BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH
Impac o he Pa ien To so Model on he Solu ion
o he In e se P oblem o Elec oca diog aphy
Milan TYSLER, Jana LENKOVA, Jana SVEHLIKOVA
Ins i u e o Measu emen Science, Slo ak Academy o Sciences, Dub a ska ces a 9, 841 04 B a isla a,
Slo ak Republic
ysle @sa ba.sk, ume macu@sa ba.sk, ume s [email p o ec ed]
Abs ac . Ca diac diagnos ics based on a solu ion o
he in e se p oblem o elec oca diog aphy o e s new
ools o isual assessmen o ca diac ischemia. The
accu acy o he in e se solu ion is in luenced by ideli y
o he pa ien o so model. As op imum, an indi id-
ual o so model wi h eal hea shape and posi ion ob-
ained om CT o MRI is desi able. Howe e , imag-
ing is no always a ailable in clinical p ac ice, hence
we in es iga ed, i a gene ic o so shape indi idually
adjus ed acco ding o pa ien ‘s ches dimensions, wi h
a simpli ied hea model placed o a e ical posi ion
ob ained om in e se localiza ion o he ea ly en ic-
ula ac i a ion can esul in an in e se solu ion close
o he esul ob ained wi h an accu a e o so model.
Simula ed in e se localiza ion o 18 ischemic lesions
o 9 subjec s showed ha he use o indi idually ad-
jus ed gene ic o so ins ead o eal o so shape led o
an accep able inc ease o he lesion localiza ion e o
om 0.7±0.7 cm o 1.1±0.7 cm when accu a e hea
model was used. Howe e , i simpli ied hea model
was used and placed in a e ical posi ion acco ding o
he V2 lead le el, he lesion localiza ion e o inc eased
o 3.5±0.9 cm. Mo ing he simpli ied hea model o
a posi ion es ima ed by he in e se solu ion dec eased
he e ical hea posi ioning e o om 1.6±2.3 cm o
0.2±1.2 cm bu wi hou adjus ing he hea shape and
o a ion he lesion localiza ion e o did no imp o e
and eached 3.7±1.0 cm.
Keywo ds
Indi idual o so shape model, in e se p ob-
lem o elec oca diog aphy, in e sely es ima ed
hea posi ion.
1. In oduc ion
Solu ion o he in e se p oblem o elec oca diog aphy
and opog aphical isualiza ion o an ca diac elec ical
gene a o is p omising ool o assessmen o a ious
ca diac diso de s including local ischemic lesions o a -
hy hmogenic subs a es. Fo an accu a e in e se so-
lu ion i is necessa y o ha e an indi idual o so model
wi h in e nal s uc u es ep esen ing a leas he main
elec ical inhomogenei ies, such as lungs and en icu-
la ca i ies illed wi h blood [1], [2]. Ano he impo an
issue discussed in he li e a u e is he la ge a iabili y
o he hea posi ion ha can a y by se e al cen ime-
e s, namely in he e ical di ec ion [3], [4]. Missing
in o ma ion on he exac hea posi ion can s ongly
in luence he esul o he in e se solu ion [5]. As op-
imum, he eal hea posi ion should be used in he
o so model a he han usually assumed posi ion el-
a i ely o ana omical landma ks, such as he ou h
in e cos al space.
To ob ain a ai h ul model o he pa ien o so, he
use o compu ed omog aphy (CT) o magne ic es-
onance imaging (MRI) echnique is p e e able. How-
e e , in clinical p ac ice hese echniques a e no always
a ailable o ca diac pa ien s. Hence i is desi able o
sea ch o he me hods how o c ea e enough accu a e
pa ien speci ic o so model wi hou he need o imag-
ing echniques.
In his simula ion s udy an app oach based on he
use o a gene ic model o he human o so con aining
simpli ied model o he en icula myoca dium was a -
emp ed. Using se e al an h opome ic measu es he
o so shape was adjus ed o ma ch wi h he o so o
an indi idual subjec . To es ima e he e ical hea
posi ion, measu ed ECG da a we e used o sol ing a
simpli ied in e se p oblem and inding he loca ion o
ea ly en icula ac i a ion ha was supposed in he
uppe pa o he sep um. The aim o he s udy was
o e i y whe he he use o he indi idually adjus ed
gene ic o so model and a simpli ied hea model placed
in he es ima ed e ical posi ion allow in e se solu ion
wi h su icien accu acy.
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2. Me hods and Ma e ial
2.1. Simula ion o Body Su ace
Po en ials
A simpli ied model o en icula myoca dium was used
o simula e no mal en icula ac i a ion and ac i a-
ion in en icles con aining single ischemic egion wi h
changed epola iza ion [8], [9]. The geome y o he
model was de ined using se e al ellipsoids and i s ol-
ume consis ed o 1×1×1 mm cubic elemen s. Each
model elemen was assigned ealis ically shaped ac ion
po en ial (AP) and he en icula ac i a ion p ocess
was simula ed by a cellula au oma on. In each ime
s ep o he ac i a ion, elemen a y dipole momen s we e
compu ed om he di e ences be ween APs o adjacen
model elemen s, hus he equi alen ca diac elec ical
gene a o was ep esen ed by a mul iple-dipole model.
Using he bounda y elemen me hod, body su ace po-
en ials (BSPs) p( )we e compu ed in poin s ep e-
sen ing elec ode posi ions on he su ace o an inho-
mogeneous o so model:
p( ) = A s( ),(1)
whe e s( )is a mul iple dipole sou ce in he en ic-
ula myoca dium model and ma ix A ep esen s he
in luence o he o so as an inhomogeneous olume con-
duc o .
F om he simula ed BSP maps he QRST in eg al
map (IM) iwas compu ed using he o mula
i=w
QRST
p( )d =w
QRST
A s( )d =Aw
QRST
s( )d =A s,(2)
whe e iis he ec o o in eg als o BSPs and s is an in-
eg al o mul iple dipole sou ce o he ca diac elec ical
ield.
To mimic he local epola iza ion changes in he is-
chemic lesions, 18 small a eas we e modeled in he en-
icula myoca dium, one a a ime. They we e o med
as sphe ical caps wi h a ying diame e and heigh , and
placed in 3 ypical egions supplied by he main co o-
na y a e ies: an e io - in he egion supplied by he
le descending a e y, pos e io – in he egion sup-
plied by he le ci cum lex a e y, and in e io - in he
egion supplied by he igh co ona y a e y. In each
egion, 3 endoca dial and 3 epica dial lesions o di e -
en sizes we e modeled. In he model elemen s wi hin
he ischemic lesions, he AP was sho ened by 20 % o
simula e he changed epola iza ion.
Fo each ischemic lesion he di e ence QRST in e-
g al map (DIM) ∆i was calcula ed by sub ac ing he
IM compu ed o he no mal ac i a ion om he IM
compu ed in he p esence o he pa icula lesion as
∆i =ii−in=Asi−Asn=A(si−sn) = A∆s,(3)
whe e iiand in ep esen he ec o s o QRST in e-
g als o BSPs in case o ischemia and du ing no mal
ac i a ion, ∆s ep esen s he di e ence be ween he in-
eg al mul iple dipole sou ce unde no mal condi ions
and du ing ischemia. The DIM hus ep esen s he
opog aphical changes in he su ace ca diac elec ical
ield due o he local ischemia.
2.2. In e se Localiza ion o an
Ischemic Lesion
To iden i y he ischemic lesion by an in e se solu ion,
equi alen in eg al gene a o ep esen ing he o iginal
mul iple dipole gene a o ∆s should be de e mined.
Because his in e se p oblem is gene ally ill-posed, ad-
di ional cons ain s a e needed o i s unique solu ion.
The cons ain used in his s udy was he assump-
ion ha he equi alen in eg al gene a o ep esen ing
he small ischemic a ea can be ep esen ed by a sin-
gle dipole. The magni ude, o ien a ion and posi ion o
he dipole can be sea ched as pa ame e s o a “mo ing
dipole”, wha yields a nonlinea p oblem. In his s udy
ano he app oach was used: only dipole magni ude and
o ien a ion we e de e mined o dipoles in p ede ined
possible posi ions. In his way he p oblem was con-
e ed o a linea one, howe e , he pa ame e s o an
equi alen in eg al dipole (EID) had o be compu ed
o many posi ions wi hin he en icula myoca dium
and hen he p ope posi ion had o be selec ed. To
achie e su icien esolu ion o he dipole localiza ion,
he mean dis ance be ween he neighbo ing possible
dipole posi ions less han 1 cm was selec ed. Fo e -
e y p ede ined posi ion j, he dipole momen djwas
compu ed as
dj=A+
j∆i,(4)
whe e A+
jis he pseudo-in e se o a subma ix Ajo
he ma ix A ha ep esen s he ela ion be ween he
EID placed in he posi ion jand he DIM. The equa-
ion (4) is o e de e mined and i s unique solu ion exis s
o each posi ion o he EID. To compu e he pseudo-
in e se, singula alue decomposi ion was applied o
he subma ix Aj.
To ind he bes ep esen a i e gene a o o he le-
sion, o each posi ion j he su ace map qiwas com-
pu ed using co esponding EID as he gene a o . This
map was compa ed wi h he inpu DIM using he el-
a i e oo mean squa e di e ence RMSDIFj:
RMSDIFj=sX
k
(qj,k −∆ik)2/sX
k
(∆ik)2,(5)
whe e kis he numbe o elec odes on he o so su -
ace. The EID in a posi ion ha p oduced he map
wi h smalles RMSDIFjwas selec ed as he bes ep-
esen a i e o he lesion.
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The dis ance be ween he selec ed EID posi ion and
he g a i y cen e o he simula ed lesion was de ined
as he lesion localiza ion e o (LE) and was used o
e alua e he accu acy o he in e se lesion localiza ion.
2.3. Ve ical Hea Posi ion
Es ima ion
F om he obse ed high a iabili y o he e ical hea
posi ion ela i ely o he ana omically ixed elec ode
posi ions (Fig. 1) i is appa en ha adjus men o he
e ical hea posi ion is highly desi able.
Fig. 1: Gene ic o so model (le ) and 3 examples o eal ches
models o subjec s used in he s udy. Do s indica e
elec ode posi ions, e ical posi ion o ECG lead V2
is ma ked by a ho izon al line.
In Fig. 1 he in e -indi idual a iabili y o he e -
ical dis ance be ween he hea posi ion and he le el
o ECG lead V2 de ined in he 4 h in e cos al space
is demons a ed. I he same gene ic o so and hea
model (Fig. 1 le ) is used o all subjec s, his e ical
dis ance is assumed o be ze o wha appa en ly may
no be co ec .
The possibili y o es ima e he indi idual e ical po-
si ion o he hea by in e se localiza ion o he ea ly
en icula ac i a ion was s udied using eal ECG sig-
nals measu ed in 9 subjec s (7 men, 2 women) pub-
lished in [3]. The ECG signals in each subjec we e
eco ded by 62 leads o he Ams e dam lead sys em.
Realis ic o so models, as well as he elec ode posi-
ions o hese subjec s, we e ob ained om MRI scans.
Fo each subjec ECG signals we e eco ded o 10 sec-
onds wi h a sampling a e o 1000 Hz. Low-pass il e
wi h 50 Hz s op-band was applied and he signals we e
ime a e aged o c ea e ep esen a i e signal o one
hea cycle in each lead [11]. Finally, he baseline o
a e aged signals was adjus ed by se ing he mean po-
en ial o he PQ in e al o ze o. The ime ins an
o he QRS onse was se manually om ms signal
compu ed om all measu ed leads.
The in eg al map (IM) o he i s 20 ms o he
en icula depola iza ion ( om he QRS onse ) was
compu ed o each subjec and used as he ep esen a-
i e o he ca diac elec ical gene a o du ing he ea ly
en icula ac i a ion ha no mally occu s in he up-
pe pa o he le endoca dial sep um [11].
Si e o he ini ial en icula depola iza ion was es i-
ma ed om he IM using he in e se solu ion in homo-
geneous o so model. Simila app oach as desc ibed
in sec ion 2.2. was applied. The egion ac i a ed
du ing he ea ly depola iza ion was assumed o be
small enough o be ep esen ed by single EID ha was
sea ched in he whole modeled en icula myoca dium
olume in p ede ined posi ions placed in egula 3 mm
g id. Fo each subjec he posi ion j o he ea ly ac-
i a ed a ea was de e mined as he si e in which he
RMSDIFj be ween he IM and he map gene a ed by
he EID was minimal. The hea model was hen e -
ically shi ed so ha he si e o he ea ly en icula
ac i a ion e ically coincided wi h he ana omically
de e mined a ea in he uppe pa o he le endo-
ca dial sep um. The e ical e o s be ween he eal
hea posi ion and he in e sely es ima ed hea posi-
ion, as well as he s anda d hea posi ion ( ep esen -
ing he si ua ion wi h no indi idual in o ma ion abou
he hea posi ion), we e hen e alua ed.
The desc ibed me hod o in e se es ima ion o he
e ical hea posi ion was used in his s udy o c e-
a e one ype o he indi idual o so models o each
subjec .
2.4. To so Models Used in he S udy
To so models o 9 heal hy subjec s in oduced in sec-
ion 2.3. ob ained om MRI scans and desc ibed
by iangula ed su aces o o so, lungs and en icu-
la myoca dium we e used in he s udy. The posi ions
o 62 ECG elec odes we e also included in he o so
models.
Modi ied Dalhousie o so [6] con aining he simpli-
ied en icula myoca dium model [8] desc ibed in sec-
ion 2.1. and placed in ana omically de ined s anda d
posi ion was used as he gene ic model o a human
o so.
Fig. 2: Indi idual adjus men o he simpli ied hea model ge-
ome y o he hea o a pa icula subjec ( on al
iew): 1 – subjec ’s hea geome y, 2 – simpli ied hea
model in s anda d posi ion, 3 – simpli ied hea model
o a ed along he long (A-S) and sho (L-R) axis and
scaled along he long axis o bes co espondence o he
subjec ’s hea geome y.
To ha e compa able hea ana omy o o wa d sim-
ula ions in all subjec s, he simpli ied en icula my-
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Fig. 3: Fou ypes o o so models used o each subjec in he s udy: A - o iginal o so model ob ained om MRI wi h a simpli ied
model o en icles placed, o a ed and scaled o co espond o he subjec ’s eal hea . B - gene ic o so model adjus ed
o bes ma ch wi h subjec ’s o so shape wi h he en icles as in case A. C – adjus ed gene ic o so shape as in case B
bu wi h a simpli ied model o en icles in s anda d posi ion, D – adjus ed gene ic o so shape as in cases B and C bu
wi h a simpli ied model o en icles e ically shi ed o a e ical posi ion based on he in e sely es ima ed si e o ea ly
en icula ac i a ion.
oca dium model desc ibed in sec ion 2.1. bu ad-
jus ed o he hea geome y o each subjec was used
(Fig. 2). Fo each subjec he long hea axis ( om
apex A o poin S in he sep um) and sho hea axis
( om poin L in he le en icula ee wall o poin
R in he igh en icula ee wall) we e de ined. Then
he simpli ied en icula model was posi ioned so ha
i s axes coincided wi h he axes in he hea o he eal
subjec and was p ope ly scaled along i s long axis.
Fo all 9 subjec s body su ace po en ial maps
(BSPMs) co esponding o no mal ac i a ion as well
as o ac i a ion in case o 18 modeled ischemic lesions
we e simula ed and single DIM was compu ed o each
case. Realis ic inhomogeneous o so models based on
subjec s’ MRI scans, con aining lungs and hea ca -
i ies illed wi h blood we e used in he simula ions.
Indi idually adjus ed simpli ied geome ical models o
he en icles desc ibed abo e we e inse ed in o each
o so. Respec i e elec ical conduc i i ies assigned o
he lungs and hea ca i ies we e 4 imes lowe and 3
imes highe han he a e age conduc i i y o he es
o he o so. The DIMs we e compu ed om 62 sim-
ula ed leads placed on he o so su ace acco ding he
Ams e dam lead sys em and used as inpu o he in-
e se solu ions.
To s udy he impac o he o so model shape and
hea posi ion on he nonin asi e in e se localiza ion
o ischemic lesions, se e al ypes o o so models we e
used in he in e se compu a ions (Fig. 3).
Model A – he same o so model as used in he o -
wa d simula ions. I consis s o ealis ic ou e
o so shape and elec ode posi ions based on MRI
scan, lungs, and indi idually adjus ed simpli ied
hea model ha was placed, o ien ed and scaled
o bes co espondence wi h he subjec ’s hea
model ob ained om MRI.
Model B – o so shape c ea ed om he gene ic o so
model by adjus ing i s shape acco ding o 10 an-
h opome ic measu es o he subjec (see Fig. 4)
as p oposed in [7]. The same indi idually adjus ed
simpli ied hea model as in o so model A was
used.
Model C – he same adjus ed gene ic o so shape
wi h elec odes as in model B bu wi h a gene ic
hea model placed and o ien ed in a s anda d way
– as i no knowledge abou he hea posi ion, o i-
en a ion and size was a ailable. The e ical posi-
ion o he hea model is in he le el o he s an-
da d ECG lead V2.
Model D – he same adjus ed gene ic o so shape
wi h elec odes as in models B and C bu wi h a
gene ic hea model e ically shi ed acco ding o
he esul o he in e se es ima ion o he e ical
hea posi ion.
Fig. 4: Selec ed 10 an h opome ic measu es o subjec -
speci ic adjus men o he gene ic o so shape.
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The e o s o he in e se localiza ion o all 18 mod-
eled lesions we e e alua ed o each o he 9 subjec s
and each ype o he o so model. The esul s o di -
e en o so model ypes we e compa ed.
3. Resul s
3.1. Ve ical Hea Posi ion
Es ima ion
The in e sely es ima ed si es o ea ly en icula depo-
la iza ion we e ound in he uppe sep al a ea o all
9 in es iga ed subjec s. Thei posi ions ( ans o med
o a single s anda d simpli ied en icula model) a e
depic ed in Fig. 5 oge he wi h hei mean posi ion
(la ge ma ke ) compu ed as he g a i y cen e o he
esul s o indi idual subjec s. The a e age spa ial dis-
ance be ween he indi idual posi ions o he ea ly de-
pola iza ion si es om hei mean posi ion was 1.6±0.6
cm and he s anda d de ia ion o he e ical posi ion
o esul s o indi idual subjec s was ±1.3 cm. These
numbe s indica e he possible e o ange when assum-
ing ha he ea ly ac i a ion si e should se e as a e e -
ence poin o adjus men o he e ical hea posi ion.
Fig. 5: The es ima ed si es o ea ly en icula depola iza ion
o 9 s udied subjec s (small ma ke s) and he g a i y
cen e o he posi ions (la ge ma ke ) depic ed in s an-
da d simpli ied en icula model.
While he a e age e ical e o ( o all 9 subjec s)
be ween he eal posi ion o he hea en icles and
posi ion o he s anda d en icula model (ma ked as
"s and. pos.") was 1.6±2.3 cm, he a e age e ical
e o be ween he eal posi ion o he en icles and
he posi ion o en icles es ima ed om he si e o
ea ly en icula ac i a ion (ma ked as "ea ly dep.")
d opped o 0.2±1.2 cm. The esul s o all 9 subjec s
a e shown in Fig. 6. These esul s indica e ha despi e
he ague de ini ion o he si e o he ea ly en icula
ac i a ion as a e e ence poin , i s in e se es ima ion
can imp o e he e ical posi ioning o he hea model
i no o he in o ma ion on he hea posi ion in he
o so is a ailable.
Fig. 6: E o s o e ical posi ion o he hea models o all
s udied subjec s: Diamonds – e o s be ween eal po-
si ions o en icles and posi ions es ima ed om he
ea ly en icula ac i a ion. Squa es - e o s be ween
eal posi ion o en icles and he posi ion o s anda d
simpli ied en icula model.
3.2. Impac o App oxima e To so
Shape on he In e se Solu ion
To s udy he impac o he use o an app oxima e o so
shape c ea ed by adjus ing a gene ic o so shape ac-
co ding 10 an h opome ic pa ame e s o he subjec ,
esul s o he in e se solu ions wi h o so models A and
B we e compa ed. As i can be seen in Fig. 7, he LE
alues ob ained wi h app oxima e o so model B ( om
0.6±0.4 cm o 1.6±1.1 cm) wi h he mean LE o all
subjec s o 1.1±0.7 cm we e only sligh ly wo se han
he LE alues ob ained wi h he o so model A c ea ed
om MRI scans ( om 0.5±0.3 cm o 0.8±0.9 cm) wi h
mean LE o all subjec s o 0.7±0.7 cm. In all subjec s,
he mean LE was sligh ly wo se when o so model B
was used, wi h he excep ion o subjec s7, whe e he
alues we e equal.
This esul sugges s ha he use o indi idually ad-
jus ed gene ic o so shape in he in e se solu ion can
be accep able i no imaging da a a e a ailable.
3.3. Impac o he Ve ical Hea
Posi ion Es ima ion on he
In e se Solu ion
To s udy he impac o he e ical posi ioning o he
hea model, esul s o he in e se lesion localiza ion
wi h o so models C and D we e e alua ed and com-
pa ed also wi h esul s wi h o so model B. In all hese
models indi idually adjus ed gene ic o so shape was
used. When he o so model C wi h he hea model
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Fig. 7: Mean e o s o he in e se lesion localiza ion compu ed
o all 18 modeled lesions in 9 s udied subjec s (s1–s9)
and using 4 o so and hea model con igu a ions (mod-
els A, B, C, D).
loca ed in s anda d e ical posi ion gi en by he le el
o ECG lead V2 was used in he in e se solu ion, he
mean LE alues a ied om 3.0±0.5 cm o 4.5±0.7
cm, wi h he mean LE o all subjec s o 3.5±0.9 cm.
Fo o so model D, whe e he hea model was e i-
cally mo ed o he in e sely es ima ed posi ion, he LE
alues anged om 2.8±1.2 cm o 4.6±0.5 cm, wi h a
no iceably lowe alue o 1.6±1.4 cm o he subjec s5.
The LE a e aged o all subjec s was 3.7±1.0 cm.
These esul s show, ha despi e he imp o ed e i-
cal posi ioning o he hea model in o so model D in
compa ison wi h o so model C, in all bu wo subjec s
(s5 and s7) he esul s wi h model D we e e en wo se
han hose wi h o so model C. Compa ison wi h much
be e esul s ob ained wi h o so model B indica es
ha me ely posi ioning o he hea model wi hou i s
p ope o a ion and scaling does no yield accep able
e o s o he in e se lesion localiza ion.
4. Discussion
The expe imen al in e se localiza ion o he ea ly en-
icula ac i a ion in 9 subjec s indica ed ha he si e
o he ini ial ac i a ion can be es ima ed wi hin abou
1.6±0.6 cm. In all s udied subjec s he ound posi ions
we e in ag eemen wi h Du e ’s indings [11] ha he
en icula ac i a ion in heal hy subjec s s a s in en-
doca dial a eas o he le en icula ca i y nea sep-
um. Al hough he achie ed a e age e o o he es i-
ma ed e ical posi ion was only 0.2 cm, i s s anda d
de ia ion o ±1.2 cm is qui e la ge and e o s o almos
2 cm we e ound in subjec s s6, s8 and s9 (Fig. 6). In
spi e o his, he me hod gene ally imp o ed he e i-
cal posi ioning o he hea model in compa ison wi h
he e o o 1.6±2.3 cm in a si ua ion when no in o -
ma ion on he hea posi ion was used and he en ic-
ula model was posi ioned wi h he use o ana omical
landma ks. The eason o he emaining inaccu acy o
he es ima ed e ical hea posi ion could be he indi-
idual a iabili y o he no mal en icula ac i a ion
sequence as well as neglec o o so inhomogenei ies in
he in e se compu a ions. Howe e , se ious limi a ion
o his me hod is he impe a i e o no mal ini ial en-
icula depola iza ion.
F om he esul s wi h he o so model B in he sec-
ond pa o he s udy i implies ha adjus men o a
gene ic o so shape acco ding o indi idual an h opo-
me ic measu es o he subjec and main aining eal
elec ode posi ions is a p omising way how o ob ain
subjec -speci ic o so geome y accu a e enough o he
in e se solu ion. Howe e , om he esul s ob ained
wi h o so models C and D he g ea impac o he
used hea model on p ecision o he in e se solu ion is
also appa en .
In he hi d pa o he s udy he me hod o indi id-
ual assessmen o he e ical hea posi ion using he
in e se localiza ion o ea ly en icula ac i a ion was
used in 9 subjec s o c ea e hei indi idual o so mod-
els (model D). F om he g aph o model D in Fig. 7
i is appa en ha he imp o emen o e ical posi-
ion o he hea , wi hou i s addi ional adjus men by
p ope o a ion and scaling did no dec ease he lesion
localiza ion e o in he in e se solu ion. Indi idual
posi ioning o he hea model in 3D space along all
h ee coo dina es based on he es ima ed si e o he
ea ly en icula ac i a ion was no used because i was
no always possible o i he hea model in he o so
wi hou addi ional hea scaling.
The impo ance o in o ma ion abou hea size and
o a ion sugges s he necessi y o some hea imaging
(e.g. USG, CT o MRI) e en i he whole o so imaging
is no a ailable. This issue should be s udied u he .
The limi a ion o he o wa d simula ions used in he
s udy was he simpli ied model o he hea ac i a ion
and ca diac elec ical gene a o . Howe e , i was su -
icien o demons a e he impo ance o indi idually
adjus ed o so and hea models used in he in e se
solu ion o each examined subjec .
The p incipal limi a ion o he p esen ed in e se
me hod is he need o BSPMs measu ed du ing he
ischemia (wi h changed epola iza ion phase o he my-
ocy es AP) and also in a si ua ion wi hou he ischemia
mani es a ion. Bo h measu emen s in he same subjec
a e necessa y o compu a ion o he DIM ha is used
as he inpu o he in e se solu ion. To ha e such da a
o a pa ien admi ed wi h acu e myoca dial in a c ion
would be ex emely di icul . Howe e , such da a can
be ob ained when ischemia is e oked in con olled con-
di ions, e.g. be o e and a e he exe cise s ess es
o by epea ed examina ions. Ano he possible appli-
ca ion o he in e se me hod could be in e ealing o
egions esponsible o ansien bea - o-bea changes
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in ECG, e.g. hose exp essed as changes o he non-
dipola i y index in in eg al BSPMs epo ed in [12].
5. Conclusion
F om he esul s ob ained in his s udy i is appa en
ha he use o a gene ic o so model wi h pa ien -
speci ically adjus ed o so shape and wi h elec ode
posi ions de ined in acco dance wi h hei eal place-
men allows accep able in e se localiza ion o pa ho-
logical ca diac e en s based on a dipole model o he
ca diac elec ic gene a o . Accu acy o he solu ion is
only sligh ly wo se han ha ob ained wi h indi idual
o so model c ea ed om MRI scans. Howe e , he use
o easonably accu a e hea model is s ill necessa y.
The use o in o ma ion om measu ed ECG signals
can imp o e he indi idual posi ioning o he hea
model in he o so in compa ison o he s anda d hea
posi ion based on he ECG lead V2 le el. Howe e , in
spi e o his esul , such in o ma ion wi hou p ope
o a ion and scaling o he hea model does no lead
o imp o ed accu acy o he in e se solu ion. Hence
some hea imaging allowing he c ea ion o a pa-
ien /speci ic hea model seems una oidable e en i
he whole o so imaging is no a ailable.
Acknowledgmen
The au ho s hank o D . Hoekema and p o . an
Oos e om o p o iding he measu ed ECG da a and
MRI based eal o so models used in his s udy.
The p esen s udy was suppo ed by he esea ch
g an 2/0131/13 om he VEGA G an Agency and
by he g an APVV-0513-10 om he Slo ak Resea ch
and De elopmen Agency.
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Abou Au ho s
Milan TYSLER was bo n in P ague, Czech Re-
public. He ecei ed his M.Sc. in Compu e Science
om Facul y o Elec ical Enginee ing, Slo ak Tech-
nical Uni e si y in B a isla a in 1974, Ph.D. deg ee
om he Ins i u e o Measu emen Theo y, Slo ak
Academy o Sciences in 1982 and became associa e
p o esso o Technical Uni e si y in Kosice in 2006.
His esea ch in e es s include biosignal p ocessing,
modeling o biological p ocesses o ien ed o he human
ca dio ascula sys em and de elopmen o in elligen
biomedical ins umen a ion.
Jana LENKOVA was bo n in P eso , Slo akia. She
ecei ed he M.Sc. in Biomedical Enginee ing om
Facul y o Elec ical Enginee ing, Uni e si y o Zilina
in 2009. Cu en ly she inished he Ph.D. s udy in he
Ins i u e o Measu emen Science, Slo ak Academy
o Sciences. He esea ch in e es s include ca diac
elec ical ield modeling and esea ch o he ole o
indi idual o so geome y in he o wa d and in e se
p oblem o elec oca diog aphy.
Jana SVEHLIKOVA was bo n in B a isla a,
Slo akia. She ecei ed he M.Sc. in Biocybe ne ics
om Facul y o Elec ical Enginee ing, Slo ak Tech-
nical Uni e si y in B a isla a in 1986 and he Ph.D.
deg ee om he Ins i u e o Measu emen Science,
Slo ak Academy o Sciences in 2011. He esea ch in-
e es s include modeling o he hea elec ical ac i i y,
o wa d and in e se p oblem o elec oca diog aphy
and eal- ime biosignal measu emen .
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