Model-based Assessment of Local Ischemia - Criteria for Localization Credibility

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1 MEASUREMENT SCIENCE REVIEW, Volume 7, Secton, No. 6, 7 Model-based Assessment of Local Ischema - Crtera for Localzaton Credblty E. Hebláková, M. Turzová, J. Švehlíková, M. Tyšler Department of Bomeasurements, Insttute of Measurement Scences, SAS, Dúbravská cesta 9, Bratslava, Slovaka Emal: umerhebl@savba.sk Abstract. A method for nonnvasve dentfcaton of local schemc lesons from dfference ntegral (DI) maps, based on dpolar representaton of the leson, was prevously reported. Am of ths study was to fnd some crtera enablng to recognze DI maps representng large or multple schemc lesons when the dpole-based method s not sutable for schema localzaton and to estmate the level of nose n DI maps. One or two smultaneous schemc lesons wth dfferent szes and postons n the myocardum were modeled and correspondng DI maps were computed and contamnated by varous degree of random nose. Relatve dfference between square values of dpole and dpole-and-quadrupole resdual maps (shares of DI maps not represented by a dpole or dpole and quadrupole) was proposed to dentfy large or multple lesons whle mean square value of gradents n dpole resdual maps was proposed to estmate the nose level. Accordng to our smulatons, these crtera can help to estmate the credblty of the nonnvasve assessment of local schema. Keywords: body surface potental mappng, dpole model of cardac generator, nonnvasve assessment of schemc lesons The summaton was done over all mapped 1. Introducton Prevously we reported a model based nverse method for dentfcaton of local myocardal schema usng dfferences n QRST ntegral maps obtaned n condtons wth and wthout schema manfestaton. Equvalent dpole (ED) was used as a model ponts on the torso surface and the crteron was evaluated for all possble ED postons. Values of R D can be understood as values of a crteron functon wth a mnmum n poston of the best ED. DI maps of large or multple lesons or DI maps wth hgh level of nose cannot be properly represented by of the cardac generator representng sngle ED and R D s supposed to reach changes of myocytes repolarzaton n the schemc regon and dentfyng possble poston of the schema. Crteron for ts fndng was the mnmal relatve rms hgher values. Magntude of R D was therefore used as an ndcator of credblty of the localzaton. However, accordng to our smulaton experments, localzaton dfference R D between the orgnal error of the dpole ncreases substantally dfference ntegral (DI) map and map generated by the ED: wth growng extent of the schemc regon or when multple lesons are present whle t ( D O ) ncreases only slghtly wth bgger nose n (1) DI maps. Mean localzaton error for (1) all = R D O O values n orgnal DI map of the leson, D values n map computed from ED generator. schemc lesons from maps wthout nose was 11.1 mm and ncreased to 13.3 mm when large nose of 4 mv.ms (rms) was added. In contrary, for small subendocardal and subepcardal lesons, the mean localzaton error was 8.9 mm and ncreased 5

2 MEASUREMENT SCIENCE REVIEW, Volume 7, Secton, No. 6, 7 to 17.5 mm for large transmural lesons even f no nose was present n DI maps (Fg.1) []. m ean localzaton error [m m] small leson large leson no nose N1 N N3 N4 nose degree Fg. 1. Mean localzaton error for dfferent szes of schemc lesons and ts dependency on varous degree of nose present n correspondng DI maps. In ths study, possble crtera for dstngushng between these two cases were nvestgated to assess applcablty of the method for partcular data and to estmate the relablty of the schema assessment.. Subject and Methods Electrcal actvty of the heart, ncludng ts depolarzaton and repolarzaton phase durng one cardac cycle was smulated usng a model of cardac ventrcles wth analytcally defned geometry [1]. Ischemc lesons were modeled by shortenng of the normal acton potental duraton by % n three regons n heart ventrcles usually nfluenced by stenoss of man coronary arteres: 1) n antero-septal part of the left ventrcle near apex (anteror - A), ) n postero-lateral part of the left ventrcle close to the heart base (posteror - P) and 3) n md postero-septal part of the left and rght ventrcle (nferor-i). One epcardal and three endocardal lesons of dfferent szes (3-1% of the ventrcular volume) were created at each poston. To smulate multvascular damage, combnatons of two smultaneous endocardal lesons (A and P, P and I) were also modeled. In forward computatons [], body surface potentals correspondng to normal and pathologcal repolarzaton were computed n 19 torso surface leads of a 16 x 1 mappng grd. DI maps representng dfferences between normal QRST ntegral maps and QRST ntegral maps wth manfestaton of schema were calculated. Several levels of nose (1,, 3 or 4 mv.ms, rms) representng random nfluences due to dsturbances n the ECG sgnals (caused manly by baselne shfts), were added to DI maps. From smulated DI maps, correspondng ED source was nversely estmated for each vertex of the trangulated epcardal and endocardal surface [3]. Among them, best estmaton of the ED was selected usng the R D crteron (1). Two parameters were suggested to recognze whether the schemc regon s large (or fragmented) and the nverse method s not sutable for partcular case or whether the data are only contamnated wth hgher level of nose. The frst parameter representng some measure of nose n DI maps was the mean square value of gradent of resdual map MSG, the resdual map was defned as the dfference between a map generated by an ED and the orgnal DI map (.e. a resduum that the dpole was not able to represent): [ grad ( D O )] MSG = () m ( n 1 ) m, n numbers of columns and rows n the mappng grd, O values n orgnal DI map of the leson, D values n map computed from the best ED generator. Presumng that MSG represents local varatons n the map, t should be lttle dependent on the sze of the schemc leson and could help to dstngush cases R D reaches large values only because of nose 53

3 MEASUREMENT SCIENCE REVIEW, Volume 7, Secton, No. 6, 7 present n nput DI maps whle localzaton of the leson stll may be farly relable. To recognze large or multple lesons, multpolar representaton of the source ncludng equvalent dpole and quadrupole (EDQ) was used to comprse more complcated (but not random) character of the source representng the schemc leson. Value of relatve rms dfference R DQ between the orgnal DI map and map approxmated by an EDQ generator can be understood as a part of the DI map that EDQ s not able to represent, partcularly the nose. The dfference between R D and R DQ thus can represent some non-random component n DI map that s not generated by sngle dpole: ( D O ) ( DQ O ) (3) D R DQ = O QP = R O values n orgnal DI map of the leson, D values n map computed from ED generator, DQ values n map computed from ED plus quadrupole generator. Ths parameter was proposed to dentfy large or multple lesons and was expected to be farly nose ndependent. 3. Results The average values of MSG for all types and szes of lesons were., 5.76, 16.9, and 61.6 for data wth nose of, 1,, 3 and 4 mv.ms, respectvely (Fg.). MSG crteron acheved approxmately 3 tmes greater value for DI maps contamnated wth nose of 4 mv.ms than for smulated maps wthout any nose. The bgger was the nose, the better was the dfferentaton of partcular level of nose contamnaton. Bar graph n Fg. shows that MSG crteron was only slghtly senstve to the sze or complexty (multplcty) of schemc regons. 8 ( m V. m s. m ¹ ) ² A1 A A3 AE I1 I I3 IE P1 P P3 PE A1P1 P1I1 1 no nose N1 N N3 N4 nose level Fg.. MSG - mean square gradent of resdual maps (as a measure of nose) for all postons and types of lesons and for dfferent levels of nose. Leson poston: A anteror, I nferor, P posteror, leson types: E- epcardal, 1 small endocardal, medum endocardal, 3 large transmural, A1P1 and P1I1 multple small endocardal lesons. 54

4 MEASUREMENT SCIENCE REVIEW, Volume 7, Secton, No. 6, no nose N1 N N3 N A1 A A3 AE I1 I I3 IE P1 P P3 PE A1P1 P1I1 type of leson Fg. 3. QP parameter, averaged values for data wthout nose and wth dfferent levels of nose N1 N4, for all postons and types of lesons. Leson types and postons are the same as n Fg.1. Value of QP parameter (Fg.3) was bgger for double lesons A1-P1, P1-I1 and for large transmural lesons I3 and P3 than for other small and medum endocardal and epcardal lesons. Ths behavour dd not hold for the large anteror transmural leson A3 also the value of R DQ was hgh. However, n general, value of QP dd not sgnfcantly change wth vared value of the nose n DI maps. 4. Dscusson and Concluson Two crtera were proposed to estmate the credblty of the nverse soluton when dentfyng local schemc lesons: MSG crteron () and QP parameter (3). Choce of the MSG crteron was based on the assumpton that pattern of resdual map s more fragmented when nose s present and dfferences between map values n neghbourng ponts are bgger. Sgnfcant dfferentaton between maps wth varous level of nose confrmed ths expectaton. Hgh value of QP should reveal large or multple schemc sources assumng that contrbuton of hgher components of the multpole expanson of the real source (beng stll not random) was smaller than that of the random nose. Another presumpton to use the QP parameter was that large schemc regon should be represented mostly by dpole and quadrupole whle hgher components of the multpole expanson can be neglected. However, small value of QP parameter resultng from hgh values of R D and also R DQ ndcates that the feld generated by transmural A3 schemc regon was not suffcently approxmated even by equvalent dpole plus quadrupole and probably also hgher multpolar components were needed (Fg.4). Despte that, smulated DI maps of multple lesons were clearly dstngushed from small sngle lesons by the QP parameter. To sum up, the mean square gradent of resdual maps (MSG) exhbted low senstvty to the sze or complexty of the leson and seems to gve a good estmate of the nose n the nput data. The QP parameter was suggested to detect events the use of the method mght be napproprate, namely cases of large or multple schemc lesons n the myocardum. 55

5 MEASUREMENT SCIENCE REVIEW, Volume 7, Secton, No. 6, RD² RDQ² RD² - RDQ² AE IE PE A1 I1 P1 A I P A3 I3 P3 A1P1 P1I1 small medum large double type of leson Fg. 4. Average of RD and RDQ and ther dfference - QP parameter for lesons of dfferent types and szes. On smulated data, the appled crtera were helpful n dstngushng between cases of large or multple regons of changed repolarzaton propertes and cases wth hgh level of random dsturbances n DI maps. However, t was mportant to consder both parameters wth respect to each other. Ablty of the nverse method for dagnostc nterpretaton of body surface potental maps based on dpolar source model and beneft of the parameters proposed n ths study should be further verfed on real measurements. Acknowledgements Ths work was supported by grants /79/7 from the VEGA grant agency and APVV from the APVV agency. References [1] Szathmáry V., Osvald R.: An nteractve computer model of propagated actvaton wth analytcally defned geometry of ventrcles, Comput. Bomed. Res., 1998, 7, pp.7-38 [] Tyšler M., Turzová M., Švehlíková J., Hebláková E., Flpová S.: Nonnvasve detecton of schemc regons n the heart. IFMBE Proceedngs, vol. 11, 5, [3] Tňová M., Tyšler M., Turzová M., Švehlíková J.: Inverse localzaton of preexctaton stes usng "Jumpng dpole". In: Electrocardology '97, Proceedngs of the XXVth nternatonal congress on electrocardology. Eds.: Bacharova l., Macfarlane P.W., Sngapore, New Jersey, London, Hong Kong, World Scentfc,