The electrical restitution of the non-propagated cardiac ventricular action potential

Sudden changes in pacing cycle length are frequently associated with repolarization abnormalities initiating cardiac arrhythmias, and physiologists have long been interested in measuring the likelihood of these events before their manifestation. A marker of repolarization stability has been found in the electrical restitution (ER), the response of the ventricular action potential duration to a pre- or post-mature stimulation, graphically represented by the so-called ER curve. According to the restitution hypothesis (ERH), the slope of this curve provides a quantitative discrimination between stable repolarization and proneness to arrhythmias. ER has been studied at the body surface, whole organ, and tissue level, and ERH has soon become a key reference point in theoretical, clinical, and pharmacological studies concerning arrhythmia development, and, despite criticisms, it is still widely adopted. The ionic mechanism of ER and cellular applications of ERH are covered in the present review. The main criticism on ERH concerns its dependence from the way ER is measured. Over the years, in fact, several different experimental protocols have been established to measure ER, which are also described in this article. In reviewing the state-of-the art on cardiac cellular ER, I have introduced a notation specifying protocols and graphical representations, with the aim of unifying a sometime confusing nomenclature, and providing a physiological tool, better defined in its scope and limitations, to meet the growing expectations of clinical and pharmacological research.

Complexity reduction in human atrial modeling using extended Kalman filter

Human atrial tissue electrophysiology is modeled upon biophysical details obtained from cellular level measurements. Data collected for this purpose typically represent a unique state of the tissue. As reproducing dynamic cases such as subject-varied and/or disorder-varied electrophysiological properties is in question, such complex models are typically hard to use. Hence, there is a need for simpler yet biophysically accurate and mathematically tractable models to be used for case-specific reproductions and simulations. In this study, a scheme for parameter estimation of a phenomenological cardiac model to match a targeted behavior generated from a complex model is used. Specifically, an algorithm incorporating extended Kalman filter (EKF) into the scheme is proposed. Its performance is then compared to that of particle swarm optimization (PSO) and sequential quadratic programming (SQP), algorithms that have been widely used for parameter optimization. Both robustness and adaptability performance of the algorithms are tested through various designs. For this, reproducing action potential (AP) waveforms of varying remodeling states of atrial fibrillation (AF) at different stimulus protocols was targeted. Also, randomly generated initial parameter sets are included in the tests. In addition, AP duration (APD) restitution curve (RC) is used for a multiscale evaluation of fitting performance. Finally, wavefront propagation on 2D of a selected AF remodeling state using parameter solutions from each of the algorithms is simulated for a qualitative evaluation. In general, PSO yielded superior performances than EKF and SQP with respect to fitting AP waveforms. Considering both AP and APD RC, however, EKF yielded the best accuracies. Also, more accurate spiral wave reentry is obtained with EKF. Overall, EKF algorithm yielded the best performance in robustness and adaptability. Graphical Abstract.