A model-independent technique for eigenvalue identification and its application in predicting cardiac alternans
Predicting cardiac alternans is a crucial step toward detection and prevention of ventricular fibrillation, a heart rhythm disorder that kills hundreds of thousands of people in the US each year. According to the theory of dynamical systems, cardiac alternans is mediated by a period-doubling bifurcation, which is associated with variations in a characteristic eigenvalue. Thus, knowing the eigenvalues would allow one to predict the onset of alternans. The existing criteria for alternans either adopt unrealistically simple assumptions and thus produce erroneous predictions or rely on complicated intrinsic functions, which are not possible to measure experimentally. In this work, we present a model-independent technique to estimate a system's eigenvalues without requirements on the knowledge of the underlying dynamic model. The method is based on principal components analysis of a pseudo-state space; therefore, it allows one to compute the dominant eigenvalues of a system using the time history of a single measurable variable, e.g. The transmembrane voltage or the intracellular calcium concentration in cardiac experiments. Numerical examples based on a cardiac model verify the accuracy of the method. Thus, the technique provides a promising tool for predicting alternans in real-time experiments.