) and magnetization left from the last breath (10), as follows:

Transcription

1 RSNA, /radiol Appendix E heory Fracional venilaion (FV) for a volume elemen in he lung is a nondimensional meric defined as he raio of he inspired gas added o ha elemen o he oal gas space a he end of inspiraion (9). oal gas can be expressed as he combinaion of inspired gas and residual volume: Vf Vf FV V V V f r, where V is he oal volume and is composed of Vf (he inhaled fresh gas) and Vr (he residual volume). Fracional venilaion is relaed o he more widely known parameer, specific venilaion (SV), which is he raio of he inspired gas volume o he residual gas volume in a small region of he lung (5). N idenical hyperpolarized gas breahs (here, n = 6) were delivered o he subjec (images 6 in Fig, A). An image of hyperpolarized gas disribuion was acquired during a shor end-inspiraory breah hold afer each breah (here, approximaely second). Signal buildup corresponding o N consecuive hyperpolarized gas breahs was fi o a recursive buildup equaion o yield fracional venilaion on a regional basis. he available signal a each breah, SA(j), is a funcion of fresh gas (wih source magneizaion S ) and magneizaion lef from he las breah (0), as follows: S j FV S FV S j exp D, S 0 0, (E) A A A where D sands for all he inernal local relaxaion mechanisms, including radiofrequency depolarizaion, oxygen-induced relaxaion, and oher negligible facors like wall decay (6). his equaion can be wrien in a closed form as ' n n S n S [ FV exp D ], A ' FV S FV exp D. he exernal relaxaion of 3 He polarizaion in he reservoir is negligible due o he relaively longer relaxaion ime consans compared wih he imaging ime. A longer image acquisiion (breah hold, approximaely 2 seconds) wih a low-flip-angle wo-dimensional gradien-echo pulse sequence was performed a he end of he six ime poins of he mulibreah maneuver when he 3 He signal is a is maximum o exrac he voxel-by-voxel signal drop of each image and hereby derive he local oxygen relaxaion and radiofrequency depolarizaion, which could hen be correced for. Figure, A, schemaically shows he mulibreah sequence used for his combined imaging echnique. Alhough he analysis is performed by using a simulaneous fi of all imaging (E2) Page of 5

2 ime poins corresponding o each voxel, imaging condiions were chosen o approximaely separae he effecs of venilaion (images 6), radiofrequency depolarizaion (images 7 and 8), and PAO2 (images 8 0). he regional fracional venilaion and PAO2 were hus derived by fiing each voxel s ime series o he coupled equaions describing signal (SA) and alveolar oxygen (PAO2) evoluion in an ieraive manner, as follows: SA i FV SA i cos α FV S ex (E3) and npe PAo2, i i i i p FV F o R PAo PAo V FI, (E4) 2 i 2 i 2 i i in which fracional venilaion, hyperpolarized gas magneizaion S, flip angle, iniial oxygen ension PAO2 (0), and oxygen upake rae R are allowed o vary. he number of phase-encodes (npe) was 48 and he O2-induced depolarizaion rae was = 2.6 bar second (7). he ieraions sop when he change in he average regional venilaion in each sep is less han Noe ha he iniial calculaed PAo 2 value used in he exponen of Equaion (E3) refers o an average PAO2 midway beween imes i and i (in our case abou 6 seconds), wih he assumpion of linear oxygen upake during he breah hold. I is measured from he four imepoin scheme described before (8). Applying his PAO2 value for correcion of relaxaions ha occurring during he -second breah hold in which venilaion images were acquired would inroduce a bias. We aemped o correc his bias by calculaion of R (linear apparen rae of oxygen rae) as is inroduced in Equaion (E4) o be able o calculae PAO2 for any given ime. Dead Space Model he dead space (refer o Fig E) is composed of dynamic volume (VD, upper airways and he porion of he gas delivery sysem afer he respiraor valve) and saic volume (VS, he porion of he device ha carries he source gas o he respiraor valve). Some of he gas from he previous breah remains in he VD and is subsequenly reinhaled wih each new inspiraion, a concep known as rebreahing (0). Accouning for his phenomenon required modificaion of he magneizaion buildup by replacing S wih he combinaion of he hyperpolarized 3 He arriving from he ransmission line and he residual exhaled gas from he previous breah. Defining, FVS = V/VS, where V is he idal volume and VS he saic volume, he apparen fracional venilaion, FVA, can be defined as follows (0): S j FV S j FV S j exp D, A A A A S 0 FV S, and S j S. S Whole-Lung (Global) Fracional Venilaion For he whole lung, fracional venilaion can be defined as he raio of idal volume breahed in o he end-inspiraory volume (EIV), which consiss of funcional residual capaciy (FRC) and idal volume: ξ (E5) Page 2 of 5

3 V V EIV FRC+V (E6) FV. V can be exraced from he breahing curves generaed from he delivery device, and endinspiraory volume was esimaed from he 3 He spin-densiy maps. o compue he whole-lung fracional venilaion direcly from signal buildup, he sums of all voxels signal inensiy buildup in six consecuive images were used in a global recursivefiing model. he available signal a each breah, SA(j), is a funcion of fresh gas (wih source signal S ) and signal lef from he las breah. For he firs breah, in which here is no prior magneizaion in he lung, we can express SA() as follows: S V V V S, S 0 0. (E7) A S D A For he second breah, we can express he oal signal in he same manner by considering boh fresh gas and signal from he previous breah: V V V S V V S V S e S D A 2 D FRC Dead Space FRC V VDead Space where VDead Space is he physiologic anaomic dead volume. Replacing fracional venilaion from Equaion (E6) and SA() from Equaion (E7) and coninuing he same process, we can derive SA(j), as follows: S j V S S j V S Device A FV FRC V ) D A Dead space [ FV ] FRC V VDead Space (E8) e, FRC V where VDevice is he gas delivery device dead volume afer he respiraor valve (approximaely 50 ml). he global fracional venilaion hen can be compued from a recursive fiing of he whole-lung sum of all voxels signals (SA[] o SA[6]) acquired from he mulibreah wash-in images o he model explained in Equaions (E7 E9). By neglecing he minimal difference in signal dynamics beween anaomic dead space and parenchyma, VDead Space can be eliminaed from Equaion (E8) o derive a simpler equaion in a closed form. In he ypical case of having V larger han dead-space volume (V > V), he equaion can be rewrien as Image Analysis ( FV) n e V SA n S V FV e n. Device n FV ( FV). Image analysis was performed by H.H. (a bioengineer wih 0 years of experience) using cusom sofware developed in he MALAB environmen (MahWorks, Naick, Mass). he signal in he, (E9) (E8) V Page 3 of 5

4 acquired image was bias-correced for he background noise according o, where σ B 2/ π and B was he average background noise of a 0 0-pixel region far away from he lung in he acquired image. Auomaic conras-limied adapive hisogram equalizaion (CLAHE) wih a gray-scale hreshold was hen applied o mask he background noise and segmen he lung (9). Each voxel s signal inensiy buildup in six consecuive images were fi o a recursive model o compue S and iniial FVA (20) as was explained in deail in he las secion. Each voxel s signal inensiy drop for he las breah hold was fi o a PAO2 model as described in (6) o calculae S0 (iniial signal),, and PAo 2. he global fracional venilaion was compued by an iniial ieraive fi o Equaion (E8) followed by an ieraive fi o boh Equaions (E4) and (E5) a he same ime o compue regional fracional venilaion while accouning for rebreahing and all he relaxaion mechanisms. Voxels wih calculaed values ouside he range of 0 < fracional venilaion <, 0 < PAO2 < 200 mm Hg, or flip angles ouside 0 < < 0 were excluded. A nonrigid affine-based coregisraion was performed on spin-densiy maps from all seven ime poins before he fiing process (2). ranslaion, roaion, and scaling were used for he wo-dimensional maps of each secion; shearing was se o zero. Accouning for Venilaion Defecs o ake he effec of venilaion defecs ino consideraion, segmened maps of boh hydrogen ( H) and 3 He spin-densiy maps were coregisered and he voxels wih no 3 He signal (a he las breah) were assumed o be unvenilaed; a fracional venilaion value of zero was assigned o hem. he mean whole-lung fracional venilaion was hen correced by using hese venilaion defecs. o coun he venilaion defecs, he abovemenioned segmenaion echnique (CLAHE) was used for boh H and 3 He images, followed by a morphology-based coregisraion (22) beween he H and 3 He in he same manner as described by Kirby e al (3). Gas Delivery Device A cusom-buil, passive-driven respiraory gas mixing and adminisraion device allowed delivery of hyperpolarized gas over a series of breahs a a prescribed volume and fracion of inspired oxygen (FIO2) and a breahing paern synchronized wih image acquisiion. Alhough he deails of he design are described by Emami e al (23), he general concep is o use MR imaging compaible differenial pressure pneumoachomeers ha independenly repor he flow rae of each gas componen, riggering he pneumaic valves and he MR imaging uni when he arge volume is reached. he subjec hen commis a volunary breah hold during which images are acquired, exhales freely, and he sequence is repeaed as desired. In his sudy, mixures of hyperpolarized 3 He-N2 and O2 were prepared in wo separae bags (final mixure 3 He:N2:O2 approximaely :3:) adminisered over seven breahs while monioring blood oxygenaion, hear rae, blood pressure, and respiraory rae. V, FIO2, and he duraion of inspiraion were measured a all seven wash-in breahs for each subjec o es he precision of he gas delivery device. he overall deviaion of V from he se poin was 34 ml ± 30 in all subjecs, and overall deviaion from he normoxic FIO2 was.23% ± 0.86 (absolue). Previous research (23) demonsraed an overall precision of 50 ml. he overall variabiliy of V (ie, sandard deviaion) in one experimen beween he seven breahs for Page 4 of 5 Ŝ = S 2 -s 2

5 all subjecs was 23 ml ± 3, and he variabiliy of FIO2 was 0.65% ± Subjecs ineviably inhaled he gas a varying speeds and volumes, and heir breahing paerns were no very consisen. he firs breah of he imaging scheme when he subjec iniiaed he proocol showed a paricularly high level of variabiliy (refer o Fig 2b[ID]FIG2[/ID]). One way o address his issue would be o allow he subjec o firs inhale wo or hree breahs of room air before inroducion of he imaging gas. Hyperpolarized 3 He Producion Imaging gas ( 3 He:N2 = 99.9:0.8, Linde, Branchburg, NJ) was polarized using a commercial polarizer (IGI 9600.He, GE Healhcare, Durham, NC) hrough spin-exchange collisions wih opically pumped rubidium aoms. Approximaely 30% polarizaion was aained afer approximaely 5 hours of opical pumping. Hyperpolarized 3 He gas was dilued wih medicalgrade nirogen gas, and oxygen was added jus before gas adminisraion wih FIO2 approximaely 2% (raio of :3:, respecively). he V adminisered was based on he subjec s weigh (0 ml/kg) rounded o he neares of hree calibraed se poins (700, 800, or 900 ml). he gas mixures were brough o he MR imaging uni sored in edlar bags (Jense Iner Producs, Coral Springs, Fla) and hen conneced o he gas delivery device. References 6. Hamedani H, Kadlecek SJ, Emami K, e al. A mulislice single breah-hold scheme for imaging alveolar oxygen ension in humans. Magn Reson Med 20;67(5): Hamedani H, Kadlecek SJ, Ishii M, e al. A variabiliy sudy of regional alveolar oxygen ension measuremen in humans using hyperpolarized (3) He MRI. Magn Reson Med 203;70(6): Hamedani H, Shaghaghi H, Kadlecek SJ, e al. Verical gradiens in regional alveolar oxygen ension in supine human lung imaged by hyperpolarized 3He MRI. NMR Biomed 204;27(2): Hamedani H, Kadlecek SJ, Ishii M, e al. Aleraions of regional alveolar oxygen ension in asympomaic curren smokers: assessmen wih hyperpolarized (3)He MR imaging. Radiology 205;274(2): Emami K, Xu Y, Hamedani H, e al. Mulislice fracional venilaion imaging in large animals wih hyperpolarized gas MRI. NMR Biomed 202;25(9): Wang H, Dong L, O Daniel J, e al. Validaion of an acceleraed demons algorihm for deformable image regisraion in radiaion herapy. Phys Med Biol 2005;50(2): Bricaul I. A fas morphology-based regisraion - applicaion o compuer-assised bronchoscopy. In: CVRMed-MRCAS 97 Proceedings of he Firs Join Conference on Compuer Vision, Virual Realiy and Roboics in Medicine and Medial Roboics and Compuer- Assised Surgery. London, England: Springer-Verlag, 997; Emami K, Hamedani H, Han B, Kadlecek S, Xu Y, Rizi RR. Auomaic respiraory gas delivery device for noninvasive adminisraion of hyperpolarized gaseous conras agens o consciously breahing subjecs [absr]. AS J 202;85():A2045. Page 5 of 5