MRI-Based Computational Torso/Biventricular Multiscale Models to Investigate the Impact of Anatomical Variability on the ECG QRS Complex

phys-10-01103 Augus 24, 2019 Time: 16:24 # 1 ORIGINAL RESEARCH published: 27 Augus 2019 doi: 10.3389/ phys.2019.01103 Edi ed by: Ja ie Saiz, Poly echnic Uni e si y o Valencia, Spain Re iewed by: A un V. Holden, Uni e si y o Leeds, Uni ed Kingdom Gunna Seemann, Uni e si y Hea Cen e F eibu g, Ge many *Co espondence: Ana Mincholé [email p o ec ed] †These au ho s ha e con ibu ed equally o his wo k as i s au ho s ‡These au ho s ha e con ibu ed equally o his wo k as senio au ho s Special y sec ion: This a icle was submi ed o Compu a ional Physiology and Medicine, a sec ion o he jou nal F on ie s in Physiology Recei ed: 08 Ma ch 2019 Accep ed: 08 Augus 2019 Published: 27 Augus 2019 Ci a ion: Mincholé A, Zacu E, A iga R, G au V and Rod iguez B (2019) MRI-Based Compu a ional To so/Bi en icula Mul iscale Models o In es iga e he Impac o Ana omical Va iabili y on he ECG QRS Complex. F on . Physiol. 10:1103. doi: 10.3389/ phys.2019.01103 MRI-Based Compu a ional To so/Bi en icula Mul iscale Models o In es iga e he Impac o Ana omical Va iabili y on he ECG QRS Complex Ana Mincholé1*†, E nes o Zacu 2†, Rina A iga3, Vicen e G au2‡and Blanca Rod iguez1‡ 1Depa men o Compu e Science, Uni e si y o Ox o d, Ox o d, Uni ed Kingdom, 2Ins i u e o Biomedical Enginee ing (IBME), Uni e si y o Ox o d, Ox o d, Uni ed Kingdom, 3Di ision o Ca dio ascula Medicine, Radcli e Depa men o Medicine, Uni e si y o Ox o d, Ox o d, Uni ed Kingdom Aims: Pa ien - o-pa ien ana omical di e ences a e an impo an sou ce o a iabili y in he elec oca diog am, and hey may comp omise he iden i ica ion o pa hological elec ophysiological abno mali ies. This s udy aims a quan i ying he con ibu ion o a iabili y in en icula and o so ana omies o di e ences in QRS complexes o he 12-lead ECG using compu e simula ions. Me hods: A compu a ional pipeline is p esen ed ha enables compu e simula ions using human o so/bi en icula ana omically based elec ophysiological models om clinically s anda d magne ic esonance imaging (MRI). The en icula model includes memb ane kine ics ep esen ed by he biophysically de ailed O’Ha a Rudy model modi ied o issue he e ogenei y and includes ibe o ien a ion based on he S ee e ule. A popula ion o 265 o so/bi en icula models was gene a ed by combining en icula and o so ana omies ob ained om clinically s anda d MRIs, augmen ed wi h a s a is ical shape model o he body. 12-lead ECGs we e simula ed on he 265 human o so/bi en icula elec ophysiology models, and QRS mo phology, du a ion and ampli ude we e quan i ied in each ECG lead o each o he human o so-bi en icula models. Resul s: QRS mo phologies in limb leads a e mainly de e mined by en icula ana omy, while in he p eco dial leads, and especially V1 o V4, hey a e de e mined by hea posi ion wi hin he o so. Di e ences in en icula o ien a ion wi hin he o so can explain mo phological a iabili y om monophasic o biphasic QRS complexes. QRS du a ion is mainly in luenced by myoca dial olume, while i is ha dly a ec ed by he o so ana omy o posi ion. An a e age inc ease o 0.12 ±0.05 ms in QRS du a ion is ob ained o each cm3o myoca dial olume ac oss all he leads while i ha dly changed due o changes in o so olume. F on ie s in Physiology | www. on ie sin.o g 1Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 2 Mincholé e al. Impac o Ana omy on ECG QRS Complex Conclusion: Compu e simula ions using popula ions o human o so/bi en icula models based on clinical MRI enable quan i ica ion o ana omical causes o a iabili y in he QRS complex o he 12-lead ECG. The human models p esen ed also pa e he way owa d hei use as es beds in silico clinical ials. Keywo ds: clinical MRI-based o so/ en icula ana omical models, compu e simula ions, elec oca diog am, compu a ional modeling, ca diac magne ic esonance imaging INTRODUCTION The elec oca diog am (ECG) is he mos widely used clinical ool o e alua ion o ca diac unc ion. I eco ds he elec ical ac i i y o he hea om elec odes posi ioned on he pa ien ’s o so, and he du a ion, ampli ude, and mo phology o ECG wa e o ms in he di e en leads a e used o pa ien s’ diagnosis (Mac a lane and Law ie, 2010). Elec oca diog am ea u es, and speci ically i s QRS complex, a e a ec ed no only by mic os uc u al and physiological ac o s such as ibe o ien a ion, Pu kinje, myoca dial conduc ion pa hways and ionic cu en s (Boineau and Spach, 1968), bu also by ana omical cha ac e is ics such as hea size and o ien a ion, en icula wall hickness, and body mass index (Hoekema e al., 1999, 2001; an Oos e om e al., 2000;Co lan e al., 2005). Quan i a i e in o ma ion on he la e is, howe e , sca ce. An expe imen al s udy showed la ge changes in QRS wi h a ying hea loca ions, using one isola ed pe used dog hea suspended in an elec oly ic o so ank (MacLeod e al., 2000). Compu e simula ion s udies a e ideally placed o p o ide insigh on he unde lying basis o he ECG. Mos o he p e ious compu a ional s udies ocused on simula ing he ECG using a single hea ana omy as (Kelle e al., 2010;Zemzemi e al., 2013;Zemzemi and Rod iguez, 2015;Neic e al., 2017; Po se, 2018). Mo e ecen ly, a compu a ional s udy using o so- bi en icula ana omical models o i e pa ien s wi h hea ailu e showed ha hea posi ion and o ien a ion s ongly al e ed QRS ampli ude, bu only sligh ly, QRS du a ion (Nguyên e al., 2015). Sánchez e al. (2018) also p o ided insigh s in o he key ac o s de e mining he ECG cha ac e is ics based on da a o six hea ailu e pa ien s. These s udies highligh he po en ial o compu e simula ion s udies using image-based models o shed ligh in o he ana omical basis go e ning ECG a iabili y and he QRS complex. Whe eas he dense olume ic in o ma ion and high esolu ion o cu en CT scans is a clea ad an age in he cons uc ion o ca diac ana omical models (Naza ian and Halpe in, 2018) o ECG simula ions, he adia ion in ol ed limi s hei use, o example in heal hy subjec s. The al e na i e o using magne ic esonance imaging (MRI) scans is e y a ac i e as hey p o ide good quali y ca diac images sa ely and non-in asi ely. Clinical p o ocols, howe e , ocus on he hea and he e o e in o ma ion on he o so is sca ce. This is why p e ious s udies ha e used MRI scans ob ained using dedica ed imaging p o ocols, no sui able o ou ine clinical p ac ice (Po se e al., 2014;Sánchez e al., 2018). Me hodological ad ances a e he e o e needed o exploi clinically s anda d MRI da abases in compu e simula ions s udies using image-based human o so/bi en icula ana omical models. The goal o his s udy is o conduc a compu e simula ion s udy using a popula ion o 265 o so- en icula ana omical models based on clinically s anda d MRI o dissec and quan i y he indi idual con ibu ion o en icula and o so ana omy on QRS bioma ke s in he 12-lead ECG. We hypo hesize ha QRS complexes in each o he s anda d 12-lead ECGs a e a ec ed di e en ly by geome ical ac o s such as en icula ana omy, hea o ien a ion and loca ion, o o so ana omy. To es his hypo hesis, we de elop a compu a ional pipeline o conduc high- pe o mance compu ing (HPC) elec ophysiological simula ions using biophysically de ailed compu a ional human models wi h en icula and o so ana omies ob ained om clinically s anda d ca diac MRI acquisi ions. In a clinical scena io, he new insigh s could acili a e an imp o ed disc imina ion in clinical ECG eco dings be ween he con ibu ions o pa ien ’s ana omical ea u es and hose a ising om a ca diac condi ion o disease. MATERIALS AND METHODS Recons uc ion o Ven icula and To so Ana omical Meshes F om Clinical MRI In his s udy, a o al o 265 combined o so- en icles ana omical models we e conside ed o quan i y he e ec o en icula and o so olumes, and hea posi ion and o ien a ion on he QRS complex. Ini ially, as desc ibed in Figu e 1, wen y- i e human hea - o so models we e gene a ed by combining he bi- en icula geome ies (H1–H5) and o sos (T1–T5) (including co esponding hea o ien a ions and posi ions) ex ac ed om clinical MRI acquisi ion om 5 heal hy subjec s. The MRI da ase s we e selec ed o include en icula end dias olic myoca dial olumes be ween 75 and 170 cm3and o so olumes be ween 23 and 54 dm3. Then, ei he o a ion o ansla ion was applied o each bi- en icula model wi hin each o so. 5◦s eps up o (±40◦we e conside ed bo h a ound he long axis (LA) and a ound he le - o- igh - en icle axis (LR) (Nguyên e al., 2015). T ansla ion was conside ed in 1 cm s eps up o (±4 cm ei he along he la e al o along c anio-caudal di ec ions. The MRI scans we e ob ained in i e heal hy subjec s ( h ee emales and wo males) wi h a ange o en icula end-dias olic myoca dial olumes be ween 75 and 170 cm3and o so olumes be ween 23 and 54 dm3, ec ui ed a John Radcli e Hospi al, Ox o d, Uni ed Kingdom. Subjec s we e non-smoke s wi hou ca dio ascula disease, hype ension o diabe es, and no amily his o y o ca diomyopa hy o sudden ca diac dea h (SCD). F on ie s in Physiology | www. on ie sin.o g 2Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 3 Mincholé e al. Impac o Ana omy on ECG QRS Complex FIGURE 1 | (A) Compu a ional pipeline om clinical MRI segmen a ions h ough cons uc ion o hea and o so geome ies o he HPC simula ion o elec ophysiology om ionic o body su ace po en ials. Following MRI segmen a ions, hea su ace is ob ained by emo ing b ea h misalignmen and o so su ace by using he spa se in o ma ion om he MRI con ou s oge he wi h a s a is ical body shape model. Wi h he olume ic meshes, elec ophysiological p ope ies such as an ac ion po en ial model and an ac i a ion model a e used o simula e elec ical ac i i y om cell o o so and calcula e he 12-lead ECG. (B) 25 o so- en icula ana omical models combining i e o sos (T1–T5) and i e en icles (H1–H5) o a ying olumes. (C) Hea pose wi hin he o so de ined as he ans o ma ion om a canonical coo dina e sys em o he en icula geome y o he o so coo dina e sys em. Clinically s anda d cine ca diac MRI acquisi ion was pe o med o each subjec , including long axis (LAX) and a s ack o sho axis (SAX) iews. Mo e speci ically, o each subjec , he da a includes a 2 chambe LAX iew, 4 chambe iew, and a s ack o SAX iew om apex o base wi h 10 mm o sepa a ion be ween adjacen slices in he s ack (8 mm slice hickness plus 2 mm gap). Image esolu ion anges om 1.4 o 1.6 mm pe pixel. An expe wi h se e al yea s o expe ience in ca diac MRI segmen ed he images a end-dias ole including he ollowing s uc u es: le epica dium, le en icle (LV) endoca dium excluding he papilla y muscles, and igh en icle (RV) endoca dium (see Figu e 1A, Segmen a ion). As he image esolu ion in s anda d MRI acquisi ions does no allow o di e en ia e igh en icula epica dial and endoca dial con ou s in he igh en icle, we syn hesized igh epica dial con ou s by a 3.5 mm o se om he endoca dial con ou s (P akash, 1978). Spa ial misalignmen s in slice images and spa ial disc epancies be ween he con ou s due o acquisi ions a di e en b ea h holds we e co ec ed by aligning in ensi y p o iles o in e sec ing slices using a 3D igid ans o ma ion o each image (Villa d e al., 2017) (see Figu e 1A, Con ou s alignmen ). Bi- en icula geome ies we e buil om he aligned con ou s using he end-dias ole ames om he s anda d CINE acquisi ion as in Villa d e al. (2018) and Zacu e al. (2017). Fo he cons uc ion o he o so geome ies, semi-au oma ic ools we e de eloped and used o delinea e he o so skin and lungs (Zacu e al., 2017). In b ie , on each subjec , he scou images (localize s), as well as, mos o he MRI images (SAX and LAX images) wi h a la ge enough ield o iew we e used and con ou ed. The spa se 3D geome ical in o ma ion om he o so images is insu icien o he use o classical segmen a ion o su ace me hods such as isocon ou ing ools (Figu e 1A, 3-Dimensional o so a angemen ). Thus, we de eloped and applied a me hodology o i a s a is ical shape model o he human body o he skin con ou s (Zacu e al., 2017). The o so con ou s oge he wi h subjec heigh , weigh and gende in o ma ion we e used o econs uc a body su ace belonging o a lea ned class o plausible body shapes om he s a is ical shape model (Pishchulin e al., 2017;Zacu e al., 2017). The a e age disc epancy be ween MRI-based con ou s and model su ace is F on ie s in Physiology | www. on ie sin.o g 3Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 4 Mincholé e al. Impac o Ana omy on ECG QRS Complex FIGURE 2 | (A) Endoca dial ac i a ion maps o he i e en icula geome ies. In o ma ion abou en icula olumes is also p o ided. (B) Homologous 12-lead elec ode posi ions o he i e i ualized subjec s. In o ma ion abou he o so olumes is p o ided. FIGURE 3 | E ec o en icula geome y on QRS du a ion, and S and R wa e ampli ude. (A) Simula ed QRS complexes ob ained o i e en icula geome ies placed in he o so-pose o Subjec 3 (T3). (B) QRS du a ion (le ), S and R ampli ude (middle and igh , espec i ely) ob ained om simula ions using he i e en icula geome ies (H1 o H5) placed in each o he i e o so-poses (T1 o T5). The e m “a.u.” s ands o a bi a y uni s. 3 mm in e ms o oo mean squa e, being he 90 h pe cen ile 5 mm. A empla e-based app oach was used o place o he in e nal s uc u es such as he lungs and he ibs (Figu e 1A, Su ace meshes). Full de ails abou he p ocedu e a e p o ided in Zacu e al. (2017). All su aces we e emeshed wi h di e en elemen sizes o ensu e nume ical con e gence o he ini e elemen so wa e Chas e o elec ophysiological simula ions (Pi - F ancis e al., 2009;Du a e al., 2016) as desc ibed in Supplemen a y Ma e ial S1. Finally, e ahed al olume ic F on ie s in Physiology | www. on ie sin.o g 4Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 5 Mincholé e al. Impac o Ana omy on ECG QRS Complex meshes we e cons uc ed om hese su aces (see Supplemen a y Ma e ial S1). The su ace and olume ic meshes can be downloaded om h p://www.cs.ox.ac.uk/ccs/home. Figu e 1B shows he econs uc ed en icula geome ies and, he o so geome ies including hei co esponding hea o ien a ions and posi ions, cons ained by ches bounda ies. The gene a ion o a new i ual o so- en icula geome y equi es he ans o ma ion o he en icula geome y om a canonical e e ence ame o he posi ion de ined by he o so (pose, see Figu e 1C). He eina e , o so-pose is de ined as he o so geome y including he hea pose, which ep esen s he coo dina e sys em and loca ion o he hea . This o so- pose linking is suppo ed by physical cons ain s such as ches bounda ies, since one speci ic o so ana omy does no allow any hea posi ion (Engblom e al., 2005). Fu he in o ma ion is ound in Supplemen a y Ma e ial S1. Elec ophysiological Simula ions The ana omical o so- en icula model combina ions desc ibed abo e we e used o compu e 265 QRS complexes om compu e simula ions as ollows. The p opaga ion o he elec ical ac i i y in he human en icles and o so was modeled using he ully coupled hea - o so bidomain equa ions and sol ed wi h he Chas e so wa e (Pi -F ancis e al., 2009). Human en icula memb ane kine ics we e simula ed wi h a modi ied e sion o he O’Ha a-Rudy ac ion po en ial model (O’Ha a e al., 2011) published in Du a e al. (2017). Myoca dial and o so conduc i i ies, and, myoca dial ibe s uc u e we e se as desc ibed in Supplemen a y Ma e ial S2. An aniso opic myoca dial ibe a chi ec u e was implemen ed using he S ee e ule (S ee e e al., 1969). The h ee o ho opic in acellula and ex acellula myoca dial conduc i i ies we e se as in Ca done-Noo e al. (2016). T ansmu al, apex- o-base and in e en icula cell elec ophysiological he e ogenei ies we e in oduced based on expe imen al and clinical da a and as desc ibed in Supplemen a y Ma e ial S2. The QRS complex is ha dly a ec ed by he elec ophysiological he e ogenei ies included in ou models as hey mainly a ec he epola iza ion p ope ies and he T wa e. Howe e , hey p o ide ou compu a ional pipeline wi h all he s a e o he a capabili ies o ex end he wo k o in es iga e a iabili y in T wa e mo phology, as well as unde disease and d ug ac ion. Sinus hy hm was simula ed using a phenomenological ac i a ion model wi h ea ly endoca dial ac i a ion ini ia ed by oo nodes and a as endoca dial laye ep esen ing a igh ly packed endoca dial Pu kinje ne wo k (Ca done-Noo e al., 2016). In sho , 7 oo nodes a e posi ioned in he en icles on he endoca dium: ou in he LV (LV mid sep um, LV an e io pa asep al, and wo LV mid-pos e io ) and h ee in he RV (RV mid sep um, wo RV ee wall), as shown in Supplemen a y Ma e ial S2. Simula ed en icula ac i a ion imes o hese models show he LV endoca dial su aces a e ully ac i a ed wi hin a ange o 39 o 51 ms, and he la es momen s o ac i a ion occu s in a ange om 57 o 76 ms. This is in ag eemen wi h he ex i o mic oelec ode eco dings by Du e e al. (1970) epo ing a ound 45 ms in endoca dial LV ac i a ion, and om 60 o 80 ms he la es momen s o whole en icula ac i a ion. The aim o his s udy is o in es iga e, analyze and quan i y he e ec o ana omical/geome ical a iabili y on he QRS complexes in an elec ophysiological compu e simula ion amewo k. I is no o cons uc pe sonalized elec ophysiology models o eplica e each o he pa ien s’ da a. In o de o isola e he e ec o en icula ana omy om di e ences in ac i a ion pa e ns, he endoca dial speed was se o 120 cm/s in all models, and he loca ions o he oo nodes we e mapped o ana omically homologous loca ions om he geome y used in a p e ious s udy (Ca done-Noo e al., 2016). The coupled epica dial, RV and LV endoca dial su aces and en icula inse ion poin s om he o iginal geome y (Ca done-Noo e al., 2016) we e di eomo phically egis e ed o each en icula geome y using a composi ion o app oxima ed Thin-Pla e Splines (TPS) de o ma ions (Roh e al., 2001). The de o ma ion me hod was guided by an i e a ed closes poin be ween he co esponding sou ce and a ge su aces/s uc u es (le and igh endo- and epica dial su aces, a io- en icula planes, and an e io and pos e io in e en icula g oo es). The successi e de o ma ions we e pe o med by ollowing an annealing p ocess in he smoo hness pa ame e o app oxima ed TPS (Ambe g e al., 2007). The esul ing egis e ed de o ma ion was applied o he ea ly ac i a ion si es om he o iginal geome y esul ing in he ana omically homologous loca ions ha lead o simila ac i a ion sequences (see Figu e 2A). The esul ing de o ma ions and he mapped ac i a ion si es we e isually e alua ed and app o ed by an expe ca diologis . This echnique was used gi en i s b oad accep ance and success in he medical imaging and shape analysis ield bu he uni e sal en icula coo dina es could ep esen an al e na i e (Baye e al., 2018). QRS complexes om he 12-lead ECGs we e simula ed by placing i ual elec odes in he s anda d 12-lead ECG posi ions o each o so. Since he s a is ical shape model used o econs uc ing he o sos is based on ana omical co espondences, he i ual elec odes a e loca ed in ana omically homologous loca ions o all he o sos (see Figu e 2B). These elec ode posi ions co espond o analogous in e cos al spaces o all subjec s. Elec ode coo dina es a e gi en o each o he o so geome ies, and can be downloaded om h p://www.cs.ox.ac.uk/ccs/home. To simula e he QRS complex o 265 combina ions o en icula / o so posi ions and o ien a ions while minimizing he numbe o expensi e HPC simula ions, ex acellula po en ials we e compu ed om he en icula po en ials ollowing he in eg al o dipole sou ce densi y o mula ion (Gima and Rudy, 2002;Plonsey and Ba , 2007) as: φ(e)=Z  −D∇Vm·∇1 || −e||d , whe e e=ex,ey,eza e he elec ode posi ion coo dina es, Dis he di usion enso , and Vmis he memb ane po en ial. The in eg al is calcula ed o e he whole myoca dium olume, . Bidomain simula ions coupled wi h he Poisson equa ion o p opaga e he elec ical ac i i y o he body su ace we e compa ed o he in eg a ion o dipole sou ce densi y o mula ion o he o so p opaga ion. The esul ing QRS complexes we e e y simila as shown in Supplemen a y Figu e S3 om F on ie s in Physiology | www. on ie sin.o g 5Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 6 Mincholé e al. Impac o Ana omy on ECG QRS Complex Supplemen a y Ma e ial S2. The p opaga ion model based on he in eg a ion o dipole sou ce densi y o mula ion was chosen in o de o simpli y he nume ical complexi y o he compu a ions and o a oid e-meshing he o so olume o each scena io in which he en icula geome y was o a ed, ansla ed o pe mu ed. Al hough his me hod does no allow he inclusion o issue inhomogenei ies in he o so, se e al s udies sugges minimal di e ences in he esul ing body su ace po en ials and he QRS complex when assuming homogeneous o inhomogeneous o so models (Ramana han and Rudy, 2001; Genese e al., 2008). Quan i ica ion o QRS-Based Fea u es and Desc ip o s Clinically used ea u es om he QRS, such as du a ion and ampli ude, we e ex ac ed o each o he simula ed 12-lead ECGs. QRS du a ion is calcula ed by using a ela i e h eshold on he absolu e alue o he slopes o he ECG signal o iden i y QRS onse and o se as in Ma ínez e al. (2004). We compa ed he simula ion esul s wi h hose epo ed in he li e a u e and also clinical ECG eco dings om heal hy olun ee s, as pa o a p ospec i e s udy app o ed by he Na ional Resea ch E hics Commi ee (REC e 12/LO/1979). In o med w i en consen was ob ained om each pa icipan (Lyon e al., 2018a). Fu he mo e, in o de o quan i y he e ec o ana omical a iabili y in QRS mo phology, we p oposed a simila i y measu e o quan i y QRS mo phological di e ences, in a ian o QRS ampli ude and du a ion. The new me ic (PC∗) is based on a con inuous gene aliza ion o he Pea son coe icien (PC), which in o de o ensu e independence om QRS du a ion, includes he in a iance o a uni o m wa ping ( ime scaling) in ime o he QRS complex. The e o e, PC∗be ween wo QRS complexes is 1 when hese ha e he same mo phology ega dless o he ampli ude o he du a ion. Le and gbe wo unc ions de ined on he domains dom( )=h 0, 1iand dom(g)= g 0, g 1, espec i ely. Le ’s assume ha dom( )∩dom(g)6= ∅ and le ’s conside he combined domain [ 0, 1]= dom( )∪dom(g), whe e 0= min 0, g 0and 1= max 1, g 1. On his combined domain, le ˜ be he eplica ed ex ension o he o iginal unc ion , ˜ =       ( )i ∈h 0, 1i ( 0)i < 0 ( 1)i < 1 and equi alen ly o ˜ g. Ou p oposed gene alized PC is gi en by PC ,g=1 1− 0 1 Z 0 ˜ ( )−µ˜ σ˜ ·˜g( )−µ˜g σ˜g d (1) whe e µ˜ and µ˜ga e means, and σ˜ and σ˜ga e he s anda d de ia ions o he unc ions ˜ ( ) and ˜ g( ), espec i ely, µ˜ =1 1− 0 1 Z 0 ˜ ( )d , σ˜ = u u u 1 1− 0 1 Z 0˜ ( )−µ˜ 2d and equi alen ly o µ˜gand σ˜g. The sub ac ion o he means µ˜ and µ˜gin Eq. (1) ensu es he in a iance o PC unde changes in he baseline le els. Likewise, no maliza ions by σ˜ and σ˜g, endow PC wi h in a iance o scaling. The no maliza ion by ( 1− 0) allows independence om ime uni s. Thus, PC alues a e wi hin he [–1, 1] in e al. In o de o ensu e independence om QRS du a ion, we include he in a iance o a uni o m wa ping ( ime scaling) in ime h ough he ollowing simila i y measu emen PC∗: PC ∗ ,g= max s∈R+PC (·),g(s·), whe e g(s·) is a uni o mly ime-wa ped e sion o g. I is wo h men ioning ha since domg(s·)= 1/s· dom(g)= g 0/s, g 1/s, he in eg al in e al in Eq.(1) is upda ed acco dingly, and he esul ing PC∗keeps ha ing compa able alues. In he ollowing, we will explain how o quan i y a global simila i y o a se o N unc ions  1(·), 2(·),· · · , N(·). We p opose o compu e, he bes ime wa ping ac o s o he N unc ions simul aneously, in o de o op imally align he se . The e o e, we sea ch o {s1,s2,...,sN}= a gmax s1,...,sN∈R+ min i= 1...N j=i+1...N PC i(si·), j(sj·) Once hese op imal ime wa ping ac o s ha e been compu ed, he global simila i y o he unc ions  1(·), 2(·),· · · , N(·) is gi en by PC∗ 1, 2,... N= max i= 1...N j=i+1...N PC i(si·), j(sj·) wi h his, he wo s aligned pai de ines he simila i y o he whole se . RESULTS E ec o Ven icula Geome y on QRS Du a ion and Ampli ude Figu e 3 illus a es he e ec o di e en en icula geome ies wi hin he same o so wi h co esponding hea posi ion (he eina e e e ed o as o so-pose) on QRS du a ion and ampli ude. Figu e 3A shows he QRS complexes ob ained in leads I, II and V1–V6 o each o he i e en icles (H1–H5) placed in he o so-pose o Subjec 3 (T3). Figu e 3B shows QRS complex du a ion as well as S and R wa e ampli ude o all 25 o so-pose and en icula combina ions. Fo all o so-poses, QRS complexes dec ease in ampli ude and inc ease in du a ion F on ie s in Physiology | www. on ie sin.o g 6Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 7 Mincholé e al. Impac o Ana omy on ECG QRS Complex wi h an inc ease in myoca dial olume (g een e sus black aces co esponding o he la ges e sus he smalles en icula olumes, espec i ely). An a e age inc ease o 0.12 ±0.05 ms in QRS du a ion o each cm3o myoca dial olume ac oss all he leads was ound. Rela ionships be ween QRS du a ions and en icula myoca dial olumes o each o he leads is shown in Supplemen a y Ma e ial S4.Supplemen a y Figu e S4 shows he 12 lead QRS complexes o di e en en icula geome ies wi hin he same o so-pose o each o he i e subjec s. E ec o To so-Hea Posi ion on QRS Du a ion and Ampli ude Figu e 4 shows he e ec o di e en o so-poses on QRS du a ion and ampli ude. Figu e 4A shows as an example, he QRS complexes ob ained o he en icula geome y H3 when placed in all he o so-poses, and Figu e 4B p o ides quan i ica ion o QRS du a ion and R and S wa e ampli udes o he i e en icula geome ies. QRS du a ion does no change subs an ially o di e en o so-poses, and his sugges s ha QRS du a ion is mainly de e mined by he en icula geome y. Indeed, a sligh inc ease in QRS du a ion o 0.01 ±0.03 ms o dm3o o so olume ac oss all leads is obse ed ( u he in o ma ion ega ding he ela ionship be ween QRS du a ion and o so olume can be ound in Supplemen a y Ma e ial S4). Howe e , bo h S and R wa e ampli udes a e mainly de e mined by o so olumes, wi h la ge QRS ampli udes co esponding o smalle o so olumes. Excep ionally, QRS complexes in T4 wi h a o so olume o 27 dm3exhibi la ge ampli udes in V1 o V3 compa ed o T5 (23 dm3) ha exhibi la ge ampli udes in V4 o V6. Fo hese wo o sos wi h simila olumes, hea posi ion plays an impo an ole in QRS ampli ude. By compa ing he en icula posi ions o T4 and T5 (see Figu e 2), we obse e ha o T5, V5 and V6 elec ode posi ions a e close o he en icles esul ing in la ge QRS ampli udes, whils V2 and V3 elec odes a e u he away, esul ing in smalle ampli udes. E ec o Ven icula Geome y and To so-Pose on QRS Mo phology Figu e 5A displays he simila i y measu emen compu ed om he modi ied Pea son co ela ion PC∗, which measu es di e ences in QRS mo phology due o di e ences in en icula geome y and o so-pose. Resul s show ha o limb leads (I, II, aVR, aVL and aVF), and V5, QRS mo phology is mo e simila (and PC∗highe ) o ixed en icula geome y (wi h a ying o so-pose) han o ixed o so-pose (wi h a ying en icula geome y). The e o e, in hese leads, he en icula geome y mainly de e mines he QRS mo phology. On he con a y, o leads V1 o V4 and V6, QRS mo phology is mo e simila (as shown by he highe PC∗ alues) o ixed o so-poses han o ixed en icula geome y. Thus, in hese leads, QRS mo phology is mos ly de e mined by o so-pose a he han by en icula geome y. These esul s a e u he illus a ed in Figu es 5B,C o wo ep esen a i e leads, aVL and V1. Simula ed QRS mo phology is mos ly de e mined by he en icula geome y and o so- pose in leads aVL and V1, espec i ely. Simula ed QRS complexes ob ained wi h he same en icula geome y a e shown in he same ow while hose ob ained wi h he same o so-pose a e shown in he same column. The wa ped QRS complexes om which PC∗is compu ed a e shown in Supplemen a y Ma e ial S5. E ec o Hea O ien a ion and Posi ion on he QRS Mo phology Figu es 6,7illus a e he esul s ob ained om he 265 simula ions conduc ed o e alua e he e ec o o a ion a ound he long axis and le - o- igh en icle di ec ions and ansla ion along he la e al and c anio-caudal di ec ions o he en icles wi hin he o so in he QRS complex. Figu e 6 displays simula ed QRS complexes ob ained o a ep esen a i e ana omical model (H3 wi hin T3), whe eas Figu e 7 shows quan i ica ion o he QRS mo phology simila i y me ic (PC∗) o all subjec speci ic o so- en icula geome ies. As shown in Figu es 6A,7A, o a ion along he long axis mainly a ec s he R and S ampli udes o leads V1 o V3. The ampli ude o he R wa e is la ge when he LV aces he ches plane (o ange aces) and dec eases as he RV ge s posi ioned be ween he LV and he ches (blue ace). The ampli ude o he S wa e also dec eases in he p eco dial leads in en icula posi ions whe e he RV aces he ches . Quan i a i e esul s ega ding changes in QRS ampli udes wi h hea o ien a ion and posi ion can be ound in Supplemen a y Ma e ial S6. Figu es 6B,7B show ha o a ion a ound he le - o- igh en icle axis se e ely a ec s he QRS mo phology in leads II, and V1 o V5. Mo e ho izon al hea s (o ange aces) esul in la ge R wa e ampli udes in leads I, V1, and V6 while mo e e ical ones (blue aces) esul in la ge R and S wa e ampli udes in leads V2 o V5. Figu es 6C,7C show ha hea s loca ed in mo e medial posi ions esul in alle R and S wa es in sep al V1 o V3 leads while sho e R wa es a e obse ed in he p eco dial la e al leads V5 and V6. This is due o he close en icula loca ion o V1 o V3 elec ode posi ions and u he om V5 and V6. On he o he hand, hea s loca ed in mo e la e al posi ions ( owa d he le -a m) displayed nega i ely de lec ed S o e en QS complexes in he sep al V1 o V2 leads and la ge R wa e ampli udes in V5 o V6 (blue solid lines). Figu es 6D,7D show he e ec o shi ing he en icles up along he c anio-caudal (supe io -in e io ) di ec ion leads o la ge R wa e ampli udes in lead I, and longe R and S wa es in V1 o V5 (blue lines). Howe e , shi ing he hea down leads o sho e R wa es in leads I, V1 and V6 (o ange line). The changes would be equi alen o changing he elec ode posi ion wi h espec o he en icles. Compa ison o Clinical Da a Simula ed ECGs ob ained om ou popula ion o models exhibi QRS axis (compu ed om QRS complexes in leads I and III) anging om 50◦ o 75◦[no mal ange –30◦ o 90◦as shown in Engblom e al. (2005)], QRS du a ions pe lead om 45 o 80 ms [no mal ange including all leads 78 ±8 ms as shown in an Oos e om e al. (2000)], and ampli udes om 0.5 o 3.5 mV [heal hy: 2 ±0.6 mV as shown in an Oos e om e al. (2000)]. F on ie s in Physiology | www. on ie sin.o g 7Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 8 Mincholé e al. Impac o Ana omy on ECG QRS Complex FIGURE 4 | E ec o o so-pose on QRS du a ion, and S and R wa e ampli ude. (A) Simula ed QRS complexes ob ained using he en icula model om Subjec 3 (H3) placed in he i e di e en o sos-poses. (B) QRS du a ion (le ), and S and R ampli udes (middle and igh , espec i ely) om simula ions using each o he i e hea s (H1 o H5) placed in he di e en o so-poses (T1 o T5). Thus, all hese quan i a i e measu emen s a e in ag eemen wi h clinical ECGs om heal hy subjec s ( an Oos e om e al., 2000;Engblom e al., 2005;S ewa e al., 2011), suppo ing he c edibili y o he simula ions. Figu e 8 shows a compa ison o he a iabili y exhibi ed in simula ed and clinical 12 lead ECG QRS complexes. Simula ed QRS complexes show a iabili y in e ms o mo phology, especially in he p eco dial leads. The no mal up igh (posi i e) QRS complexes in bo h, lead I and lead aVF, esul in a no mal QRS axis. Fu he mo e, simula ed QRS complexes show posi i e de lec ion wi h la ge, up igh R wa e in leads I, II, V4–V6 and a p edominan nega i e de lec ion wi h a la ge, deep S wa e in aVR, V1 and V2 (see Figu e 8A). This is in ag eemen wi h he h ee clinical eco dings shown in Figu e 8B. Lead III in simula ed ECGs shows biphasic QRS complexes wi h a nega i e de lec ion ollowed by a posi i e one as in he clinical eco ding o Subjec 1 (Figu e 8B). On he con a y, simula ed lead aVL shows biphasic QRS complex wi h i s a posi i e de lec ion ollowed by a nega i e one, as in clinical eco dings o Subjec s 1 and 3 (Figu e 8B). P eco dial QRS complexes show R wa e p og ession om V1 o V6, wi h an inc easing R wa e and a dec easing S wa e when mo ing om V1 o V6. This p og ession is obse ed in bo h simula ed (Figu e 8A) and clinical ECGs (Figu e 8B). QRS complexes in lead V1 show mo phological a iabili y om biphasic QRS complexes (posi i e-nega i e de lec ions) o down igh QRS complexes (Figu e 8A). This is in ag eemen wi h he a iabili y in clinical eco dings (Figu e 8B). DISCUSSION The p esen s udy demons a es he compu a ional e alua ion o he e ec o hea - o so posi ion and ana omy on he QRS complex using human o so/bi en icula elec ophysiology models de i ed om clinically s anda d MRI. The i s con ibu ion o he s udy is he compu a ional pipeline o build he o so/bi en icula ana omies ini ia ing om s anda d clinical ca diac MRI augmen ed wi h a s a is ical shape model o he body (Zacu e al., 2017). This me hodology enables exploi ing clinical da abases o e alua e he unc ional impac o MRI-ex ac ed ana omical and s uc u al ea u es (Lyon e al., 2018b). Fu he mo e, human MRI-in o med modeling and simula ion based on his echnology could accele a e he de elopmen o ailo ed pha macological and elec ical he apy F on ie s in Physiology | www. on ie sin.o g 8Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 9 Mincholé e al. Impac o Ana omy on ECG QRS Complex FIGURE 5 | (A) Simila i y measu emen (PC∗) o he simula ed QRS mo phologies o ixed en icula geome y (and a ying o so-pose) (blue), and o ixed o so-pose (and a ying en icula geome y (g ay). Panels (B,C) Simula ed QRS mo phologies ob ained wi h he i e en icula geome ies (H1 o H5) placed in he i e o so-poses (T1 o T5) o leads aVL (B) and V1 (C). and he goal o p ecision ca e. Fi s ly, being able o econs uc he pa ien ’s speci ic o so and en icula model om s anda d ca diac MRI is a s ep o wa d o pe sonalized compu e modeling and simula ion. The human models cons uc ed ha e he biophysical de ail equi ed o enable u u e simula ion s udies in o he esponse o disease and pha macological ea men . Addi ionally, he simula ion esul s demons a e he in luence o ana omical ea u es on he QRS complex in heal hy con ol condi ions. This quan i ica ion o no mal QRS complex a iabili y is impo an o in o m he e alua ion o esponse o disease and ea men . Analysis o he simula ed QRSs yields he ollowing indings: (i) QRS mo phologies in limb leads I and II a e mainly de e mined by he geome y o he en icles whe eas QRS mo phologies in he p eco dial leads, and especially V1 o V4, a e de e mined by he o so-pose. (ii) QRS du a ion is mainly in luenced by myoca dial olume while i is ha dly a ec ed by he o so geome y o hea posi ion; (iii) QRS ampli ude inc eases wi h la ge en icula olumes and dec eases wi h la ge o so olumes. Quan i ica ion o he con ibu ion o he indi idual hea s uc u e, o ien a ion and body habi us on he ECG is c i ical o aid he clinical in e p e a ion o po en ial ECG abno mali ies d i en by disease o pha macological ea men . In syne gy wi h clinical da abases, hey could also d i e he pe sonaliza ion o sco e me ics o isk s a i ica ion by disc imina ing in clinical eco dings be ween he con ibu ion o each pa ien ’s speci ic ana omy and hose a ising om hei disease s a e. Popula ions o Hea -To so Elec ophysiological Models F om S anda d Clinical MRI In his pape , we p esen mul iscale elec ophysiological simula ions using hea - o so ana omical models om s anda d ca diac MRI acquisi ions (Figu e 1). The gene a ion o he subjec -speci ic geome ies is pe o med om s anda d ca diac MRI acquisi ions allowing o be used di ec ly on a ailable clinical da ase s. The sca ce in o ma ion o o so ana omy om s anda d ca diac MRI acquisi ions makes he use o adi ional F on ie s in Physiology | www. on ie sin.o g 9Augus 2019 | Volume 10 | A icle 1103 phys-10-01103 Augus 24, 2019 Time: 16:24 # 16 Mincholé e al. Impac o Ana omy on ECG QRS Complex Villa d, B., Zacu , E., Dall’A mellina, E., and G au, V. (2017). “Co ec ion o slice misalignmen in mul i-b ea h-hold ca diac MRI scans,” in P oceedings o he STACOM 2016: S a is ical A lases and Compu a ional Models o he Hea . Imaging and Modelling Challenges (Lec u e No es in Compu e Science). In e na ional Wo kshop on S a is ical A lases and Compu a ional Models o he Hea , (A hens: Sp inge ), doi: 10.1007/978-3-319-52718-5-4 Wallman, M., Smi h, N. P., and Rod iguez, B. (2014). Compu a ional me hods o educe unce ain y in he es ima ion o ca diac conduc ion p ope ies om elec oana omical eco dings. Med. Image Anal. 18, 228–240. doi: 10.1016/j. media.2013.10.006 Zacu , E., Minchole, A., Villa d, B., Ca apella, V., A iga, R., Rod iguez, B., e al. (2017). “MRI-based hea and o so pe sonaliza ion o compu e modeling and simula ion o ca diac elec ophysiology,” in P oceedings o he Imaging o Pa ien -Cus omized Simula ions and Sys ems o Poin -o -Ca e Ul asound Lec u e No es in Compu e Science, (Cham: Sp inge ), 61–70. doi: 10.1007/978- 3-319-67552-7-8 Zemzemi, N., Be nabeu, M. O., Saiz, J., Coope , J., Pa hmana han, P., Mi ams, G. R., e al. (2013). Compu a ional assessmen o d ug-induced e ec s on he elec oca diog am: om ion channel o body su ace po en ials. B . J. Pha macol. 168, 718–733. doi: 10.1111/j.1476-5381.2012.02200.x Zemzemi, N., and Rod iguez, B. (2015). E ec s o L- ype calcium channel and human e he -a-go-go ela ed gene blocke s on he elec ical ac i i y o he human hea : a simula ion s udy. Eu opace 17, 326–333. doi: 10.1093/eu opace/ euu122 Con lic o In e es S a emen : The au ho s decla e ha he esea ch was conduc ed in he absence o any comme cial o inancial ela ionships ha could be cons ued as a po en ial con lic o in e es . Copy igh © 2019 Mincholé, Zacu , A iga, G au and Rod iguez. This is an open- access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (CC BY). The use, dis ibu ion o ep oduc ion in o he o ums is pe mi ed, p o ided he o iginal au ho (s) and he copy igh owne (s) a e c edi ed and ha he o iginal publica ion in his jou nal is ci ed, in acco dance wi h accep ed academic p ac ice. No use, dis ibu ion o ep oduc ion is pe mi ed which does no comply wi h hese e ms. 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