe Mass flow rate leavg rght ateror daphragmatc brochus m R ap Mass flow rate to the rght apcal brochus m R ap lobe Mass flow rate leavg rght apcal brochus m R ap wall Mass flow rate due to rght apcal lobe wall movemet m ma Mass flow rate to the ma broch m R broch The sum of m R post daph, m R at daph, m R majdaph ad m R card m R card Mass flow rate to the rght cardac brochus m R card lobe Mass flow rate leavg rght cardac brochus m R card wall Mass flow rate due to rght cardac lobe wall movemet m R daph lobe Mass flow rate to rght daphragmatc lobe m R majdaph lobe Mass flow rate leavg rght major daphragmatc brochus m R daph wall Mass flow rate due to rght daphragmatc lobe wall movemet m R ma Mass flow rate to the rght ma brochus m R majdaph Mass flow rate to the rght major daphragmatc brochus m R post daph Mass flow rate to the rght posteror daphragmatc brochus m R post daph lobe Mass flow rate leavg rght posteror daphragmatc brochus m sec to Mass flow rate a secto xxv

25 m up trachea Mass flow rate to the upper trachea N Number of cycles N S Number of tme steps per cycle N SN Number f specal odes ω P yclg frequecy Pressure P atm Atmospherc Pressure P terface Pressure patet terface P L card Pressure left cardac brochus P L card lobe Pressure the left cardac lobe P L daph lobe Pressure the left daphragmatc lobe P lobe Absolute pressure wth a secto P low trachea Pressure lower trachea P L ma Pressure left ma brochus P L majdaph Pressure left major daphragmatc brochus P L post daph Pressure left posteror daphragmatc brochus P pleural Pleural Pressure P R at daph Pressure rght ateror daphragmatc brochus P R ap Pressure rght apcal brochus P R ap lobe Pressure the rght apcal lobe P R card Pressure rght cardac brochus P R card lobe Pressure the rght cardac lobe P R daph lobe Pressure the rght daphragmatc lobe P R ma Pressure rght ma brochus P R majdaph Pressure rght major daphragmatc brochus P R post daph Pressure rght posteror daphragmatc brochus P up trachea Pressure upper trachea xxv

26 P upwd Pressure o the upwd boudary of a lumped segmet P sec to Absolute pressure wth a secto Q Volume flow rate ρ r R Desty Radus of a bubble Specfc gas costat of ar R (t) Tme varyg radus of a bubble R Re Best-ft coeffcet Reyolds umber R lobe Arway Resstace a lobe R lobes total Total arway resstace of all lobes t T Tme T cycle ycle tme v V Temperature Kelv Velocty of the bulk flud Volume V cycle yclc volume of bubble V L card Volume of left cardac brochus V L card lobe Volume of the left cardac lobe V L daph lobe Volume of the left daphragmatc lobe V L ma Volume of left ma brochus V L majdaph Volume of left major daphragmatc brochus V lobe Volume of a lobe V low trachea Volume of lower trachea V L post daph Volume of left posteror daphragmatc brochus V max Maxmum bubble volume V mea Mea bubble volume V m Mmum bubble volume V pleural Volume of pleural flud xxv

27 V R ap Volume of rght apcal brochus V R ap lobe Volume of the rght apcal lobe V R at daph Volume of rght ateror daphragmatc brochus V R card Volume of rght cardac brochus V R card lobe Volume of the rght cardac lobe V R daph lobe Volume of the rght daphragmatc lobe v rel Relatve velocty of the bubble terface v relbot Velocty at the mdpot of the upwd ode v reltop Velocty at the mdpot of the dowwd ode V R ma Volume of rght ma brochus V R majdaph Volume of rght major daphragmatc brochus V R post daph Volume of rght posteror daphragmatc brochus V sec to Volume of a secto V up trachea Volume of upper trachea WOB Mea work of breath WOB exp Mea work of breath durg exprato WOB sp Mea work of breath durg sprato WOB total Mea work of breath oe breath cycle ξ x Dampg factor Dstace x L card wall Dsplacemet of left cardac wall x L daph wall Dsplacemet of daphragmatc wall x lobe wall Dsplacemet of a lobe wall x pleural Dsplacemet of pleural compartmet x R ap wall Dsplacemet of rght apcal wall x R card wall Dsplacemet of rght cardac wall x R daph wall Dsplacemet of rght daphragmatc wall Z L Respratory system mpedace xxv

28 ABBREVIATIONS BPD BVV BS FD PAP T ERV fps FO FR HFFI HFJV HFO HFPPV HFPV HFV I IMV IRV KOH MV PAP Nal NIUs PaO PaO PBS PV PFV PIP PSD P-V Brochopulmoary dysplasa Bologcally varable vetlato aptve bubble surfactometers omputatoal flud dyamcs otuous postve arway pressure omputer tomography Expratory reserve volume Frames per secod Fracto of spred oxyge Fuctoal resdual capacty Hgh-frequecy flow terrupto Hgh-frequecy jet vetlato Hgh-frequecy oscllato Hgh-frequecy postve pressure vetlato Hgh-frequecy percussve vetlato Hgh-frequecy vetlato Ispratory capacty Itermttet madatory vetlato Ispratory reserve volume Potassum Hydroxde Mechacal Vetlato Nasal cotuous postve arway pressure Sodum chlorde Neoatal tesve care uts Partal pressure of arteral carbo doxde Partal pressure of arteral oxyge Pulsatg bubble surfactometers Pressure-cotrolled vetlato Photro Fastcam Vewer Peak spratory pressure Power spectral desty Pressure-Volume xxv

29 RDS RV SIMV TL TV V VV WOB WTP Respratory dstress sydrome Resdual volume sychrozed termttet madatory vetlato Total lug capacty Tdal volume Vtal capacty Volume-cotrolled vetlato Work of breathg Work-tme product xxx

30 HAPTER. Itroducto.. Backgroud The most commo reaso to tate vetlato of a eoate (ewbor fat) s respratory falure. Ths ca be caused by codtos that arse ether from a falure of the cetral ervous system or where there s a vetlato-perfuso msmatch caused by physologcal dsruptos. odtos arsg from the frst type are apoea due to prematurty, tracraal haemorrhage, brth asphyxa ad drug overdose. I these cases, the eoate does ot breathe because the respratory drve s suppressed ad hece mechacal vetlato (MV) s absolutely ecessary. I the secod type, pulmoary gas exchage s adequate to susta requred partal pressures of arteral carbo doxde (PaO ) ad oxyge (PaO ). The adequacy gas exchage s caused by dseases stemmg from physologcal chages, flammato ad fecto of membraes the respratory system, such as respratory dstress sydrome (RDS), peumoa, peumothorax, daphragmatc hera ad tumours []. Of specfc terest for ths research s RDS (prevously called hyale membrae dsease). Respratory dstress sydrome s the most commo respratory lless to affect eoates. It remas the leadg cause of fat mortalty ad morbdty. Wth the progress techology, there are creasg optos for provdg qualty respratory vetlato for eoates. Irrespectve of the type of respratory vetlato, the goals of vetlato rema the same, amely to mata adequate gas exchage the lugs ad reduce the work of breath (WOB) of the patet whle mmzg jury to the lugs ad matag the hghest level of patet comfort. The tradtoal method of respratory vetlato has bee mechacal vetlators. However, the use of such vetlators o

31 delcate premature lugs causes may of the survvors of RDS to develop brochopulmoary dysplasa (BPD) resultg from barotrauma [-4]. Vetlato at low lug volumes also worse lug jury due to the repettve opeg ad closg of collapsed regos (atelectrauma) [5, 6].A varety of other respratory support techques have bee admstered sce a effort to reduce the possblty of over-dsteso of the arways ad shear stresses o the epthelal walls, as s commo mechacal vetlato. The Bubble otuous Postve Arway Pressure (PAP) System developed by Fsher & Paykel Healthcare s oe such respratory support devce whch combes the effects of tradtoal PAP ad pressure oscllatos. It has clcally reported beefts over mechacal vetlato [7-4]; however, the mechasms of lug recrutmet ad the role that the pressure oscllatos may play optmsg the operato of the system requre more ad s thus the subject of vestgato ths thess... Respratory Dstress Sydrome Respratory dstress sydrome s caused by suffcet surfactat producto the alveol (ar sacs) ad uderdeveloped lug structure [, 5-7]. Surfactat ad lug structure developmet ca be explaed the cotext of gestatoal age wth the ad of Fgure. [, 5]. Lug developmet s parttoed to fve phases: () Embryoc phase (3-6 weeks), () Pseudogladular phase (6-6 weeks), (3) aalcular phase (6-6 weeks), (4) Saccular phase (6-36 weeks), (5) Alveolar phase (36 weeks 3 years). The expected date of delvery s calculated at 40 weeks of pregacy. Normal pregacy s cosdered to occur betwee 37 to 4 weeks. Ifats bor before 37 weeks of age are cosdered to be preterm ad fats are termed as eoates up to 8 days after brth. Brth (± weeks) Preterm Neoatal (Brth 8 days) weeks 6-6 weeks 6-6 weeks 6-36 weeks 36 weeks 3 years Fgure. Huma lug developmet wth gestato.

32 Surfactat s produced by the alveolar type II cells lamellar bodes. It performs the fucto of decreasg the surface teso forces at the ar-lqud terface the alveol ad s therefore a prerequste to breathg. Oce secreted by the lamellar bodes, the surfactat s trasported to the ar-lqud terface where t spreads as a moolayer ad acts to reduce the surface teso. Ths process starts aroud week 6 post cocepto ad s ot yet fully completed the saccular phase (6-36 weeks). Ifats bor ths perod have lugs wth suffcet surfactat ad alveol to facltate adequate vetlato. A lack of surfactat preterm fats meas that the surface teso forces ther alveol are much hgher ad act to decrease the surface area of the alveol to such a extet that they collapse, markg the oset of RDS. Tradtoal surfactat therapes ad vetlato techques have bee used eoatal tesve care uts (NIUs) to treat RDS. These are dscussed Sectos.. ad.. respectvely.... Surfactat Therapy Natural surfactats that are curretly used the treatmet of RDS are lpd extracts of bove lug mce (Surfactat TA ad Survata), extracts of bove lug washes (Ifasurf, Alveofact ad BLES) ad extracts of porce lug mce (urosurf). Examples of sythetc surfactats are Exosurf ad Pumactat. The ma cetve towards ther developmet s the hgh prce of atural surfactat. They are usually hghly smplfed mxtures of phospholpds ad do ot cota the surfactat protes that atural surfactats cota whch usually ehace the surface teso lowerg ablty of the surfactat. Surfax ad Vetcute cota addtves that have surfactat prote-lke propertes. However, to date there s o clcal evdece to suggest whch atural surfactat s superor ad whether sythetc surfactats are superor to atural preparatos [8, 9]. Surfactat treatmets have show to mprove oxygeato ad lug mechacs as well as lower the mea arway pressures ad the percetage cocetrato of oxyge the gas (fracto of spred oxyge - FO ) delvered by vetlators to premature fats wth RDS. Surfactat ca be admstered ether prophylactcally (wth te mutes of 3

33 brth), as a early treatmet (wth hours of brth) or as a rescue treatmet (whe RDS has bee establshed). Although there are o trals comparg prophylactc treatmet wth early treatmet, clcal trals have bee doe to show that early treatmet s deftely more effectve tha delayg treatmet utl RDS has bee establshed [, 8, 9].... Tradtoal Vetlato Treatmets It was ot utl the 970s that the practce of eoatal mechacal vetlato advaced ad dramatcally mproved the treatmet of eoates wth RDS. Tradtoal modes of mechacal vetlato clude termttet madatory vetlato (IMV) ad sychrozed termttet madatory vetlato (SIMV) wth pressure ad volume cotrol modes. Early techques of IMV fuctoed by takg over the role of the respratory muscles by facltatg gas exchage. The vetlator could be pre-set to delver "mechacal breaths" at regular breath cycles. The dsadvatage was that fats ofte breathed asychroously wth the mechacal breaths, whch lead to effcet gas exchage, gas trappg ad ar leaks [0-]. Ths o-sychrozato betwee the fat ad the vetlator led to the developmet of a mproved type of vetlator called sychrozed termttet madatory vetlato (SIMV). Ths type of vetlator sychrozed the mechacal breaths wth the fat's spotaeous breath. I smpler terms, the vetlator looked for a spotaeous breath from the patet wth a tmg wdow each tme t was supposed to cycle ad would ether start or delay the mechacal breaths f a spotaeous breath was detected [0, ]. Although ths sychrozed the spratory process, the expratory process was stll subject to asychroy. lcas have the opto wth a vetlatory mode to choose betwee pressurecotrolled vetlato (PV) or volume-cotrolled vetlato (VV). otrollg the appled pressure works such that f a cosstet peak spratory pressure (PIP) were set, the volume of ar delvered to the patet would be depedet o the complace of the lug. Ths meat that f the complace was poor, the fat would receve a lower volume tha requred ad f the complace mproved, the fat would receve a hgher volume. otrollg the tdal volume however, does ot preset much mprovemet of 4

34 the udesrable possblty of geeratg hgh pressures the lug. A reduced complace, creased resstace or actve exhalato creases the rsk of vetlatorduced lug jury such as BPD [0-]. Brochopulmoary dysplasa s a type of lug jury preterm fats brought o by too much oxyge ad mechacal vetlato [, 0, 3-5]. Mechacal vetlato ot oly causes damage ad flammato the delcate premature lugs but also mpars the lugs' ablty to repar tself ad develop further. lcal vestgatos usg mechacal vetlato performed o a umber of speces showed that lugs that were exposed to hgh levels of oxyge a attempt to acheve hgher levels of oxyge saturato the blood, developed sgfcat persstet lug dsease [5]. Studes o preterm amals also showed that mechacal vetlato damaged lugs by causg a flammatory respose [4, 6, 7]. Due to the hgh rsks volved wth mechacal vetlato, other getler techques have bee developed such as hgh-frequecy vetlato (HFV), bologcally varable vetlato (BVV) ad PAP to avod eoates from progressg to respratory falure. HFV s characterzed by hgh frequecy rates up to 5 Hz at volumes less tha the dead space of the lug whle BVV uses a computer cotroller to delver typcal physologcal varatos tdal volume ad breath rate. These methods alog wth the tradtoal method of PAP are dscussed detal Secto.. The Bubble PAP System s a modfed form of tradtoal PAP ad s dscussed further detal here Secto.3 sce t s the focus of ths research..3. The Bubble PAP System The Bubble PAP System by Fsher & Paykel Healthcare was released the year 000 wth Hudso progs. The system was desged to offer respratory support to spotaeously breathg eoates sufferg from RDS. It apples a mea PAP accompaed by pressure oscllatos to the arways ad alveol throughout the respratory cycle. Ths matas a degree of lug flato durg exprato, thus prevetg lug collapse ad makg t easer for the eoate to breathe sce a partally flated alveolus s easer to expad tha a fully collapsed oe. 5

35 Poeerg work uderpg the Bubble PAP System was performed at olumba Presbytera Medcal etre by Dr. Je-Te Wug ad colleagues 974 [3]. The studes focused o tryg to provde respratory support to eoates wth RDS to prevet them from progressg to respratory falure. The early system (Fgure.) cossted of a humdfer, a crcut for gas flow, a asal prog to coect the crcut to the fat's arway ad a bottle cotag water to whch the dstal ed of the expratory tubg s mmersed to create a postve pressure the crcut. The Bubble PAP System operates uder the same prcples but has bee mproved wth addtoal features that offer more accuracy matag requred mea pressures ad flows ad further features that cosder patet comfort. The system (Fgure.3) cludes a delvery system ad a patet terface. The delvery system cossts of the MR90 humdfcato chamber, a sgle-heated breathg crcut, PAP geerator, ad pressure mafold. The patet terface cossts of the asal tubg, asal progs ad fat boet. Head gear may be used place of the boet ad ch straps (ot show) may also be added to the patet terface to optmse the effect of Bubble PAP. The dvdual compoets (show as they would appear operato Fgure.3) are brefly descrbed as follows. Fgure. Ital Bubble PAP as used by olumba Presbytera Medcal etre [8]. 6

36 Ispratory Le Expratory Le Pressure Mafold MR90 Humdfcato hamber MR850 Humdfer Nasal Progs Ifat Boet Nasal Tubg Adjustable PAP Probe PAP Geerator Delvery System Patet Iterface Fgure.3 Bubble PAP System ompoets..3.. MR90 Humdfcato hamber The chamber s the source of the humdty requred by the eoate. Sterle water s fed to the chamber from a flexble bag. The water level s cotrolled by a dual float mechasm. The float prevets the chamber from floodg ad provdes a closed system ad a costat mea PAP pressure..3.. Sgle-Heated Breathg rcut The breathg crcut (cosstg of the spratory ad expratory les) lks the flow source, humdfcato chamber, patet terface ad PAP geerator. The spratory le coects the humdfer to the patet terface ad the trasparet expratory le coects the patet terface to the PAP geerator. 7

37 .3.3. Pressure Mafold The pressure mafold s a pressure relef mechasm stuated upstream of the eoate that lmts the maxmum pressure the system to 7 cm H O at a flow rate of 8 L/m the evet of a occluso the delvery system. It also has measuremet ports for pressure ad ar/oxyge aalyss PAP Geerator The PAP geerator s the ovatve verso of the early system of Bubble PAP used at the olumba Presbytera Medcal etre sce 974. Ether lowerg or rasg the adjustable probe the water cotaer creates the requred level of postve pressure the crcut. Achevable mea pressures rage from 3 to 0 cm H O. Excess water splls out to a overflow cotaer esurg that the mea PAP pressure s costat. As ar eters the water through the PAP probe, t creates bubbles, whch tur create pressure oscllatos about a mea PAP level Nasal Tubg, Nasal Progs ad Ifat Boet The asal tubg drects the ar to the eoate ad allows a balaced flow to the ares. Nasal progs of dfferet szes, to address the varety of are dameters ad septum gaps, ca be attached oto the ed of the asal tubg. The specally desged fat boet allows for the asal tubg to be fxed posto ad allows repostog of the asal progs wth the fat's movemets. Head gear as a alteratve to the fat boet s also avalable. h straps are also avalable to prevet excessve leaks from the mouth thereby prevetg sgfcat pressure loss. lcal studes o Bubble PAP have show that ts use decreases mute vetlato, respratory rate [], the eed for vetlato [8] ad the umber of days o respratory support [9]. It has also bee speculated that the vbratos produced by the pressure oscllatos ehace gas exchage ad respratory mechacs [3]. However, these fdgs relato to the curret research wll be further dscussed hapter..4. Respratory System Structure ad Fucto The prmary fucto of the respratory system s to supply the blood wth oxyge ad to eable carbo doxde to move out. It s made up of a gas exchage orga (the lugs) 8

38 ad a respratory pump (the chest wall ad respratory muscles). The orgas ad process of resprato are explaed ths secto [5, 9-3]..4.. Aatomy The respratory system cossts of several orgas that clude the asal cavty, throat (pharyx), voce box (laryx), wd ppe (trachea), broch, lugs ad respratory muscles. Ths s llustrated Fgure.4. The ostrls ad proceedg asal cavty herald the begg of the huma respratory tract. Ther prmary fuctos are to flter out mechacal aeral cotamats ad to warm ad humdfy the haled ar. The terveg pharyx acts prmarly as a codut betwee the aforemetoed passages ad the trachea. The trachea tself s a musculo-cartlagous tube, whch further mostes the flowg ar ad addtoally flters smaller dameter partcles. The trachea tur braches at the cara (Fgure.4) to the prmary coductg arways supplyg each lug,.e. the rght ad left prmary broch. Hereafter, each brochus dvdes aga, formg secodary, tertary ad smaller broch (Fgure.5) Fgure.4 Respratory System Orgas [30]. 9

39 such that they become smaller ad more umerous as they peetrate deeper to the lugs, formg lobar, the segmetal broch. Fgure.5 also shows the 5 lobes of the lugs (3 the rght lug ad the left lug). The dvso of the broch cotues dow to the termal brocholes (the smallest arways wthout alveol). The arways from the trachea to the termal brocholes are called the coductg arways. Ther fucto s to lead the spred ar from the exteror to the gas exchage rego or respratory zoe of the lug (show Fgure.6). The respratory zoe s made up of respratory brocholes (whch have occasoal alveol buddg from ther walls), alveolar ducts ad alveol. There are about 300 mllo alveol the huma lug, each about /3 mm dameter. Fgure.5 Brachg of coductg arways the lug [3]. 0

40 The dstace from the termal brochole to the most dstal alveolus s oly a few mllmetres but the respratory zoe costtutes most of the lug. The alveol are surrouded by pulmoary capllares whch form a dese etwork the walls of the alveol (Fgure.6) such that t forms a almost cotuous sheet of blood o the alveolar wall surface (whch s about m adult humas). The barrer betwee the ar ad the blood s oly about 0.5 µm apart such that oxyge ad carbo doxde ca dffuse through the barrer wth ease. Four geeratos of respratory brocholes develop before brth ad several mllo alveol form the last few weeks of brth, uderscorg the mportace of the last few weeks of gestato [6]. Fgure.6 Respratory zoe of the lug [3].

41 Premature fats bor before or durg ths mportat stage of alveolarzato are subjected to mechacal vetlato before the developmet of alveol. Ths could dsrupt the ormal process of lug developmet ad lead to BPD [6, 9, 30, 3]. The alveol are led by two types of epthelal cells (as see Fgure.7). Type I cells are the prmary lg cells. Type II cells are thcker ad secrete surfactat. The alveol also cota macrophages whch clea off haled dust partcles ad mcroorgasms. Fgure.7 also shows the pulmoary capllares ad red blood cells (erythrocytes). Fgure.7 ells the alveol [3]..4.. Isprato, Exprato ad the Respratory Muscles The sprato ad exprato processes durg quet breathg are llustrated Fgure.8 ad Fgure.9 respectvely ad explaed as follows [9-3]. Isprato s a actve process. The most mportat muscle of sprato s the daphragm whch accouts for 75% of the chage trathoracc volume. It s a th dome-shaped sheet of muscle that s attached at the bottom of the thoracc cage.

42 (a) (b) Fgure.8 Isprato process durg quet breathg [3]. It moves dowward lke a psto whe t cotracts ad the vertcal dmeso of the chest cavty s creased (Fgure.8a). The exteral tercostals muscles ru oblquely forward ad dowward, coectg the rbs. Whe they cotract, they pull the rbs upward ad forward ( a bucket-hadle moto) such that the sterum s also pushed outward. The scalee muscles also elevate the frst two rbs. There s lttle actvty by the scalee muscles durg qute breathg but they may cotract vgorously durg exercse. The crease trathoracc volume by the cotracto of all the respratory muscles causes a decrease pressure the lug accordg to the deal gas law sce the volume creases due to temperature chages are small (Fgure.8b). Ths causes ar to rush to the lug from the atmosphere sce flud flows dow alog a pressure gradet. As a result, the pressure wth the lug (trapulmoary pressure) decreases to egatve values durg sprato. The sprato process eds whe the trapulmoary pressure ad the atmospherc pressure become equal. Exprato s a passve process that t depeds o the elastcty of the lugs ad the chest wall. As the daphragm ad other spratory muscles relax, the lugs ad chest wall recol to ther restg posto (Fgure.9a). Thus the lug volume s decreased ad the trapulmoary pressure creases to postve values durg exprato. The pressure 3

43 gradet ow forces ar out of the lugs (Fgure.9b). Durg exercse, however, exprato becomes actve. (a) (b) Fgure.9 Exprato Process durg quet breathg [3]. The teral tercostals muscles cotract, pullg the rb cage dowward ad thereby decreasg the thoracc volume. Muscles the abdome also cotract, rasg the traabdomal pressure, thus pushg the daphragm upward. The lugs ad the chest wall are elastc structures that are coected by a commo pleural cavty ad pleurae as see Fgure.0. The pleura s a membrae that folds back o tself to create a double-layered membrae. The paretal pleura (outer pleura) s attached to the chest wall ad the vsceral pleura (er pleura) s attached to the lug surface. The th space betwee the pleura (the pleural cavty), s flled wth a lubrcatg flud called the pleural flud. The pleural flud allows the lug to slde easly o the chest wall ad prevet pleural separato due to the surface teso of the pleural flud. Ths s ak to two most peces of glass that ca slde o each other but resst beg separated. Thus, the pressure the pleural cavty (the trapleural pressure) s subatmospherc. The tedecy for the chest wall to recol at the ed of quet exprato s balaced by the tedecy for the lug to recol away from the chest wall. If the chest wall s opeed, the lugs collapse ad f the lugs lose ther elastc recol, the chest expads ad becomes barrel shaped. 4

44 Fgure.0 The pleural cavty [3] Respratory Volumes ad apactes The respratory or lug volumes ad the ames appled to combatos of them (the respratory capactes) are show Fgure. [6, 3]. Durg quet breathg, the amout of ar that moves to the lugs wth ormal sprato (or the amout that moves out durg exprato) s called the tdal volume (TV). The amout of ar that ca be forcbly spred beyod the tdal volume s the spratory reserve volume (IRV). The volume of ar that ca be forcbly exhaled after quet exprato s the expratory reserve volume (ERV). The ar left the lugs after a forced exprato s the resdual volume (RV), whch helps to keep the arways ope ad hece prevet lug collapse. The volume of the coductg zoe of the lugs s called the respratory dead space sce there s o dffuso of respratory gases to ad out of the blood ths secto of the lug. Respratory capactes always corporate two or more lug volumes. The spratory capacty (I) s the sum of the TV ad the IRV ad s the amout of ar that ca be spred after a quet exprato. The amout of ar that remas the lugs after a quet exprato s the fuctoal resdual capacty (FR). Ths combes the RV ad the ERV. The vtal capacty (V) s the sum of the TV, ERV ad IRV, whch s 5

45 effectvely the total amout of exchageable ar. The sum of all the lug volumes s kow as the total lug capacty (TL). TL Ispratory apacty Ispratory Reserve Volume Vtal apacty Total Lug apacty FR RV Fuctoal Resdual apacty Resdual Volume Tdal Volume Expratory Reserve Volume 0 Fgure. Respratory Volumes ad apactes..5. Mechacs of Resprato Ths secto troduces the mechacal aspects of ar flow the respratory system. The parameters troduced are commoly used parameters clcal practce ad expermetato to assess respratory mechacs ad performace. They deal wth the forces that move the lug ad chest wall ad the resstg forces that they have to overcome..5.. Arway Resstace Arway resstace s the major source of o-elastc mpedmet ecoutered the lug. It ca be measured at the arway opeg as the total resstace ecoutered all the arway braches combed. I the lug, a pressure dfferece exsts betwee the atmosphere ad the alveol where the arways are a seres of brachg tubes betwee. Each arway ca be cosdered as a tube where a pressure dfferece ( ) 6 Parway exsts betwee the eds whch s a fucto of the rate ad the patter of flow ( Q ). I lamar flow, Parway s proportoal to Q ad a costat K. such that:

46 P arway = KQ (.) However, turbulet flow, Parway s ot proportoal toq, but to ts square. I a complex system of brachg tubes such as the brochal tree, wth ts varous bfurcato agles, surface roughesses ad dameters, the applcato of a smple expresso for Parway s dffcult. Lamar flow s most lkely to occur the termal brocholes ad fully developed turbulet flow s most lkely to occur the trachea. However, for most of the brochal tree, the flow s most lkely to be trastoal..5.. omplace The complace s the rato of the chage pressure ( P ) ad the chage volume ( V ) ad reflects the elastc propertes of the respratory system. The lug complace ( L ) s expressed as L = V P = E L (.) where the elastace of the lug ( E ) s the recprocal of the lug complace ( ). L Statc lug complace measuremets ca be made by measurg the traspulmoary pressure (whch s the pressure dfferece betwee the alveolar ad pleural pressure) before ad after flato wth a kow volume. Ths s measured at the mouth ad oesophagus. The chest wall complace ( W ) ca be measured a smlar maer by recordg the dfferece betwee pleural ad atmospherc pressures. A pressure-volume curve ca be made by recordg the pressures at several dfferet volumes. Fgure. shows typcal lug ad chest wall expaso curves for a eoatal lug [3]. The sum of the two s the total complace ( ). It s apparet that the complace s ot lear T across the etre rage of expaso, wth the complace gettg smaller at hgher expadg pressures, as see by the flatter slope of the curves at hgher pressures. omplace s a useful measure of dseased states. It s reduced codtos of pulmoary fbross, alveolar edema ad atelectass whch prevet the flato of the L 7

47 lug. omplace creases pulmoary emphysema ad the agg lug where the elastc propertes of the tssue alter. % Total Lug apacty Total [Lug hest Wall] hest Wall FR RV Lug Pressure Fgure. Neoatal lug ad chest wall complace Impedace The mpedace of the respratory system ( Z ) s a expresso of the overall mpedmet to flow the respratory system [33]. It s the result of a combato of the resstve, elastc ad ertve elemets ad s gve by L Z L = P Q (.3) where P s the stataeous pressure at the arway opeg Alveolar Surface Teso Alveolar surface teso s the force actg across a magary le ( cm legth) o the lqud lg of surfactat ad hece has the SI uts of N/m but s commoly expressed the lterature as dyes/cm. It s a mportat factor that affects the pressure-volume relatoshp of the lug. Ths ca be measured by flatg excsed 8

48 lugs wth sale at varous volumes, to abolsh the ar-lqud terface the alveol, thereby reducg the surface teso to almost zero. A typcal resultg pressure-volume curve such as that see Fgure.3 [9, 3] s oe that measures oly the tssue elastcty, whereas smlar measuremets doe wth ar measure the effects of both tssue elastcty ad surface teso. Fgure.3 shows that the sale flled lugs have a hgher complace ad less hysteress tha ar-flled lugs, dcatg that surface teso cotrbutes to a large part of the statc recol force of the lug. The surface teso-reducg mechasm of surfactat ca be better uderstood by lookg at the termolecular forces betwee the surfactat molecules. Pulmoary surfactat s made up of 90% phospholpds ad 0% protes. Phospholpd s the prmary surface-teso lowerg compoet of pulmoary surfactat ad makes up most of ts mass. The protes ehace the surface teso lowerg ablty of the surfactat. The surfactat assocated protes are SP-A, SP-B, SP- ad SP-D. Fgure.4 shows the composto of mammala surfactat. Although there s some varato surfactat across speces, the compostos gve are represetatve sce composto mammals geeral s cosdered to be smlar. Phospholpd cotet ca be dvded 5-30% dpalmtoylphospatdylchole (DPP), 5-30% usaturated phospatdylchole (P), 0-5% phosphatdylglycerol (PG) plus phosphatdylostol (PI), 5-0% eutral lpds, 5-0% protes ad about % each of sphgomyel (SM) ad lyso-bs-phosphatc acd (LYSO). Sale-flled Volume Ar-flled Pressure Fgure.3 Pressure-volume curves of ar-flled ad sale-flled lugs. 9

49 LYSO ~ % SM ~ % NEUTRAL LIPIDS 5-0% PROTEIN 5-0% DPP 5-30 % PE - 3% PG&PI 0-5% P 5-30% Fgure.4 Mammala surfactat composto. Phospholpds are maly resposble for gvg the surfactat ts surface tesoreducg capacty ad ths s dscussed greater detal as follows. Phospholpd molecules cota a hydrophobc tal ad a hydrophlc head (Fgure.5) ad exst as aggregates because they are soluble the aqueous mxture that les the alveol. At the ar-lqud terface of the alveol, water molecules are attracted to each other ad to molecules the bulk lqud, thereby creatg a cotractve force kow as surface teso. The surface teso acts to reduce the surface area of the ar-lqud terface to create a stable posto at mmal surface area. Surface teso has a value of 0.7 mn/cm for water at 37 o (more commoly expressed as 70 dyes/cm). Ths ressts expaso of the alveol the lug dseased states where there s o surfactat. To crease the surface area suffcetly for adequate vetlato requres large amouts of dstedg pressure to be geerated ad hece, more work. Ths explas why a premature fat, who s uable to produce pulmoary surfactat, s faced wth the further dffculty of havg to perform more muscle work to couter the tedecy of the alveol to collapse. 0

50 Phospholpd Molecule Hydrophobc Tal Hydrophlc Head Fgure.5 Phospholpd Molecule. I the presece of surfactat a healthy lug, the hydrophlc heads of the phospholpds teract wth the water molecules ad the hydrophobc tals exted towards the ar (as see Fgure.6). Ths dsplaces the water molecules at the arlqud terface (whch are attracted to each other by electrostatc forces kow as Va de Waals forces), thus reducg the surface teso to equlbrum values of approxmately 5 dyes/cm [6, 34]. Surface teso forces the alveol ca be descrbed by the statc Youg-Laplace equato [, 3, 34] most commoly appled to a small sphercal ar bubble a surfactat suspeso whch s pulsated at regular frequeces betwee a fxed mmum ad maxmum radus (Equato (.4)). γ P = (.4) r Here P s the pressure drop across the ar-lqud terface that s eeded to stablze the system, r s the radus of the bubble ad γ s the surface teso. ar Phospholpd Molecules Fgure.6 Phospholpd molecules at the ar-lqud terface.

51 I the absece of surfactat, the surface teso creases ad Equato (.4) llustrates that more dstedg pressure s requred to stop the alveol from collapsg. If the radus of the alveolus s small, ths too ecesstates a larger dstedg pressure to keep t ope. I a premature fat whose alveol are defcet surfactat ad aturally smaller radus tha ormal fats, surfactat therapes ad vetlato are thus requred to expad the alveol to prevet collapse at the ed of exprato. Equato (.4) gores the dyamc effects of surface dlatoal vscosty κ whch affects the terfacal pressure drop whe the bubble chages dyamcally. A complete descrpto of the terfacal behavour s gve by Equato (.5) whch s a fucto of radus r, surface teso γ ad surface dlatoal vscosty κ [35]: γ 4κ r P = (.5) r r These effects, f gored durg expermets, ca result sgfcat errors, however for the purposes of a basc explaato, the Youg-Laplace equato suffces Work of Breath Geerally, the work of breath (WOB) refers to the mechacal work performed by the respratory muscles agast the lug ad chest wall durg resprato [9, 3]. It s most coveet to measure work as the product of pressure ad volume chage whch has the same uts as work (Nm). The work of breath ca be calculated from a relaxato pressure curve such as prevously show Fgure.. The work of breath s complex ad dffcult to measure wthout sophstcated aalyss to quatfy the movemet ad dstorto of the chest wall [3, 36]. However, may cases, measurg the work performed agast a exteral load may provde suffcet formato for the purposes of respratory performace [36]. The work measured at the mouth or arway opeg estmates the work performed by all the respratory muscles. Alteratvely, t ca be measured usg the traspulmoary pressure for measuremet of the chest wall ad ts muscles agast the lug ad arways.

52 The work of breath ca be expressed as the work doe per breath, work per mute or work per ltre [37]..6. losure Ths chapter has troduced the backgroud of RDS ad the role of vetlato ad surfactat therapy ts treatmet. The Bubble PAP System has bee troduced wth further detals o clcal trals to be dscussed the followg chapter. The aatomy ad physology of the respratory system relevat to ths research have bee hghlghted ad the mechacs of resprato ad the fucto of surfactat have also bee explaed. 3

53 HAPTER. Lterature Revew.. Itroducto Ths chapter presets a revew of the relevat research performed o oscllatory vetlato techques to treat RDS. HFV ad BVV are dscussed wth ther proposed mechasms of mprovemet. The clcal research performed o the use of the Bubble PAP System s also preseted to hghlght the potetal beefts t offers wth the troducto of pressure oscllatos supermposed o the mea PAP pressure. The research to date o the modelg of respratory system mechacs ad surfactat dyamcs the alveol are also dscussed. The objectves of the research are the preseted the hopes of extedg the use of eoatal mechacal ad surface teso models to study the effect of pressure oscllatos o eoatal respratory performace... Vetlato Techques usg Pressure Oscllatos The use of pressure oscllatos vetlato before the troducto of Bubble PAP was ot etrely ukow. Ths secto presets a revew of the lterature focusg o the descrpto of the vetlato techques that use pressure oscllatos, ther clcal beefts ad proposed mechasms of mprovemet.... Hgh Frequecy Vetlato Hgh frequecy vetlato was a radcal departure from mechacal vetlato that t delvered gas at small tdal volumes (less tha the dead space of the lug) at frequeces up to 5 Hz. The pulses of small gas volumes at rapd rates created lower pressures the alveol, decreasg the cdece of lug tssue jury [38-4]. It has bee suggested 4

54 that the vbratory or pulsg ature of the arflow causes a "sloshg moto" of ar the lugs, kow as pedelluft ad that ths feature of HFV may offer better gas trasport to the respratory zoe of the lug [4, 43]. lcal results [44, 45] have show that early, exclusve use of HFV decreases the cdece of BPD premature fats wth RDS whe compared to mechacal vetlato. Ifats also requred a much shorter perod o vetlator support. A umber of mechasms of gas trasport durg HFV have bee suggested. Durg ormal breathg frequeces, bulk covecto ad molecular dffuso take place. These mechasms also occur durg HFV but other mechasms have also beg suggested. hag [4] proposed that the followg modes of gas trasport are collectvely resposble durg HFV: Drect alveolar vetlato - Alveol that le proxmal to the trachea stll receve drect vetlato. Eve though the tdal volumes are small, as log as they are above a certa lmt, some alveol wll receve fresh gas wth every sprato. Pedelluft - Whe eghbourg regos the lug are dfferet complace, resstace ad tme costats of flato ad deflato, ths leads to fast uts whch fll faster ad more easly (Fgure.a) ad slow uts whch may stll be the process of halato whe the fast uts are exhalg (Fgure.b). Durg hgh velocty flow ths pheomeo s magfed ad the eghbourg uts mutually exchage gas a effect kow as pedelluft. As a result, there s a more homogeeous mxg of gas, allowg the use of smaller volumes of gas to reach more alveol ad as a result decrease the requred tdal volume requred for resprato. Fast Ut Slow Ut Fast Ut Slow Ut (a) (b) Fgure. Pedelluft pheomeo showg fllg ad emptyg of uts. 5

55 ovectve Gas Trasport - Durg sprato the velocty profle of the gas s parabolc (Fgure.b) but durg exprato the velocty profle s flatter (Fgure.c). The resultg dsplacemet of a partcle of gas that was stuated the cetre of the arway at the start of sprato (Fgure.a) s ow stuated to the rght (Fgure.d) (.e. workg ts way dow the tracheo-brochal tree to the alveol) ad the gas partcles ear the walls are stuated to the left of ther orgal posto. Facltated dffuso - The fast pulses of low volumes HFV move dow the arways wth larger axal spkes (Fgure.3b) tha slower pulses (Fgure.3a) whch create a larger boudary for lateral dffuso of oxyge ad carbo doxde lamar flow. (a) Gas partcle velocty profle at start of sprato (b) Gas partcle velocty profle durg sprato (c) oflctg Ispratory ad Expratory Profles (d) Resultg Dsplacemet at ed of exprato Fgure. Velocty profles durg covectve gas trasport. 6

56 (a) Slow pulse (b) Fast pulse Fgure.3 Facltated Dffuso durg HFV. Lateral dffuso ca also occur turbulet flow ad at bfurcatos due to eddes. Thus, t sad that dffuso s facltated these cases. Molecular Dffuso - Ths refers to the molecular dffuso of respratory gases at the alveolar-capllary membrae. Ths mechasm always exsts as alog as gas exsts there at a temperature above absolute zero ad hece s ot a HFV-specfc mechasm. Molecular dffuso of oxyge ad carbo doxde wll occur across the alveolarcapllary membrae to mata a equlbrum betwee partal pressures of these gases. De Jog [34] also suggested that aother factor of mportace for HFV s surfactat effcecy. The fact that HFV has lower pressures may mea that they do ot dsturb the crtcal alveol (whch have a relatvely low surfactat cocetrato) ad so they wll ot collapse. Although all sx modes of gas trasport dscussed may exst durg HFV, t s possble that certa modes are more domat certa regos of the respratory system. It has bee suggested that drect vetlato ad facltated dffuso domate vetlato the trachea, whle pedelluft or covectve gas trasport domate the medum-szed arways. Smaller arways are vetlated by pedelluft ad alveol by molecular dffuso. There are may varats of the HFV techque, but they all cota three basc elemets, a hgh pressure flow geerator, a valve for flow terrupto ad a breathg crcut to be coected to the patet. Varats clude hgh-frequecy jet vetlato (HFJV), hgh-frequecy flow terrupto (HFFI), hgh-frequecy (push- 7

57 pull) oscllato (HFO), hgh-frequecy postve pressure vetlato (HFPPV) ad hgh-frequecy percussve vetlato (HFPV).... otuous Postve Arway Pressure (PAP) wth Pressure Oscllatos Nasal otuous Postve Arway Pressure (PAP) s a o-vasve type of respratory support comparso to edotracheal vetlato. It apples a cotuous postve pressure to the alveol (through asal progs or tubes) throughout the respratory cycle ad has bee creasgly used hosptals to treat eoates wth RDS [0, 46]. The postve pressure appled to the lug s created by a varable resstace at exhalato. It produces a more regular breathg patter whe compared to mechacal vetlato sce t allows the fat to breathe spotaeously. The cotuous dstedg pressure provded by PAP creases lug volume ad promotes better gas exchage the alveol by keepg them ope [6, 0]. Studes have show that PAP reduced the eed for mechacal vetlato eoates wth moderate RDS ad proved to be a adequate form of vetlato by mprovg oxygeato wthout posg ay addto harmful sde effects [0, 47-50]. The Bubble PAP System as dscussed hapter uses a water colum rather tha a varable resstor to produce the requred PAP to the alveol. The bubbles produced the PAP bottle as the ar leaves the system produce pressure oscllatos (reported to be betwee 5-30 Hz []) addto to the mea pressure. There has bee some evdece based o studes o fats betwee 750 ad 500g brthweght that usg Bubble PAP decreases the respratory rate ad mute vetlato eoates wth RDS wthout decreasg alveolar vetlato [], meag that the fat has to perform less muscle work to acheve adequate resprato. It was proposed that Bubble PAP may facltate better gas exchage the lug whch may be caused by mechasms see HFV. Hosptal ad clcal studes have detfed several beefts of Bubble PAP that make t a feasble devce for maagg RDS eoates. Hosptal studes o preterm ad extremely low brthweght fats cocluded that the use of Bubble PAP reduces the possblty of lug jury by reducg the eed ad umber of days requred for mechacal vetlato [0, 5, 5]. Studes also showed that hosptals that used Bubble 8

58 PAP to a greater extet o preterm fats wth RDS reported a sgfcatly lower rate of BPD tha hosptals that dd ot [4, 48, 53]. A otable study by Pllow et al. [3] o preterm lambs showed that ( comparso to costat pressure PAP) Bubble PAP mproved arteral oxyge levels (due to the mproved gas exchage offered by the pressure oscllatos), stablsed lug volumes at low pressure ad ehaced lug mechacs (by creasg complace ad FR ad decreasg arway resstace). Also, studes o preterm lambs have show that Bubble PAP mproves the complace of the lug by prevetg repettve flammatory stresses o the preterm lug ad preservg surfactat fucto better tha mechacal vetlato []. It has also bee speculated that the osy pressure sgal may also promote surfactat secreto the lug [7]. The mprovemets oted vetlatory parameters durg Bubble PAP could be due to a umber of physologcal, chemcal ad mechacal mechasms. These clude the avodace of aggressve tato of vetlato wth hgh tdal volumes ad advertet hypervetlato of the lug [, 5], those smlar to those see HFV [] ad that of stochastc resoace resultg from the supermposed osy pressure sgal from the bubblg acto [3]. However, the relatve cotrbutos of the dfferet proposed mechasms are yet to be establshed. The essece of stochastc resoace relato to the Bubble PAP System ca be explaed as follows. Whe ose s added to the put to a o-lear system (lke the lug), the respose s frst mproved. However t s possble that f the tmg or the pressure ampltude of the ose s creased further t ca produce a detrmetal effect. Ths suggests that ose ca be tued such a way to provde optmal vetlato [54, 55]. Ths mprovemet has bee llustrated terms of the et volume recruted due to the o-learty of the pressure-volume curves of the lug. However, the stochastc resoace effect due to the overall mechacal respose of the respratory system s yet to be determed ad s of terest to ths research. 9

59 To date o clcal studes have vetured so far as to determe the optmum ampltude ad frequeces of pressure oscllatos the treatmet of RDS. Some aalytcal studes [56, 57] have bee doe that demostrate the ablty of usg the Bubble PAP System to optmse the ampltudes ad frequeces of pressure oscllatos produced by the system but these rema to be valdated by clcal studes...3. Bologcally Varable Vetlato Bologcally varable vetlato or osy vetlato has bee clcally show to have beefts as well. BVV uses a computer cotroller to mmc the ormal varablty a spotaeously breathg lug by producg radom varatos tdal volume ad breath rate. Studes o porce [58, 59] ad rodet [54] models showed that such techques mprove the oxygeato of arteral blood ad have ehaced the performace of mechacal vetlators. Mathematcal models [55] that were developed also suggest that mechacal vetlato accompaed by radomly varyg breath patters mproved alveolar recrutmet by opeg collapsed alveol ad creasg the et lug volume wthout causg creases mea arway pressures. The mechasms of alveolar recrutmet for ths techque are also ot fully uderstood, although theores do exst o the mechasms of gas trasport. These are mostly assocated wth the beefts due to the better mxg of gases osy vetlato [4, 43, 60]. Varous authors suggest that osy vetlato (lke BVV ad Bubble PAP) s a example of stochastc resoace [54, 55, 58, 59]. Studes o small amals [54, 59] have show that respratory support systems ca optmze lug recrutmet by tug parameters such as the tmg ad ampltude of the pressure fluctuatos. Whether ths s applcable to larger amals ad humas remas to be prove...4. The Role of Vbrato The pressure oscllatos produced Bubble PAP ot oly facltate gas trasport but also vbrate the lug ad chest wall. These ca be felt f oe s had s placed o the fat's chest. Ivestgatos o the mechacal respose of the lug walls to hgh 30

60 frequeces are a recet feld of study ad the relatoshp s ot fully developed. Smulatos of ormal adult lugs [6] ad expermets o cae lugs [6] show that the geometry ad mechacal propertes of the lug are mportat factors the mechacal respose of the lug. Furthermore, t s suggested that vbratos caused by pressure oscllatos mprove the elastc codto of the lug walls [6, 6] ad that the behavour of the lug s susceptble to the frequecy of those pressure oscllatos [56, 57, 63]. However, ay effect that pressure oscllatos have o respratory parameters due to the mechacal propertes ad dyamcs of the respratory system s ukow. Logtudal vbratos (up to 37 Hz) to cae trachea smooth muscles [64] showed a decrease muscle stffess wth a crease vbrato frequecy. A three-fold reducto stffess was recorded for frequeces aroud 35 Hz. It was postulated that mechacally ducg vbratos to lug tssue dsrupted the cohesve mechacal teractos betwee prote flamets (cross brdges) durg cotracto, resultg a legtheg or relaxato of the tssue. However, studes by other authors propose a dfferet mechasm [65-67] related to lug relaxato sayg that t s cocevable that vetlators such as BVV, oscllatory PAP ad HFV whch duce lug vbrato at frequeces of 8-8 Hz, postvely affect breathg by stmulatg pulmoary receptors whch sed formato to the bra...5. Overvew There have bee a varety of respratory vetlators developed to combat the egatve effects of mechacal vetlato. lcal ad aalytcal studes have show that there are physologcal beefts to addg pressure oscllatos to respratory treatmet. However, the mechasms for gas trasport ad the effect of the mechacal ad surfactat propertes o the dyamc respose of the lugs stll requre further study. The cocept of stochastc resoace or tug the ampltude ad frequecy of pressure oscllatos vetlato has bee proposed ad studes o smaller amals support such theores. Whether the same apples to huma eoatal lugs s stll to be determed, addto to the optmal frequeces requred for ay partcular lug. To summarse, t s apparet that vbratos or pressure oscllatos affect dfferet elemets of the respratory system dfferet ways as see Fgure.4. I the cotext 3

61 of eoatal respratory mechacs, lug maturty ad surfactat fucto are the major cotrbutors to lug dsease ad so the curret thess focuses o the effect that pressure oscllatos have o respratory performace due to mechacal ad surface teso effects of the lug. Quattatve clcal ad aalytcal studes o the optmal frequecy ad ampltude geerato capable by the Bubble PAP System are stll ther facy ad deped o accurate mathematcal models of the eoatal lug. Sectos.3 ad.4 dscuss the respratory models foud the lterature ad ther usefuless predctg the respose of eoatal lugs to respratory support techques. Secto.3 detals the morphometrc ad mechacal models whch ca be bult o to assess the mechacal effect of pressure oscllatos o respratory performace lobes ad at the arway opeg. Secto.4 detals the models to date o surfactat dyamcs whch ca be used to assess the effect that oscllatos have o surfactat fucto the alveol. Respratory Elemets Mechasms Assessmets Mechacal Effects Surfactat Dyamcs Smooth Muscle Dyamcs Gas Trasport Stochastc resoace Icreased complace Icreased surfactat secreto Icreased surfactat cocetrato Dsrupto of act-flamet crossbrdges Pedelluft Molecular & facltated dffuso Work of Breath Respratory Impedace Dyamc Surface Teso Force-Legth Relatoshps Blood Gas Parameters Efferet Actvty Trggerg of efferet sgals Respratory Muscle Work Fgure.4 The effect of pressure oscllatos of dfferet elemets of resprato. 3

62 .3. Modellg Respratory System Dyamcs A varety of models are avalable the lterature whch clude poroelastc, computatoal flud dyamcs (FD), morphometrc ad mechacal models. A search of the lterature reveals that the approach ad complexty of modellg the respratory system depeds o the research questo. The effects of gas mxg, efferet actvty ad vetlato-perfuso effects are ot studed ths work. Models that corporate geometrc, physcal, mechacal ad flow characterstcs are cosdered, so a revew o the morphometrc ad mechacal models foud the lterature s dscussed ths secto..3.. Morphometrcs Models Morphometrc models represet the brachg structure of the arways alog wth other data such as the dmesos, brachg agles as well as cross sectoal areas ad volumes of alveol. Webel [68] developed a symmetrc model of the huma adult lug lug whch corporated 3 geeratos of symmetrcally dvdg tubes ad 300 mllo alveol. The Webel model s wdely used aalytcal ad umercal predcto because of the coveet symmetrc structure [34]. However, the arway brachg the real lug does ot ed abruptly at geerato 3, so Hase ad Ampaya [69] refed the Webel model by performg detaled aalyses of the alveolar regos, cocludg that the lug has 7 geeratos of arways. Also, the system developed by Webel wth the doublg of the arways at each geerato was replaced by a system where the umber of arways was creased at each geerato up to geerato 4, the decreased utl geerato 7. Hase ad Ampaya dstgushed 6 dfferet types of alveol ad cocluded that there were fact 450 mllo alveol the lug. Horsfeld [70] developed a more realstc model where the brachg structure of the arways s asymmetrc but ths patter of asymmetry s costat. I realty, the termal brocholes requre a dfferet patter of asymmetry, so for more sophstcated computatoal aalyses, computer models developed from computer tomography (T) scas show more promse [7]. For the curret research, however, the terest arway brachg structure s focused o the frst few geeratos ad so the Webel ad Horsfeld models are adequate. 33

63 .3.. Mechacal Models omputer models that use lumped parameters to descrbe lug mechacs are ofte used to vestgate the effects of lug developmet ad dseases o respratory measuremets. Such models ca also be used to determe the teracto of the respratory system wth respratory support equpmet ad vetlato techques. The smplest model to descrbe lug mechacs s a sgle compartmet model (Fgure.5a) cosstg of a sgle complace ad a sgle resstace R (the R model) [7]. Ths model s sutable for smple tdal breathg predctos but s adequate for hgher frequecy aalyss due to the lack of ertace I. Addg ertace to the model (the RI model Fgure.5b) meas that t s useful the study of smple maturato studes due to the small umber of requred model parameters [73]. Mead [74] suggested a model wth seve parameters (Fgure.5d); ertace I, cetral ad perpheral resstaces (R c ad R p ) ad lug, chest wall, brochal ad extrathoracc complaces ( l, w, b ad e ). Although t cosders these further propertes ad s able to smulate the flueces of mask leaks ad complace o the respratory system as well as the effects of brochole obstructo, t stll remas a exteded verso of a sgle compartmet model ad caot smulate ueve vetlato. Vscoelastc models that separate arway ad tssue propertes to separate regos are also avalable the lterature. Athaasades et al. [75] used a vscoelastc model (show Fgure.6) to calculate the work of breath ormal adults. R u, R c, R s ad R ve are the upper arways, collapsble arways, small arways ad vscoelastc elemet resstaces. c, l, ve ad cw are the collapsble arways, lug tssue, vscoelastc elemet ad chest wall complaces. P mus ad P atm are the pressure due to muscle actvty ad the atmosphere. Lu et al. [76] used the same type of model but added a pulmoary crculato model (to descrbe gas exchage at the alveolarcapllary membrae) whch could accurately predct the expred gas cocetratos. These models however, do ot clude the ertace whch make t adequate for smulatos that volve frequeces much hgher tha breathg frequeces ad also 34

64 lke the Mead model [74] are sgle compartmet models as well whch lmt ther use vetlato dstrbuto studes. Fgure.5 Lug models to model respratory system mechacs [73]. Fgure.6 Vscoelastc model as used by Athaasades et al. [75]. 35

65 Tomlso et al. [77, 78] also uses a sgle compartmet model of a adult lug to smulate pressure, flow ad volume. However, ulke Mead [74] ad Athaasades [75], the Tomlso model cludes flow-depedat resstace the upper arways as well as lug ad chest wall vscoelastcty ad ertace. More expermetal data s stll requred to correlate wth the model, however, t does show promse beg used dyamc studes. A two-compartmet model (Fgure.5c) as proposed by Schmdt [73] ad rooke ad Head [79] s well suted to vestgatos of ueve vetlato. The values of, I ad R ca be adjusted to reflect dfferet pathologes. These models ca predct tdal volumes, flows ad pressures each compartmet that could be of terest to clcas. The models however do ot clude arway ad chest wall complace. These types of models, although a mprovemet from the sgle compartmet model, do ot cosder flow depedat resstace whch s mportat descrbg the upper arways [80]. A model by Polak ad Lutche [8] uses a asymmetrc Horsfeld brochal tree that leads to several depedet alveolar compartmets. Vscoelastc propertes of the lobes ad the erta of arway walls are eglected. Also, the mechacal propertes are assumed ot to vary betwee compartmets such that the oly source of compartmetal flow heterogeety s the asymmetry of the brochal tree. The model predcts expratory flow ad pressure but predctos are ot dyamc or valdated Overvew A revew of the morphometrc ad mechacal models avalable the lterature have bee preseted. Sgle compartmet models, regardless of the varous regoal resstaces ad complaces that may be corporated are stll ot able to model the effects of ueve vetlato. Mult-compartmetal models the lterature eglect ertace, chest wall mechacs or a varato mechacal propertes betwee compartmets. Thus, there exsts a eed for models that corporate ertace to eable aalyss at frequeces hgher tha typcal breathg frequeces ad multple compartmets that have dvdual mechacal ad physcal propertes to better model the ueve dstrbuto of vetlato dseased lugs. Also, model predctos the lterature mostly represet adult values wth oly a few fat models predctg overall 36

66 respratory varables. The lack of eoatal lug parameters makes t dffcult to accurately quatfy predctos for eoates..4. Modellg Surfactat Dyamcs Surfactat dysfucto plays a major role RDS. Uderstadg the mechasms of surfactat trasport durg oscllatory treatmets such as Bubble PAP wll help uderstad the possble beefts of usg surfactat therapy cojucto wth Bubble PAP. Measuremets o dyamc surfactat fucto (as occurs the alveol) have bee performed usg surface teso measurg devces such as pulsatg bubble surfactometers (PBS) ad captve bubble surfactometers (BS). Mathematcal models have also bee developed that help to uderstad the mechasms of surfactat trasport uder dfferet vetlato types ad surfactat therapes. They are frequetly approxmated as a sgle sphercal alveolus surrouded by flud. A revew of the mathematcal models developed to date are preseted ths secto due to ther promse beg used the preset research to detfy the possble surface teso beefts of troducg pressure oscllatos at the level of the alveol. Hor ad Davs [8] were the frst to troduce a comprehesve model that descrbed surface teso surfactat that uderwet dyamc area chages. The alveolus was approxmated as a sphercal elastc membrae that cotaed a shell of compressble lqud surroudg a gas. The gas-lqud terface (as wth subsequet models) s the ste of surfactat actvty. The model cosdered dffuso ad adsorpto of surfactat molecules ad vscoelastc behavor of the bulk ad terface. They cocluded that although bulk vscosty dd ot cotrbute to lug hysteress (sce the alveolar lg s too th), surface vscosty had sgfcat effects. The use of the Hor ad Davs model s restrcted to ear equlbrum behavour however, sce t made o provso for overcompresso or squeeze-out of surfactat from the surfactat layer at the gas-lqud terface. Ots et al. [83] modelled surfactat behavour of Surfactat TA as observed a PBS. The problem was smplfed by assumg that the sphercal bubble of ar was surrouded a fte soluto of surfactat. The adsorpto ad desorpto of surfactat to ad from the gas-lqud terface was characterzed by Lagmur ketcs 37

67 ad three terfacal surfactat cocetrato regmes. Dffuso was eglected but realty a dffusoal boudary layer wll develop aroud the gas-lqud terface makg the trasport through ths boudary layer more complex. However, the model dd have success descrbg the steady-state oscllatory dyamcs that t provded good agreemet wth expermetal values at steady state for a varety of cyclg frequeces (-00 cycles/m) ad bulk cocetratos. Morrs et al. [84, 85] corporated the effects of dffuso to the Ots model. By usg the methods of hag ad Frases [86], they corporated the covecto-dffuso equato to the model such that the bulk cocetrato becomes tme ad space depedat. The Morrs model was able to smulate traset effects ad surfactat cocetratos just below the gas-lqud terface. It also showed a creased agreemet wth expermetal results o urosurf (a commercal surfactat) performed by Schurch et al. [87]. To date, the models dscussed have bee used to vestgate surface teso behavour uder typcal breathg frequeces ad ampltudes. Its ablty to be used to vestgate the effect of addg pressure oscllatos supermposed o the breath sgal have ot yet bee performed. Also, o such expermets o surface teso measurg devces have bee performed to date wth whch to valdate such predctos..5. Research Pla ad Objectves A revew of the lterature reveals that although there are a varety of respratory system models the lterature, predctos o eoatal respratory parameters stll remas largely udefed mostly due to the lack of put parameters. Models that clude vscoelastc ad ertve propertes ofte are sgle-compartmet models ad multcompartmet models ether gore ertace or have uform mechacal propertes across compartmets. Prevous models have maaged to smulate respratory behavour durg ormal ad forced breathg movemets ad durg vetlato. The respose of the respratory system to oscllatory techques such as the Bubble PAP System s stll to be accurately modelled. 38

68 Thus, there s a eed for more descrptve mult-compartmetal models that seek to model the effect of pressure oscllatos o eoatal respratory performace. Also, surfactat behavor has bee modelled the lterature for ormal breathg frequeces ad volume excursos. The behavor of surface teso the alveol uder the fluece of added pressure oscllatos has ot bee modelled or expermetally determed. Therefore, the objectves of the curret research are to: reate a orgal mult-compartmetal model of the eoatal lug that cludes compartmet-specfc ertace ad vscoelastcty as well as better defed mechacal ad physcal parameters determed from measuremets o actual eoatal lugs. Valdate the model wth expermetal data obtaed from clcal trals. Use the model to determe the mechacal effect of pressure oscllatos as produced by the Bubble PAP System o respratory performace. Determe the role that frequeces of oscllato play provdg the optmal respratory support. Buld a surface teso model that smulates surface teso dyamcs a alveolus exposed to pressure oscllato frequeces the rage typcally produced by the Bubble PAP System. Valdate the surface teso model wth expermets coducted o a custom-bult PBS..6. losure Ths chapter preseted the kowledge to date o the kow effects ad mechasms of mprovemet of vetlatory treatmets that use pressure oscllatos. HFV, BVV ad the 39

69 Bubble PAP System were hghlghted as the major examples. lcal studes proposg the beefts of usg Bubble PAP have bee dscussed. The relevat models that have bee developed to date o respratory mechacs ad surfactat dyamcs were metoed ad the value of those models to the curret research feld was oted. As a result, the objectves of the research were developed to further expermetally ad theoretcally vestgate the mechacal effect of pressure oscllatos o eoatal respratory performace. 40

70 HAPTER 3 3. Respratory System Model 3.. Itroducto Ths chapter cotas the complete dervato of the ove respratory system model used to predct the work of breath (WOB) at predefed locatos wth the respratory system. Also, the parameters used the model are fully defed for both 8 day (preterm) ad 4 day (ear-term) gestato lambs ths chapter. Secto 3. dscusses the phlosophy of the model formulato ad descrbes the lumped parameter model used ths research. Expressos for the pressures each detfed secto of the lumped model are derved. Secto 3.3 descrbes the expressos of the mass flow rates each secto, derved from the o-dmesoal, emprcal Reyolds-Lee relatoshps for the arways ad from smple resstace relatoshps for the lobes. Secto 3.4 cotas the dervatos that descrbe the wall moto each lobe ad the pleural compartmet. The methods ad results for the emprcally measured parameters (lug/lobe masses, pressure-volume curves ad arway dmesos) that were eeded for the model are preseted Secto 3.5. Parameters that were obtaed from the exstg lterature for the model are summarsed Secto 3.6. The Smulk model ad ts use wth the Matlab evromet s descrbed Secto Model Formulato The brochal tree s a complex bfurcatg etwork of arways whch accordg to the Webel model [68] dvdes 3 tmes before formg mllos of alveolar sacs humas. However, whe defg the dfferet elemets of the respratory system usg lumped parameter modellg, the complexty of the mathematcal model ca be reduced so that pressures, flows ad volumes are assumed to be uform wth well defed cotrol 4

71 volumes. The lug ca the be descrbed as a system of brached arways, cosstg of the trachea (wdppe) ad broch (subsequet arways), leadg to 5 chambers that represet the 5 separate lobes preset the actual lug. Each lobe has ts ow set of mechacal propertes that are descrbed terms of elastcty, erta ad dampg elemets. As a result, the model developed ths chapter s able to accout for the behavour of a 5-compartmet lug wth dfferg mechacal propertes ad lug capactes, as well as dspartes betwee spratory ad expratory arway resstaces. It was ot physcally possble to accurately obta emprcal measuremets such as pressure-volume, mass ad dmeso measuremets for sub-lobar segmets to determe regoal mechacal ad physcal propertes wth each lobe, thus restrctg the curret model to a maxmum of 5 compartmets. The output of the model cludes arway pressures, flow rates ad volumes at the arway opeg ad at the dvdual lobes. These are used to calculate the WOB at each locato as a measure of respratory performace uder dfferet vetlato strateges. The ove respratory system s modelled ths chapter. Preterm ad ear-term respratory outputs ca be modelled by chagg the parameters to sut. Ove lugs are used frequetly clcal trals o eoatal respratory mechacs due to the smlarty sze, physologcal parameters ad establshed relatoshps betwee ove ad huma gestatos. Moreover, lmtatos o huma expermetato make the ove model a attractve alteratve to vestgate respratory parameters. The arways ad 5 lobar regos represeted the ove respratory system model are show Fgure 3. (ot to scale) ad amed Table 3. such a way as to reflect aatomcal locato. The dyamcs of the model are formulated by assumg that a uform (but tme varyg) pressure exsts each secto ad that the rate of chage of that pressure s depedet o the flow to ad out of the secto as well as ay elastc, resstve or ertve forces preset. A schematc dagram of the lumped sectos of the lug s show Fgure 3.. The tracheo-brochal tree, startg from the trachea, dvdes successvely to the varous secodary broch that lead to ther respectve lobes. The 4

72 respectve pressures ad mass flow rates preset each secto are show the fgure ad defed more detal thereafter. The umbers correspod to those Table Fgure 3. The elemets of the ove respratory system model. Table 3. The 7 elemets of the ove respratory system model. - Upper trachea 0 - Rght posteror daphragmatc brochus - Lower trachea - Left posteror daphragmatc brochus 3 - Rght apcal brochus - Rght ateror daphragmatc brochus 4 - Rght ma brochus 3 - Rght apcal lobe 5 - Left ma brochus 4 - Rght cardac lobe 6 - Rght cardac brochus 5 - Left cardac lobe 7 - Left cardac brochus 6 - Rght daphragmatc lobe 8 - Rght major daphragmatc brochus 7 - Left daphragmatc lobe 9 - Left major daphragmatc brochus 43

73 P terface m up trachea m R ap wall 3 P R ap lobe m R ap lobe P R ap 3 m R ap m md trachea m low trachea P up trachea m ma P low trachea m R card wall 4 P R card P R post daph P R maj daph P R at daph P R card lobe m R card lobe m 0 6 P R ma m R post daph R post daph lobe m R card m m R majdaph 8 m R ma R broch m R at daph m L ma 4 5 m R at daph lobe m R majdaph lobe m m L majdaph L broch 9 P L ma m L card m L post daph m L majdaph lobe 7 m m L post daph lobe P L card lobe m L card wall 5 L card lobe P L card P L post daph P Lmaj daph P L daph lobe P R daph lobe 6 m R daph wall 7 m L daph wall Fgure 3. Schematc dagram of the lumped respratory system (showg secto umberg) 44

74 3... Model Assumptos Humdty effects are eglected ad all physcal propertes ad costats are evaluated at a costat temperature of 39 o (3 K).e. lamb rectal temperature. Resstaces of the arways the lobe ad the collectve resstace of the lobes are assumed to be costat ad the oly teracto betwee lobes s assumed to occur at the brach pots of the broch leadg to the lobes. Ideal gas s assumed ad gas compressblty s eglected sce the Mach umbers have bee calculated to be <0. for typcal flows all arways. Lobe surface area s assumed to rema costat ulke realty where the area chages wth lug volume. Sce ths relatoshp s ucharactersed for premature lambs, a costat surface area s assumed. Lobe ad arway pressures are assumed to be uform. Although realty there are varatos pressure wth the lobe, ths assumpto s adequate for the preset level of vestgato where the treds overall dffereces respratory parameters across lobes are of cosderato. Such effects ca be added to the model the future by addg more compartmets to the dvdual lobes to accout for regoal pressure varatos. The arways are assumed to be straght wth costat crcular cross-secto. Arways ca also be modelled as collapsble tubes f desred, based o the crosssectoal area-trasmural pressure relatoshp. Ths relatoshp s udefed the lterature for premature eoatal lambs. The trachea ad prmary broch cota cartlage ad some remats of cartlage whch are stll preset at the level of the secodary broch. Ths makes these arways more rgd tha the rest of the coductg arways. Therefore, to reduce the complexty of the model ad crease solver effcecy, elemetary dsspatve pressure losses a bfurcatg arway system s modelled as the prmary pressure-loss pheomeo. However, the model retas fudametal features of arway brachg, mechacal ad physcal propertes. It s also costructed so as to facltate the addto of brochal wall complace future studes that may be coducted ths area Model Developmet The rate of chage of pressure sectos - ca be derved from the deal gas equato of state. 45

75 Psec tovsec to = msec to RT (3.) where P sec to s the absolute pressure wth the secto (Pa) V sec to s the volume of the secto (m 3 ) m sec to s the mass of ar the secto (kg) R s the specfc gas costat of ar at 3 K (Pa.m 3 /(kg.k)) T s the temperature Kelv (K) If we cosder a tme varyg pressure ay partcular secto, equato (3.) becomes d( Psec to Vsec to ) d( msec to RT ) = (3.) dt dt Assumg V sec to, R ad T costat, equato (3.) becomes dp sec to dt RT dmsec to = (3.3) V dt sec to Applyg the coservato of mass to a secto gves the chage the mass of ar that secto, m sec to. Ths ca be wrtte as m sec = m m (3.4) to out where m s the mass that eters the secto ad secto. For a tme varyg system, m out s the mass that leaves the dm dt d( m mout = (3.5) dt sec to ) 46

76 ad thus dm sec to dt = d dt ( m mout ) = m m out (3.6) Equato (3.3) ca ow be wrtte as dp sec to dt = RT V sec to ( m m ) out (3.7) For regos 3 to 7 (the lobes), where the volume of the rego vares wth tme, equato (3.3) chages to d( P lobe dt V lobe ) = dm dt lobe RT (3.8) whch ca be expaded to the followg form. dp lobe dt V lobe dvlobe Plobe = ( m m out )RT (3.9) dt Equatos (3.7) ad (3.9) ca be used to obta expressos of the pressure the dvdual arway segmets ad lobes respectvely. The mass flow rates ad pressures volved are those preseted Fgure 3.. Applyg equato (3.7) to sectos - leads to: dp dt up trachea up trachea ( m m ) RT = up trachea md trachea (3.0) V for the upper trachea, where m m m md trachea = (3.) low trachea R ap 47

77 For the lower trachea dp low trachea dt RT = ( m low trachea m ma ) (3.) V low trachea where m = m m (3.3) ma L ma R ma For the rght apcal brochus dp dt R ap R ap ( m m ) RT = R ap R ap lobe (3.4) V For the rght ma brochus dp dt R ma RT = ( m R ma m R broch ) (3.5) V R ma where m = m m m m (3.6) R broch R card R majdaph R post daph R at daph For the left ma brochus dp dt L ma RT = ( m L ma m L broch ) (3.7) V L ma where m = m m m (3.8) L broch L card L majdaph L post daph For the rght cardac brochus dp dt R card RT = ( m R card m R card lobe ) (3.9) V R card For the left cardac brochus 48

78 dp dt L card RT = ( m L card m L card lobe ) (3.0) V L card For the rght major daphragmatc brochus dp R majdaph dt R majdaph ( m m ) RT = R majdaph R majdaph lobe (3.) V For the left major daphragmatc brochus dp L majdaph dt L majdaph ( m m ) RT = L majdaph L majdaph lobe (3.) V For the rght posteror daphragmatc brochus dp R post daph dt R post daph ( m m ) RT = R post daph R post daph lobe (3.3) V For the left posteror daphragmatc brochus dp L post daph dt L post daph ( m m ) RT = L post daph L post daph lobe (3.4) V For the rght ateror daphragmatc brochus dp R at daph dt R at daph ( m m ) RT = R at daph R at daph lobe (3.5) V Usg equato (3.9), the pressure each lobe (regos 3-7) ca be wrtte as follows. For the rght apcal lobe dp R ap lobe dt V R ap lobe dvr ap lobe PR ap lobe = ( m R ap lobe m R ap wall )RT (3.6) dt 49

79 For the rght cardac lobe dp R card lobe dt V R card lobe dvr card lobe PR card lobe = ( m R card lobe m R card wall )RT (3.7) dt For the left cardac lobe dp L card lobe dt V L card lobe dvl card lobe PL card lobe = ( m L card lobe m L card wall )RT (3.8) dt For the rght daphragmatc lobe dp R daph lobe dt V R daph lobe dvr daph lobe PR daph lobe = ( m R daph lobe m R daph wall )RT (3.9) dt where m = m m m (3.30) R daph lobe R majdaph lobe R post daph lobe R at daph lobe For the left daphragmatc lobe dp L daph lobe dt V L daph lobe dvl daph lobe PL daph lobe = ( m L daph lobe m L daph wall )RT (3.3) dt where m = m m (3.3) L daph lobe L majdaph lobe L post daph lobe I ths secto, expressos have bee derved to descrbe the chage pressure each secto due to the flow rates ad physcal propertes of each secto. The mass flow rates equatos (3.0) to (3.3) stll eed to be determed by separate relatoshps to resolve the model. These are derved the followg secto. 50

80 3.3. Mass Flow Rate Expressos Thus far, the mass flow rates the dervato represet the mass flow at specfc pots.e. at the boudares of each secto. The walls sectos - cota varyg amouts of cartlage ad so may be cosdered to be vastly more rgd tha subsequet arways. I order to smplfy the model for the purposes of ths study, sectos - are assumed to be rgd. Ths mples that there s o varato mass sectos -. The sectos are also very short ( the order of a few cetmetres) such that ay pressure varatos wth the secto are very small ad ca be gored. It ca thus be assumed that the pressure at each boudary s equal to the pressure the secto that s stuated upwd from that boudary. I the smplest case, mass flow rate ca be determed by the pressure-flow characterstcs as descrbed by Poseulle s equato for lamar flow straght, crcular tubes. However, the mass flow rate a moopodal brachg etwork ca be more accurately determed by emprcal relatos developed by Reyolds ad Lee [88] where the total pressure loss a cae arway segmet Ptotal was foud to be related to the flow rate ad ts square for Reyolds umbers tested up to 0,000. The followg calculatos show how the Reyolds-Lee equatos [88] ca be used to descrbe the spratory ad expratory mass flows the tracheal ad brochal segmets as a fucto of Poseulle pressure drop across that segmet ( Number (Re). Pposeulle ) ad the Reyolds Reyolds ad Lee descrbe ther data usg a dmesoless Rohrer equato: total ( a b ) Pposeulle P = Re (3.33) where a ad b are scalg coeffcets as defed by Reyolds ad Lee ad are lsted Table 3. for the trachea ad subsequet arways. The values of a are much larger for exprato tha for sprato for a gve arway, meag that statc pressure drop s much larger for exprato tha sprato. The values for b rema smlar for both 5

81 sprato ad exprato a partcular arway. Reyolds ad Lee attrbute the creased loss pressure durg exprato to the effects of the bfurcatos precedg tracheal flow as ar travels up from the smaller arways, out to the arway opeg. Table 3. Scalg factors Reyolds-Lee equato [88]. Isprato Exprato a b a b Tracheal Segmets All Arways Below Trachea The statc pressure drop across the secto P sec to ca be expressed as: P = P P = ( a b Re) Pposeulle sec to upwd sec to (3.34) where P upwd s the pressure o the upwd boudary ad 8µ L Pposeulle = m sec to (3.35) πd ρ sec to 4 sec to I equato (3.35) respectvely. L sec to ad D sec to are the legth ad dameter of the secto m sec to s the mass flow through the secto ad µ ad ρ are the dyamc vscosty ad desty of the ar at 3.5K. ombg equatos (3.34) ad (3.35) ad solvg for the mass flow rate gves 4 Psec to πdsecto ρ = (3.36) m ( a b Re) 8µ Lsecto Substtutg values for a ad b for each respectve arway, we arrve at the followg expressos for the dvdual arway segmets (sectos to ). 5

82 For sprato: The mass flow rate the upper trachea s 4 Pterface Pup trachea πdup trachea ρ up trachea = (3.37) m ( Re) 8µ Lup trachea The mass flow rate the lower trachea s P P 4 up trachea low trachea πdlow trachea ρ low trachea = (3.38) m ( Re) 8µ Llow trachea The mass flow rate the rght apcal brochus s 4 Pup trachea PR ap πdr ap ρ R ap = (3.39) m ( Re) 8µ LR ap The mass flow rate the left ma brochus s 4 Plow trachea PL ma πdl ma ρ L ma = (3.40) m ( Re) 8µ LL ma The mass flow rate the rght ma brochus s 4 Plow trachea PR ma πdr ma ρ R ma = (3.4) m ( Re) 8µ LR ma The mass flow rate the left cardac brochus s 4 PL ma PL card πdl card ρ L card = (3.4) m ( Re) 8µ LL card The mass flow rate the left major daphragmatc brochus s 4 PL ma PL majdaph πdl majdaph ρ m L majdaph = (3.43) ( Re) 8µ LL majdaph 53

83 The mass flow rate the left posteror daphragmatc brochus s 4 PL ma PL post daph πdl post daph ρ L post daph = (3.44) m ( Re) 8µ LL post daph The mass flow rate the rght cardac brochus s 4 PR ma PR card πdr card ρ R card = (3.45) m ( Re) 8µ LR card The mass flow rate the rght major daphragmatc brochus s 4 PR ma PR majdaph πdr majdaph ρ R majdaph = (3.46) m ( Re) 8µ LR majdaph The mass flow rate the rght posteror daphragmatc brochus s 4 PR ma PR post daph πdr post daph ρ R post daph = (3.47) m ( Re) 8µ LR post daph The mass flow rate the rght ateror daphragmatc brochus s 4 PR ma PR at daph πdr at daph ρ R at daph = (3.48) m ( Re) 8µ LR at daph For exprato: The mass flow rate the upper trachea s 4 Pt Pup trachea πdup trachea ρ up trachea = (3.49) m ( Re) 8µ Lup trachea The mass flow rate the lower trachea s 54

84 P P 4 up trachea low trachea πdlow trachea ρ low trachea = (3.50) m ( Re) 8µ Llow trachea The mass flow rate the rght apcal brochus s 4 Pup trachea PR ap πdr ap ρ R ap = (3.5) m ( Re) 8µ LR ap The mass flow rate the left ma brochus s 4 Plow trachea PL ma πdl ma ρ L ma = (3.5) m ( Re) 8µ LL ma The mass flow rate the rght ma brochus s 4 Plow trachea PR ma πdr ma ρ R ma = (3.53) m ( Re) 8µ LR ma The mass flow rate the left cardac brochus s 4 PL ma PL card πdl card ρ L card = (3.54) m ( Re) 8µ LL card The mass flow rate the left major daphragmatc brochus s 4 PL ma PL majdaph πdl majdaph ρ L majdaph = (3.55) m ( Re) 8µ LL majdaph The mass flow rate the left posteror daphragmatc brochus s 4 PL ma PL post daph πdl post daph ρ L post daph = (3.56) m ( Re) 8µ LL post daph The mass flow rate the rght cardac brochus s 55

85 4 PR ma PR card πdr card ρ R card = (3.57) m ( Re) 8µ LR card The mass flow rate the rght major daphragmatc brochus s 4 PR ma PR majdaph πdr majdaph ρ R majdaph = (3.58) m ( Re) 8µ LR majdaph The mass flow rate the rght posteror daphragmatc brochus s 4 PR ma PR post daph πdr post daph ρ R post daph = (3.59) m ( Re) 8µ LR post daph The mass flow rate the rght ateror daphragmatc brochus s 4 PR ma PR at daph πdr at daph ρ R at daph = (3.60) m ( Re) 8µ LR at daph The mass flow rates that eter the lobes are depedet o the coductace of the dvdual lobes ad the dfferece pressure betwee the lobe ad the secto precedg t. Values for the total coductace of the arways that make up the dvdual lobes are assumed to be costats. The mass flow rate to a partcular lobe may be expressed as ( Psecto Plobe ) lobe m = (3.6) Applyg ths to each lobe gves the followg mass flow rates: The mass flow rate to rght apcal lobe R ap lobe ( PR ap PR ap lobe ) R ap lobe m = (3.6) 56

86 The mass flow rate to the rght cardac lobe R card lobe ( PR card PR card lobe ) R card lobe m = (3.63) The mass flow rate to the rght daphragmatc lobe from the rght major daphragmatc brochus R majdaph lobe ( PR majdaph PR daph lobe ) R daph lobe m = (3.64) The mass flow rate to the rght daphragmatc lobe from the rght posteror daphragmatc brochus R post daph lobe ( PR post daph PR daph lobe ) R daph lobe m = (3.65) The mass flow rate to the rght daphragmatc lobe from the rght ateror daphragmatc brochus R at daph lobe ( PR at daph PR daph lobe ) R daph lobe m = (3.66) The mass flow rate to the left cardac lobe L card lobe ( PL card PL card lobe ) L card lobe m = (3.67) The mass flow rate to the left daphragmatc lobe from the left major daphragmatc brochus L majdaph lobe ( PL majdaph PL daph lobe ) L daph lobe m = (3.68) The mass flow rate to the left daphragmatc lobe from the left posteror daphragmatc brochus L post daph lobe ( PL post daph PL daph lobe ) L daph lobe m = (3.69) m R ap wall, R card wall m, R daph wall m, L card wall m ad m are caused by the dsplacemet L daph wall of the lobe walls ad wll be defed the followg secto. 57

87 3.4. Lobe Dyamcs Assumptos ad Justfcatos The 5-lobe model preseted ths secto s well suted to descrbe the ueve dstrbuto of vetlato across the lobes ad the homogeetes eoatal lug mechacs. The cosderato of the dfferet propertes of each lobe creases the umber of parameters sgfcatly. So far, the practcal value of such a model for smulato studes premature eoates s lmted because a great umber of referece values ad parameters are ukow. However, sectos 3.5 ad 3.6, t wll be demostrated how the varous parameters for a premature ove lug requred for the model were collected through expermet ad calculatos based o referece values from the lterature. A mechacal model whch allows drect substtuto of most measured parameters s used to descrbe the mechacs of each lobe. The cocept of a movg psto of a mass M lobe forms the bass of the model. It accouts for the moto of the lobe wall ad the gas flow effects. A varable sprg stffess ( k lobe ) descrbes the elastc propertes of the lobe ad a costat vscous resstace ( f lobe ) descrbes the vscous resstace of the lug tssue. The ertve, elastc ad vscous forces caused by these elemets act o the psto (lobe) area ( the pressure the lobe ( P lobe A lobe ), whch s equvalet to the lobe wall. The psto s subject to ) ad the pleural pressure ( P pleural ). Lobe pressures are assumed to be uform ad the area of the psto remas costat, although realty there are varatos pressure wth the lobe ad the surface area of the lobe chages wth a chage volume (chagg the predcted pressures the lobe). Such effects ca be added to the model the future by addg more compartmets to the dvdual lobes to accout for regoal pressure varatos ad by determg the surface arealug volume relatoshp to accout for the chagg surface area Lobe Dyamcs Developmet A geeral form of the equato of moto s derved based o the schematc dagram Fgure 3.3. Subsequetly, the dvdual expressos for each lobe are preseted. 58

88 Brochus leadg to Lobe k lobe P P lobe pleural f lobe x lobe wall Fgure 3.3 Geeral schematc for a lobe sprg mass damper system. Applyg Newto s secod law, the equato of moto for the lobe wall ca be wrtte as: dx dt d x ( Plobe Ppleural ) Alobe M lobe lobe wall lobe wall k lobexlobe wall flobe = (3.70) dt d xlobe wall dx wall where, dt dt of the lobe wall respectvely. lobe ad lobe wall x are the accelerato, velocty ad dsplacemet The mass flow rate of ar caused by the moto of the lobe wall may be expressed as: dxlobe wall m lobe wall = ρalobe (3.7) dt where ρ s the ar desty at 3.5K. The lobe volume ( V lobe ) s regarded as a cotrol volume whch s determed from the dsplacemet of the lobe wall ( x lobe wall ) multpled by the psto surface area ( A lobe ), such that V = A x (3.7) lobe lobe lobe wall 59

89 Usg equatos (3.70) to (3.7), the equvalet expressos for each dvdual lobe are obtaed. For the rght apcal lobe dxr ap wall d xr ap wall k R ap xr ap wall f R ap ( PR ap lobe Ppleural ) AR ap = M R ap (3.73) dt dt dx wall m A R ap R ap wall = ρ R ap (3.74) dt V = A x (3.75) R ap lobe R ap R ap wall For the rght cardac lobe dx d x ( PR card lobe Ppleural ) AR card M R card R card wall R card wall k R card xr card wall f R card = (3.76) dt dt dxr card wall m R card wall = ρar card (3.77) dt V = A x (3.78) R card lobe R card R card wall For the rght daphragmatc lobe dxr daph wall k R daph xr daph wall f R daph = dt ( PR daph lobe Ppleural ) AR daph M R daph 79) d x R daph wall dt (3. dxr daph wall m R daph wall = ρar daph (3.80) dt 60

90 V = A x (3.8) R daph lobe R daph R daph wall For the left cardac lobe dx d x ( PL card lobe Ppleural ) AL card M L card L card wall L card wall k L card xl card wall f L card = (3.8) dt dt dxl card L card wall = ρal card (3.83) dt m wall V = A x (3.84) L card lobe L card L card wall For the left daphragmatc lobe dxl daph wall k L daph xl daph wall f L daph = dt ( PL daph lobe Ppleural ) AL daph M L daph d x L daph wall dt (3.85) dxl daph wall m L daph wall = ρal daph (3.86) dt V = A x (3.87) L daph lobe L daph L daph wall The Pleural ompartmet ad hest Wall The pleural compartmet s modelled alog smlar les to the lobes as see Fgure 3.4. However, t has two otable dffereces, () there s o ar flow to or out of the compartmet ad () t s a closed compartmet that s flled wth pleural lqud (stead of ar as the lug). A equvalet varable stffess ( k pleural ) s assumed to represet the elastc propertes of the rbcage, daphragm ad pleural flud ad tssue. Also, these propertes geerate a equvalet vscous resstace ( f pleural ) whch s assumed to act o the pleural wall of a 6

91 equvalet surface area x ) A pleural. The combed movemet of the lobe walls ( lobe wall total s the sum of x R ap wall, R card wall x, x R daph wall, x L card wall ad x L daph wall. The pleural compartmet expereces forces geerated by the pleural pressure ( P pleural ), atmospherc pressure ( P atm ) ad the thoracc force ( F th ). These forces act to chage the volume of the compartmet. F th s the force geerated by the rbcage ad daphragm muscles due to the eurogec sgals set by the bra to drve lug moto to create the tdal volume. It s the ma drvg force of the model ad dealsed as actg o a sgle pot of the pleural surface. It s commoly defed as a sgal wth a profle that follows the shape (but ot the magtude) of the tdal volume [78]. I realty, t s far more complex wth the force adaptg tself to respod to the chagg levels of oxyge ad carbo doxde the blood stream. The physologcal aspects of gas exchage ca be troduced to the model through addtoal subsystems that accout for gas dffuso at the alveolar level, the partal pressures of oxyge the bloodstream ad the resultg eural cotrol of breathg. These elemets, however, are out of the scope of ths research whch cocetrates purely o the mechacal aspects of resprato. I ormal adult resprato, regoal varatos pleural pressure exst due to the dowward-actg weght forces of the lug. However, sce eoatal subjects recevg respratory support are ever uprght, the regoal dffereces pleural pressure are much less sgfcat ad so ca be gored for the purposes of ths model. Usg Newto s secod law, the equato of moto of the pleural wall s: dx F = dt ( Ppleural Patm ) Apleural M pleural pleural pleural th kpleuralxpleural fpleural (3.88) d x dt where ad d xpleural M pleural s the mass of the movg part of the chest wall ad dt, dx pleural x pleural are the accelerato, velocty ad dsplacemet of the pleural wall dt respectvely. 6

92 P pleural P atm F th k pleural f pleural x lobe wall total x pleural Fgure 3.4 Schematc of pleural compartmet ad chest wall. Sce the flud sde the pleural compartmet s lqud, the rate of chage of the pleural pressure depeds o the expaso ad compresso of the pleural flud ad may be derved by usg the effectve bulk modulus ( B pleural ). By defto: B pleural dp pleural = dt (3.89) dvpleural Vpleural dt Rearragg, gves: dp pleural dt B = V pleural pleural dv dt pleural (3.90) dv pleural The chage the pleural compartmet volume s determed by the dt dsplacemet of the pleural ad lobe walls ad so equato (3.90) s expaded to gve: 63

93 dp pleural dt B = V pleural pleural A A pleural R daph dx pleural dt dx dt A R daph wall R ap A dx R ap wall L card dt dx A L card wall dt R card A dx R card wall L daph dt dx L daph wall dt (3.9) 3.5. Emprcally Measured Model Parameters Ths secto descrbes the procedures used ad results obtaed to determe legths ad dameters of the arways specfed Table 3., the masses of the dvdual lobes ad the chest wall ad the pressure-volume (P-V) curves of the whole lug, left lug ad rght lug. The above parameters were determed for both 8 day ad 4 day gestato lambs. Lambs were delvered va caesarea secto at 8 day ad 4 day gestato ad mmedately receved a lethal dose (00 mg/kg) of petobarbtoe (Vrbac, NSW, Australa). They were the weghed ad radomly assged to ether be used to make lug casts or coduct P-V curves o. The costat phase model [89] uses -vvo mpedace data to characterse respratory parameters such as resstace, ertace, tssue dampg ad tssue elastace. However, values calculated ths fasho are ether dffcult to covert to ther proper SI uts to ft the curret model or expressos of overall lug propertes Lug asts The followg method of producg lug casts was devsed for the purposes of ths research. Table 3.3 lsts a summary of the amals each gestato that were used to make the lug casts. Followg delvery ad euthaasa, subjects were placed the supe posto. A 5 cm slt from the base of the laryx was made through the fur, sk ad surroudg tssue to expose the trachea. Just below the laryx, a axal cut was made half way through the trachea ad a pece of a 4.5 mm teral dameter edotracheal tube was serted. Two tes were used to faste the tube to avod slppage. A syrge was placed at the etrace of the tube ad used to suck out ay excess fetal lug flud. 453g of slcoe rubber (Dow org 30 RTV mxed wth 45 g of S type catalyst) was chose as the jecto materal due to ts flexblty ad fast curg tme. Slcoe was the jected to the trachea (at 0ml/kg brthweght) usg a 60 ml syrge. A moderate to heavy pressure was ecessary to allow fuso over 0 mutes. Oce the slcoe was jected, a haemostat was used to clamp the edotracheal tube at 64

94 the etrace. The subject was the placed the proe posto ad left for hours for the slcoe to cure. Table 3.3 Descrpto of lambs used lug casts. 8 day 4 day Number of subjects 8 4 Male/Female 4/4 3/ Body weght, kg (±SD).85 (0.34) (0.44) After hours, the lug was removed from the chest cavty ad a strg was ted aroud the trachea ad suspeded from a support to a bucket of 0M soluto of potassum hydroxde (KOH). The lug was mmersed the soluto for 4 hours. After 4 hours, the lug was removed from the soluto ad ay macerated tssue that was clgg to the cast was rsed off uder cold rug water. If requred, the cast was the placed a fresh soluto of KOH for aother -4 hours ad rsed aga thereafter to reveal the complete cast. Fgure 3.5 shows the lug cast before ad after macerato by KOH. It ca be see that the slcoe reaches the level of the termal brocholes ad alveol to create a complete cast. The cast was the hug ad ar dred. Legths ad dameters of the arways detfed Table 3. were measured o all casts wth verer calpers. Table 3.4 lsts the average legth per ut brthweght measured for all 8 day ad 4 day gestato lambs. Table 3.5 lsts the average dameter per ut brthweght measured for all 8 day ad 4 day gestato lambs. A B Fgure 3.5 Lug casts before (a) ad after (b) macerato by KOH. 65

95 Table 3.4 Average arway legths per ut brthweght for 8 day ad 4 day gestato lambs. Arway Number ad Descrpto Legth/brthweght, mm/kg (±SD) 8 Day 4 Day - Upper trachea 37. (.7).9 (3.) - Lower trachea 8.85 (.0) 6.06 (0.49) 3 - Rght apcal brochus.48 (0.38).7 (0.45) 4 - Rght ma brochus 3.59 (0.40).50 (0.) 5 - Left ma brochus.74 (0.30).04 (0.4) 6 - Rght cardac brochus.08 (0.36).39 (0.34) 7 - Left cardac brochus.99 (0.7).06 (0.) 8 - Rght major daphragmatc brochus.83 (0.47).56 (0.3) 9 - Left major daphragmatc brochus.5 (0.3).3 (0.) 0 - Rght posteror daphragmatc brochus.56 (0.3). (0.03) - Left posteror daphragmatc brochus.88 (0.40).64 (0.6) - Rght ateror daphragmatc brochus.75 (0.3).68 (0.63) Table 3.5 Average arway dameters per ut brthweght for 8 day ad 4 day gestato lambs. Arway Number ad Descrpto Dameter/brthweght, mm/kg (±SD) 8 Day 4 Day - Upper trachea.64 (0.0).73 (0.8) - Lower trachea.48 (0.4).6 (0.) 3 - Rght apcal brochus.35 (0.7).44 (0.) 4 - Rght ma brochus.9 (0.7).48 (0.6) 5 - Left ma brochus. (0.9).38 (0.9) 6 - Rght cardac brochus.6 (0.3).4 (0.8) 7 - Left cardac brochus.36 (0.6) 0.93 (0.06) 8 - Rght major daphragmatc brochus.03 (0.3) 0.69 (0.8) 9 - Left major daphragmatc brochus.08 (0.) 0.73 (0.4) 0 - Rght posteror daphragmatc brochus 0.84 (0.8) 0.59 (0.07) - Left posteror daphragmatc brochus 0.84 (0.) 0.57(0.09) - Rght ateror daphragmatc brochus 0.89 (0.) 0.63(0.09) Pressure-Volume urves Table 3.6 lsts a summary of the amals each gestato that were used the P-V curves. Repeated P-V curves for each cycle of flato ad deflato due to gas trappg the lug. Therefore, each measuremet was doe oly oce o each lug ad 66

96 the same lug could ot be used for both whole-lug ad half-lug P-V curves. For each gestato, the same group of amals was used to determe the P-V curves for both the rght ad left lug. Followg delvery ad euthaasa, subjects were placed the supe posto. The rbcage was opeed ad separated from the daphragm to reveal the chest cavty (Fgure 3.6), takg care ot to pucture the lug. The cso was exteded from the top of the chest to the base of the laryx through the fur, sk ad surroudg tssue to expose the trachea. Just below the laryx, a axal cut was made half way through the trachea ad a 4.5mm teral dameter edotracheal tube was serted to the upper trachea. Two tes were used to faste the tube to the trachea to esure o slppage of the tube or leakage of ar. A syrge attached to a maometer (show Fgure 3.7) was attached to the edotracheal tube. The lug was frst flated ad the deflated at set pressures from 0 40 cm H O cremets of 5 cm H O. The volume was read from the markg of the graduated syrge at each cremet. The dead space of the syrge was also measured at the prescrbed cremets of pressure ad subtracted from the flato ad deflato volumes measured. A 50 ml syrge was used for whole-lug measuremets, whle a 60 ml syrge was used for half-lug measuremets. For the half-lug measuremets, haemostats were used to clamp the respectve broch to allow flato of the selected areas. The left ma brochus was clamped wth a haemostat to flate/deflate the rght lug. After testg the rght lug, the haemostat was the removed ad used to clamp the rght apcal brochus ad the rght ma brochus to allow the left lug to be flated/deflated. Table 3.6 Descrpto of the amals used pressure-volume curves. 8 Day 4 Day Whole Lug Rght & Left Lugs Whole Lug Rght & Left Lugs Number Body weght, kg (±SD) 3.05 (0.48) 3. (0.46) 4.99 (0.69) 5.07 (0.6) 67

97 Edotracheal Tube Exposed Lug Ope hest Wall Fgure 3.6 Subject supe posto wth ope chest exposg lug. Graduated Maometer Syrge oecto to Edotracheal Tube Exposed Lug Fgure 3.7 Measurg P-V curves wth syrge ad maometer setup. Table 3.7 shows the average volume per brthweght measured at each pressure cremet of all lugs tested at both 8 day ad 4 day gestatos. The resultg P-V curves are plotted Fgure 3.8 ad Fgure 3.9 for 8 day ad 4 day gestatos respectvely. 68

98 Table 3.7 Pressure-volume data for 8 day ad 4 day gestato lugs. Pressure (cm Water) Average Volume/Brthweght, ml/kg (±SD) 8 Day 4 Day Whole Lug Rght Lug Left Lug Whole Lug Rght Lug Left Lug (0.47) 0.66(0.5) 0.48(0.6).7(.44).7(.3).4(.33) 0.35(.5).53(.06) 0.73(0.78) 5.4(3.8) 6.46(4.) 4.59(.97) 5.3(.47).9(.06).(0.88).4(6.3).0(7.) 7.35(4.8) (.33) 4.47(.7).60(.3) 7.33(5.98) 4.90(9.6) 0.56(5.) (3.4) 5.98(.89).90(.3).66(6.65) 8.66(0.70) 3.34(5.56) (4.39) 7.36(.9) 5.0(.79) 8.48(8.55) 3.07(0.3) 6.3(7.7) (4.30) 7.30(.3) 4.83(.) 7.50(8.34).8(0.30) 5.46(6.47) (3.94) 6.39(.5).86(.7) 3.8(6.76) 8.85(9.7) 3.88(5.96) (3.39) 5.90(.58).9(.03).0(6.47) 6.97(9.).84(5.5) 0 5.(.50) 5.5(.68).5(0.95) 0.7(5.85) 6.7(8.90).0(5.6) (.90) 4.47(.45).77(0.79) 9.8(5.60) 3.86(7.39).8(5.37) (0.74).3(.87) 0.79(0.5) 9.98(.03) 8.96(3.79) 8.9(6.00) 4 Average Volume/brthweght (ml/kg) Whole Lug Rght Lug Left Lug Pressure (cm Water) Fgure 3.8 Average P-V curves for 8 day gestato whole, rght ad left lugs. 69

99 Average Volume/brthweght (ml/kg) Whole Lug Rght Lug Left Lug Pressure (cm Water) Fgure 3.9 Average P-V curves for 4 day gestato whole, rght ad left lugs. The P-V curves were measured for the left ad rght lug sce t was ot possble to dvde the lug further to test P-V curves o dvdual lobes whch would have bee the deal measuremets to make order to get the parameters for the model. Nevertheless, the rght ad left lug P-V curves were measured to ga some basc sghts to how the P-V curve of the whole lug relates to the P-V curve of dvdual lobes. Possble stress relaxato of the tssue, the large stadard devatos data ad leaks through the maometer equpmet coectos ad perforatos o the surface of the lug meat that the average volumes the rght ad left lug do ot exactly add up to the average volumes the whole lug. To the best of our kowledge, there s o avalable lterature that determes the relatoshp betwee the whole-lug P-V curves ad dvdual lobe P-V curves for ewbor lambs. Mortola et al. [90] have publshed data for kttes where dvdual lobe ad whole lug P-V curves are expressed as a percetage of the maxmum volume. They otced o systematc dfferece the statc behavour of the dvdual lobes comparso to the whole lug. The same shape was retaed ad the maxmum volume was always approxmately tmes the volume at FR for kttes. 70

100 To determe whether smlar relatos are appled to the lamb lug, Fgure 3.0 ad Fgure 3. show the P-V curves plotted as a percetage of the maxmum volume of each type of lug for 8 day ad 4 day gestatos respectvely. The P-V curves of the 4 day lug (Fgure 3.) show behavour cogruet to that descrbed by Mortola et al. [90] ad so t ca be assumed that the P-V curves of the dvdual lobes wll follow the same shape ad statc behavour of the whole-lug whe expressed as a percetage of the maxmum volume. Thus, kowg the maxmum volume of each lobe, oe s able to calculate the P-V curve of the dvdual lobe based o the shape of the whole-lug P-V curve. These calculatos are performed Secto 3.6. It s oted that the half-lug P-V curves of the 8 day lug (Fgure 3.0) does ot follow such a close relato to the whole-lug P-V curves as those for the 4 day lug (Fgure 3.) because there s a lot of varablty the data measured. The large stadard devatos the 8 day lugs may dcate the large bologcal varablty premature lambs, or that there s o relatoshp to be draw at all betwee the P-V curves of half-lugs ad whole-lugs. Due to the exploratory ature of the tal vestgatos ths study ad the fact that the half-lug measuremets the 8 day lug stll le wth the stadard devato of the whole lug measuremets, the relatoshp ca be assumed to be that of the smplest case where the shape ad statc behavour of the half-lug P-V curves the 8 day lug also follow the same treds as the P-V curves of the whole-lug. I dseased states realty, ths relatoshp wll ot hold due to the heterogeety of the dseased lug. However, oce characterzed, these relatoshps ca be added to the preset model to exted ts capabltes descrbg vetlato durg dseased states. Ths data s used the followg secto to estmate the stffess-volume relatoshp for each lobe based o assumpto derved from the lterature. 7

101 % Maxmum Average Volume/brthweght (ml/kg) Whole Lug Rght Lug Left Lug Pressure (cm Water) Fgure 3.0 Average P-V curves as a percetage of maxmum volume for 8 day gestato whole, rght ad left lugs. % Maxmum Average Volume/brthweght (ml/kg) Whole Lug Rght Lug Left Lug Pressure (cm Water) Fgure 3. Average P-V curves as a percetage of maxmum volume for 4 day gestato whole, rght ad left lugs. 7

102 Lug ad Lobe Masses After coductg the P-V curves, lugs were separated to the dfferet lobes ad weghed. The chest wall (.e. the rbcage wth the tercostal muscles) was also weghed. Table 3.8 descrbes the amals used measurg the masses. Table 3.9 cotas the average masses per brthweght for the chest wall, total lug, left lug, rght lug ad all the dvdual lobes for both 8 day ad 4 day gestato lambs. The mass dstrbuto of the lobes, rght ad left lug ad the chest wall as a percetage of the total lug mass s also calculated. These percetages wll be useful the allocato of surface areas, resstaces ad lug volumes the followg secto. Table 3.8 Descrpto of amals used to measure lug, lobe ad chest wall masses. 8 Day 4 Day Number of subjects 8 7 Body weght, kg (±SD) 3. (0.45) 5.0 (0.50) Table 3.9 Masses of lugs, lobes ad chest wall of 8 day ad 4 day gestato lambs. 8 Day 4 Day Average % of Average Average % of Average Mass/Brthweght, Total Mass, Mass/Brthweght, Total Mass, g/kg (±SD) (±SD) g/kg (±SD) (±SD) hest Wall 74.83(6.8) 56.07(3.9) 69.5(7.0) 05.04(3.57) Total Lug Mass 9.30(.37) 00.00(0.00) 33.94(3.37) 00.00(0.00) Left Lug Mass.45(.4) 4.50(.8) 4.45(.38) 4.66(.70) Rght Lug Mass 6.85(.43) 57.50(.8) 9.49(.47) 57.34(.70) Rght Apcal Lobe 4.0(0.84) 3.65(.44) 4.38(0.97).8(.00) Rght ardac Lobe.64(0.4) 9.06(.67).6(0.69) 7.66(.54) Rght Daphragmatc Lobe 0.9(0.84) 34.79(.63).49(.) 36.86(.7) Left ardac Lobe 3.95(0.48) 3.44(0.94) 4.3(0.56).77(.50) Left Daphragmatc Lobe 8.5(0.7) 9.06(.53) 0.3(0.98) 9.89(.83) 73

103 3.6. Lterature Derved Model Parameters Some of the model parameters were derved from values foud the lterature. Ths secto detals the calculatos ad estmatos performed to geerate parameters sutable for the preset model Volumes ad Surface Areas Ashraf et al. [9] measured both the weght ad volume of the left ad rght lug ewbor lambs. Also, Tg et al. [9] measured the surface area dstrbuto across the rght ad left lug ewbor lambs by electro mcroscopy. These data are summarsed Table 3.0. They suggest that the volume ad surface area dvde themselves across the left ad rght lug smlar proportos to the mass of the lug. It ca therefore be reasoed that the surface areas ad lobe volumes for the lugs measured Secto ca be calculated by assumg that the percetage dstrbuto of surface area ad lobe volume across the lobes s the same as the percetage dstrbutos of masses detfed Table 3.9. The total surface area per ut brthweght for 40 day gestato lambs s gve as 3.39 m /kg by Lpsett et al. [93] ad 4.85 m /kg by Tg et al. for ew bor lambs [9]. A average value of 4. m /kg s take as the value for a 4 day gestato lamb (ear term). The surface area per ut brthweght s less for the smaller 8 day lug, wth less alveol to cotrbute to surface area. It s felt that the best way to estmate the surface area for the 8 day gestato lug s by multplyg the value at 4 day gestato by the rato of the 8 day brthweght to the 4day brthweght (.e. 0.56), sce brthweght s commoly used to scale physologcal data. The surface area/ut brthweght for a 8 day gestato lamb s thus calculated as.3 m /kg. Average brthweght values are calculated from all amals used emprcal measuremets (.e. values from Tables 3.8 ad 3.6) The resultg surface areas for each lobe, as determed by the allocated percetage area dstrbuto, s show Table 3. for both 8 day ad 4 day gestato lugs. 74

104 The maxmum volume acheved the whole lug the pressure-volume data Table 3.7 s 8.5 ml for a 4 day lug ad 8.59 ml for a 8 day lug. The maxmum volume acheved each lobe s the calculated ad gve Table 3. by usg the allocated percetage dstrbuto of volume. These values wll be used to calculate the dvdual pressure-volume ad elastace-volume relatoshps as follows. Table 3.0 Weght, volume ad surface area dstrbuto ewbor lambs. Weght (%total lug weght) Volume (%total lug volume) Surface Area (%total lug surface area) Rght Lug Left Lug Lterature Referece Ashraf et al. [9] 58 4 Ashraf et al. [9] Tg et al. [9] Table 3. Surface areas per ut brthweght for dvdual lobes for 8 day ad 4 gestato lugs. 8 Day 4 Day Surface % of Total Surface % of Total Area/Brthweght, Surface Area Area/Brthweght, Surface Area m /kg m /kg Rght Apcal Lobe Rght ardac Lobe Rght Daphragmatc Lobe Left ardac Lobe Left Daphragmatc Lobe Table 3. Maxmum lobe volume per ut brthweght for dvdual 8 day ad 4 gestato lobes. 8 Day 4 Day Volume/Brthweght, % of Maxmum Volume/Brthweght, % of Maxmum ml/kg Whole Lug Volume ml/kg Whole Lug Volume Rght Apcal Lobe Rght ardac Lobe Rght Daphragmatc Lobe Left ardac Lobe Left Daphragmatc Lobe

105 3.6.. Pressure-Volume ad Elastace-Volume urves To formulate the P-V curves for dvdual lobes, the value at 00% of maxmum volume whole-lug P-V curves Fgure 3.0 ad Fgure 3. s set to the maxmum volume of each lobe calculated Table 3., such that the P-V data for each lobe s as descrbed Table 3.3. Table 3.3 Scaled pressure-volume data for each lobe 8 day ad 4 day gestato lugs. Pressure (cm HO) Scaled Volume/Brthweght, ml/kg 8 Day 4 Day Rght Apcal Rght ardac Rght Daph Left ardac Left Daph Rght Apcal Rght ardac Rght Daph Left ardac Left Daph Veegas et al. [94] demostrated a sgmodal relato that fts wth excellet precso the flato ad deflato P-V curves of lugs as show by equato (3.9). b V = a e ( Pc) / d (3.9) where V s the volume, P s the pressure ad a,b,c ad d are fttg parameters. I addto to characterzg the P-V curve, equato (3.9) ca also accurately estmate respratory parameters such as the elastace whch ca be expressed as 76

106 ( Pc) / d [ e ] P d Elastace = = (3.93) V b ( Pc) / d e The P-V data Table 3.3 was ftted usg equato (3.9) Mcrosoft Excel by usg the least squares method where the sum of the squared resduals was mmzed yeldg estmates of the fttg parameters a,b,c ad d ad the best-ft coeffcet R. Table 3.4 shows the fttg parameters ad best ft coeffcet for the deflato data of each lobe for both 8 day ad 4 day gestato lugs. The deflato data s used sce t s closer to P-V curves realty (sce the flato curve starts from a completely collapsed lug whch has ever bee vetlated before). Usg the values Table 3.4 ad equatos (3.9) ad (3.93), the volume ad elastace values at each dstedg pressure (from 0-40 cm H O cremets of 0. cm H O) are determed ad mplemeted the model as Look-Up Tables wth the Smulk model. Table 3.4 Fttg parameters ad best-ft coeffcet for dvdual lobe deflato curves for 8 day ad 4 day gestato lugs. 8 Day 4 Day Rght Rght Rght Left Left Rght Rght Rght Left Left Apcal ardac Daph ardac Daph Apcal ardac Daph ardac Daph a b c d R Lobe Resstaces The values of the collectve arway resstace each lobe (defed here as the equvalet resstace of all arways from Webel geerato 3-3 each lobe) for 8 day ad 4 day gestato lambs are ot avalable the lterature ad so are estmated the followg maer. Values of total arway resstace (equvalet resstace of all Webel geeratos from 0-3) for a 5 (~8) day ad 46 (~4) day gestato lamb s gve by Pllow et al. [95] as 3.45 ad.6 (cm H O/(L/s))/kg respectvely. The 77

107 collectve arway resstace ca be estmated by usg the relatos developed by Kobayash et al. [96] whch determed the percetage dstrbuto of arway resstace across each Webel geerato humas (Fgure 3.). Although the symmetrc Webel model s ot used the preset study, the Kobayash relatoshp s the oly study foud the lterature to develop such a relatoshp that ca be used for the preset purposes. From Fgure 3. t ca be see that the collectve resstace of the trachea, prmary ad secodary broch s 39.8% of the total arway resstace ad the collectve resstace of the lobes (.e. geeratos 3-3) costtute 60.8% of the total arway resstace. However, the ove lug has a dfferet structure to the huma lug. The secodary brochus leadg to the rght upper lobe the huma lug les the same geerato as the rest of the secodary broch. I the sheep lug, stead of rug off the rght prmary brochus, the secodary broch that leads to the rght apcal lobe rus off the mddle of the trachea. Although ths structure s dfferet, t may be assumed that the collectve resstace of the sheep trachea, prmary broch, secodary broch ad brochus leadg to the rght apcal lobe s stll 39.8% of the total arway resstace. 5 Resstace (% Total Resstace) Webel Geerato Number Fgure 3. Dstrbuto of arway resstace across each Webel geerato humas. 78

108 Assumg the same percetage dstrbuto of resstace to apply for the eoatal lamb brachg structure, the collectve resstace of the lobes ( R lobes total ) s calculated to be.0 (cm H O/(L/s))/kg for the 8 Day lamb ad.58 H O/(L/s))/kg for the 4 Day lamb. The ext step s to separate the collectve resstace of all the lobes to resstaces for each dvdual lobe. The lobe resstaces ca be cosdered to be coected parallel sce flow dvdes at each brachg pot of the arway etwork. A larger lobe wll have less arway resstace ad a smaller lobe wll have more arway resstace sce the flow gog through the smaller lobe s less. There s o measured data the lterature o how the resstace splts betwee the lobes. Asghara ad Prce [97], determed that flow the huma lug dvdes tself such a maer that 60% goes to the rght lug ad 40% goes to the left lug. Ths s smlar to the percetage dstrbutos of weght, lobar volume ad surface area. The resstace s versely proportoal to flow so t ca be extrapolated that the percetage dstrbuto of the resstace of each lobe wll be versely proportoal to the prevously defed percetage dstrbutos of flow, weght, lobar volume ad surface area across each lobe. A more coveet expresso s that of the coductace of each lobe ( lobe ) as calculated by Lobe Volume lobe = = R R Total Lobe Volume (3.94) lobe lobes total The coductace per ut brthweght of dvdual lobes both 8 day ad 4 day gestato lugs are determed usg equato (3.94) ad lsted Table

109 Table 3.5 oductace of dvdual lobes both 8 day ad 4 day gestato lugs. 8 Day 4 Day oductace ((kg/s)/pa)/kg % of Total Lug Mass oductace ((kg/s)/pa)/kg % of Total Lug Mass Rght Apcal Lobe 8.77E E-09.8 Rght ardac Lobe 5.8E E Rght Daphragmatc Lobe.4E E Left ardac Lobe 8.64E E Left Daphragmatc Lobe.87E E Pleural Volume Noppe et al. [98] measured the pleural flud adult lugs to be 0.6 ±0. ml/kg ad suggest that ths was ot age depedat ad ca be extrapolated to fats. Lght ad Hamm [99] suggest that pleural flud formato ca be extrapolated from humas to sheep. Hece, the value from Noppe et al. [98] of 0.6 ml/kg for both 8 day ad 4 Day lambs s used Dampg coeffcets The dampg coeffcet (c damp ) s chose as a sgle value, calculated at the FR volume. For each lobe, the elastace at the chose dstedg pressure s calculated usg equato (3.93) ad the multpled by the square of the lobe surface area to determe the equvalet stffess (k lobe ). Equato (3.95) s used to calculate the dampg coeffcet (c damp ) for each lobe [00]. damp ξ = (3.95) k c lobe M lobe The dampg factor ξ has bee reported for a over-damped d order system for a adult huma lug to be 8.45 [78]. Sce huma ad ove lugs are cosdered to be physologcal smlar a umber of cases ths research, t s used ths work to determe the mechacal dampg coeffcet (c) for premature lambs. 80

110 Tdal Volumes ad Respratory Rates The followg values of tdal volumes ad respratory rates are ot used drectly the smulatos sce these values are set accordg to the chose expermetal breath patter uder cosderato for better model-expermet comparso. They are descrbed here however to demostrate typcal values practce ad durg smulato. Davs et al. [0] measured the tdal volume of 45 day lambs to be. ml/kg. Wllet et al. [0] measured a value of 7.8 ± 0.4 ml/kg for tdal volume for 8 Day lambs. Durg mechacal vetlato Pllow et al. [95] reported adjustg vetlator settgs to mata a tdal vetlato of less tha 0ml/kg for both 5 ad 46 Day lambs. Respratory rates have bee reported to be approxmately 40 breaths per mute (bpm) for 5 day ad 35 day gestato lambs ad 30 bpm for 46 day lambs [95, 0] Smulk Model Separate models were formulated for 8 day ad 4 day gestato lambs. The Smulk models cotaed look-up tables whch cota put ad output umerc values to descrbe the relatoshp betwee elastace ad lobe volume for each lobe. Sce these relatoshps were dfferet at each lobe ad at each gestato, two separate models were created. The model s able to predct the pressure, flow rate ad volume at each of the 7 sectos detfed Table 3.. Fgure 3.3 shows the 3 ma subsystems of the model wth the Smulk evromet.e. the tracheo-brochal subsystem, the vscoelastc subsystem. ad the respratory support devce subsystem. Each subsystem s a modular, coectable subroute (cosstg of may smaller subroutes) based o the equatos derved ths chapter. The tracheo-brochal system cotas equatos (3.0) to (3.5) ad (3.37) to (3.60). The vscoelastc system cotas equatos (3.6) to (3.3), (3.6) to (3.69) ad (3.73) to (3.9). 8

111 Fgure 3.3 Elemets of the Smulk Model. Fgure 3.4 shows the geeral form of the block dagrams used for equatos (3.0) to (3.5) ad (3.37) to (3.60) the trachea-brochal system, usg the geeral forms equatos (3.7) ad (3.36). Ths arragemet costtutes the subsystems the model that calculate the mass flow rates ad pressures each arway secto. Fgure 3.5 shows the geeral form of the block dagrams used for equatos (3.6) to (3.3) ad (3.6) to (3.69) the vscoelastc system, usg the geeral forms equatos (3.9) ad (3.6) Ths arragemet costtutes the subsystems the model that calculate the pressures each lobe ad the mass flow rates to the lobes from the coectg arway sectos. 8

112 m out P upwd m _ V RT sec to s P sec to _ 4 sec to πd a b Re 8µ L ρ sec to Fgure 3.4 Geeral form of the block dagram for equatos (3.0) to (3.5) ad (3.37) to (3.60). m out P sec to m _ RT V lobe s P lobe _ lobe Fgure 3.5 Geeral form for the block dagram for equatos (3.6) to (3.3) ad (3.6) to (3.69). Fgure 3.6 shows the geeral form of the block dagrams used for equatos (3.73) to (3.87) the vscoelastc system, usg the geeral forms of equatos (3.70) to (3.7). Ths arragemet costtutes the subsystems the model that calculates the dvdual lobe wall movemet due to the varous forces actg o the lobe walls ad hece the mass flow rate geerated by each lobe due to patet breathg. Fgure 3.7 shows the block dagram for equato (3.88) the vscoelastc system. Ths arragemet costtutes the subsystem the model that calculates the movemet of the pleural wall due to the forces that act o t. Fgure 3.8 shows the block dagram for equato (3.9) the vscoelastc system. Ths arragemet costtutes the subsystem the model that calculates the pleural pressure whch acts o the wall of the dvdual lobes. 83

113 f lobe ρ A m out lobe P pleural P lobe _ A lobe M lobe s s x lobe lobe x A lobe X k lobe Lug Volume-Stffess Relatoshp V lobe (Look-Up Table) Fgure 3.6 Geeral form for the block dagram for equatos (3.73) to (3.87). f pleural x pleural P atm P pleural _ A pleural M pleural s x pleural s F th k pleural x pleural Fgure 3.7 Block dagram for equato (3.88). 84

114 x R ap wall A R ap x pleural A pleural x R card wall A R card B V pleural pleural s P pleural x R daph wall A R daph x L card wall A L card x L daph wall A L daph Fgure 3.8 Block dagram for equato (3.9). The respratory support devce subsystem s the Smulk model developed prevously by the author [56] whch models the Bubble PAP devce. The mass flow rate geerated by the patet ( m up trachea ) flows to the patet terface of the Bubble PAP devce ad cotrbutes to the pressure geerated at the terface ( P terface ) whch tur acts o the upper trachea as equato (3.37). The Bubble PAP System ca be substtuted for ay other model of a respratory devce (.e. PAP, HFV, MV etc.) The parameters for the model are stored a Matlab m-fle whch s loaded before performg ay smulato. Aga, separate m-fles are created for 8 day ad 4 day gestato lamb models due to the dfferet parameters ad physcal relatoshps. Desred outputs (.e. pressure, flow rate ad volume) are obtaed by placg scopes the desred locatos (.e. sectos ad 3-7) whch log the data to arrays the Matlab workspace. The sample tme for all smulatos s secods (50Hz) sce frequeces up to 5Hz were used. The ode3s varable-step cotuous solver Smulk was used. It computes the model's state at the ext tme step usg a modfed Rosebrock formula of the order. It s a oe-step solver, eedg oly the soluto to the precedg tme pot. It showed more effcecy at the crude toleraces that were used the smulato. 85

115 After smulato, the power spectral desty ad work of breath (WOB) calculatos are performed Matlab at each specfed locato ad the stored a Excel spreadsheet for further aalyss. The detals of each smulato wth results are dscussed hapter losure Models of the 8 day ad 4 day gestato ove respratory system have bee developed ths chapter. Frst, the equatos to predct pressure ad mass flow rate were developed. The emprcal ad lterature derved parameters requred for the model were the detfed ad defed. The elemets of the Smulk model ad ts use wth the Matlab evromet were descrbed. I the followg chapter, the smulatos ad expermets performed to valdate the model are preseted. 86

116 HAPTER 4 4. Model Valdato ad Results 4.. Itroducto Ths chapter begs by descrbg the expermetal procedure used to collect data from 33 day gestato lambs (Secto 4.). Secto 4.3 the compares the expermetal data collected wth the predctos from the Smulk model developed hapter 3. Secto 4.4 presets the model predctos of the effect of usg pressure oscllatos o the WOB. The method of calculatg WOB s frst descrbed (Secto 4.4.) ad a comparso of the WOB betwee premature (8 day gestato) ad ear term (4 day gestato) lugs s the establshed (Secto 4.4.). The predctos of WOB at specfed locatos the 8 day lug are the performed by addg pressure oscllatos at the PAP geerator (Secto 4.4.3) ad at the patet terface (Secto 4.4.4). These WOB calculatos help determe f WOB creases from prematurty to ear-term upo addto of partcular pressure oscllato frequeces. 4.. ollato of Expermetal Data The expermetal sets of data used to valdate the 8 day gestato model were obtaed from a earler study performed by Pllow et al. [3] o 33 day gestato lambs (the closest gestatoal data avalable). The protocols were a collaboratve study betwee The cat hldre s Hosptal Medcal etre, cat, Oho; The School of Wome s ad Ifats Health, The Uversty of Wester Australa, Perth, Australa; ad Fsher & Paykel Healthcare Ltd, Aucklad, New Zealad. Ivestgatos were approved by the Amal Ethcs ommttee of the Wester Australa Departmet of Agrculture ad cat hldre s Hosptal Medcal etre. 87

117 The study proved that a ove model of preterm lug dsease, treatmet wth Bubble PAP mmedately after brth ehaces gas exchage, lug mechacs, gas mxg effcecy ad lug volume compared wth costat pressure PAP. A bref summary of the methods as publshed Pllow et al. [3] s gve as follows. Lambs were delvered by caesara secto at 33 day gestato, dred ad tubated wth a 4.5 mm teral dameter cuffed, tracheal tube. They were the treated wth PAP usg heated humdfcato wth 00% oxyge. The usedated, spotaeously breathg lambs were radomzed to 3 groups: Group - ostat Pressure PAP wth a bas flow of 8L/m (=) Group - Bubble PAP wth a bas flow of 8 L/m (=) Group 3 - Bubble PAP wth a bas flow of L/m (=0) The depth of the PAP probe the Bubble PAP System was adjusted to mata smlar mea pressures as those obtaed wth PAP. Lambs were delvered to a moble radat warmer (osyot Ifat Warmer, Fsher & Paykel Healthcare) ad covered occlusve wrap to mata body temperature at approxmately 39 o (see Fgure 4.). At study completo (50 mutes) a varety of physologcal measuremets were performed whch cluded arteral blood gases, oxygraphy, capography, multple breath washout ad lug mechacs. Of terest to ths study are the flow rate, tdal volume ad pressure measuremets recorded at a samplg frequecy of 00 Hz at the arway opeg. Table 4. lsts a summary of the amals of terest to ths study.e. amals group ad. The average brthweght, tdal volume ad respratory rate are lsted the table for each group. Typcal pressure, volume ad flow rate sgals are preseted Appedx A for each amal. 88

118 Vetlato Tube Peumotach Edotracheal Tube Occlusve Wrap Oxmeter Probe osyot Ifat Warmer Fgure 4. Amal prepared for trals o fat warmer wth occlusve wrap. Table 4. Detals of amals ad vetlato strateges used expermets. Bubble PAP PAP Number of amals Average Brthweght ± SD (kg) 3.5±0.5 3.±0.7 Average Tdal Volume ± SD (ml/kg) 5.38±.3 4.7±.4 Average Respratory Rate ± SD (bpm) 68.83± ±5.0 For the purposes of valdato, however, typcal pressure, volume ad flow rate sgals of oly amal were used to compare the model results to the expermetal values. The amal whose tdal volume was closest to the average value of the sample populato was chose for comparso purposes ad s further detaled Secto omparso of Model ad Expermetal Results The frst step of the modellg process before proceedg to subsequet smulatos was to valdate the model predctos of pressure, flow rate ad volume at the arway opeg wth expermetal data collected Secto omparso of Model Predctos wth PAP measuremets The detals for the amal selected for comparso are show Table 4.. The amalspecfc parameters the 8 day gestato model were adjusted to match those of Table

119 Table 4. Detals of selected amal from group. Treatmet Type PAP Brthweght (kg) 3.5 Tdal Volume (ml/kg) 4.65 Respratory Rate (bpm) 60 Mea PAP (cm HO) 6.75 As metoed hapter 3, the profle of the thoracc force was defed so as to follow the shape (but ot magtude) of the tdal volume profle. To show a more fathful comparso, the thoracc force s set to match the tdal volume profle of the expermetal tdal volume (Fgure 4.). The magtude of the thoracc force s set by creasg ts value utl the tdal volume of the model predcto matches that of the expermetal tdal volume. Ths, effect, calbrates the drvg put of the system. Ths method assumes, however, that the relatoshps of all other parameters the model are accurate. The result of matchg the model tdal volume to the expermetal tdal volume of a 8 day gestato lamb recevg PAP s show Fgure 4.. The model predctos comparso to the expermetal values of arway opeg pressure ad flow are show Fgure 4.3 ad Fgure 4.4 respectvely. Fgure 4.3 ad Fgure 4.4 show a close correlato betwee expermetal ad model results. The devato of the model results from the expermetal results are quatfed as a percetage dfferece wth respect to the expermetal results at the pots of maxmum, mmum ad mea pressure ad flow (Table 4.3). Of partcular terest RDS s the ueveess vetlato across dfferet lobes the lug due to ther wdely dfferg mechacal propertes. Model predctos for the pressures, flow rates ad volumes each lobe are show Fgure 4.5. Fgure 4.5 (a) to (c) show the pressures, flow rates ad volumes respectvely for lobes the left lug.e. the left cardac lobe ad the left daphragmatc lobe. Fgure 4.5 (d) to (f) show the pressures, flow rates ad volumes respectvely for lobes the rght lug.e. the rght apcal lobe, the rght cardac lobe ad the rght daphragmatc lobe. 90

120 Fgure 4. Model-expermet tdal volume calbrato of a 8 day gestato lamb. Fgure 4.3 Model-expermet comparso of arway opeg pressure for a 8 day gestato lamb recevg PAP. 9

121 Fgure 4.4 Model-expermet comparso of arway opeg flow rate for a 8 day gestato lamb recevg PAP. Table 4.3 Percetage dfferece of pressure ad flow betwee model ad expermet. % Dfferece Pressure % Dfferece Flow Max Mea M Max Mea M The pressures the lobes show hgher mea values ad larger pressure swgs tha those predcted at the arway opeg. The pressure the rght daphragmatc lobe (the largest lobes) shows the smallest pressure swgs. The left daphragmatc lobe (whch s slghtly smaller tha the rght daphragmatc lobe) shows a slghtly greater pressure swg. The left cardac lobe ad rght apcal lobe (whch are smlar sze ad smaller tha the daphragmatc lobes) show smlar magtudes of pressure swgs to each other whch are larger tha those for the daphragmatc lobes. The rght cardac lobe (whch s the smallest lobe) shows the largest pressure swg durg exprato but pressure swgs rema betwee the rght apcal ad rght daphragmatc lobe durg sprato. The rght daphragmatc lobe has the hghest flow rate, followed by the left daphragmatc lobe. The left cardac ad rght apcal lobes have smlar flow rates whle the rght cardac lobe has the lowest flow rate. Hece, the larger the lobe, the larger the 9

122 flow rate geerated. A smlar relatoshp exsts for the lobe volumes (at both FR ad peak sprato) as see Fgure 4.5 (c) ad (f). a d b e c f Fgure 4.5 Model predctos for lobe pressures, flows ad volumes a 8 day gestato lamb recevg PAP. 93

123 4.3.. omparso of Model Predctos wth Bubble PAP measuremets The respratory parameters of a subject recevg Bubble PAP s of prmary terest to ths research. More specfcally, the model s used to determe the pressure, flow rate ad volume profles at the level of the dvdual lobes. As Secto 4.3., the amal group whch had the tdal volume closest to the average tdal volume of the sample populato was chose for the purposes of comparso. The amal-specfc parameters the model were adjusted to those descrbed Table 4.4. All other parameters ad settgs were left uchaged. I addto to the prescrbed level of mea PAP (6.75 cm H O) as used the tal smulato, a typcal sgal of the supermposed pressure oscllatos geerated at the level of the PAP geerator of the Bubble PAP System s troduced to the model. Ths was obtaed from prevous measuremets by Malal [56]. The comparsos of pressure, flow ad volume predctos of the model to the expermetal measuremets are show Fgure 4.6 to Fgure 4.8 respectvely. Overall, the model predctos show good comparsos wth the expermetal data. The supermposed pressure oscllatos are clearly vsble Fgure 4.6. Because of the radom ature of the bubble oscllatos, the expermetal ad model values do ot match exactly but le the same pressure rage. Due to the hgh ampltude of pressure oscllatos relatve to that of the breath patter aloe, the breath patter the pressure values of Fgure 4.6 s ot as dstctly vsble at the arway opeg durg Bubble PAP as compared to PAP. The breath patter s clearly vsble Fgure 4.7 wth supermposed oscllatos. Table 4.4 Detals of selected amal from group. Treatmet Type Bubble PAP Brthweght (kg) 3. Tdal Volume (ml/kg) 4.7 Respratory Rate (bpm) 98 Mea PAP (cm HO)

124 The tdal volume values durg Bubble PAP (Fgure 4.8) show some ueveess profle due to the pressure oscllatos whch are ot as dstct as those see the pressure ad flow profles. The tdal volume s calculated the model (as well as measured clcal practce) by the mathematcal tegrato of the flow rate sgal ad so the oscllatos preset the flow rate measuremets have effectvely bee tegrated out process of calculatg the tdal volume. Varous questos have arse regardg the trasmsso of pressure oscllato ampltude ad frequecy from the arway opeg to the dvdual lobes. I the hope of aswerg such questos, the model was also used to predct the respratory parameters the dvdual the lobes durg Bubble PAP as see Fgure 4.9 to Fgure 4.4. The oscllatos pressure ad flow are vsble at the level of the dvdual lobes. The magtude of the pressure oscllatos Fgure 4.9 ad Fgure 4.0 are ot markedly decreased to those compared wth Fgure 4.6. The magtude of the flow oscllatos Fgure 4. ad Fgure 4. shows a decrease magtude to those compared wth Fgure 4.7. Aga, the volumes the lobes (Fgure 4.3 ad Fgure 4.4) show o otceable chage profle wth the addto of oscllatos. I-vvo expermetal values of pressure ad flow rate each lobe durg Bubble PAP has ether bee measured prevous work by the author or recorded the lterature due to the dffcult ad mpractcal ature of the testg. Thus, the model predctos rema uvaldated ad oly serve as a dcato of the trasmsso of the pressure oscllatos. The accuracy ad utlty of the predctos are further dscussed hapter 6. 95

125 Fgure 4.6 Model-expermet comparso for arway opeg pressure a 8 day gestato lamb recevg Bubble PAP. Fgure 4.7 Model-expermet comparso for arway opeg flow rate a 8 day gestato lamb recevg Bubble PAP. 96

126 Fgure 4.8 Model-expermet comparso for tdal volume a 8 day gestato lamb recevg Bubble PAP. Fgure 4.9 Pressures left lobes of a 8 day gestato lamb recevg Bubble PAP. 97

127 Fgure 4.0 Pressures rght lobes of a 8 day gestato lamb recevg Bubble PAP. Fgure 4. Flow left lobes of a 8 day gestato lamb recevg Bubble PAP. 98

128 Fgure 4. Flow rght lobes of a 8 day gestato lamb recevg Bubble PAP. Fgure 4.3 Volume left lobes of a 8 day gestato lamb recevg Bubble PAP. 99

129 Fgure 4.4 Volume rght lobes of a 8 day gestato lamb recevg Bubble PAP Model Predctos of Pressure Oscllato Effects Before cotug wth smulatos o the effect of pressure oscllatos, a dstcto must be made betwee the respratory parameters of a healthy ad uhealthy lug. The WOB s used to demostrate respratory ad devce performace ths secto ad s calculated for lambs of 8 day gestato (represetg a premature lug) ad 4 day gestato (represetg a ear-term lug) alculatg the WOB The WOB calculates the combed effort of all the respratory compoets of the eoatal respratory system ad the devce durg a breath cycle ad s the mechacal work doe o the specfed cotrol volume. Sce the tdal volume, respratory rate ad work doe by the eoatal lug are ot altered across smulatos, ay chages WOB are due to the work doe by the devce. Although complex tegratos of dvdual pressure-volume loops are requred for more sophstcated estmates of WOB, a expresso of the mea WOB over sprato ad exprato are calculated ths aalyss as t provdes suffcet formato for the purposes of descrbg the dfferece betwee the premature ad ear term lug as well as the overall mprovemet of addg oscllatos to eoatal breathg. 00

130 To determe the WOB, the work-tme product (WTP) s calculated by tegratg the stataeous work (.e. the product of pressure ad tdal volume vs. tme) over tme (.e. Wdt ). A more coveet expresso of the WTP s the mea WOB ( WOB ) geerated over a certa tme as per equato (4.) (WOB ) = WTP/samplg perod (4.) For example, f WTP s calculated for sprato, the the samplg perod s the durato of sprato ad f WTP s calculated for exprato, the the samplg perod s the durato of exprato. The mea WOB doe oe complete breath WOB total s the sum of the mea WOB durg sprato WOB sp ad the mea WOB durg exprato WOB exp WOB omparso of premature ad ear-term lugs The WOB total was calculated for both a 8 day (premature) ad 4 day (ear term) lamb from the model smulatos. The amal specfc parameters for the 8 day model are those used Table 4.. Sce o -vvo measuremets o 4 day lambs were avalable to produce valdated pressure, flow ad volume predctos for that gestato, the tdal volume/kg brthweght, respratory rate ad mea pressure were those of Table 4. ad the brthweght was set at 5.0 kg as per the average measured brthweght for 4 day gestato lambs Table 3.8. Other gestato specfc parameters used the 4 day model are as defed Secto 3.5. The WOB total at the specfed locatos for both gestatoal ages are show Appedx B ad ormalzed wth respect to the dvdual values at each locato for the 8 day gestato lamb Fgure

131 Work of Breath (%Work of Breath of 8 Day) Day 4 Day 0 Rght ardac Rght Apcal Left ardac Left Daphragmatc Rght Daphragmatc Upper Trachea Fgure 4.5 Normalzed values of WOB of 8 day ad 4 day gestato lambs recevg 6.75 cm H O PAP. Fgure 4.5 shows that WOB total s hgher for the 4 day gestato lamb due to the hgher tdal volume resultg from the added brthweght ad complace of the lug ad the added muscle eergy avalable to a larger amal. The percetage crease WOB total at each locato for the 4 day gestato whe compared to values at the 8 day gestato are preseted Table 4.5. The 4 day gestato, beg ear term, represets healther values of WOB. Ay crease of WOB total from the values at the 8 day gestato due to the addto of the varous vetlato profles used subsequet smulatos s see as beefcal that they perform the addtoal work requred to crease caot perform tself. WOB total, whch the eoate Table 4.5 Percetage crease WOB total at each locato. Locato Percetage crease WOB total (%) from values at 8 day gestato Rght ardac Lobe 3 Left ardac Lobe 43 Rght Apcal Lobe 49 Left Daphragmatc Lobe 76 Rght Daphragmatc Lobe 88 Upper Trachea 76 0

132 Addg pressure oscllatos at the PAP geerator I order to quatfy the effect of oscllatos o the respratory parameters, the followg procedure was adopted for the subsequet smulatos. A whte ose pressure sgal (a sgal that cotas all frequeces equal amouts) was troduced at the PAP geerator place of the Bubble PAP pressure oscllato sgal. The use of the whte ose sgal stems from the power spectral desty (PSD) aalyss egeerg where t has prove to be a useful test sgal to determe the frequecy respose of o-lear systems [00]. I terms of stochastc resoace, the whte ose sgal effectvely allows the lug to select the frequeces t prefers to tate ay resoacebased mprovemets. The ose could be added at ay pot the system, but sce the PAP geerator s the source of the oscllatos practce, t presets the most practcal place to troduce whte ose to the system realty. The stadard devato of the whte ose pressure sgal was set to equal that of the Bubble PAP pressure sgal (.e. ±.58 cm H O). The whte ose sgal cotas pressure oscllato frequeces up to 5 Hz sce prevous vestgatos by other authors [, 56] have revealed that o sgfcat frequeces are preset Bubble PAP above ths rage. A PSD aalyss of the stataeous work (.e. the product of pressure ad tdal volume vs. tme) at the arway opeg ad at the level of the dvdual lobes was the performed to determe the frequeces that cota the hghest power (.e. those that cotrbute the most to the value of the work). The ormalzed power (the power expressed as a fracto of the hghest magtude of power preset the data set) at the arway opeg for a 8 day gestato lamb recevg PAP ad whte ose s show Fgure 4.6. For the purposes of the curret vestgato, the frequecy wth the strogest power ad all other frequeces whch have magtudes that are greater tha 40% of the maxmum powers are defed as frequeces of sgfcat power. The spectrum Fgure 4.6 shows sgfcat power at 9 ad 3 Hz. The power spectra of the stataeous work calculated at the level of the dvdual lobes detfy the same strog frequeces wth oly very slghtly dfferet magtudes relatve to the hghest power. The powers of sgfcat frequeces ormalzed to the maxmum power each data set at each locato are summarzed Table

133 The power spectrum detfyg sgfcat frequeces wll chage wth the mechacal propertes of the lug [56]. The values of frequeces detfed ths work are oly vald for 8 day gestato ove lugs. A seres of subsequet smulatos were performed to predct the respratory parameters of a 8 day gestato lamb recevg PAP supermposed wth oscllatos at the dvdual frequeces detfed Fgure 4.6. Smulatos were also performed for a sgal cotag equal magtudes of both strog frequeces as well as for vetlato uder Bubble PAP. Oce aga, the magtude of the oscllatos was set to ±.58 cm H O (.e. stadard devato of the osy Bubble PAP oscllatos). For all smulatos, the mea WOB for sprato ( WOB sp ), exprato ( WOB exp ) ad the total breath ( WOB total ) were determed at the arway opeg ad each dvdual lobe. These values are archved Appedx. The values relatve to the at PAP-oly treatmet are show Fgure 4.7 for each locato. WOB total value Although the relatve magtudes at each locato are vastly dfferet, whe the results are ormalzed relatve to the PAP-oly WOB value at each locato, as see Fgure 4.7, the upward treds are the same for all locatos. 9Hz 0.8 Normalsed Power Hz Frequecy (Hz) Fgure 4.6 Power spectrum of the stataeous work at the arway opeg of a 8 day gestato lamb recevg PAP ad whte ose. 04

134 Table 4.6 Normalzed power of sgfcat frequeces at dfferet locatos o addto of whte ose at the PAP geerator. 9Hz 3Hz Arway Opeg 0.40 Left ardac Lobe Rght ardac Lobe 0.44 Rght Apcal Lobe Left Daphragmatc Lobe 0.4 Rght Daphragmatc Lobe 0.49 The WOB for the vetlato profle that uses a oscllato frequecy of 9 Hz s hgher tha that whch uses 3 Hz. The largest crease WOB (4-6% crease across all locatos) s observed whe both sgfcat frequeces (9 ad 3 Hz) are combed oe vetlato profle. Both vetlato profles show a hgher WOB tha usg Bubble PAP. The model predcts that usg Bubble PAP shows a -% crease WOB across all locatos whe compared to usg PAP aloe. The average WOB at the arway opeg calculated from the -vvo measuremets of the groups of amals recevg PAP ad Bubble PAP (groups ad ) Secto 4. are preseted Fgure 4.8 after beg corrected for brthweght ad tdal volume. The -vvo measuremets show that usg Bubble PAP creases the WOB at the terface by 4% whe compared to PAP aloe. The dffereces betwee the values predcted by the model ad the -vvo measuremets are dscussed hapter 6. The sgfcat frequeces preset Bubble PAP are of terest to uderstad the role that ay frequeces there play the WOB calculato whe compared to the other vetlato profles. The PSD of the stataeous work calculated at the arway opeg durg the model smulato s show Fgure 4.9. Sgfcat frequeces are preset at 7 Hz ad 3 Hz, close to the most powerful frequeces detfed Fgure 4.6. Other peaks, although below 40% of the maxmum power, are preset at 9 Hz ad 33 Hz ad cotrbute to the calculated value of the WOB. 05

135 Smlar frequeces were detfed whe performg PSD calculatos o the -vvo data acqured from the Bubble PAP amals (group ) detfed Secto 4. ad are show Table 4.7. The values calculated from the model are hghlghted grey to llustrate that they le wth the rage of typcal expermetal values. Work of Breath (% of WOB usg PAP Oly) PAP Oly PAPWhte Nose B-PAP 9Hz 3Hz 9 & 3Hz Rght ardac Rght Apcal Left ardac Left Daphragmatc Rght Daphragmatc Upper Trachea Fgure 4.7 WOB (relatve to PAP-oly treatmet) at specfed locatos for a varety of oscllatory treatmets o a 8 day gestato lamb. Fgure 4.8 Average WOB (relatve to PAP-oly treatmet) at the patet terface calculated from expermetal data 06

136 7 Hz 0.8 Normalsed Power Hz 9 Hz 33 Hz Frequecy (Hz) Fgure 4.9 Power spectrum of the stataeous work at the arway opeg of a 8 day gestato lamb recevg Bubble PAP. Table 4.7 Sgfcat frequeces detfed PSD aalyss of expermetal data. (Key: Stem uts=0 Hz, Leaf uts= Hz) STEM LEAF Addg pressure oscllatos at the patet terface Eve though frequeces up to 5 Hz were recorded the PAP geerator of the Bubble PAP devce, the atteuato of frequeces above 45 Hz through the expratory lmb makes t mpossble to determe the effect of hgher frequeces o respratory parameters [56]. To determe ths effect, the whte ose pressure sgal s added at the patet terface stead of at the level of the PAP geerator. Sce the expratory tube s elmated from the system, pressure oscllatos wll ot be atteuated at the patet terface, thus allowg vestgatos of the effect of hgher frequeces. Frst, a smulato was performed for PAP wth whte ose at the terface up to 5 Hz. The PSD s calculated at the arway opeg ad at the level of the dvdual lobes 07

137 to determe the frequeces wth the strogest power. Fgure 4.0 shows the PSD of the stataeous work at the arway opeg. The sgfcat frequeces are oted o the fgure. The power spectra of the stataeous work calculated at the level of the dvdual lobes detfy the same strog frequeces of oly very slghtly dfferet magtudes relatve to the hghest power. A seres of subsequet smulatos were performed to predct the respratory parameters of a 8 day gestato lamb recevg PAP supermposed wth oscllatos at the terface usg the dvdual frequeces detfed Fgure 4.0. A smulato was also performed for a sgal cotag equal magtudes of all frequeces. Oce aga, the magtude of the oscllatos was set to ±.58 cm H O. Normalsed Power Hz 49Hz 8Hz 9Hz 44Hz 33Hz 99Hz 54Hz 88Hz 3Hz Hz 3Hz Frequecy (Hz) Fgure 4.0 Power spectrum of the stataeous work at the arway opeg of a 8 day gestato lamb recevg PAP ad whte ose at the terface. WOB total, WOB sp ad WOB exp at each specfed locato for each smulato are archved Appedx D. At each locato, the values of WOB total relatve to the value of PAP-oly treatmet are calculated ad show Fgure 4. to Fgure 4.3 for the upper trachea, rght lobes ad left lobes respectvely. Fgure 4. to Fgure 4.3 show smlar treds WOB ad also show that addg sgle frequeces as well as a equal mxture of all sgfcat frequeces creases 08

138 WOB above the values calculated for PAP-oly treatmet. The amout of crease WOB for ay partcular sgle frequecy used s cogruet wth the stregth of the frequecy detfed Fgure 4.0, such that the crease WOB at 8, 88 ad 99Hz, (whch show the hghest power cotrbutos to the work Fgure 4.0) s greater tha that at 3 Hz whch shows the lowest power cotrbuto of the sgfcat frequeces. Work of Breath at Upper Trachea (% of WOB usg PAP Oly) PAP Oly Whte Nose 9Hz 3Hz 8Hz 33Hz 44Hz 49Hz 54Hz 8Hz Modulatg Frequeces used w th PAP 88Hz 99Hz Hz 3Hz All Frequeces Fgure 4. WOB (relatve to PAP-oly treatmet) at the upper trachea for a varety of oscllatory treatmets o a 8 day gestato lamb. Work of Breath Rght Lobes (% of WOB usg PAP Oly) Rght ardac Rght Apcal Rght Daphragmatc 96 PAP Oly Whte Nose 9Hz 3Hz 8Hz 33Hz 44Hz 49Hz 54Hz 8Hz Modulatg Frequeces used w th PAP 88Hz 99Hz Hz 3Hz All Frequeces Fgure 4. WOB (relatve to PAP-oly treatmet) at the rght lobes for a varety of oscllatory treatmets o a 8 day gestato lamb. 09

139 0 Left ardac Left Daphragmatc Work of Breath Left Lobes (% of WOB usg PAP Oly) PAP Oly Whte Nose 9Hz 3Hz 8Hz 33Hz 44Hz 49Hz 54Hz 8Hz Modulatg Frequeces used w th PAP 88Hz 99Hz Hz 3Hz All Frequeces Fgure 4.3 WOB (relatve to PAP-oly treatmet) at the left lobes for a varety of oscllatory treatmets o a 8 day gestato lamb. The greatest crease WOB s observed whe all sgfcat frequeces are combed, showg a 4-0% crease WOB across all locatos. The larger daphragmatc lobes show a slghtly greater percetage crease WOB whe compared to the smaller apcal ad cardac lobes losure The procedure ad results of the amal expermets have bee preseted ths chapter ad compared to the model predctos to valdate the model. The calculato of the WOB the cotext of ths research was descrbed ad the the WOB was calculated for both premature (8 day) ad ear-term (4 day) lugs to establsh the basele ad desred WOB. Smulatos to determe the effect of addg pressure oscllatos o the value of WOB were the performed o the 8 day gestato model to observe the treds towards the WOB value of a 4 day gestato lug. The results geerated ths chapter are dscussed hapter 6. 0

140 HAPTER 5 5. Surface Teso Model 5.. Itroducto Surfactat s mportat at brth because t prevets the lugs from collapsg. Surfactat defcecy s a mportat cause of RDS fats. Natural surfactats are curretly used the treatmet of RDS but are expesve. Newer, cheaper, effectve techologes that ca reduce the expese of or optmze surfactat use are sought. Ths research seeks to determe whether atural surfactat (urosurf) accompaed wth pressure oscllatos at the level of the alveol ca reduce the surface teso the lug, thereby makg t easer for the fat to mata the requred level of FR wthout collapse. Ths chapter cotas the complete dervato ad umercal methods used to costruct the computatoal model that predcts the effect of usg modulated waveforms o the surface teso the alveol. The modellg methods follow those of Morrs et al. [84, 85]. The dscretzato, umercal modellg steps ad adjustmets of adsorpto ad dffuso parameters eeded to be performed by the author ad so are show ths chapter. The model predctos are compared wth expermets performed o urosurf a PBS whch smulates the oscllatg ar-lqud terface of the alveol. Secto 5. presets the dervato of the covecto-dffuso equato used to descrbe the trasport of surfactat to the ar-lqud terface of the bubble. The boudary codtos ad the three regmes of mass trasport that gover surfactat movemet at the terface are descrbed. The umercal methods are also descrbed wth the dscretzato of all approprate elemets of the model Secto 5.3. Fally, the tr-dagoal matrx, whch forms the framework of the model, s preseted followed by demostrato of the proper fuctoalty of the model Secto 5.4. Secto 5.5 detals the equpmet setup,

141 methodology ad results of the expermetal valdato performed usg a custom-bult PBS. Fally, Secto 5.6 compares the mmum ad maxmum surface teso values durg a breath cycle (at dfferet frequeces ad ampltudes) measured by expermetal results wth the model predctos. 5.. omputatoal Model Formulato Ths secto presets the dervato of the computatoal model llustratg the dffusve covectve effects. The surfactat dyamcs are also govered by Lagmur ketcs ad mass trasport pheomea whch are explaed detal. The umercal methods appled to solve the covecto-dffuso equato are also gve. Fally, the fuctoalty of the model s llustrated by comparso wth data from the lterature ovecto-dffuso Equato A dcato of how surfactat wll perform physologcally s the varato of surface teso a small sphercal ar bubble surrouded by surfactat. As see Fgure 5., the ar bubble serves to smulate a alveolus durg a breath cycle. The tme-varyg terface betwee the bulk lqud ad the ar bubble s of terest sce ths smulates the th flm or lqud layer of surfactat coatg a alveolus. As the flm expads ad cotracts durg the breath cycle, the surfactat molecules move betwee the bulk lqud ad the terface, thereby resultg a perodc varato of surface teso. Surroudg Bulk Lqud Surfactat r R (t) x Surfactat Molecules Sphercal Ar Bubble Alveolus apllary Tube Fgure 5. Schematc of a bubble a bulk lqud cotag surfactat.

142 The movemet of surfactat molecules to ad from the terface s govered by adsorptve ad desorptve effects at the terface as well as covectve ad dffusve effects through the bulk lqud. Adsorpto s the process whereby a molecule forms a bod to a surface. Dffuso s the spotaeous, atural process where a substace dffuses from a rego of hgher cocetrato to lower cocetrato. ovecto s the trasfer of solute wth the curret the flud. The equatos that gover these pheomea are troduced ad appled to the stuato depcted Fgure 5.. The dervato for the covecto-dffuso equato based o Fck s secod law [03] s well establshed ad preseted Appedx E. Usg sphercal coordates, the covecto-dffuso equato ca be wrtte as t v r = D r r r r (5.) where s the cocetrato (kg.m -3 ), D s the dffuso coeffcet (m.s - ), v s the velocty of the flud (m.s - ) ad r s the bubble radus (m). Alteratvely, the covecto-dffuso expresso for sphercal co-ordates ca be more descrptvely wrtte as [85, 86] ( r, t) ( r, t) ( r, t) v( r, t) = D r t r r r r (5.) Equato (5.) s used to model surfactat trasport to ad from a bulk suspeso to the terface of a sphercal ar bubble. Workg a coordate system movg relatve to the movg terface, r s the radal dstace from the cetre of the bubble such that r = x R(t) (5.3) 3

143 where R (t) s the tme-varyg radus of the bubble ad x s the dstace to the bulk from the bubble radus R (t). Substtutg equato (5.3) to the equato (5.) trasforms t to the followg form [85]. ( x, t) ( x, t) D vrel ( x, t) = t x x ( x R( t) ) ( x, t) x ( ) x R( t) (5.4) To ga a expresso for ( x, t), a sphercal bubble a fte amout of lqud s cosdered. v rel Workg sphercal coordates ad cosderg coservato of mass for a bubble a fte lqud mass requres that [86, 04] F( t) v rel ( r, t) = (5.5) r where F (t) s the force o a rgd partcle the bulk flow. I the case of a ar-lqud terface there s o mass trasport across the terface so the relatve velocty of the flud at the bubble radus ( R (t) ) s the same as the velocty of the movg terface, whch s expressed as: F( t) dr( t) v rel ( R, t) = = (5.6) R ( t) dt Therefore dr( t) F( t) = R ( t) (5.7) dt 4

144 Substtutg ths to equato (5.5) gves R ( t) dr( t) v rel ( r, t) = (5.8) r dt A expresso for v rel ( x, t) ca ow be obtaed as v R ( t) dr( t) dr( t) R ( t) dr( t) x, t) = vrel ( r, t) vrel ( R, t) = = r dt dt r (5.9) dt ( rel Substtutg r = x R(t) to equato (5.9), gves R( t) dr( t) v rel ( x, t) = (5.0) x R( t) dt Substtutg to equato (5.4) gves the fal form of the covecto-dffuso equato as ( x, t) R( t) dr( t) ( x, t) D = t ( ) x R( t) dt x x x R( t) ( x, t) x ( ) x R( t) (5.) 5... Ital ad Boudary odtos A tal codto ad two boudary codtos are requred to solve equato (5.). Ital odto: It s assumed that tally (.e. at t = 0 ), the surfactat cocetrato s uform throughout the bulk lqud at a cocetrato of : bulk ( x,0) = (5.) bulk 5

145 Boudary odto : Sce the bulk lqud s modelled as beg spatally fte, the mass trasport to ad from the terface of the bubble s assumed to have o effect o the cocetrato far from the bubble terface. The cocetrato at fty ca be cosdered to rema at the tal bulk cocetrato: (, t) = (5.3) bulk Boudary odto : Havg establshed the boudary codto at x =, the boudary codto at x = 0.e at the ar-lqud terface s requred. The boudary codto s specfed as a flux codto ad equates the terfacal mass flux to the dffusve mass flux at the surface. Applyg Fck s law at the terface J dm = dt A( t) (0, t) = D x (5.4) J s the dffusve flux ad M s the mass of surfactat at the terface gve by M = A( t) Γ( t) (5.5) where A (t) s the tme varyg area of the bubble (alveolus) (where A( t) = 4πR ( t) ) ad Γ (t) s the terfacal cocetrato (kg.m ). Substtutg equato (5.5) to (5.4) gves d [ A( t) ( t) ] Γ (0, t = A( t) D ) dt x (5.6) 6

146 [ A( t) Γ( t ] d ) dt represets the mass trasport to ad out of the terface as s characterzed by three dfferet regmes whch more accurately descrbes surfactat trasfer a oscllatg bubble Regmes of Mass Trasport Ths secto descrbes the three regmes of mass trasport whch arse as a result of the establshed geeral behavour of a pulsatg surfactat bubble [83, 85]. For clarty, the theory of the geeral behavour s frst preseted ths secto, followed by the resultg equatos that gover mass trasport these regmes Secto The domas of the regmes are defed by the value of Γ (t), the terfacal * cocetrato, the equlbrum terfacal cocetrato ( Γ ) ad the maxmum terfacal cocetrato ( Γ max ). Γ (t) s the umber of occuped bdg stes per ut area by surfactat molecules o the terface of the bubble (as see the vsual represetato of Fgure 5.) ad s hece used to calculate the surface teso at the terface (as further llustrated Secto 5..5). Startg at A Fgure 5. ad followg a clockwse drecto, the bubble s compressed tll pot E ad the expaded from E to A. For a clearer uderstadg, the bubbles are also marked as a percetage of the maxmum terfacal area such that bubble A s at 00%, bubble B s at 99% of the maxmum terfacal area ad so forth. These percetages are typcal values but chage for dfferet types of surfactat, cocetratos ad cyclg tmes. The regmes whch arse from the terfacal cocetrato Γ (t) are oted at each labelled bubble. The locatos of the three regmes o a typcal surface teso-area ( γ A ) loop ca be see Fgure 5.3. The γ A loop s a typcal surface teso vs. area relatoshp for a ar bubble surrouded a bulk flud carryg surfactat whch ca be derved from expermets o a PBS or prevous mathematcal models. 7

147 66% * Γ < Γ 78% * Γ < Γ 00% Γ < Γ * 63% Γ = Γ * Regme 99% * Γ < Γ 57- Γ * < 63% Γ < Γmax Regme Regme 3 Regme 95% * Γ = Γ 57% Γ = Γ max 90% Γ = Γ max Γ % * < Γ < Γ max Fgure 5. Vsual represetato of the terfacal cocetrato Γ (t). Regme - Segmet F Regme - Segmets D & EF Surface Teso (dye/cm) E F G γ = γ eq * * Γ = Γ ; γ = γ Γ = Γ ; γ = H max γ m Adsorpto Desorpto Isoluble D Regme 3 - Segmet DE A B Area (mm ) Fgure 5.3 The locatos of the three regmes o the γ A loop [83, 85]. 8

148 The arrows ormal to the loop dcate whether the mass flux moves to or out of the terface durg dfferet regmes or parts thereof. The black arrows dcate a flux of surfactat to the bubble terface ad the whte arrows dcate a efflux, such that the et flux to or out of the terface s zero, makg the γ A loop represetatve of a steady state process. Each regme ad the relatoshp betwee the terfacal cocetrato ad surface teso are descrbed more depth as follows: Regme Followg a clockwse fasho, regme correspods to the surface tesos o the curve Fgure 5.3 from F to. The correspodg pctograms of Γ (t) at pots F, G, H, A, B ad are show Fgure 5.. At equlbrum (pots F ad ) there s a maxmum umber of bdg stes that ca be occuped at the terface ad s kow as * Γ (defed the maxmum terfacal cocetrato that correspods to a mmum equlbrum surface teso measuremet for a partcular value of o a PBS. Hece, the frst regme s sad to occur whe * γ bulk determed by equlbrum measuremets * Γ < Γ. Γ s drectly related to the surface teso γ. A greater amout of surfactat molecules at the terface (a larger Γ ) meas that there s a greater dsrupto of the attractg forces of the lqud molecules at the terface (a smaller γ ). Hece, whe Γ approaches * Γ, γ approaches (le F Fgure 5.3). * γ, whch s kow as the mmum equlbrum surface teso Regme Regme occurs two parts of the * γ A loop (D ad EF). Here, Γ(t) exceeds Γ due to dyamc compresso of the terface durg the cyclg of the area A. The surfactat molecules are packed so tghtly that t ca be cosdered to be a soluble moolayer (as see Fgure 5.3 bubbles -D ad E-F). However Γ (t) s stll less tha Γ max, whch s the maxmum terfacal cocetrato possble.e. the most dese 9

149 packg of surfactat molecules possble a moolayer. Hece, regme occurs whe * Γ < Γ < Γmax. Regme 3 I the thrd regme (segmet DE), whe Γ (t) reaches the value of Γ max the surface teso reaches a mmum value γ m. I ths regme the surfactat molecules are packed as tghtly as possble ad a further compresso of the terface results a squeeze out of extra surfactat molecules to the bulk. Ths squeeze-out of extra molecules meas that the terfacal cocetrato remas at Γ max whle the area decreases from pot D to E such that Γ = Γmax ad γ = γ m for the segmet DE Mass trasport equatos for each regme Regme * Sce regme occurs whe Γ < Γ, mass trasport s govered by adsorpto ad desorpto of surfactat molecules to ad from the terface as well as the subsurface cocetrato 83, 05]: s. Ths ca be expressed usg the followg Lagmur relatoshp [8, d [ A( t) Γ( t) ] dt = dm dt = A k * [ ( Γ Γ) k Γ] s (5.7) where k s the adsorpto coeffcet ad k s the desorpto coeffcet. Regme Sce the surfactat behaves as a soluble moolayer ths regme, there s o mass trasport to ad from the terface, so that d [ A( t) Γ( t) ] dt = dm dt = 0 (5.8) 0

150 Regme 3 Sce to be: Γ = Γmax regme 3, the rate of chage of mass at the terface ca be cosdered d [ A( t) Γ( t) ] dm d[ A( t) Γ ] dt = dt = dt max = Γ max da dt (5.9) A expresso for * Γmax Γ s foud by sertg γ = γ m to the sotherm equato (equato (5.3)), whch s descrbed the followg secto. To summarze, the mass flux at the terface for the three dfferet regmes, gves the followg equato d [ A( t) Γ( t) ] dt = A k * [ ( Γ Γ) k Γ] s whe * Γ < Γ d [ A( t) Γ( t) ] dt = 0 whe * Γ < Γ < Γmax (5.0) d [ A( t) Γ( t) ] dt = Γ max da dt whe Γ = Γmax Equato (5.0) alog wth the covecto-dffuso equato (equato (5.)) ad the equatos descrbg the tal ad boudary codtos (equatos (5.), (5.3) ad (5.6)) wll be quattatvely determed after usg the umercal methods Secto Isotherm The relatoshp betwee the ormalzed terfacal cocetrato * Γ Γ ad the surface teso γ s foud from a sotherm whch s assumed to be a fucto of oly terfacal cocetrato. Ths s descrbed Ots et al. [83], Morrs et al. [85] ad Morrs [84] ad summarzed here as follows.

151 The sotherm s defed by two lear slopes, m ad m as see Fgure 5.4 whch reflects the chage of surface teso at the terface of the bubble as a fucto of the surfactat coverage at the terface. Slope m occurs durg regme where the surface teso les betwee pots correspodg to Γ Γ * = 0 ad Γ Γ * =. The surface teso at Γ Γ * = 0 s the surface teso of pure water, γ 0 ad the surface teso at Γ Γ * = s the maxmum equlbrum surface teso of the surfactat. A lear form of the sotherm was assumed as a smple ad reasoable approxmato of the surface teso. The surface teso regme s thus expressed as Γ γ = γ 0 m (5.) * Γ ad m ca be smply expressed as m * = γ 0 γ. Ots et al. [83] derved a expresso for m based upo average expermetal γ A data. The resultg expresso for m s * ( γ γ ) m m = (5.) * A Aγ m γ m m * Γ Γ Fgure 5.4 Isotherm relatg surface teso (γ ) to surface cocetrato ( Γ * Γ ) of surfactat.

152 where * A ad Aγ m are the terfacal areas correspodg to * γ at the oset of regme compresso ad γ m at the ed of regme compresso respectvely. These occur at pots ad D Fgures 5. ad 5.3. The surface teso relatoshp for regme s * Γ γ = γ m * (5.3) Γ 5.3. Numercal Soluto I ths secto the partal dfferetal equatos that specfy the mass trasport of surfactat molecules to ad from the bubble terface are solved usg umercal methods. Numercal methods have bee used the lterature to successfully model oscllatory surfactat dyamcs [83, 85, 86]. Ths work follows the method proposed by Morrs [84] where a cotrol volume approach s used where the bulk s spatally dscretzed to odes wth each ode at the cetre of a cotrol volume. The mplct Euler scheme [06, 07] s used to smultaeously approxmate the future values of all odes at the ext tme step (referred to here as the st tme step) by usg a system of lear equatos Dscretzato of Tme A apprecato of how tme s dscretzed the model s show Fgure 5.5 as bubble dsplacemet vs. the umber of tme steps per cycle ( N S ) where the bubble s cycled from a mmum to maxmum dsplacemet ad back to the mmum value. T cycle s the tme take for a cycle ad hece s equal to ω, where ω s the cyclg frequecy. N S s chose as 000 (the smallest value that was foud to produce accurate results) [84]. t s the tme step ad s set to be N S ω. 3

153 T cycle Bubble Dsplacemet t Number of tme steps per cycle ( N ) S Fgure 5.5 Dscretzato of tme Dscretzato of Space A oe dmesoal dscretzato of the space s show Fgure 5.6. The bulk s dscretzed to a amout of odes that are x apart. The 0 th ad st (subsurface) odes are located at a dstace x from the terface such that durg the subsequet umercal procedures, the terfacal flux occurs at the mdpot of the 0 th ad st odes, allowg a more accurate ad elegat soluto. The dstace x s the dstace betwee the terface ad the th ode ad s gve by R x X x x x x x x x 0 th Node st Node (Subsurface) th Node Iterfacal Mass Flux Iterface Fgure 5.6 Dscretzato of space. 4

154 x = x (5.4) At the st tme step, the bubble radus s R ad the dstace from the cetre of the bubble to the th ode s X = R x (5.5) Next, we defe the spatal cremet x as half the characterstc dffuso legth l D, (the dstace travelled by the surfactat molecules for a tme step of t ). l D ca thus be expressed as l D = Dt (5.6) where D s the dffuso coeffcet wth the uts of cm /s ad so Dt x = (5.7) By makg the mesh sze smaller tha the dffuso legth, we esure that the mesh sze s small eough to resolve the computatos ecessary to descrbe the dffuso process. The umber of specal odes relatoshp N SN N SN s related to the depth of the bulk L by the = L x. The depth of the bulk L s chose to be 5 tmes the adsorptve legth ( l A ) or dffusve characterstc legth ( l D ), whchever s larger for the process. Ths ca all be expressed as N SN ( l l ) L 5 D or = = x x A (5.8) 5

155 We ow fd dvdual expressos for l D x ad l A x. If t s the total tme of the smulato ad N s the umber of cycles the smulato, the the total tme of the smulato ca also be expressed as t = N N t, such that S l D = x Dt x = DN S x N t = DN S N Dt t = N S N (5.9) Sce Dt x = N S N, x = N Dt N DN N S S = S N = N t N S D ω (5.30) l A x ca ow be evaluated as l A Γ N S Γ = = x x D ω * bulk * bulk (5.3) A ew operator A, B s defed, to deote the greater of A ad B, so N SN ca be expressed as N SN = 5 ( N ) S N Γ, D ω * bulk (5.3) 6

156 Dscretzato of Bubble Dmesos The bubble volume V (t) s prescrbed for the model as equato (5.33) ad s show Fgure 5.7. The volumes Fgure 5.7 ca be related to those of the alveol durg a typcal breath cycle as follows: Vcycle π V ( t) = Vmea s πωt (5.33) V max V cycle V mea V m Fgure 5.7 Dscretzato of bubble dmesos. V m s the volume of a alveolus whe the lug volume s at FR. V cycle s the cyclc volume chage that the alveol goes through durg the TV of the lug. V max s the volume of a alveol whe the lug s at FRTV. V mea ca be expressed as FR 0.5TV. The dscretzed form of the bubble volume s V = V mea V cycle π s πωt (5.34) 7

157 where V s the volume at the th tme step, 4 V π ( R ) 3 the bubble follows sphercal geometry ad behavour, the radus =. Usg the assumpto that 3 R ad terfacal area 3 R = ad 4π V A ca be calculated as 3 A = 4π ( R ) respectvely Dscretzato of ross-sectoal Area Mass flux betwee two adjacet odes passes through the surface area at the mdpot of the odes as oted Fgure 5.8. The otatos Fgure 5.8 are explaed as follows: The surface area at the mdpot of odes ad at the st tme step s deoted by A., The surface area at the mdpot of odes ad - at the st tme step s deoted by A,. The surface area at ode at the st tme step s deoted by A, or more succctly as A. The terfacal surface area at the st tme step s deoted by A, or more succctly as A subsequet operatos. 0 x X x 0 - A, 0 A, A, A, Fgure 5.8 Dscretzato of the cross sectoal area. 8

158 Followg the relatoshp of sphercal geometry, the dscretzed equatos for the area are A, = x 4π X ( X ) A, = A, = 4π (5.35) A, = x 4π X Dscretzato of the Dffuso Equato Here, the covecto-dffuso equato s dscretzed usg the mplct Euler scheme [06, 07] wth a cotrol volume approach. The cetred-fte dfferece formulas are used to dscretze the equatos. Both the covecto ad dffuso terms are dealt wth. A upwd scheme [07] s ecessary to better approxmate the covecto term. Prelmary Dervato A three grd-pot cluster for a oe dmesoal cotrol volume approach s show Fgure 5.9. It s used to defe the cocetrato at each ode where: s the cocetrato at the th ode s the cocetrato o the east sde (the postve drecto) s the cocetrato o the west sde (the egatve drecto) bot s the cocetrato at the mdpot of ad top s the cocetrato at the mdpot of ad v relbot s the relatve velocty betwee the flud ad the movg terface at mdpot of ad v reltop s the relatve velocty betwee the flud ad the movg terface at the mdpot of ad 9

159 bot top v relbot v reltop Fgure 5.9 A three grd-pot cluster for a oe dmesoal cotrol volume approach. The goverg dfferetal equato s t v rel x = D x (5.36) It follows ow to dscretze each term of equato (5.36) by usg the otatos the three grd-pot cluster. For the frst term, t t (5.37) Oe could assume that the cocetrato at the mdpot of adjacet odes (whch s fact the terface of the cotrol volume) s the average value of the cocetrato of the two adjacet odes, top ad bot. However, t has bee reported that usg ths assumpto wll oly be able to produce realstc results for low Reyolds umbers ad may cause the soluto to dverge ad thus to seek a better formulato, the upwd scheme (also kow as the upwd dfferece scheme, the upstream-dfferece scheme, the door-cell method, etc) [07] s employed. A better prescrpto s preseted by the upwd dfferece scheme by assumg that the value of the cocetrato at the cotrol volume terface s equal to the value of at the grd pot o the upwd sde of the face. 30

160 top ad bot ca thus be reformulated as whe v < 0 (5.38) top = = whe v > 0 (5.39) top reltop reltop = whe v < 0 (5.40) bot whe v > 0 (5.4) bot = relbot relbot Recallg a prevously troduced operator A, B, whch deotes the greater of A ad B, the upwd scheme ca be more compactly wrtte as: v reltop top = vreltop, 0 vreltop,0 (5.4) v relbot bot = vrelbot,0 vrelbot,0 (5.43) For the secod term, usg the cetred-fte dfferece formula for the frst dervatve, gves v rel x v reltop top x v relbot bot x (5.44) For the thrd term, usg the cetred-fte dfferece formula for the secod dervatve, gves D x = D ( ) D ( ) x x (5.45) ollectg all the terms, the dscretzed goverg equato ow becomes 3

161 3 x v x v t bot relbot top reltop ( ) ( ) x D x D = (5.46) To arrage the equato more compactly, both sdes of the equato are multpled by t to obta x t v x t v bot relbot top reltop ( ) ( ) x t D x t D = (5.47) The equato ca be further smplfed by settg x t D = α. Ths s kow as the dmesoless dffuso coeffcet. For preset purposes, the dffuso coeffcet s assumed to be costat sce the bulk s assumed to be well mxed such that x t D x t D = = α (5.48) to get the followg x t v x t v bot relbot top reltop ( ) ( ) = α α (5.49) ad cosequetly by substtutg equatos (5.4) ad (5.43), we get x t v x t v reltop reltop,0,0 0,,0 = relbot relbot x t v x t v α α α α (5.50) At ths pot, the volume flow rate s defed as Q, such that

162 33, = reltop A Q v ad, = relbot A Q v (5.5) ollectg all lke terms equato (5.50), gves α α x t v x t v relbot reltop 0,,0 = x t v x t v relbot reltop 0,,0 α α (5.5) Sce, 0, = reltop reltop A Q v x t v α (5.53) ad, 0, = reltbot relbot A Q v x t v α (5.54) Equato (5.5) ca be smplfed to read ( ) relbot reltop relbot reltop v v v v = (5.55) Substtutg the values of, = reltop A Q v ad, = relbot A Q v to equato (5.55), gves,,,, = A Q A Q A Q A Q (5.56)

163 34 Assumg that the surface area at ode s approxmately equal to the areas located at the mdpot betwee the two odes o ether sde of t,,, = = A A A (5.57) Ths allows equato (5.56) to be smplfed to = Q Q Q Q A (5.58) By defto = = = (5.59) So equato (5.58) ca be rewrtte as Q Q Q Q A = Q Q Q Q (5.60) ollectg all lke terms, the fal dscretzed form of the covecto-dffuso equato s ( ) Q Q A Q Q ( ) Q Q Q Q = (5.6) Q s the mass flux betwee adjacet odes wth the uts of kg/s Defg the Volume Flow Rate To defe the Q terms ( Q ad Q ) equato (5.6), the relatoshps equatos (5.53) ad (5.54) are recalled to arrve at

164 t t Q = A, α vreltop, 0 ad Q = A, α vrelbot, 0 (5.6) x x The Dmesoless Dffuso oeffcet Dt Because the spatal cremet s set as x =, the Dt x = 4 = α (5.63) Therefore, the dmesoless dffuso coeffcet α has a set value of Dscretzato of Relatve Veloctes The relatve velocty s gve by equato (5.0) terms of x ad R (t). To defe the relatve velocty terms of area, both sdes of the equato are multpled by 4 π as follows R t dr v = ( ) rel x R t 4π 4π dt ( ) (5.64) so that v rel R t dr R t 4π ( ) 4π 4π ( ) dr = = x R t 4π dt [ x R t ] dt ( ) 4π 4π ( ) (5.65) The term 4 R ( t) π represets the surface area at the terface ad [ ] 4π x R( t) represets the surface area at ode as see Fgure 5.0(a). To ga a dscretzed expresso of v reltop ad v relbot usg equato (5.65), we use the otato Fgure 5.0 (b) to ga v reltop ad v relbot terms of A, ad A, respectvely. 35

165 R (t) x R x x R(t) (a) th ode A, A, (b) Fgure 5.0. Notatos used to dscretze relatve veloctes. Thus at A, v reltop 4π ( R ) = A, dr dt (5.66) ad at A, v relbot 4π ( R ) = A, dr dt (5.67) To ga a physcal apprecato, t s worthy to ote that at the terface,0 = 4 ( R ) A π such that the relatve velocty of the flud s zero as show equato (5.68). v rel 4π = ( ) R 4 ( ) dr = π R A, 0 dt 4π ( R ) dr dt = 0 (5.68) Also, for odes far away from the terface, the area s much larger tha that of the 4πR terface such that the term A approaches 0 ad hece 36 v rel dr =. dt

166 Dscretzato of the Boudary odtos Usg Fgure 5., the boudary codto at the terface (equato (5.6)) s dscretzed. A, 0 0 x x 0 th ode Iterface st ode Fgure 5. Dscretzato at the terface. The mass flux across the terfacal area A ca be expressed as,0 M t (0, t) D = A x αx t (0, t x ) = A,0,0 (5.69) where αx D = t from the prevously establshed relatoshp equato (5.48). Usg the cetral dfferece approxmato for the frst dervatve, the term dscretzed as (0, t) x s x 0 = x = x 0 (5.70) 37

167 38 otg that ths case, the spatal cremet betwee the terface ad the two adjacet odes, odes 0 ad, s x as see Fgure 5.. ( ) 0,0 0,0 = = t x A x t x A t M α α (5.7) ad so ( ) 0,0 = x A M α (5.7) whch ca be rearraged as follows ( ) 0,0 = A x M α (5.73) the the rght had sde s equal to the flux term betwee the 0 th ad st odes. The flux term betwee the 0 th ad st odes s also cotaed equato (5.6) (the dscretzed covecto-dffuso equato) for the case of =. Lookg at equato (5.6), we substtute for = to get ( ) Q Q A Q Q ( ) Q Q Q Q = (5.74) ollectg all terms cotag 0 Q to the left had sde, reveals ( ) Q Q Q Q ( ) ( ) Q Q Q A = 5.75) Rearragg, gves

168 39 ( ) ( ) Q Q ( ) ( ) Q Q Q A = (5.76) ad subsequetly ( ) ( ) ( ) Q Q Q A Q 0 0 = (5.77) where the term ( ) 0 0 Q s actually the flux term betwee the 0 th ad st odes. Equatg ths to equato (5.73), gves ( ) ( ) x M A Q = = 0,0 0 0 α (5.78) Substtutg x M to equato (5.77) gves the fal dscretzed form as ( ) ( ) Q Q Q A x M = (5.79) Dscretzato of the equatos descrbg the three regmes Regme Lagmur Regme The Lagmur equato as see equato (5.0) ca be smply dscretzed as ( ) [ ] * Γ Γ Γ = k k A t M (5.80) where s whch s the subsurface cocetrato s actually substtuted for the dscretzato sce t represets the same quatty at the st tme step. As t stads, equato (5.80) caot be solved a mplct scheme because t cotas the o-lear product betwee the subsurface cocetrato ad terfacal mass

169 40 ( = Γ A M ). A learzato eeds to be doe where the terms ad M are expressed terms of the preset tme value plus the chage that value gog to the ext tme step, such that ( ) = ad ( ) M M M =. Expadg equato (5.80) gves * Γ Γ Γ = k A k A k A t M * k M k M k A Γ = ( ) ( ) ( ) ( ) * k M M k M M k A Γ = (5.8) Isolatg term ( ) ( ) k M M ad smplfyg, gves ( ) ( ) ( )( ) M k M k k M M = M k M k M k M k = (5.8) Neglectg the secod order term M k ad collectg lke terms reveals the term to be ( ) M M M k. Substtutg ths back to equato (5.8), ad expadg gves ( ) ( ) ( ) * k M M M M M k k A t M Γ = M k M k M k M k M k k A k A Γ Γ = * * (5.83) ollectg lke terms reveals the fal form of the equato ( ) [ ] M k M A k M A k M k k t * * Γ = Γ (5.84)

170 Regme No Mass Trasport From equato (5.0), the mass trasport for regme s descrbed by dm dt = 0 (5.85) A dscretzato of equato (5.85) s smply M = 0 (5.86) Regme 3 Squeeze Out Regme From equato (5.0), the mass trasport equato for regme 3 s dm dt da = Γ max (5.87) dt A dscretzato of equato (5.87) s M t A = t Γ max where A = A A (5.88) so that M = A Γ A Γ = A Γ A max max max Γ (5.89) The dscretzato of the equatos goverg mass trasport the three regmes ca be expressed as 4

171 k t k M * [ k ( A M )] k * Γ = Γ A M k M * Γ < Γ M = 0 Γ Γ < Γmax (5.90) * M = A Γ A Γ Γ = Γ max max Soluto of the Tr-dagoal Matrx The dscretzed equatos goverg dffuso ad the boudary codtos are assembled to a tr-dagoal matrx [08]. Equato (5.90) s the frst le of the matrx followed by equato (5.79) the secod le. Ths followed by m- equatos (where m s the umber of spatal odes) of the form equato (5.6). The last row of the matrx corporates the boudary codto at fty whch s always at bulk ad so there s o chage the cocetrato hece = 0. m The equato s show equato (5.9) for the frst regme. For the secod ad thrd regmes, the frst row of equato (5.9) s chaged to equatos (5.9) ad (5.93) respectvely. The vector of ukows to be solved s [ M,,, ], m ad s added to the vector of curret tme values to produce the future tme vector of cocetratos at whch pot all matrces are recalculated ad the loop begs aga. The computatoal model s solved Matlab, the umercal code of whch s attached Appedx F. 4

172 43 ( ) Γ m m m m m m m M Q Q A Q Q Q Q A Q Q Q Q A x M A k k k t 3 3 * ( ) ( ) [ ] [ ] Γ = * m m m m m m m Q Q Q Q Q Q Q Q Q M k M A k (5.9) [ ][ ] [ ] = M (5.9) [ ][ ] [ ] Γ Γ = A A M max 0 0 (5.93) 5.4. Model Valdato To valdate the model, the umercal code Appedx F was appled to match the expermetal data of Schurch et al. [87] where a bubble was oscllated a mg/ml soluto of urosurf. The model parameters used the smulato (Table 5..) were adopted from Morrs [84] who successfully used the model to match the same set of data from Schurch et al. [87]. The results of the smulato ad the comparso to the expermetal data by Schurch et al. [87].e. the A γ loops at steady state are show Fgure 5.. The preset code shows a smlar match of the expermetal data to that of Morrs [84], thus demostratg proper fucto of the Matlab code.

173 Table 5. Model parameters used by Morrs [84] to match expermetal data of Schurch et al [87]. Parameter Value Uts ω 0 cycles/m bulk mg/ml * γ 5 dy/cm γ m dy/cm m 00 dy/cm D x 0-9 cm /sec k 0.07 x 0 5 ml/(g.m) k. x 0 5 ml/g k * Γ 3 x 0-7 g/cm m = γ water * γ 70 5= 45 dy/cm Γ * * = Γ ( γ γ ) m ] 3x0-7 [(5-)/00] = 3.7x0-7 g/cm max [ m Surface Teso (dye/cm) A Relatve Area (%) B Fgure 5. omparso of γ A loops at steady state for (A) expermetal data from Schurch et al.[87], (B) match of Schurch data usg computatoal model Expermets o urosurf usg Modulated Frequeces Prevous expermets o urosurf [87] have oly bee doe o cyclg frequeces the order of breathg frequeces. ommercal PBS devces to date have therefore bee desged to have pumps that delver the oscllatg tdal volume ad software ad camera resolutos to sut [83, 86, 87, 09]. Sce the preset study uses oscllatg frequeces that are beyod the rage of commercal pump, camera ad software 44

174 operato, a custom bult surfactometer had to be made. The am of the expermetato was to determe the surface teso of a oscllatg bubble mmersed a surfactat soluto thus smulatg surface teso dyamcs the alveol uder the followg codtos: Oscllato at a breathg frequecy of 0.5 Hz ad V m /V max of 70% V m /V max s the rato of the mmum volume over the maxmum volume. These values were chose to represet the breath cycle of a 4 day gestato lamb where the tdal volume (TV) = 8 ml/kg durg mechacal vetlato as Pllow et al. [95] ad FR s the value at 5 cm H O the pressure-volume curves of the samples collected hapter 3. A V m /V max rato smaller tha 70% saw the bubble dsappearg to the tube ad so restrcted the possblty of testg dfferet V m/ V max ratos wth the curret setup. Oscllato at a breathg frequecy of 0.5 Hz ad V m /V max of 70% Modulated Frequeces Frequeces from 0-70 Hz were chose for the study to represet the rage of frequeces preset the Bubble PAP System uder ormal operatg codtos. Frequeces were tested from 0 to 70 Hz at 0 Hz tervals at 3 ampltudes.e. 5% of TV,.5% of TV ad 30% of TV. Modulated ampltudes above 30% of TV caused the bubble to become ustable ad detach. Table 5. detals the codtos of each expermet (each of whch was repeated thrce). The breath cycle frequecy ad the breath cycle V m /V max rato were kept costat for all expermets at 0.5 Hz ad 70% respectvely. The expermets were performed at 39 o to represet the core temperature of ewbor lambs. 45

175 Table 5. Expermetal detals. Expermet Name Modulatg Frequecy (Hz) Modulatg Ampltude (%TV) Breath ycle 0 0 F0-A5 0 5 F0-A F0-A F0-A5 0 5 F0-A F0-A F30-A F30-A F30-A F40-A F40-A F40-A F50-A F50-A F50-A F60-A F60-A F60-A F70-A F70-A F70-A Expermetal Equpmet ad Setup The schematc dagram of the complete expermetal setup s show Fgure 5.3 ad a photograph of the actual setup s show Fgure 5.4. The bubble chamber s the focus of the expermet ad s show closer detal Fgure 5.5(a) ad (b). The bubble chamber cossts of a ml trasparet cuvette cotag a surfactat soluto wth a small ar gap. The cuvette has a flat surface to avod optcal dstorto of the bubble as s commo wth cyldrcal bubble chambers. LED backlghtg s used to lght up the bubble from behd for the best cotrast durg bubble motorg. A rubber plug s used to create a artght seal through whch two eedles are serted; () the Bubble Needle a 8 gauge o-bevelled eedle o whch 46

176 the bubble s attached ad oscllates ad () the Adjuster Needle a 8 gauge bevelled eedle used to create the tal bubble sze by suckg out ar the cuvette wth a syrge. A thermocouple wre s also serted through the plug to a depth whch allows the tp to be well mmersed the surfactat soluto. Resstve heatg elemets ad coductve paste are placed o the sdes of the cuvette ad clamped to a alumum stad. The thermocouple wre ad resstve heatg elemets are coected to a custom made temperature cotroller accurate to 0.5 o the rage of -00 o. Amplfer Osclloscope Temperature otroller Dsplay Thermocouple Mas Power RTD Trasducer Heat O/Off ELV otrolled Sgal Geerator A Power Supply Sgal Geerator B Permaet Maget Shaker Bubble hamber P wth PFV software Hgh Speed Dgtal amera Fgure 5.3 Schematc dagram of expermetal setup. 47

177 A.6 mm dameter psto s attached to a permaet maget shaker (V0/3, LDS, Mddleto, WI, USA) ad serted to a flexble tube that attaches to the bubble eedle as see Fgure 5.6. Thck petroleum jelly s used to successfully create a artght seal wth mmal frcto. The permaet maget shaker s used to delver the waveforms to smulate eoatal breathg frequeces ad the modulated frequeces from 0-70 Hz used the expermets. Fgure 5.4 Photograph of expermetal setup. A custom-bult power amplfer (Fgure 5.3) s used to exted the usable frequecy rage of the permaet maget shaker from Hz to Hz to accommodate for the low cyclg frequecy used smulate breathg frequecy.e. 0.5 Hz. The shaker s drve by the two fucto geerators.e. Model 5300A (Kroh-Hte, Brockto, MA, USA) ad Model 330A (Hewlett Packard, Eglewood, olorado, USA). A osclloscope (TDS0, Tektrox, Orego, USA) was used to vew the drvg waveforms from the fucto geerators. A regulated D power supply (EPS- 48

178 3030D, Escort, Tawa) s used to power the shaker va the power amplfer as well as the LED ad resstve heatg elemet (Fgure 5.5). A hgh speed dgtal vdeo camera (FASTAM 04 PI, Photro, Sa Dego, A, USA) wth a log dstace mcroscope (K/S IFocus, Ifty, Boulder, USA) show Fgure 5.7 where used to dgtally motor the bubble oscllatos. The Photro Fastcam Vewer (PFV) software was used to capture the dgtal mages whch were capable of beg used Matlab to measure the bubble dmesos durg data processg. oectg Tube to Shaker Bubble Needle Adjuster Needle creates tal bubble Thermocouple (wth attached bubble) Bubble Needle Thermocouple Plug Adjuster Needle Plug Wres to LED Backlghtg Resstve Heatg Elemets Resstve Heatg Elemets Bubble hamber Bubble hamber a b Fgure 5.5 Bubble chamber. 49

179 Fgure 5.6 Permaet maget shaker. Fgure 5.7 Photro hgh speed dgtal camera ad log dstace mcroscope Expermetal Methodology The followg methodology was performed for each expermet outled Table 5.. After settg up the equpmet, the samplg rate of the hgh speed camera was set to 000 frames per secod (fps) ad the shutter speed was set to /frame secod ad the scree resoluto to 640 x 58 pxels. Ths produced the optmal optcal cotrast ad samplg perod achevable for the gve samplg rate of 000 fps wth the avalable equpmet. 50

180 urosurf was suppled as a 80 mg/ml suspeso a 3 ml val. Surfactat was wthdraw from the val wth a sterle eedle ad mxed to the requred cocetrato of 0.5 mg/ml wth ormal sale (0.9% Nal) soluto. ocetratos greater tha 0.5 mg/ml redered the soluto too murky to produce dstct bubble edges the captured mages. The desty of the surfactat soluto was measured at 39 o. The soluto was the trasferred to the bubble chamber ad the plug (cotag the eedles ad thermocouple) put place. The temperature cotroller was the swtched o ad the soluto was the heated up to 39 o. are was take to esure that the eedle was vertcal, the thermocouple wre was ot terferg wth the bubble moto ad that the backlght was set such that the backgroud was as whte as possble ad the bubble as black as possble to get the best bubble cotrast. The dal o the amplfer was calbrated by performg a few prelmary measuremets so that the cyclg ampltude was set to geerate a V m /V max rato of 70%. Keepg the swtch o the amplfer whch seds the sgal to the shaker off, the frequecy ad ampltude of oscllato was set at the fucto geerator accordg to the values specfed Table 5. for the partcular expermet. The mage was calbrated to the bubble eedle by measurg the dameter pxels o the scree sce the eedle dameter s kow. A tal bubble was created by wthdrawg ar out of the bubble chamber wth the adjuster eedle. The bubble sze was set to.5 tmes the tube dameter. A few prelmary trals showed that a tal bubble sze larger tha ths value caused the bubble to detach durg oscllato whe the maxmum area was reached. Bubble szes smaller tha ths value caused the bubble to become too small durg oscllato ad the bubble would dsappear to the bubble eedle. 5

181 After creatg a tal bubble sze, the bubble was left to adsorb for 3 mutes to allow the bubble to reach equlbrum. The cyclg was the started by turg o the swtch o the amplfer to the shaker. The bubble was cycled for 0 cycles to reach steady state as determed by Schurch et al. [87]. The mages were the recorded o the PFV software for as log as the memory o the computer allowed wth the chose camera settgs, whch was approxmately 7 secods. The dgtal mages of the bubble were the aalysed a custom geerated code (See Appedx G) Matlab whch measured the dameter of the bubble both the x ad y axes. The surface teso was calculated by aother code Matlab (See Appedx H) whch was based o the umercal solutos provded by Graves et al. [0] that allow oe to relate the shape of a deformed bubble to the surface teso [33, 0] Expermetal Results Mmum ad maxmum surface teso for the purposes of ths study are defed as the surface teso at mmum ad maxmum area, respectvely. The st breath cycle of each expermet was chose to detfy mmum ad maxmum values achevable at steady state. Ths was performed to determe whether addg modulated frequeces would postvely affect the mmum ad maxmum surface tesos the alveol durg a breath cycle. The surface teso values for each expermet cludg the stadard devatos are preseted Table 5.3. The mmum ad maxmum surface teso measuremets at each modulatg frequecy are plotted Fgure 5.8 ad Fgure 5.9 respectvely, for the 3 dfferet modulatg ampltudes. The surface teso values of the breath cycle wthout modulato are also show at each frequecy for comparso. 5

182 Table 5.3 Surface teso measuremets. Expermet Average Mmum Surface Teso, dye/cm (±SD) Average Maxmum Surface Teso, dye/cm (±SD) Breath ycle 6.56 (.8) 7.5 (3.36) F0-A5 3.5 (.84) 6.76 (3.06) F0-A (0.9) 0.04 (0.63) F0-A30.45 (.43) 7.84 (.3) F0-A5. (3.84) 4.0 (3.3) F0-A (.86).74 (3.75) F0-A30. (3.5) 6. (.70) F30-A5.59 (.99) 4.39 (5.9) F30-A.5.7 (.63) 0.03 (6.6) F30-A (.4) 7.0 (.97) F40-A5.95 (0.96) 7.55 (.30) F40-A.5.9 (0.78) 6. (0.85) F40-A (.9) 6.5 (.07) F50-A (.) 0.4 (5.9) F50-A.5.79 (.6) 5.7 (.63) F50-A (.5) 5.3 (.8) F60-A5 0.0 (3.4) 3.03 (4.79) F60-A (.04) 4.4 (.04) F60-A (.0) 5.07 (.74) F70-A5.83 (3.8) 4.89 (4.96) F70-A (.60) 0.87 (0.70) F70-A (0.75) 4.88 (0.75) Fgure 5.8 ad Fgure 5.9 are preseted prmarly to observe the statstcal dffereces betwee expermets before further aalyss. The observatos o statstcal dffereces the mmum surface tesos Fgure 5.8 are as follows. The mmum surface teso usg a modulated ampltude of 5%TV s ot statstcally dfferet to the mmum surface teso durg a umodulated breath cycle for all frequeces except at 50 ad 60 Hz where the mmum surface tesos are statstcally lower at ths ampltude. The mmum surface teso usg a modulated ampltude of.5%tv s ot statstcally dfferet to the mmum surface teso durg a umodulated breath 53

183 cycle for frequeces from 0-30 Hz. The mmum surface tesos at Hz however are statstcally lower at ths ampltude. The mmum surface tesos at.5%tv are also ot statstcally dfferet to those at 5%TV for all frequeces apart from 70 Hz where t s lower. The mmum surface teso usg a modulated ampltude of 30%TV s statstcally lower to the mmum surface teso durg a umodulated breath cycle for all frequeces tested. It s however, ot statstcally dfferet to both 5%TV ad.5%tv for all frequeces, except at 40Hz, where t s lower. The observatos o statstcal dffereces of the maxmum surface tesos Fgure 5.9 are as follows. The maxmum surface teso usg a modulated ampltude of 5%TV s ot statstcally dfferet to the maxmum surface teso durg a umodulated breath cycle for all frequeces, except at 50 Hz where t s lower. The maxmum surface teso usg a modulated ampltude of.5%tv s statstcally lower tha the maxmum surface teso durg a umodulated breath cycle for all frequeces. It s also statstcally lower tha the maxmum surface teso at 5%TV for all frequeces except 0 Hz ad 30 Hz. The maxmum surface teso usg a modulated ampltude of 30%TV s statstcally lower tha the maxmum surface teso durg a umodulated breath cycle as well as ampltude modulato at 5%TV for all frequeces. It s ot statstcally dfferet to the maxmum surface teso values at.5%tv for all frequeces, except at 70Hz, where t s hgher. Although dstct statstcal dffereces surface teso betwee modulatg ampltudes ad frequeces are ot observed geeral Fgure 5.8 ad Fgure 5.9, treds of decreasg surface teso were oted wth a crease frequecy for all modulatg ampltudes. 54

184 The lear treds of mmum ad maxmum surface teso wth frequecy are show Fgure 5.0 ad Fgure 5. respectvely. Fgure 5.8 Mmum surface teso measuremets. Fgure 5.9 Maxmum surface teso measuremets. 55

185 Fgure 5.0 Treds mmum surface teso. Fgure 5. Treds maxmum surface teso. Observatos o the treds mmum ad maxmum surface teso from Fgure 5.0 ad Fgure 5. respectvely are preseted as follows. 56