Jacobian-determinant method of identifying phase singularity during reentry

Abstract

Reentrant spiral waves (also called rotors) have been observed in the heart muscle during cardiac arrhythmias and are nowadays targeted by ablation therapy in order to cure certain heart rhythm disorders. Phase singularity (PS) is considered to represent the organizing center of the spiral wave and the spatiotemporal behavior of the spiral wave can be extensively quantified by tracking PS. Recent clinical studies suggested that ablating the tissue at PS locations may cure atrial fibrillation. However, for experimental data, typically only one state variable, i.e., the voltage, is recorded. Accordingly, the calculation of phase and the identification of PSs must be carried out by using one variable. Here, a Jacobian-determinant method using one variable in reconstructed state space is proposed and the advantages of the method are demonstrated.