Control of cardiac alternans in a mapping model with memory

Abstract

A generic feature of cardiac muscle is that the duration of an action potential depends on the long-term history of previous action potentials, known as cardiac 'memory'. Even though memory is known to be an important physiological response, there have only been limited studies of its effect on cardiac dynamics. Here, we investigate a map-based model of paced myocardium in the presence of closed-loop feedback control. The model relates the duration of an action potential to the preceding diastolic interval as well as the preceding action potential duration and thus has some degree of memory. We find that the range of parameters over which control is effective can be enlarged or reduced by memory, a prediction that is independent of the specific functional form of the map. Our work suggests that modifying the degree of memory (e.g., pharmacological agents) with some form of feedback control may be an effective strategy for the maintenance of normal cardiac function.

The Interrelations among Stochastic Pacing, Stability, and Memory in the Heart

“…As reviewed in the introduction, previous works have shown, using both numerical and experimental models, interrelations between cardiac memory and cardiac electrical conduction stability (11,(15)(16)(17). Based on that notion, our work provides a theoretical mechanism for the antiarrhythmic effect of stochastic pacing found previously (7) by exploring the interrelations among stochastic pacing, stability, and memory in the heart.…”

“…Lemay et al (14) used stochastic pacing in an autoregressive moving average (ARMA) to predict alternans instability, showing that such modeling provides a superior predictive marker over standard APD restitution properties. Tolkacheva et al (15) and Fox et al (16) proposed that the standard analysis of the slope of the APDR curve does not provide an accurate prediction of stability and alternans propensity, ascribing this to the fact that the APDR curve does not sufficiently account for the APD history (i.e., cardiac memory). Using deterministic pacing, they suggested performing linearization around a fixed point of a nonlinear curve relating the APD to its history.…”

Restricted feedback control in discrete-time dynamical systems with memory

“…Variants of unrestricted TDAS have been previously analyzed in the context of controlling alternans; see, for example, [4,18,[20][21][22][23]. Regarding the application of TDAS to a restitution mapping, there is an important physiological consideration to take into account.…”

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization

“…We remark that assuming such a simple restitution relationship is done primarily for illustrative purposes, whereas it is known that cardiac cells exhibit memory with respect to the pacing history [31][32][33]. That is, A n+1 depends not only upon D n , but also on previous data such as A n and D n-1 .…”

“…Whereas such mappings can give a reasonable approximation of the dynamics, cardiac tissue is known to exhibit memory-that is, A n+1 depends not only upon D n , but also upon earlier APD and DI [31][32][33]. Fortunately, the ETDAS method can be applied even if a more sophisticated mapping model with memory is used.…”