Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, the wave-back velocity exhibits pronounced rate dependence and the wave-front velocity does not. Moreover, the discrepancy between wave-back velocity RCs is most significant for a small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wave-front and wave-back velocities. Our calculations show that rate-dependent wave-back velocity can be present even if neither APD nor wave-front velocity exhibits rate dependence.