The Bidomain Theory of Pacing

The implantable cardiac pacemaker is one of the most important medical innovations of the twentieth century.¹ Yet until recently researchers have not understood the basic mechanisms governing how a pacemaker excites the heart. The development of a mathematical model describing the electrical properties of cardiac tissue — the bidomain model — helped unravel these mechanisms. This chapter outlines several important predictions of the bidomain model related to pacing. Several other chapters in this book examine related topics.

The bidomain model^2,3 represents cardiac tissue as a multidimensional cable that can be represented by a network of resistors and capacitors. Figure 1 shows a network equivalent to the two-dimensional bidomain model. The lower grid of resistors represents the intracellular space, and the upper grid represents the extracellular space. The two spaces are coupled by resistors and capacitors representing the membrane. The electrical properties of cardiac muscle are markedly anisotropic; in Fig. 1 the resistors in the x direction may be different from the resistors in the y direction. Moreover, the degree of anisotropy differs within the intracellular and extracellular spaces. The ratio of conductivities in the x and y directions in the extracellular space is on the order of two, but in the intracellular space it is about ten, indicating the intracellular space is more anisotropic than the extracellular space.⁴ This condition of “unequal anisotropy ratios” leads to many of the interesting phenomena predicted by the bidomain model.⁵