Theoretical evaluation of space constants of electrotronic decay in resistive anisotropic media: common equation

Abstract

Pateiktas elektrotoninio potencialo pasiskirstymo trimatėje dvisritėje anizotropinėje RC terpėje (miokarde) matematinis modelis, kai srovės šaltinis yra taško, apskritimo, disko ir cilindro formos. Naudojant superpozicijos principą srovės elektrodas yra aproksimuotas taškiniais šaltiniais, išdėstytais ant apskritimo formos elektrodo perimetro dviem būdais, taip, kad a) atstumai tarp taškinių šaltinių yra vienodi metrinėje koordinačių sistemoje; b) atstumai tarp taškinių šaltinių yra vienodi normalizuotoje koordinačių sistemoje. Disko ir cilindro formos srovės elektrodai yra aproksimuoti taškiniais šaltiniais, tolygiai išdėstytais jų paviršiuje. Various physiological and pathological effects may evoke changes in the electric excitation wave of the heart that can lead to disorders in the mechanical activities of the heart. It is known that the intercellular electrical communication in the working myocardium deteriorates under some pathological conditions or factors. However, due to complexity of the myocardium structure, direct measurement of the degree of deterioration of intercellular electrical coupling is not possible. Lately, intensive works have been pursued in modeling ECG [1], cardiac pacing [2-5], excitation wave spread in the myocardium tissue under normal and pathological conditions [6-8], repolarization processes [9]. In these tasks myocardium is treated as two-dimensional or threedimensional resistive-capacitive medium [10-11], electrotonic anisotropy being characteristic of the intracellular and intercellular areas. To solve the tasks, different experimentally obtained values of the parameters of the passive electric properties of myocardium are used (such as specific resistances of the intracellular medium, plasmic (electrogenic) membrane, membrane of intercellular contacts, space constants of electrotonic decay, time constants of the plasmic membrane). However, modeling makes sense only provided the used values of parameters are most precise. One of possibilities to find the parameters is by measuring experimental space constants of electrotonic decay ( λ xe , λ ye , λe ,) (i.e. the distance at which the amplitude of potential decreases by 2.71 times) and the distribution of electrotonic potential in the cardiac tissue close to the current delivering electrode, with further analysis of data by mathematical models of resistive (R) and resistive-capacitive (RC) media[...].