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.
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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).
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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
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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
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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
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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
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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)].
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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
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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
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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
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