Reprinted from PROCEEDINGS OF THE ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, New Orleans, Louisiana, November 4-7, 1988 Multicellular and Biodomain Systems I ANISOTROPIC 2-D MODEL OF ELECTRICAL PROPAGATION IN CARDIAC MUSCLE J. Mailen Kootsey and Jiashin Wu National Biomedical Simulation Resource Duke University Medical Center Durham, NC ABSTRACT The propagation of depolarization in cardiac muscle is known to be anisotropic in several characteristics: veloc- ity of propagation, waveform of depolarization, and safety factor. Previous models, both 1-D and 2-D, have been able to account for some, but not a ll of these anisotropies. A new 2-D model is described in th is paper, using a "b ri ck wall" form of staggered transverse int er ce llul ar connections suggested by the tissue struct ur e. This new propagation model accounts for all three kinds of anisotropic charac- teristics. INTRODUCTION The basis for understanding cardiac arrhythmias is a de- tailed knowledge of the mechanism of propagation of elec- tr ical activity in heart muscle. It is we ll known that elec- trical activity trave ls from cell to cell in the heart tissue through low resistance electrical connections located in the nexus or gap junction. Early concepts of uniform, wave- like spread of el ectrical act ivation in all directions have been challenged by data showing anisotropy in velocity, waveform, and safety factor (see [1] for a review). These anisotropies are associated with the elongated shape of individual cells; characteristics of propagation parallel to the long cell axis (longitudinal propagation, LP) contrast with characteristics of propagation perpendicular to the cell axis (transverse propagation, TP) .. Known anisotropic characteristics include: 1) prop agat ion velocity of depolarization (LP fas ter than TP); 2) the max- imum rate of of the transmembrane potential during depolarization V max and the peak amplitude (both high er in TP than in LP); 3) the time constant of the fo ot of the action potential Tf oot (smaller for TP than for LP ); 4) the "safety factor" or tendency of the propagation to con- tinue under adverse conditions such as premature st imuli (TP shows a higher safety factor than LP in older tis- sues, but n'ot in younger tissues [2]). While some of these differences are small, as a whole they have clinical sig- nificance because they are associated with reentr ant ar- rhythmias a nd nonuniform drug binding. Characteristics 2) through 4) are ' particularly puzzling because they are contrary to accepted "rules" for propagation , e.g. V max is us ua ll y thought to increase with propagation ve lo city. Previous models of propagation in one [3] or two dimen- sions [ 4] have been able to account for 1) above by in- creased coupling resistance in the transverse direction and for 2) by emphasizing the discreteness of the medium. However, models of this type do not account for 4) an d the predicted changes in T foot are opposite to the experimental observations. It has been shown that the observed charac- ter istics of TP can be obtained by reducing the membrane capacitan ce to one half the normal value [2], but this model has no known physical correlate in the tissue. FIGURE 1: Circuit diagram of a small portion of the 2-D anisotropic propaga- tion model. Horizontal "cables" repre- sent elong ated rows of cell s coupled errd- to-end at int ercalated di sks and vert i- cally at staggered intervals. In each "ca- ble" , the hori zontal row of resis tors rep- resents the intracellular condu ctor and the lower conductor represents the com- mon extracellul ar space. Th e actual mo- del contained 197 membran e patches in each row (50 cells) and 50 rows, a total of 25 00 cells or 9850 membrane patches. 0956--IEEE ENGINEERING IN MEDICINE & BIOLOGY SOCIETY 10TH ANNUAL INTERNATIONAL CONFERENCE CH2566-8/88/0000--0956 $1.00 © 1988 IEEE