Accurate Prediction of Alternans in Cardiac Cells Using Stochastic Pacing and Transfer Function Analysis

Abstract

Alternans of action potential duration (APD) is a well-known arrhythmogenic mechanism. Studies based on eigenmode analysis demonstrated that alternans occurs when the eigenvalue λ_alt of the alternant eigenmode is < −1, providing an exact marker in contrast to the APD restitution slope. However, no method has been designed to estimate λ_alt experimentally. We hypothesized that λ_alt can be obtained by pacing at cycle lengths (CLs) varying stochastically around a basic CL (BCL) and analyzing the transfer function between the time series of CLs and APDs. We expected that the pole of this transfer function closest to −1 corresponds to λ_alt. We tested this hypothesis using a canine ventricular cell model in which alternans can be caused by unstable dynamics of membrane potential or of Ca2+ cycling. Control values of λ_alt were obtained analytically as a function of BCL. Stochastic pacing protocols were simulated for different BCLs and the poles and zeros of the corresponding transfer functions were estimated by fitting an autoregressive-moving-average (ARMA) model describing APD as a function of previous APDs and CLs. In all model versions, the pole closest to −1 provided an accurate estimation of λ_alt and required the analysis of 30 successive APDs and CLs. During slow ramp decreases of BCL or slow changes of ion current conductances simulating drug application, small stochastic CL variations and ARMA model identification permitted to predict the onset of alternans by extrapolating the time course of the estimated λ_alt to −1. In conclusion, stochastic pacing combined with ARMA model identification represents a novel approach to accurately evaluate the propensity to alternans. This method does not make any assumptions about the ionic mechanism of alternans and should be applicable experimentally for any type of myocardial cell.