Barotrauma during air travel: predictions of a mathematical model

Transcription

1 J Appl Physol 98: , Frst publshed December 17, 2004; do: /japplphysol Barotrauma durng ar travel: predctons of a mathematcal model Stephen Chad Kanck 1,2 and Wllam J. Doyle 1,3 1 Department of Pedatrc tolaryngology, Chldren s Hosptal of Pttsburgh, 2 Department of Chemcal and Petroleum Engneerng, Unversty of Pttsburgh, and 3 Department of tolaryngology, Unversty of Pttsburgh School of Medcne, Pttsburgh, Pennsylvana Submtted 7 September 2004; accepted n fnal form 14 December 2004 Kanck, Stephen Chad, and Wllam J. Doyle. Barotrauma durng ar travel: predctons of a mathematcal model. J Appl Physol 98: , Frst publshed December 17, 2004; do: /japplphysol Mddle ear barotrauma durng flght s a panful dsorder experenced by passengers who cannot properly regulate ther mddle ear pressure n response to the changng cabn pressures durng ascent and descent. Prevous reports emphaszed the mportant role of poor eustachan tube functon n dsease pathogeness but pad lttle attenton to other moderatng factors. Here we descrbe a mathematcal model of mddle ear pressure regulaton and smulate the pressure response to the changes n cabn pressure experenced over typcal flghts. The results document bufferng mechansms that decrease the requste effcency of actve, muscleasssted eustachan tube openng for dsease-free flght. These nclude the relatve dfference between destnaton and departure elevatons and the rato of maxmum tympanc membrane volume dsplacement to mddle ear volume, where greater absolute values requre lesser effcences for dsease-free flght. Also, the specfc type of functonal defct s mportant snce ears wth a completely obstructed eustachan tube can be less susceptble to barotrauma than those wth a eustachan tube that passvely opens but fals to dlate n response to muscle actvty. These bufferng systems can explan why some chldren and adults wth poor eustachan tube functon do not experence mddle ear barotrauma. mddle ear pressure regulaton; eustachan tube; Valsalva maneuver; tympanc membrane MIDDLE EAR (ME) barotrauma, the most common medcal dsorder assocated wth modern ar travel, affects an estmated 5% of adult and 25% of chld passengers (49). Two prmary expressons of barotrauma can be dstngushed based on sgns and pathophysology: barotts meda and baromyrngts. Barotts meda s ME mucosal (MEM) nflammaton, hemorrhage, and leakage of transudate nto the ME precptated by moderate ME underpressures relatve to the surroundng MEM. Baromyrngts s structural damage to the tympanc membrane (TM) wth severe pan caused by large pressure dfferences between ME and cabn. Sequelae of barotrauma can nclude dzzness, tnntus, and deafness (16, 45). Prevous studes descrbng the pathogeness of ME barotrauma were done on dvers or on patents beng treated n hyperbarc 2 chambers (3, 25, 32, 41), stuatons that do not share the physologcal condtons experenced durng pressurzed flght. Moreover, most publcatons and revews that specfcally focused on ME barotrauma durng flght lack emprcal data and descrbed dsease pathogeness usng broad generalzatons (2, 6, 33, 45) wth a prmary focus on the functon of the eustachan tube (ET). The nadequacy of ths approach was recently hghlghted n a study by Sade and colleagues (48) who reported dsease-free flghts for chldren and adults wth presumably poor ET functon. Here, we approach the pathogeness of ME barotrauma from the perspectve of basc physology usng both descrptve and mathematcal formats. ur goal s to clarfy the bufferng mechansms that protect the ME from barotrauma durng pressurzed flght. ME Pressure Regulaton Barotrauma s caused by an nablty to mantan near pressure equvalence between the ME (P ME ) and arplane cabn (P Cabn ) as the latter s changed rapdly durng ascent and descent. Normally, the pressure of the flud-free ME s near ambent (Pam) (P ME Pam P Cabn ), whch ensures free vbraton of the TM and effcent transducton of sound energy to the nner ear. Because the ME s usually a closed, relatvely noncollapsble, temperature-stable, mucosal-lned bony cavty, ts pressure s a drect functon of the contaned gas volume, and gas transfers to or from the ME change ts pressure. The ME conssts of two functonally dscrete but contnuous ar spaces: the anteror tympanum, whch contans the osscles, lgaments, and muscles of the sound transducer mechansm; and the posteror mastod cavty, whch s subdvded nto numerous ntercommuncatng ar cells (5). Whle the varance among ndvduals and age groups n tympanum volume (V tym ) s low (V tym 1 ml), that of the mastod (V mas ) s large (V mas 0 15 ml) due to contrbutons of age, gender, and dsease hstory effects (37, 46). The anteror wall of the tympanum s contnuous wth the osseous porton of the ET, the lateral wall ncludes the TM, the medal wall ncludes the round wndow membrane, and the posteror wall opens to the mastod ar space by way of a large ar cell, the antrum (5). Fgure 1A shows the varous gas exchange pathways for the ME when solated wthn an arplane cabn. The tympanum can exchange gas wth the external envronment va the TM and wth the nner ear va the round wndow, but expermental measurements show that transfers across these pathways are neglgble (18, 21). Therefore, n descrbng P ME regulaton, the physologcally relevant pathways are as follows: tympanum-antrum-mastod, ME-MEM-blood, and tympanum-etnasopharynx (NP). Because the tympanum and mastod are contnuous n the ar phase, al pressure dfferentals are rapdly equlbrated, and establshed gas partal-pressure dfferentals decay quckly (24). ME-MEM-blood-gas exchange s a dffusve process whose rate depends on the extant partalpressure gradents and gas-specfc exchange constants (20, 22, 23). At physologcal partal-pressure gradents between ME Address for reprnt requests and other correspondence: S. C. Kanck, Chldren s Hosptal of Pttsburgh, 3705 Ffth Ave. at DeSoto St., Pttsburgh, PA (E-mal: kancksc@upmc.edu). The costs of publcaton of ths artcle were defrayed n part by the payment of page charges. The artcle must therefore be hereby marked advertsement n accordance wth 18 U.S.C. Secton 1734 solely to ndcate ths fact /05 $8.00 Copyrght 2005 the Amercan Physologcal Socety

2 and venous blood (VB), gas exchange across ths path s prmarly attrbutable to the relatvely slow exchange of N 2, and, consequently, ths exchange s expected to have a mnmal effect on P ME over most flght duratons. In contrast, gas exchange across the ET s a rapd, gradent-dependent bolus exchange of mxed gases between NP and tympanum. Under normal physologcal condtons, ths s the only drect, potental communcaton between ME and ambent envronment and the only exchange pathway capable of reducng establshed, postve Pam-P ME gradents. The functonal anatomy of the ET has been descrbed n many publcatons (2, 5, 17, 52). Brefly, the posteror porton of the ET s a mucosa-lned, bony tube contnuous wth the anteror tympanum, whereas the anteror porton s cartlagnous medally and membranous laterally (Fg. 2). The cartlagnous porton s usually closed by a tssue pressure, ET pressure (P ET ), that equals the sum of the Pam (a consequence of the ncompressblty of body fluds) and a vascular pressure (P vas ) (17, 27). A muscle, the tensor vel palatn (mtvp), takes orgn from the membranous wall of the ET and termnates on the hamular process and wthn the palatne aponeuross (5). Actvaton of the muscle durng swallowng exerts an anterorlateral-nferor vector force (F TVP ) on the membranous wall of the ET (52). Fgure 1B depcts these functonal relatonshps. There, the ET s represented as a balloon pressure valve that s normally closed by the pressure dfference between P ET and both NP pressure (P NP ) and P ME. ET openng can be affected by passve, pressure-drven processes or by actve, pressuredrven or muscle-asssted mechansms (36, 51). Passve, pressure-drven ET openng occurs when the force, F(P), assocated wth ether P ME or P NP exceeds that of P ET. Actve, pressuredrven ET openng occurs when P NP s ncreased by Valsalva Fg. 1. Cartoon llustratng the pathways for mddle ear (ME) gas exchange (A), the factors contrbutng to passve (va pressure-nduced flow past a compressng balloon) and actve [va tensor vel palatn muscle (mtvp) muscle contracton] eustachan tube (ET) functon (B), and the effect of ME-ambent pressure (Pam) gradents on tympanc membrane (TM) dsplacement (C). See text for detals. NP, nasopharynx; IE, nner ear; P ME, ME pressure; X TM, TM dsplacement dstance; A TM, TM surface area; P Cabn, cabn pressure; P ET, ET pressure; P NP, NP pressure. BARTRAUMA DURING AIR TRAVEL 1593 Fg. 2. Component forces actng on the ET durng muscle-asssted openngs. The lumen remans open untl the force of the surroundng tssue (a functon of tssue pressure, P ET, and contact area, A ET) exceeds that exerted by the mtvp (F mtvp). Arflow through the ET s a functon of the cross-sectonal area of the lumen, related to the wdth opened, shown as X ET, and s determned n part by the mechancal stffness of the lumen and surroundng tssue, shown as K ET. P amb, Pam; P vas, vascular pressure. or other maneuvers so that the appled F(P NP ) exceeds F(P ET ), or, for some ndvduals, when F(P ET ) s reduced by yawnng or mandbular repostonng (5, 13, 17, 36). Actve, muscleasssted ET openng occurs when the mtvp contracts wth suffcent force (F TVP ) to overcome the F(P ET ) (5, 27, 28). The teleologcal effect of these normal ET openngs s to allow NP-ME gas exchange so as to mantan an approxmate equlbrum between P ME and Pam as P ME s decreased by transmucosal gas exchange and Pam fluctuates wth barometrc condtons,.e., normal P ME regulaton (5, 31, 43). Movements of the TM n response to P ME -Pam dfferentals are an mportant excepton to the assumed fxed ME volume (V ME ). There, small fluctuatons n that pressure gradent can be absorbed by V ME changes n response to pressure-drven TM movements (46, 47). Ths s llustrated n Fg. 1C, whch shows the TM response to a P ME -P Cabn gradent. As gven by Boyle s law, the magntude of ths pressure bufferng effect s a functon of the rato of TM volume dsplacement to V ME.In healthy ears, the maxmum TM dsplacement volume s 1% of the ME (.e., tympanum mastod) volume (46), and the bufferng effect of TM dsplacement on P ME s lmted. However, persstent ME dsease causes a sgnfcantly reduced V mas and can cause a hypercomplant TM (19, 26), changes that wll ncrease the determnate rato for TM bufferng and may reduce the affected ME s susceptblty to barotrauma. Normal P ME Regulaton Durng Flght Durng arplane ascent, P Cabn ( Pam) decreases, whch causes decreasng P NP, P ET, and MEM pressure (P MEM ), whereas P ME s relatvely unchanged (wth the excepton of a mnor decrease assocated wth TM bulgng) vs-à-vs takeoff. Ths results n the development of postve P ME -Pam, P ME -P NP, and P ME -P ET gradents. At tmes when F(P ME ) exceeds F(P ET ), the ET passvely opens, gas of ME composton flows from the ME to NP, and P ME s reset to the extant value of P ET. The resdual P ME -P Cabn gradent representng P vas (.e., P ET Pam), as well as any gradents that develop by trans-mem gas exchange (Pam P ME P ME, where s change) or by mnor changes n elevaton durng flght (Pam Pam P ME )

3 1594 BARTRAUMA DURING AIR TRAVEL are reduced by drectonal gas flows when the ET s actvely opened by the mtvp. n descent, Pam ncreases, causng ncreases n P NP,P ET, and P MEM, whereas P ME s relatvely unchanged vs-à-vs crusng alttude. Ths causes a rapdly developng, postve Pam-P ME (and P ET -P ME ) gradent, and a relatve P MEM overpressure wth respect to P ME. Under such condtons, nether F(P NP )orf(p ME ) wll exceed F(P ET ), and passve ET openngs are not possble. Consequently, durng descent, the passenger must perodcally open the ET actvely by swallowng to nduce mtvp actvty or by other maneuvers that cause F(P NP ) to transently exceed the extant F(P ET ) or cause F(P ET ) to decrease to less than F(P NP ). f the latter, Valsalva s the most commonly used wheren ar s forcbly expelled from the lungs whle keepng the mouth closed and pnchng the nose (6, 17, 33, 36, 45). Ths greatly ncreases the P NP and can passvely open the ET to allow for NP gas transfer to the ME. Glossary Pressures P ME P ME P Cabn P Cabn P NP P NP P ET P IET Pam P vas P ME-Cabn P ME-NP Volumes Total ME pressure ME partal pressure ( 2,C 2,N 2,H 2 ) Total cabn pressure Cabn partal pressure ( 2,C 2,N 2,H 2 ) Total NP pressure NP partal pressure ( 2,C 2,N 2,H 2 ) Tssue pressure surroundng ET lumen ET ntralumnal pressure Ambent pressure Vascular pressure ME-cabn pressure dfferental ME-NP pressure dfferental Pathogeness of Barotrauma The rapd changes n P Cabn (Pam) durng arplane ascent and descent can overtax the P ME -regulatng system and provoke barotrauma. For passengers wth excellent actve ET openng functon, P ME regulaton durng flght s a nomnal task, but for those wth less effcent ET functon, nfants and chldren, and those wth concurrent nasal nflammaton caused by colds or allergy, the task may be mpossble (6, 7, 33). If trans-et gas flow does not reestablsh a near zero P ME -Pam gradent durng descent, P ET wll exert ts force over a larger collapsble secton of the ET lumen, whch can exceed the maxmal force exerted by ether the mtvp or actve NP pressurzaton (17). Ths phenomenon, known as ET lockng, occurs at an ndvdualspecfc P ME -Pam gradent and effectvely obstructs the ET to any further gas flow. In the absence of adequate pressure regulaton, the large P ME -Pam gradents that develop durng ascent and descent cause maxmal extenson of the TM wth stretchng and tearng of ts structural elements. The TM can develop focal hemorrhages or local pocket formaton and may perforate (17, 45). At submaxmal extenson, ths s perceved as a feelng of fullness n the ear and at maxmal extenson as severe pan (16, 55). These are sgns and symptoms of baromyrngts. Alternatvely, at a specfed value of mmh 2, the postve Pam-P ME gradent that develops durng descent wll cause a larger P MEM -P ME gradent, resultng n MEM swellng, capllary dlataton, transudatve leakage, and accumulaton of flud n the ME va hydrops ex vacuo (50). Ths set of sgns presents as barotts meda. An ssue often faced by otolaryngologsts s the assgnment of ndvdual patents to rsk groups for barotrauma,.e., whch patents can fly safely and whch should take precautons before ar flght (54). Currently, such assgnments are based on hstory, clncal observatons, and, n some centers, ET functon test. We beleve that these assessments may not account for all nfluental factors that determne barotrauma rsk. Here, we take a unque approach to addressng ths ssue by frst formulatng a mathematcal model of P ME regulaton durng flght based on the physologcal consderatons outlned above and then studyng the effects on barotrauma rsk of varyng physologcal parameters ncluded wthn the model. V ME V mas V typ ET Passve penng P P ME-ET P ME-ET P NP-ET P NP-ET P C A ME A NP TM Dsplacement A TM C TM X TM ET Actve penng F ET F ST F TVP C ET X ET Q ET R A T A S f Mscellanous k METHDS Defnton of Dsease Sates ME ar space volume Mastod volume Tympanum volume ET openng pressure (reference ambent) ME-sde openng pressure (absolute) ME-sde openng pressure (reference ambent) NP-sde openng pressure (absolute) ME-sde openng pressure (reference ambent) ET closng pressure (reference ambent) ET contact area from ME ET contact area from NP TM cross-sectonal area TM complance TM lnear dsplacement ET closng force ET ntralumnal surface tenson (ST) force Force exerted by mtvp on ET lumen ET complance ET medolateral lumen wdth Trans-ET volume gas flow ET actve resstance ET openng tme Swallowng frequency Speces-specfc trans-mem exchange tme constants ( 2,C 2,N 2,H 2 ) We use the P ME-P Cabn gradent ( P ME-Cabn) as an ndex measure of barotrauma, or

4 BARTRAUMA DURING AIR TRAVEL 1595 P ME-Cabn t P ME t P Cabn t (1) where P ME and P Cabn are absolute pressures wthn the ME and cabn, respectvely, at a tme step (t). Based on the results of prevous studes, we assgned P ME-Cabn 250 mmh 2 as the threshold for onset of barotts meda (50) and P ME-Cabn 1,300 mmh 2asthe threshold for onset of baromyrngts wth severe pan (6). Gas Exchange Model The model compartments and lnkages shown n Fg. 1A depct the gas-exchange components of the ME system. All compartments are assumed to be well mxed and sothermal wth ntercompartmental communcaton defned as the transfer of gas moles down pressure gradents along the lnkages. Model compartments nclude the ME (tympanum mastod), MEM, NP, VB, and cabn. The ME s lnked perodcally to the NP durng ET openngs and contnuously wth the VB va the MEM. The cabn acts as the ambent envronment for the system, drectly affects P ET and P MEM [assumed to be nearly nstantaneous and lnear, based on the results of pressure chamber experments (30)], exerts a mechancal force on the TM, and exchanges gas wth the NP. The cabn s assumed to be an nfnte gas source/snk, and the volumes of the NP and VP are assumed to be fnte but much greater than that of the ME. Consequently, speces gas exchange between the ME and larger compartments does not affect the partal and al pressures of those compartments, but does have a sgnfcant effect on ME partal and al pressures. Cabn Pressurzaton Durng ascent, the arplane rses to a crusng alttude of 30,000 ft above sea level. To protect passengers from the adverse effects of these extreme low pressures, the cabn s pressurzed to an effectve crusng alttude of 8,000 ft (35, 45, 55). Cabn pressurzaton was modeled by ncreasng cabn alttude at a constant rate of 90 m/mn (approxmately that of a Boeng 747) from departure elevaton to the effectve crusng alttude (45). P Cabn s a functon of cabn elevaton and, assumng deal compressble gas behavor, s gven by: P Cabn t Pame mgz t BT o (2) where P Cabn s al P Cabn, t s tme, g s acceleraton due to gravty, m s the average mass of an ar molecule, B s Boltzman s constant, T o s the cabn temperature, Pam s referenced to sea level, and z(t) sthe effectve alttude of cabn pressurzaton (reference sea level). Because gas speces mole fractons are constant durng flght, cabn N 2 N (P 2 Cabn ) and 2 partal pressures (P 2 Cabn ) are calculated usng: N P 2 Cabn P 2 Cabn t 0.79P Cabn t (3) t 0.21P Cabn t (4) Smlarly, arplane descent was modeled as a lnear decrease from effectve crusng to destnaton alttudes at 90 m/mn, whle calculatng the ncreases n P Cabn(t). Pulmonary Exchange Total P NP s assumed to be equal to that of the cabn or, P NP t P Cabn t (5) whle NP gas speces pressures are assumed to be an average of the respectve cabn (experenced durng nhalaton) and alveolar (experenced durng exhalaton) values (34). Total VB pressure (P VB) s lnked to al P Cabn va nasopharyngal-pulmonary gas exchange as, P VB t P NP t (6) under the assumptons that the pulmonary-blood-gas exchange s very rapd and blood gases stored n fatty tssues would contrbute mnmally to the ME arteral supply. Throughout flght, VB partal pressures of 2 (P 2 C VB ) and C 2 (P 2 VB ) are assumed to be buffered at constant values by hemoglobn and bcarbonate reactons, the VB H remans saturated at a constant H 2 pressure (P 2 VB ), and VB N 2 pressure N (P 2 VB ) s a functon of nasopharyngeal N 2 pressure, calculated as: N P 2 VB t P NP t P 2 C VB t P 2 H VB t P 2 VB t (7) P ME Dynamcs Durng Flght The drvng mechansms ncluded n the model that affect P ME dynamcs durng flght are trans-et and trans-mem gas exchanges and the pressure effects of V ME changes due to TM dsplacement. ET openng. Durng ET openngs, gas flows between the ME and NP n response to the al extant pressure gradent. The ET opens when a force appled to the ET lumen (F ET) overcomes the ET closng force equal to the sum of the force of the mucosal tssue pressure (P ETA ET) and that attrbutable to ntralumnal surface tenson (F ST) or: F ET t P ET t A ET F ST (8) where A ET s the surface area of mucosal contact. Pressure-drven ET openng occurs when P ME (passve) or P NP (actve or passve) exerts a force (P MEA ME or P NPA NP ) on the ET lumen greater than F ET such that, P ME t F ET t A ME P ME-ET t or P NP t F ET t A NP P NP-ET t (9) where A ME and A NP are the effectve ET surface areas exposed to the ME and NP, respectvely, and P ME-ET and P NP-ET are the ME and NP openng pressures of the ET, respectvely. These openng pressures have been measured emprcally and were reported as pressure dfferentals referenced to ambent [.e., P ME-ET P ME (t) Pam(t); P NP-ET P NP (t) Pam(t)] (13, 51). We used representatve values from those data sets n ths model (see Table 1). When relatve ME overpressures cause the ET to passvely open, gas exchange contnues untl the ntralumnal ar phase pressure of the ET (P IET) equals the tssue pressure (P ET) of the ET, where P IET P ME. Ths results n a resdual ME overpressure wth respect to the NP Table 1. Average values of model parameters for normal MEs used n smulaton Parameter Descrpton Mean Unts Reference No. V ME ME volume 8.75 ml 14, 38 max V TM TM dsplacement volume ml 14, 46 A TM TM surface area 0.6 cm 2 15 TM TM stffness coeffcent 179 mmh 2/ml 26 S f Actve ET openng rate 5.2 openngs/h 53 R A ET actve resstance 2 mmhg ml 1 mn 1 11 T A ET actve openng duraton 0.25 s 11 P ME-ET ME openng pressure 350 mmh 2 51 P NP-ET NP openng pressure 600 mmh 2 13 P C Closng pressure 100 mmh 2 51 ME, mddle ear; TM, tympanc membrane; ET, eustachan tube; NP, nasopharynx.

5 1596 BARTRAUMA DURING AIR TRAVEL (P C ) that s usually referred to as the ET closng pressure and can be wrtten expressed as: P C P ET t P NP t P vas (10) Because gas flows from ME to NP, ME speces gas fractons are not affected by ths transfer, and these were calculated by multplyng the preexstng gas fractons by the revsed al P ME. As wth P ME-ET,P C has been measured emprcally (51), and representatve values are used n ths model (see Table 1). For ET openngs caused by relatve NP overpressures, gas exchange frst occurs between NP and ME, wheren those pressures are equlbrated, and then between ME and NP as P ME s reduced to the ET closng pressure. The effect of the NP-to-ME gas transfers on ME partal pressures at a tme step (dt) was modeled as the weghted average of NP and ME speces pressures as gven by: where y NP P ME dp ME dt t y NP P NP t P ME t (11) s the speces mole fracton n the NP, P NP s al P NP, and s al P ME. These partal pressures were then adjusted for the ME-to-NP gas exchange as descrbed above. Actve muscle-asssted ET openng occurs when the force of mtvp contracton (F mtvp) surpasses F ET, where F mtvp t F ET t (12) For all F mtvp satsfyng ths condton, the magntude of that muscular force determnes the ET lateral wall dsplacement as descrbed by Hooke s law: X ET t F mtvp t C ET (13) where C ET s the complance of the ET lumen, and X ET s the lumen wall dsplacement dstance. Fgure 2 provdes a detaled representaton of the forces actng on the ET durng mtvp actvty. Assumng that trans-et gas exchange follows Hagen-Poseulle flow between two parallel plates (11), then Q ET t 2 3 P ME-NP t X ET t 3 W L (14) where Q ET s the volume of gas transferred, L s the ET length, W s the superor-nferor heght of the tube lumen, X ET s the medolateral lumen wdth, s the vscosty of ar, and P ME-NP s the drvng force for transfer. Because W,, and L are constants for a gven ET and X ET s a defned functon of F mtvp, we can extract from ths equaton an analytcal expresson for the actve resstance to gas flow (R A) that s condtoned on F mtvp, or: R A t P ME-NP t Q ET 3 L (15) t 2 W F mtvp t C ET 3 Whle F mtvp s not measurable n vvo, R A s an outcome measure of the forced-response test of ET functon, whch has been used n both clncal evaluatons and expermental studes n humans (11, 12, 23, 51). In the model, R A s an nputted parameter used to descrbe mtvp effectveness wth respect to actve ET openngs wth representatve values selected from exstng data sets (see Table 1). Lackng measured values of F mtvp, we dd not nclude ET lockng n the model descrpton. Usng the emprcal measures of R A and ET openng tme (T A) reported by Cantekn and colleagues (10 12), trans-et volume gas exchange can be then be descrbed as follows: Q ET t P ME-NP t T A (16) R A Regular tubal openng by mtvp actvty occurs durng rhythmc swallowng, as reported by Tdeholm et al. (53). In ths model, we Table 2. Intal gas speces partal pressure n the ME (24), NP (34), VB, and trans-me mucosal exchange constants (21) used a normal swallowng frequency (S f) of 5.2 openngs/h durng crusng and an ncreased value of 31 openngs/h durng descent. Volume gas flow durng mtvp-nduced tubal openngs (at tmestep t) represents the drectonal movement of a proportonal number of gas moles (N) between compartments, wth the relatonshp formalzed as: N ET t P NP t Q ET t (17) K where N ET s the change n number of ET gas moles, and K s the product of ME temperature and the gas constant. Assumng an deal gas, P ME after the swallow s calculated from the sum of N ET( t) and the number of ME moles (N ME)(t) before the swallow. Ths value s then used to calculate a new V ME,V ME(t t), and P ME,P ME(t t) (see TM dsplacement secton below). The effect of these transfers on ME gas speces pressures was modeled as descrbed above for the drectonal transfers caused by passve ET openngs. MEM gas exchange. The ME exchanges gas wth the local VB by dffuson across the MEM. Here, the MEM was modeled as the VB gas source/snk for ths exchange, such that ME gas speces pressures,, are calculated as P ME Gas Speces dp ME dt t Partal Pressure, mmhg ME NP VB k P ME t P VB t (18) where k s an emprcal speces exchange constant, and P VB s VB speces pressure. Equaton 18 was appled for N 2, 2,C 2, and H 2, and al P ME was equal to the summaton: P ME t P ME t (19) Table 2 lsts the ntal gas-speces pressures for these compartments and the trans-mem tme constants measured by experment (22). The resultant P ME(t t) value followng trans-mem exchange s calculated after the V ME [V ME(t t)] s adjusted for V(t t) (see TM dsplacement secton below). TM dsplacement. Fgure 1C llustrates TM dsplacements n response to a pressure gradent across the membrane, P ME-cabn. TM deformaton s a functon of ts complance and the force appled to the TM (equal to trans-tm pressure gradent multpled by TM surface area). The deformaton s governed by Hooke s law: X TM t t P ME-Cabn t t A TM C TM (20) where X TM s the TM dsplacement dstance, A TM s the TM surface area, and C TM s the TM complance. TM volume dsplacement ( V TM) s calculated as: V TM X TM t t A TM (21) wth dsplacements constraned to the range, V max max TM V TM t t V TM Tme Constant Rate, mn 1 xygen Carbon doxde Water vapor Ntrogen Balance Balance Balance VB, venous blood. (22)

6 BARTRAUMA DURING AIR TRAVEL 1597 compartment (P Cabn, P NP, and P VB); gas speces pressures and al pressure (P ME adjusted for V TM) for the ME after trans-mem exchange; and gas speces pressures and al pressure for the ME after condtonal gas transfers through the ET based on nputted swallowng rhythm (Q ET adjusted for V TM) and/or passve openngs (P ME adjusted for V TM). RESULTS Fg. 3. Pam changes for the pressure chamber experment descrbed by Groth et al. (29) (A), and the correspondng expermental TM dsplacement data for a plot durng compresson and decompresson and the model predctons for TM dsplacement (B). Model parameters, ftted to the data, were as follows: ET openng pressure (reference ambent) (P ) 292 mmh 2, ET closng pressure (reference ambent) (P C ) 136 mmh 2, actve resstance to gas flow (R A) 7.5 mmhg ml 1 mn 1, TM complance (C TM) 425 mmhg/ml, ET openng tme (T A) 250 ms, and swallowng frequency (S f) 33 swallows/ mn. V TM, TM volume. V ME s calculated as the sum of the system V ME (V sys ME ) and the TM volume dsplacement as, V TM t t V sys ME V TM t t (23) V sys ME s the value of the closed system (.e., the ntal startng pont for TM dsplacement calculaton), equal to ether the ntal ME value [V ME (t 0)] or the value followng the prevous trans-et or trans-mem transfer. From Boyle s law (.e., P MEV ME constant), P ME s then calculated for varyng TM dsplacements, as P ME t t P ME t V ME t (24) V ME t t Smulaton Package The above-lsted equatons allow for the calculaton of the tmedependent changes n the P ME-Pam gradent durng smulated flghts. The requred nput parameters for the model are lsted n Table 1. The relevant equatons were coded nto a MatLab verson 6.1 m-fle and entered nto a loop, whch was terated usng a tme step ( t) of mn. Duratons of all flghts were obtaned from publshed flght schedules, wth domestc flghts averagng 170 mn n length. The order of sequental operatons at each tme step was the calculaton of cabn pressurzaton, gas speces pressures, and al pressure for each Model Valdaton To evaluate the predctve accuracy of the model, we smulated the P ME dynamcs for a pressure chamber experment by Groth and colleagues (29), who descrbed P ME change (measured as TM volume dsplacements) n plots exposed to hgh rates of pressurzaton (1,920 ft/mn) over short tme perods (25 s). Model parameters were estmated from the expermental data (P 292 mmh 2, P C 136 mmh 2, R A 7.5 mmhg ml 1 mn 1,C TM 425 mmhg/ml, T A 250 ms, and S f 33 swallows/mn). A comparson of model and expermental results s shown n Fg. 3. Durng ascent, Pam decreased, and the resultng ME overpressures caused outward TM dsplacement. At a relatve ME overpressure of 292 mmh 2, the ET passvely opened, and the P ME -Pam gradent was partly dsspated as gas was transferred from ME to NP, a process nterrupted when the ET passvely closed at P ME P ET. Ths was assocated wth TM repostonng to a lesser volume dsplacement. Durng smulated descent, Pam ncreased, causng nward dsplacement of the TM. At all tmes, P ET exceeded P ME and P NP, and passve ET openngs dd not occur. Rather, at semregular ntervals, swallowng caused mtvp contracton and actve ET openngs. Each openng was assocated wth a transfer of gas from NP to ME, a consequent reducton n the P ME -Pam gradent and reduced TM volume dsplacement. Sequental swallows caused a progressve lessenng of the resdual ME underpressure. Ths comparson shows that our model can accurately reproduce expermental data for P ME behavor durng smulated flghts. Flght Smulatons Fgure 4 shows P Cabn as a functon of tme durng three smulated 170-mn flghts, each departng from Pttsburgh, PA (PIT) and arrvng at PIT, Denver, C (DEN), and Mam, FL (MIA). For all flghts, P Cabn decreased durng arplane ascent, remaned relatvely constant durng crusng, and n- Fg. 4. Change n P Cabn for 170-mn flghts departng from Pttsburgh, PA (PIT) and arrvng at Mam, FL (MIA), PIT, and Denver, C (DEN).

7 1598 BARTRAUMA DURING AIR TRAVEL creased on descent. The magntude of pressure change experenced by passengers depends on the relatve pressure dfferences between departure, crusng, and destnaton elevatons. Table 3 lsts the elevaton and Pam values for these arports and for the arplane cabn at the effectve crusng alttude. Usng these three flght paths, we smulated the P ME dynamcs for a normal ME (see Table 1) and for ears wth abnormal structural (e.g., V ME, TM dsplacement) or functonal (e.g., P ME-ET,R A ) parameters. ET functon measurements n normal, dsease-free ears document passve ET openngs at moderate ME-ambent overpressures ( mmh 2 ), passve ET closng at aboveambent P ME ( mmh 2 ), and the ablty of the mtvp to open the ET over a large range of appled P ME -Pam gradents (12). The P ME changes durng a smulated flght for such an ear (all parameters equal to normal) are shown n Fg. 5A, whch demonstrates the development of relatvely low-magntude P ME -Pam gradents throughout the duraton of the flght, wth none of those gradents exceedng the threshold for ether expresson of ME barotrauma. A common treatment for otts meda s the nserton of tympanostomy tubes, small tubes placed wthn the TM that allow for constant communcaton between ME and ambent envronment (42). An abnormal physologcal condton referred to as a patulous ET also allows for constant NP-ME communcaton (4). There, functon tests show that the P ET s less than Pam, resultng n a contnuously open ET (5). Smulated flghts for ears wth ether of these condtons yeld the trval result of a0mmh 2 P ME -P Cabn gradent throughout flght and, consequently, protecton from barotrauma. Rarely, clncal tests document an ET that s physcally obstructed by enlarged adenods or by nasopharyngeal carcnoma (40, 44). More frequently, the ET s ntrnscally blocked by ntralumnal swellng and venous engorgement caused by posteror extenson of NP nflammaton that accompanes vral nfectons or allergy (5). ET functon tests for both condtons document a falure of appled ME overpressures to passvely open the ET and an nablty of the mtvp to affect ME-NP gas transfers (5). We modeled ths condton by nputtng hgh P values (P ME-ET 2,500 mmh 2, P NP-ET 2,500 mmh 2 ) and a hgh R A (1/R A 0) value (other parameters equal normal). The results for the three smulated flghts are shown n Fg. 5B. Durng ascent, the lack of passve ET openngs leads to a postve ME-cabn gradent of 2,020 mmh 2, a pressure that exceeds the threshold for pan and baromyrngts. Durng crusng, that gradent s slghtly reduced by the slow, trans-mem N 2 exchange, and, durng Table 3. Elevatons and ambent pressures for arports and arplane cabn (35) Locaton Elevaton, ft Ambent Pressure, mmhg Pttsburgh, PA 1, Mam, FL Denver, C 5, London, UK Arplane cabn 8,000 (equvalent elevaton) 577 Fg. 5. Predcted change n mddle ear-cabn pressure gradent ( P ME-Cabn) for a normal ME wth parameters lsted n Table 2 (A), for a ME wth an obstructed ET (P ME-Tssue 2,500, P NP-Tssue 2,500 mmh 2) (B), and for a ME wth poor mtvp functon (1/R A 0) (C). Barotrauma onset s specfed by the dotted-dashed ndcator lnes. descent, the gradent s decreased as P Cabn ncreases. n landng, the ME-cabn gradent [termnal pressure gradent (TPG)] depends almost exclusvely on the dfference n elevaton between departure and arrval; the TPG for a flght departng and arrvng at PIT was 202 mmh 2, for a flght arrvng n DEN was 1,070 mmh 2, and for a flght arrvng n MIA was 612 mmh 2. nly the MIA destnaton was assocated wth the expresson of barotts meda. The most common cause of ET dysfuncton s a consttutvely mpared, actve ET openng mechansm. There, functon tests document normal passve ET openng and closng pressures, but an nablty of the mtvp muscle to dlate the ET durng swallowng (5). To model these ears, we nputted normal values for the openng and closng pressures (and other varables) but constraned the actvty of the mtvp muscle by nputtng a hgh R A value (1/R A 0). Note that 1/R A s the arflow conductance of the ET durng a swallow (.e., the extent to whch the ET dlates durng mtvp contracton) and does not necessarly reflect the arflow conductance resultng from appled pressure dfferentals or the other passve propertes of the ET. Fgure 5C shows the dynamcs of the P ME -P Cabn gradent for the three smulated flghts. Durng ascent, the developng postve P ME -P Cabn gradent s repeatedly reduced to the value of P C as the ET s passvely opened at P.No barotrauma s experenced durng ths phase of flght. The

8 resdual gradent ( P ME-Cabn P C ) s slowly reduced durng flght by trans-mem N 2 exchange. However, the developng negatve ME-cabn gradent durng descent cannot be allevated by muscle-asssted ET openngs, leadng to TPGs of 1,731, 2,226, and 486 mmh 2 for landngs at PIT, MIA, and DEN, respectvely. All underpressures are of suffcent magntude to provoke barotts meda, and the former two are expected to provoke baromyrngts. The results of ths smulaton are not applcable to ears that test postve for the Valsalva maneuver, wheren large P NP gradents are generated by closed nose/mouth forced exhalatons. If the generated P NP -P ET gradent s suffcent to passvely open the ET, NP gas s transferred to the ME, and the P ME s ncreased (see Eq. 9). n descent, repetton of ths maneuver can, lke the effect of swallowng for the normal ET, mantan near-ambent P ME, establsh near 0 mmh 2 TPGs, and prevent barotrauma. The majorty of persons who fly do not exhbt these extreme forms of ET dysfuncton but rather exhbt a graded seres of actve ET openng effcences. For example, studes comparng chldren wth adults or persons wth and wthout a hstory of otts meda document smlar passve ET propertes among all groups, but less effcent actve ET openngs n the former groups (5, 8, 12). In our model, ths varablty n actve openng effcency can be represented by varyng R A. Fgure 6A shows the smulated P ME -P Cabn gradent durng the course of a PIT-MIA flght for an ear wth normal and one wth compromsed mtvp-nduced ET openngs (R A 2 and 20 mmhg ml 1 mn 1 ; other parameters normal values). The larger R A value lmts trans-et flow at each openng, BARTRAUMA DURING AIR TRAVEL 1599 Fg. 7. PIT-MIA termnal pressure gradent (TPG) as a functon of R A wth fxed TM stffness coeffcent 179 mmh 2/ml (A) and as a functon of TM stffness coeffcent ( TM) wth fxed R A 8 mmhg ml 1 mn 1 (B) over a range of V ME. Barotrauma onset s desgnated by the dotted-dashed ndcator lnes. S f was set to 1.1/h durng crusng and 20/h durng descent; other parameters were set to normal. Fg. 6. P ME-Cabn as a functon of flght tme from PIT to MIA for MEs (Table 2) wth two dfferent R A values and fxed volume normal (A) and for two dfferent volumes at fxed R A 20 mmhg ml 1 mn 1 (B). Barotrauma onset s desgnated by the dotted-dashed ndcator lnes. ther parameters were set to normal. V ME, ME volume. compromses the ablty of the ET to regulate P ME, and leads to a negatve TPG suffcent to precptate barotts on landng. V ME shows a growth-related ncrease (attrbutable prmarly to expanson of V mas ), an effect that s stunted or delayed n ears wth poor ET functon and/or a hstory of otts meda (14, 37, 38). Ths observaton causally lnks poor ET functon to small V ME. Fgure 6B shows the smulated P ME -P Cabn gradent for ears wth compromsed mtvp-asssted ET openngs (R A 20 mmhg ml 1 mn 1 ) and large and small V ME ( 50% baselne V ME ; other parameters normal values). The smaller V ME (V ME 4.4 ml) buffers the effect of the compromsed mtvp functon on P ME -P Cabn devatons and prevented the barotts documented for the larger V ME (V ME 13.1 ml). From these observatons, the ablty to mantan a near-0 mmh 2 P ME -P Cabn gradent depends on the relatve magntudes of volume gas supply and demand. In the absence of actve, pressure-drven ET openngs (e.g., Valsalva maneuver), supply s a functon of mtvp ET openng effcency (proportonal to S f T A /R A ), whle demand s a functon of both the dfference n P Cabn at effectve crusng and landng alttudes (maxmum P to be equlbrated) and V ME (moles of gas requred to equlbrate that P). Fgure 7A summarzes ths relatonshp for smulated PIT-MIA flghts by plottng the TPGs for ears wth constant S f and T A but dfferent R A and V ME values. There, low R A ( 4 mmhg ml 1 mn 1 ) allows for the exchange of suffcent gas volumes to prevent both expressons of barotrauma over all reasonable V ME ( 16 ml).

9 1600 BARTRAUMA DURING AIR TRAVEL In contrast, bufferng aganst barotrauma for ncreasng V ME was decreased wth ncreasng values of R A. In ears wth a hstory of dsease, changes n the TM are observed frequently (16). These nclude ncreases n TM complance, whch s termed atelectass. In the extreme, TM retracton can dsplace the al V tym, resultng n a V ME restrcted to that of the mastod. As noted, the magntude of P ME -Pam devatons n ears wth compromsed mtvp functon can be buffered by TM dsplacement volume (see Eq. 24). Fgure 7B shows the smulated TPG values for a ME wth compromsed mtvp functon (R A 8, other parameter values normal ) as a functon of both TM stffness ( TM 1/C TM ) and V ME (wth V max TM V tym 1 ml) after a PIT-MIA flght. The plot demonstrates the expected effect of changng the V TM -to-v ME rato on P ME -P Cabn gradents. Specfcally, greater TM values are assocated wth lesser TPG values, and the magntude of ths effect s greater for larger V ME. Conversely, hypercomplant TMs ( TM 0.14 normal TM ) protected the ME from barotts meda over all reasonable V ME. Fnally, we examned the effect of flght duraton on TPG by comparng the predcted TPG values for PIT-MIA (170 mn) and PIT to London, UK (533 mn), destnatons wth smlar elevatons (Table 3). For all ME functon and structure confguratons, the TPGs for the two flghts were smlar. Because the major dfference between these flghts s the duraton of crusng at fxed alttude, any effect of flght duraton wll be drven by the rate of trans-mem N 2 exchange, a process that was prevously measured to be extremely slow (20, 22). DISCUSSIN Unlke prevous descrptons that focused only on a categorcal representaton of ET functon (poor/good ET openng), our model of P ME regulaton durng flght s founded on mathematcal descrptons of the physology underlyng gas transfers between the ME and all adjacent compartments. Calbraton of the model parameters was done usng publshed data for dsease-free MEs, and thus ths descrpton s not applcable to the ME wth extant otts meda or MEM nflammaton. Specfcally, those condtons 1) ntroduce addtonal system compartments (e.g., effuson), 2) change the capactances of exstng compartments (e.g., ncrease MEM volume at the expense of V ME ), and 3) affect the exchange parameters for trans-mem gas transfers (e.g., ncrease MEM blood flow) (1). Nonetheless, our model does have broad applcablty to the dsease-free ME and to MEs expressng the predspostons (e.g., poor mtvp functon) and/or sequelae (e.g., altered TM complance, reduced V mas ) of those condtons. Moreover, by ncludng contnuous measures of relevant parameters, our model realstcally maps dsease expresson onto the known contnuum of underlyng ET dysfunctons. An mportant test of any model s ts predctve accuracy wth respect to descrbng and explanng well-establshed observatons. For ME barotrauma, these nclude the prevously documented ncreased rsk assocated wth young age and nasal nflammaton (concurrent colds or nasal allergy). ur model s capable of representng and explanng these effects by ncorporatng the changes n the contrbutng parameters measured by experment. For example, the age effect s explcable by the establshed mprovement n mtvp functonal effcency (modeled as progressvely decreasng R A ) wth advancng age (8, 9), and the effect of nasal nflammaton s medated by ntralumnal venous engorgement (modeled as a greater P ET ) (17). These explanatory analyses can be extended to nclude the effects of preventatve treatments, such as nasal decongestants (17, 39), that act by decreasng tssue nflammaton (decreased P ET )or of less well-establshed nterventons, such as bottle-feedng of nfants durng descent (7), where the assocated jaw movements ntate mtvp actvty (greater S f ) and/or reduce ET tssue pressure (lesser P ET ). Earler descrptons of barotrauma durng arflght usually dd not dscrmnate between barotts meda and baromyrngts n reportng results. As dscussed above, these expressons have dfferent underlyng causes wth the former, resultng from a moderate, postve MEM-P ME gradent, and the latter resultng from large postve or negatve P ME -P Cabn gradents. Consequently, baromyrngts can be experenced throughout flght and s usually assocated wth sgns of TM damage and symptoms of ear-fullness and pan, but barotts meda develops durng descent and, n the absence of baromyrngts, s often unrecognzed by the traveler. By consderng both expressons, our model predcts postflght ME barotrauma that s and s not perceved by the traveler and, by consequence, recorded as an event n the complaton of prevalence reports (49). Perhaps the most mportant feature of our model s the demonstraton of potental bufferng mechansms that modfy or prevent dsease expresson n ears wth consttutvely or stuatonally mpared ET functon. For example, we showed that, for ears wth a blocked ET (by enlarged adenods, nasopharyngeal carcnoma, nasal nflammaton due to a cold/allergy, or other condtons), hgh postve pressures and baromyrngts wll develop on ascent to crusng alttude for all flghts, but the development of barotts meda on descent wll depend on the dfference between departure and destnaton alttudes. Lkewse, for ears wth poor ET functon, a protectve effect s provded by a hgh TM volume dsplacement-to-v ME rato. Support for the physologcal relevance of these bufferng mechansms was provded n a recent paper (48) that reported a low frequency of barotrauma n ears that were expected to have poor ET functon but also had preexstng condtons that favored a hypermoble TM and small (mastod) V ME. Earler descrptons of the pathogeness of barotrauma focused prmarly on ET functon and dd not nclude these nuances. In that regard, tests of ET functon were used to screen canddates for servce as plots (29), and attempts have been made by ndustry to extend these tests to the professonal flght crews of commercal arlnes. ur results suggest that, whle good ET functon s hghly predctve of dsease-free flght, poor functon only defnes an ncreased rsk of flghtnduced barotrauma. Ths dstncton has mportant mplcatons to nterpretng the results of ET functon screenng where falure to repeatedly open the ET durng swallowng or to transfer NP gas to the ME durng Valsalva can be career lmtng. In concluson, we present a physologcal model of barotrauma development for normal MEs durng flght. The presented model smulates the emprcal data for experments conducted on plots n a pressure chamber and explans past observatons wth respect to rsk assessments. Also, our results dentfed dverse physologcal and anatomcal parameters that nteract n affectng adequate and abnormal P ME regulaton durng flght. Ths underscores the mportance of consderng contextual relatonshps n predctng the susceptblty of a gven ME to barotrauma.

10 BARTRAUMA DURING AIR TRAVEL 1601 ACKNWLEDGMENTS We thank our many colleagues at the Unversty of Pttsburgh for clncal nsghts and techncal comments. GRANTS Ths study was funded n part by Natonal Insttute on Deafness and ther Communcaton Dsorders Grant and by support from a 2003 NASA Space Grant Fellowshp. REFERENCES 1. Alper CM, Doyle WJ, and Seroky JT. Hgher rates of pressure decrease n nflamed compared wth nonnflamed mddle ears. tolaryngol Head Neck Surg 121: , Armstrong H and Hem J. The effect of flght on the mddle ear. JAMA 109: , Becker GD and Parell GJ. Barotrauma of the ears and snuses after scuba dvng. Eur Arch torhnolaryngol 258: , Bluestone CD. Eustachan tube functon: physology, pathophysology, and role of allergy n pathogeness of otts meda. J Allergy Cln Immunol 72: , Bluestone CD and Doyle WJ. Anatomy and physology of eustachan tube and mddle ear related to otts meda. J Allergy Cln Immunol 81: , Brown TP. Mddle ear symptoms whle flyng. Ways to prevent a severe outcome. 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