Unstable eigenmodes are possible drivers for cardiac arrhythmias

Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics

Single channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.

Slow Calcium-Depolarization-Calcium waves may initiate fast local depolarization waves in ventricular tissue

Intercellular calcium waves in cardiac myocytes are a well-recognized, if incompletely understood, phenomenon. In a variety of preparations, investigators have reported multi-cellular calcium waves or triggered propagated contractions, but the mechanisms of propagation and pathological importance of these events remain unclear. Here, we review existing experimental data and present a computational approach to investigate the mechanisms of multi-cellular calcium wave propagation. Over the past 50 years, the standard modeling paradigm for excitable cardiac tissue has seen increasingly detailed models of the dynamics of individual cells coupled in tissue solely by intercellular and interstitial current flow. Although very successful, this modeling regime has been unable to capture two important phenomena: 1) the slow intercellular calcium waves observed experimentally, and 2) how intercellular calcium events resulting in delayed after depolarizations at the cellular level could overcome a source-sink mismatch to initiate depolarization waves in tissue. In this paper, we introduce a mathematical model with subcellular spatial resolution, in which we allow both inter- and intracellular current flow and calcium diffusion. In simulations of coupled cells employing this model, we observe: a) slow inter-cellular calcium waves propagating at about 0.1 mm/s, b) faster Calcium-Depolarization-Calcium (CDC) waves, traveling at about 1 mm/s, and c) CDC-waves that can set off fast depolarization-waves (50 cm/s) in tissue with varying gap-junction conductivity.