Direct 4D Parametric Imaging in Dynamic Myocardial Perfusion PET

Transcription

1 Arman Rahmm et al. Drect 4D Parametrc Imagng n Dynamc Myocardal Perfuson PET Drect 4D Parametrc Imagng n Dynamc Myocardal Perfuson PET Arman Rahmm 1,2*, Jng Tang 3, and Hassan Mohy-ud-Dn 1,2 1. Department of Radology, Johns Hopkns Unversty, USA. 2. Department of Electrcal & Computer Engneerng, Johns Hopkns Unversty, USA. 3. Department of Electrcal & Computer Engneerng, Oakland Unversty, USA. Artcle nfo: Receved: June Accepted: August Keywords: Myocardal perfuson, PET, 4D reconstructon, Optmzaton transfer. A B S T R A C T Purpose: Dynamc myocardal perfuson (MP) PET magng followed by tracer knetc modelng allows quantfcaton of myocardal blood flow, thus enablng computaton of the coronary flow reserve, wth consderable clncal potentals. Nonetheless, utlzaton of short dynamc frames can lead to nosy flow estmates, an ssue that s further amplfed n parametrc magng at the voxel level. Our purpose s to utlze an enhanced mage reconstructon framework to better address ths ssue. Methods: We mplemented a novel 4D reconstructon scheme to drectly estmate MP parametrc mages from the measured dynamc datasets. Ths ncluded formulaton of a 4D log-lkelhood obectve functon relatng the knetc parameters to the proecton datasets, and mplementng numercal methods to optmze the obectve functon. We also utlzed the technque of optmzaton transfer to enable more convenent and relable parametrc magng. We smulated MP Rb-82 PET proecton datasets based on the XCAT phantom utlzng patent-based tme actvty curves for the varous organs and clncally realstc nose levels, followed by nose vs. bas analyss. Results: The proposed drect 4D methodology was shown to outperform conventonal ndrect parametrc magng, reducng nose by over 50% (matched bas), wth further reductons of 15% n nose and a factor of fve speed-up when optmzaton transfer was addtonally utlzed. Concluson: Drect 4D PET mage reconstructon s a vable and very promsng approach towards robust parametrc MP PET magng at the ndvdual voxel level. 1. Introducton M yocardal perfuson (MP) PET provdes mproved dagnostc qualty, certanty, and accuracy over conventonal MP SPECT magng [1-5]. The prognostc value n predctng adverse cardac outcomes has also been demonstrated n an ncreasng number of studes [6-8]. In partcular, dynamc MP PET magng followed by tracer knetc analyss (e.g. compartmental modellng appled to Rb- 82 [9-15]), provdes a powerful mean to estmate the tracer transport rate K1, and subsequently myocardal blood flow (MBF) whch when measured under rest and stress used to calculate the coronary flow reserve (CFR). The CFR has been shown to be related to the degree of coronary artery stenoss (CAS) [16]. It thus allows for non-nvasve assessment of the functonal mportance of CAS and may ad dentfcaton of patents wth ether dffuse, nonocclusve lumnal coronary artery narrowng or a balanced reducton n coronary artery blood flow (extensve mult-vessel coronary dsease) [17, 18]. CFR has also been shown to be reduced as a functon of varous coronary rsk factors before the onset of clncally overt dsease (e.g. n asymptomatc men wth a famly hstory of coronary artery dsease (CAD) and hgh-rsk lpd profles [19]). Degradaton of CFR based on other rsk factors (e.g. hyperlpdema, dabetes, smokng), has also been shown, supportng the benefcal effects of rsk-factor modfcatons and novel medcal therapes [20-32]. Non-nvasve MP quantfcaton may, therefore, allow early detecton of preclncal * Correspondng Author: Arman Rahmm, PhD Department of Radology, Johns Hopkns Medcal Insttutons, Baltmore, Maryland, USA. Tel: E-mal: arahmm1@hm.edu 4

2 January 2014, Volume 1, Number 1 atheroscleross, provdng an opportunty to modfy rsk factors or ntate treatment. These studes have contrbuted to a paradgm shft n the percepton of CAD, away from a pure macroscopc vew of lumnal stenoses and toward an emphass on mcrocrculaton and endothelal functon [33-35]. Specfcally, n persons wth angographcally normal arteres, CFR has been shown to be a marker of coronary mcrovascular dysfuncton [36], whch can represent a new therapeutc target. Overall, changes n CFR promse to be extremely useful n assessng the effectveness of treatment [37, 38]. Nonetheless, notwthstandng the vast potentals of the dynamc MP PET modalty, t has remaned prmarly lmted to research, and remans to be wdely adopted n clncal practce [18, 39]. In fact, dynamc MP PET magng s specfcally challenged by the presence of addtonal nose due to dvson of the data nto shorter frames, ultmately adversely mpactng absolute flow quantfcaton. In the present work, we propose a drect 4D reconstructon framework applcable to dynamc MP PET magng enablng sgnfcant reductons n nose, and n fact, enablng parametrc magng at the ndvdual voxel level. Where C a (t) and C M (t) are the concentratons of Rb- 82 n the arteral blood and the myocardum, respectvely. By measurng the concentraton C LV (t) va a small regon sze n the center of the LV cavty, nearly complete recovery of the arteral nput curve and mnmal myocardal spllover can be acheved [46], allowng a non-nvasve approach;.e. C a (t) = C LV (t). Furthermore, to address the contrbuton of blood n the myocardal measurements, one wrtes: C(t) = FC a (t) + (1 F)C M (t) (2) where C(t) s the measured concentraton of the tracer n the myocardum, and F represents the total fractonal blood volume, combnng (a) spllover due to the partal volume effect from the blood pool nto the myocardal regon or voxel of nterest as well as (b) the presence of arteral blood n the muscle. Solvng the abovementoned two equatons yelds: C(t) = FC a (t) + (1 F)K 1 exp( k 2 t)*c a (t) (3) 2. Proposed Cardac Parametrc Imagng Framework Conventonal dynamc MP PET magng conssts of reconstructng the ndvdual data frames followed by compartmental analyss to estmate knetc parameters. A novel alternatve s to nstead drectly estmate the knetc parameters from the dynamc datasets. Ths approach has been revewed elsewhere [40-42], and has typcally nvolved parametrc magng at the voxel level for bran studes, or at the ROI-level n some cardac studes. The present work elaborates upon our efforts [43-45] to develop and evaluate drect parametrc magng for dynamc cardac PET magng The Knetc Model We consder the one-tssue compartmental model (Fgure 1) as commonly nvoked n the lterature to model knetcs of Rb-82 [10, 12, 13, 15]: dc M (t) dt = K 1 C a (t) k 2 C M (t) (1) Fgure 1. One-tssue compartmental model for knetc modellng of Rb-82 MP PET magng. The ellpse ndcates the addtonal contrbuton of blood to the regon or voxel of nterest Drect 4D Problem Formulaton and Numercal Optmzaton To formulate the 4D problem, we next note that for a gven parameter set K consstng of K 1, k 2, F across the voxels, the accumulated actvty x m at any voxel for any gven dynamc frame m (spannng duraton t 1 to t 2 ) can be wrtten as: t 2 x m = C (τ )dτ (4) t 1 Where C (t) s gven by (3) for any voxel. Ths can then be used n connecton wth the system matrx to arrve at the estmated proecton-space data y = p m x m for every LOR. To acheve drect parametrc estmaton, we then note that the log-lkelhood (L) functon, to be maxmzed, s gven by: 5

3 Arman Rahmm et al. Drect 4D Parametrc Imagng n Dynamc Myocardal Perfuson PET L(y K) = y m log y m (K) y m (K) (5),m Ths s depcted n Fgure 2. where the actual measured data are denoted by y m. We then apply numercal methods to teratvely search for knetc parameters maxmzng the L functon, startng wth an ntal estmate K (0) and arrvng at subsequent updates to the parametrc set. We consdered precondtoned gradent ascent as we all as precondtoned conugate gradent algorthms, mplemented n C usng numercal recpes, ncludng ordered subsets and precondtoners. Ths s elaborated n Sec Optmzaton Transfer Asde from ts nonconvex nature, numercal maxmzaton of (5) s challenged by the computatonal burden of operatons mappng the parametrc mage estmates to the proecton-space at every teratve update. A powerful technque n optmzaton problems s to seek surrogate functons that can be more convenently optmzed, referred to as optmzaton transfer as explored n dfferent contexts n the past [47-51]. Specfcally, these technques seek a surrogate functon Q(q;q n ) dependng on the current estmated parameter set of nterest q n n the log-lkelhood functon L(y q n ) such that L(y q) Q(q;q n ) has ts mnmum when q = q n. Then, f we fnd the next estmate q n+1 that maxmzes Q(q;q n ),.e. qn+1 = arg max Q(q;q n ), t follows that q L(y q n+1 ) L(y q n ) thus guaranteeng mproved estmaton. Ths s because: ( ) ( ) L(y q n+1 ) = Q(q n+1 ;q n ) + L(y q n+1 ) Q(q n+1 ;q n ) Q(q n ;q n ) + L(y q n ) Q(q n ;q n ) = L(y q n ) The surrogate functons are desgned such that they are easer and/or less computatonally ntense to optmze than the orgnal log-lkelhood functon. As such, for every update, the optmzaton s transferred to the surrogate functon, thus the name s optmzaton transfer. We also note that a very natural specal case of the above condton s havng a surrogate functon that bounds the log-lkelhood functon from below everywhere, touchng t at qn ;.e. Fgure 2. Optmzaton usng surrogate functons that are teratvely constructed and maxmzed provdng subsequent updates. Wang and Q appled the optmzaton transfer concept to drect parametrc magng n the case of lnear knetc models [52]. They also pursued the non-lnear context developng a separable parabolodal surrogate [53] and an EM surrogate [54]. The latter approach was shown to exhbt more favourable convergence propertes, whch we also use towards dynamc MP PET magng as elaborated next. In partcular, the resultng surrogate functon to the log-lkelhood functon (5) can be shown to be: Q(K;K n ) = where ˆx m ( ( )log x m (K) x m (K)) p ˆx EM m K n (6) m EM (K n ) = x m (Kn ) p q p y m p q x qm (K n ) (7) ( K n ). s an EM update to the exstng mage estmate x m An mportant observaton s that the surrogate functon (6) s separable n voxels, and thus ts maxmzaton can be convenently carred out voxel-by-voxel: K n+1 = arg max K Q(K;K n ) (8) L(y q) Q(q;q n ) L(y q n ) = Q(q n ;q n ) Overall, nstead of performng drect parametrc magng va maxmzaton of the log-lkelhood (5), the alternatve optmzaton transfer formulaton (6), (7) and (8) 6

4 January 2014, Volume 1, Number 1 enables decouplng of the knetc-parameter-to-mage and mage-to-snogram relatonshps at each teraton, allowng more convenent and more frequent updates. Thus one starts wth an ntal estmate K (0) of the parameter set, followed by utlzaton of the snogram data to produce ˆλ EM,m accordng to (7), and subsequently usng (6) and (8) to work convenently n the mage-space doman only, performng optmzaton of Q voxel-byvoxel, to arrve at the next update parameter set K, and onwards Ordered-Subsets Method and the Detaled Numercal Implementaton Analogous to the concept of ordered-subsets (OS) as utlzed n standard OS-EM algorthms [55], t s possble to smlarly expand both aforementoned formulatons (schemes wthout and wth optmzaton transfer). In partcular, for every update, only an angular subset of the measured dynamc dataset s utlzed, n order to speed up the computatons. To compare the performance of steepest ascent vs. conugate gradent methods n the context of OS, we frst smplfy the numerc problem to the standard case of statc mage reconstructon. The standard EM algorthm can n fact be formulated as a fxed step-sze specal case of precondtoned steepest ascent (PSA), whle PSA and precondtoned conugate gradent (PCG) algorthms allow varable, optmal step-szes for each new drecton. To see ths, we note that the standard loglkelhood functon s gven by: L(y x) = y log y y (9) where y = p x (10) Furthermore, the EM algorthm maxmzng the above log-lkelhood functon s gven by [56, 57]: x (t +1) = x (t ) p q p y (t ) p q x q (11) Where t denotes the teratve update number. It s easy to see [58-60] that the EM algorthm s effectvely a fxed step-sze specal case of precondtoned gradent ascent: consder a precondtoner C and step-sze α. Then, the update teraton s as follows: x (t +1) = x (t ) + αc L(y x) x (t ) (12) Notng that: L(y x) = x p y p p q x q q (13) It follows that (11) and (12) are equvalent f α = 1 and the precondtoner s set as follows: C = x (t ) p (14) For our drect 4D parametrc magng framework (5), we utlzed a general form somewhat smlar to (12) but optmzed wth respect to the knetc parameters K p (p=1,2,3; where for a gven voxel, three parameters K 1, k 2, F LV are to be estmated): K p,(t +1) = K p,(t ) + αc p L(y K) K p,(t ) Wth our precondtoners set to: C p = K p,(t ) p (15) (16) The numercal update algorthm then optmzes n each teraton for steepest ascent, thus arrvng at PSA. We also mplemented a PCG varant, nvolvng the Fletcher-Reeves-Polak-Rbere method [61]. The OS technque, commonly appled to acheve OS-EM, was then appled to result n OS-PSA and OS-PCG varants. 3. Expermental Desgn 3.1. Smulatons We generated myocardal perfuson Rb-82 PET datasets usng the XCAT phantom [62], combned wth analytc smulatons, ncludng the effects of attenuaton and normalzaton. The geometry of the GE Dscovery RX PET [63] was consdered, ncludng realstc average counts and nose levels based on clncal studes of fve patents wth healthy myocarda at the Johns Hopkns PET Center, as we also prevously utlzed n a dfferent context [64]. Rb-82 PET patent organ tme actvty curves for the varous organs n the feld-of-vew were acqured (Fgure 3) and ftted to generate a set of knetc parameters for the organs. The resultng para- 7

5 Arman Rahmm et al. Drect 4D Parametrc Imagng n Dynamc Myocardal Perfuson PET metrc mages (Fgure 4) served as the bass, and reference truth, for the realstc smulatons. For quanttatve assessment of the results, polar maps were created from the estmated K 1 values on the left ventrcular myocardum. The polar maps were subdvded nto 10 sub-regons as depcted n Fgure 5, for addtonal regonal quanttatve analyss. Fgure 3. Average organ tme actvty curves from 5 patents wth healthy myocarda. Fgure 5. Masks to dvde the polar map nto dfferent segments for analyss. Fgure 4. A transaxal slce of the K1, k2, and FLV parametrc mages generated for the NCAT phantom, and used for subsequent smulatons Quanttatve Analyss To track convergence of OS methods, we computed a metrc, referred to as the asymptotc normalzed loglkelhood dfference (NLD), gven by: NLD(n) = L(y ˆx) L(y x(n) ) L(y ˆx) L(y x (0) ) (17) where ˆx denotes a reference mage after substantal teratons (.e. at near convergence). Ths enabled us to dentfy whether OS-PSA or OS-PCG s more approprate as method of choce for numercal optmzaton (Sec. 4.1). The three approaches of () conventonal reconstructon followed by compartmental fttng, as well as drect 4D parametrc magng () wthout and () wth optmzaton transfer, as elaborated n Sec. 2, were consdered. Comparsons were performed usng nose vs. bas trade-off curves as generated wth ncreasng teratons nto the reconstructons. Ths was performed for the entre LV myocardum, as well as the 10 segments shown above. 4. Results 4.1. Optmzaton Methods n the Context of OS For our ntal studes n the case of statc magng, PSA and PCG algorthms were seen to converge as fast as the EM algorthm, whle producng overlappng nose vs. bas trade-off curves (not shown). However, when utlzng subsets, the OS-PCG algorthm was seen to converge relatvely poorly relatve to both OS-EM and OS-PSA algorthms, as shown n Fgure 6 (normalzed lkelhood dfference, computed by (17), was seen to be larger by factors of 1.8 and 2.5 respectvely). We attrbute ths to the fact that whle the PCG technque has theoretcal advantages compared to movng n the drecton of steepest ascent, ths effect dsappears for OS data due to nherent nconsstences between the data subsets. We thus concluded that usage of the PCG algorthm n the OS context s not recommended, whle OS-PSA and OS-EM algorthms pose more favorable 8

6 January 2014, Volume 1, Number 1 alternatves. In applcatons where the EM soluton does not exst (e.g. non-lnear 4D parametrc magng pursued n ths work), usage of OS-PSA optmzaton s nstead recommended, whch s what we utlzed n the rest of ths work. Fgure 6. In the context of OS, PCG s seen to converge relatvely slowly compared to the PSA and EM counterparts. 4.2 Drect 4D Parametrc Imagng wthout Optmzaton Transfer Analyss of nose (normalzed standard devaton) vs. bas (normalzed mean squared error) trade-off curves, as generated by varyng the teratons, revealed sgnfcant mprovements for the proposed 4D method n the entre polar map and n all ndvdual regons of nterest (apex, anteror, lateral, nferor and septal) relatve to conventonal ndrect parametrc magng, as seen Fgure 7. Nose vs. bas curves (generated by varyng the teratons) for the entre K1 polar map and for the ndvdual segments. The 4D drect reconstructon outperforms conventonal compartmental fttng followng reconstructon of ndvdual frames. 9

7 Arman Rahmm et al. Drect 4D Parametrc Imagng n Dynamc Myocardal Perfuson PET Fgure 8. Polar maps wth matched bas for (left) conventonal ndrect knetc parameter estmaton, and (rght) proposed drect 4D parametrc magng. Clearly suppressed nose levels are observed. n Fgure 7. For vsual nspecton, Fgure 8 shows the two polar maps whch were pcked n such a way to be quanttatvely matched n terms of bas: clearly reduced nose levels are observed; n fact, the proposed 4D technque produced over 50% overall reducton n nose, wth matched bas Drect 4D Parametrc Imagng wth Optmzaton Transfer A sgnfcant factor-of-fve mprovement n computatonal effcency was acheved for 4D parametrc magng utlzng optmzaton transfer compared to the 4D approach not utlzng optmzaton transfer. Ths s due to the decouplng between the snogram and mage space domans, as dscussed n Sec Moreover, nose vs. bas trade-off analyss, as shown n Fgure 9, revealed enhanced quanttatvely performance for optmzaton transfer, as could also be detected va vsual Fgure 10. Polar maps obtaned usng drect 4D reconstructon (left) wthout and (rght) wth optmzaton transfer. nspecton (Fgure 10): over 15% reducton n nose was obtaned, wth matched bas. 5. Dscusson 5.1 Parameter Estmaton Outsde the Myocardum An area of cauton n drect parametrc magng s the nherent assumpton that the compartmental model of nterest s vald everywhere wthn the mage. Otherwse, f the model s naccurate outsde a regon of nterest, errors can stll be propagated to the regon [65, 66], unlke the conventonal ndrect estmaton framework where knetc fttng s ndependently performed for each voxel or regon of nterest. In any case, n our context of Rb-82 MP PET, our prelmnary analyss ndcated that tme actvty curves outsde the myocardum were approprately ft usng the standard one-tssue compartment model (no systematc resdual errors). It s worth notng, at the same tme, that we do not nterpret the fts outsde the myocardum, though Rb-82 has been proposed as a tracer wth potental for renal blood flow magng, ncludng demonstraton of approprate fts n the kdney usng the one-tssue compartmental model [67]. 5.2 Addressng the Partal Volume Effect (PVE) Fgure 9. Nose vs. bas curves (generated by varyng the teratons) for the entre K1 polar map. The approach utlzng optmzaton transfer s seen to perform favorably compared to the baselne drect 4D reconstructon methods. One presented ssue n both statc and dynamc magng s PVE, whch arses from the contrbutons of resoluton degradng phenomena [68]. In the case of dynamc magng, an attempt to address PVE has been through addtonal parameters n the knetc modellng analyss [15, 69-74] (e.g. note that the fractonal blood volume F as mplemented n Sec. 2.1 s amed, n part, to model the spllover from the blood pool to the myocardum). However, use of addtonal varable(s) can degrade estmaton robustness. Other alternatves explored for cardac magng nclude post-reconstructon partal volume correcton (PVC) [75-79] or reconstructon-based reso- 10

8 January 2014, Volume 1, Number 1 luton modellng [80-82]. In fact, n one explct comparson by Nuyts et al. [75], PVC was seen to outperform the expanded knetc modellng approach. A downsde to drect 4D parametrc estmaton s that because ndvdual mages are not reconstructed, PVC cannot be appled as such to fnal reconstructed ndvdual mages; however, t s possble to nvestgate applcaton of PVC to the fnal parametrc mage, though ths s not an equvalent approach. By contrast, resoluton modellng can be easly ncorporated n the context of 4D mage reconstructon. However, resoluton modellng tself s an area that needs to be approached wth cauton, especally n the context of quanttatve magng [83] because even though t leads to mproved resoluton and contrast recovery (reduced quanttatve bas) t can amplfy varablty (.e. reduce reproducblty) for small regons of nterest, and can lead to edge artfacts [84]. 6. Summary A drect 4D parametrc magng method was developed ncorporatng knetc modelng wthn the reconstructon of dynamc cardac PET data. Wth realstc smulatons, we demonstrated mproved quanttatve performance of the proposed technque over conventonal ndrect quantfcaton of myocardal blood flow followng reconstructon of ndvdual mages. Optmzaton transfer va constructon of an mage-doman surrogate functon was seen to notably enhance computatonal as well as quanttatve performance of drect parametrc mage estmaton. Acknowledgment Ths work was n part supported by the NIH grant 1S10RR and the NSF grant ECCS The authors wsh to thank Dr. Bengel for helpful dscussons, and Andy Crabb for computatonal support. References [1] Go, R.T., et al. (1990). A Prospectve Comparson of Rubdum-82 PET and Thallum-201 SPECT Myocardal Perfuson Imagng Utlzng a Sngle Dpyrdamole Stress n the Dagnoss of Coronary Artery Dsease. J Nucl Med, 31(12), [2] Stewart, R.E., et al. (1991). Comparson of rubdum-82 postron emsson tomography and thallum-201 SPECT magng for detecton of coronary artery dsease. Am J Cardol, 67(16), [3] Machac, J. (2005). Cardac postron emsson tomography magng. Semn Nucl Med, 35(1), [4] Bateman, T.M., et al. (2006). Dagnostc accuracy of rest/ stress ECG-gated Rb-82 myocardal perfuson PET: comparson wth ECG-gated Tc-99m sestamb SPECT. J Nucl Cardol, 13(1), [5] Sampson, U.K., et al. (2007). Dagnostc accuracy of rubdum-82 myocardal perfuson magng wth hybrd postron emsson tomography/computed tomography n the detecton of coronary artery dsease. J Am Coll Cardol, 49(10), [6] Marwck, T.H., et al. (1997). Incremental value of rubdum-82 postron emsson tomography for prognostc assessment of known or suspected coronary artery dsease. Am J Cardol, 80(7), [7] Yoshnaga, K., et al. (2006), What s the Prognostc Value of Myocardal Perfuson Imagng Usng Rubdum-82 Postron Emsson Tomography? J Am Coll Cardol, 48(5), [8] Schenker, M.P., et al. (2008). Interrelaton of coronary calcfcaton, myocardal schema, and outcomes n patents wth ntermedate lkelhood of coronary artery dsease: a combned postron emsson tomography/computed tomography study. Crculaton, 117(13), [9] Herrero, P., et al. (1992). Implementaton and Evaluaton of a 2-Compartment Model for Quantfcaton of Myocardal Perfuson wth Rb-82 and Postron Emsson Tomography. Crculaton Research, 70(3), [10] Coxson, P.G., et al. (1995). Varablty and Reproducblty of Rb-82 Knetc-Parameters n the Myocardum of the Anesthetzed Canne. Journal of Nuclear Medcne, 36(2), [11] Yoshda, K., Mullan, N., and Gould, K.L. (1996). Coronary flow and flow reserve by PET smplfed for clncal applcatons usng rubdum-82 or ntrogen-13-ammona. Journal of Nuclear Medcne, 37(10), [12] Coxson, P.G., Huesman, R.H. and Borland, L. (1997). Consequences of usng a smplfed knetc model for dynamc PET data. Journal of Nuclear Medcne, 38(4), [13] Golanowsk, L., et al. (2000). Varance and Covarance of 82Rb Knetc Parameters: Computer Smulatons and Dynamc PET Studes, n Proceedngs of the 22nd Annual Internatonal Conference of the IEEE Engneerng and Medcne n Bology Socety, pp [14] El Fakhr, G., et al. (2005). Quanttatve dynamc cardac Rb-82 PET usng generalzed factor and compartment analyses. Journal of Nuclear Medcne, 46(8), [15] Lorte, M., et al. (2007). Quantfcaton of myocardal blood flow wth Rb-82 dynamc PET magng. European ournal of nuclear medcne and molecular magng, 34(11), [16] Uren, N.G., et al. (1994), Relaton between myocardal blood flow and the severty of coronary-artery stenoss. N Engl J Med, 330(25), [17] Parkash, R., et al. (2004). Potental utlty of rubdum 82 PET quantfcaton n patents wth 3-vessel coronary artery dsease. Journal of Nuclear Cardology, 11(4), [18] Lodge, M. and Bengel F. (2007). Methodology for quantfyng absolute myocardal perfuson wth PET and SPECT. Current Cardology Reports, 9(2),

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