Figure 1

Propagation of a planar cardiac action potential (shaded gray) in the $x$-direction, with fibers at an angle $45°$ with respect to the $x$ axis. The sum of the intracellular and extracellular current densities ${\mathit{J}}_{\mathit{i}}+{\mathit{J}}_{\mathit{e}}$ is not, in general, zero; there is, in this case, a net current in the $y$ direction [18]. The intracellular and extracellular displacements, while in opposition, are not equal in magnitude; observe, however, that displacements are greatest at the site of maximum current density $\frac{x}{L}=0$, as we expect. Hydrostatic pressure is found to buildup within the region of the action potential and peak before, and not at, the boundary $\frac{x}{L}=1$. We label this buildup before the boundary $\Delta p$, which diminishes with increasing $K$. The dashed line indicates the intracellular pressure distribution with infinite stiffness; in this case $u_y=w_y=0$ and there is no displacement. Our estimate of $K$ is somewhat small to exaggerate the effects in the plot. Large $K$ make displacements and pressure buildup significantly smaller.Reuse & Permissions

Figure 2

Cardiac tissue with a boundary between an ischemic region (shaded gray) and a nonischemic region with fiber angle again $45°$. We assume a free boundary at infinity, allowing displacements to increase. Negative $x$ displacements are found to increase with distance from the ischemic boundary, suggestive of a situation where the fibers are trying to right themselves perpendicular to the ischemic boundary. The dotted line indicates displacements with infinite stiffness, which is not zero; instead, with infinite stiffness we find $u_y=w_y$ (not necessarily zero) and the tissue behaves like a monodomain. For an infinite stiffness, we observe the pressure is discontinuous across the boundary, while for a finite stiffness it is smoothly varying between these two values.Reuse & Permissions