Measurements of curvature in an ionic model of cardiac tissu

To quantify the effect of curvature on propagation in ventricular cardiac muscle we selected two cases of propagation where wavefronts of pronounced curvature were present: propagation through a narrow hole in an impermeable screen, and propagation after point-stimulation in a homogeneous medium. Those two situations were simulated in a computer model of a two-dimensional isotropic medium incorporating the Luo-Rudy equations to describe the ventricular muscle membrane. A planar wave initiated in the proximal side of the screen was diffracted at the hole creating a curved wavefront. Its propagation velocity beyond the hole first decreased and then increased as it propagated away from the hole. The minimum velocity of propagation was a function of the hole size. When the size of the hole was smaller than 175 μm, propagation through the hole was impossible. After point stimulation in a homogeneous medium a wavefront with a circular shape was initiated. The velocity of the propagating wave increased as the radius of the wavefront increased. To initiate a propagating wave, a circle with a diameter of 450 μm had to be activated. Considering the reciprocal of half the size of the hole as an estimation of the maximum curvature imposed by the hole, and the reciprocal of the radius of the wavefront as the curvature in the case of point-stimulation, in the two cases studied the propagation velocity decreased linearly with increasing curvature. Wavefronts whose curvature was higher than a critical value did not propagate. Therefore, in cardiac ventricular muscle, the curvature of the wavefront can be a cause of slow conduction and block.