Memory-induced nonlinear dynamics of excitation in cardiac diseases

Abstract

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.

Bifurcations Caused by Feedback between Voltage and Intracellular Ion Concentrations in Ventricular Myocytes

“…A key step is to define the function g in Eq.2. As shown in our previous study [22], when [Na + ] i is clamped at a constant, g is a sole function of c n , and thus is one-dimensional. However, here g is a two-dimensional function depending on both c n and s n , which becomes nontrivial to be defined.…”

“…The rationale for choosing linear iterated map equations for c n and s n is as follows: for a fixed T, after a sudden shortening of APD, the ion concentration decays exponentially toward a new steady state [22]. Based on our simulations, the steady state concentrations increase with APD but decrease with T. We have the following equations for c and s: c = c 1 (T )a n + c 0 = 0.2 T + 2.1 a n + c 0 (6) s = s 1 (T )a n + s 0 = 0.03 T + 2.8 a n + s 0…”

Short-Long Heart Rate Variation Increases Dispersion of Action Potential Duration in Long QT Type 2 Transgenic Rabbit Model

“…Due to its relatively rapid turnover of expression, it has been linked to pacing-induced T-wave memory 55,56 . I to has been also implicated in the genesis of APD alternans 57 and EAD-induced complex APD instability through its modulation of short-term cardiac memory 58 . In our current stimulation protocol with short-long CLs, the short CL n−2 can accelerate inactivation of I to and the long CL n−1 can provide the sufficient time to recover from the inactivation, which exposes the largest impact of I to heterogeneity on APD and may increase APD dispersion.…”

Control of voltage-driven instabilities in cardiac myocytes with memory

“…In both cases, the steep APD response combined with the memory effect results in complex APD dynamics, which are purely voltagedriven instabilities. 45,46 We show that under normal conditions in which the memory effect is minimal, all three controlling methods can effectively stabilize instabilities caused by steep APD restitution. However, under diseased conditions, constant-DI pacing control is the least effective controlling algorithm, almost completely failing to stabilize the APD.…”

“…As shown in a study by Sun et al, 44 the presence of memory drives alternans and more complex behaviors in AV nodal conduction. Our recent studies 45,46 showed that the steep dependence can indeed exist under certain diseased conditions, i.e., the all-or-none behaviors caused by the diseases result in steep APD dependence on the memory variables, which causes complex APD dynamics.…”