Impact of the patient torso model on the solution of the inverse problem of electrocardiography

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. c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 58 BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH 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. c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 59 BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH 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- c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 60 BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH 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. c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 61 BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH 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 c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 62 BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH 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 c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 63 BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH 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. Re e ences [1] HUISKAMP, G. and A. VAN OOSTEROM. Tai- lo ed e sus ealis ic geome y in he in e se p oblem o elec oca diog aphy. IEEE T ansac- ions on Biomedical Enginee ing. 1989, ol. 36, iss. 8, pp. 827–35. ISSN 0018-9294. DOI: 10.1109/10.30808. [2] BRUDER, H., B. SCHOLZ and K. ABRAHAM- FUCHS. The in luence o inhomogeneous olume conduc o models on he ECG and he MCG. Physics in Medicine and Biology. 1994, ol. 39, iss. 11, pp. 1949–1968. ISSN 0031-9155. DOI: 10.1088/0031-9155/39/11/010. [3] HOEKEMA, R., G. J. UIJEN, L. VAN ERN- ING and A. VAN OOSTEROM. In e indi- idual a iabili y o mul ilead elec oca dio- g aphic eco dings: in luence o hea posi- ion. 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ISBN 80-8070-443-0. c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 64 BIOMEDICAL ENGINEERING VOLUME: 12 |NUMBER: 1 |2014 |MARCH [12] DURRER, D., R. T. VAN DAM, G. E. FREUD, M. J. JANSE, F. L. MEIJLER and R. C. ARZBAECHER. To al exci a ion o he iso- la ed human hea . Ci cula ion. 1970, ol. 41, iss. 6, pp. 899–912. ISSN 1941-3149. DOI: 10.1161/01.CIR.41.6.899. [13] METTINGVANRIJN, A. C., A. P. KUIPER, A. C. LINNENBANK and C. A. GRIMBER- GEN. Pa ien isola ion in mul ichannel bioelec ic eco dings by digi al ansmission h ough a sin- gle op ical ibe . IEEE T ansac ions on Biomedi- cal Enginee ing. 1993, ol. 40, iss 3, pp. 302–308. ISSN 0018-9294. DOI: 10.1109/10.216416. [14] KOZMANN, G., K. HARASZTI and I. PREDA. Bea - o-bea in e play o hea a e, en- icula depola iza ion, and epola iza ion. Jou nal o Elec oca diology. 2010, ol. 43, iss. 1, pp. 15–24. ISSN 0022-0736. DOI: 10.1016/j.jelec oca d.2009.08.003. 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 . c 2014 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 65