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We propose hybrid automata (HA) as a unifying framework for computational models of excitable cells. HA, which combine discrete transition graphs with continuous dynamics, can be naturally used to obtain a piecewise, possibly linear, approximation of a nonlinear excitable-cell model. We first show how HA can be used to efficiently capture the action-potential morphology--as well as reproduce typical excitable-cell characteristics such as refractoriness and restitution--of the dynamic Luo-Rudy model of a guinea-pig ventricular myocyte. We then recast two well-known computational models, Biktashev's and Fenton-Karma, as HA without any loss of expressiveness. Given that HA possess an intuitive graphical representation and are supported by a rich mathematical theory and numerous analysis tools, we argue that they are well positioned as a computational model for biological processes.

We introduce cycle-linear hybrid automata (CLHA) and show how they can be used to efficiently model dynamical systems that exhibit nonlinear, pseudo-periodic behavior. CLHA are based on the observation that such systems cycle through a fixed set of operating modes, although the dynamics and duration of each cycle may depend on certain computational aspects of past cycles. CLHA are constructed around these modes such that the per-cycle, per-mode dynamics are given by a time-invariant linear system of equations; the parameters of the system are dependent on a deformation coefficient computed at the beginning of each cycle as a function of memory units. Viewed over time, CLHA generate a very intuitive, linear approximation of the entire phase space of the original, nonlinear system. We show how CLHA can be used to efficiently model the action potential of various types of excitable cells and their adaptation to pacing frequency.

We present an efficient, event-driven simulation framework for large-scale networks of excitable hybrid automata (EHA), a particular kind of hybrid automata that we use to model excitable cells. A key aspect of EHA is that they possess protected modes of operation in which they are non-responsive to external inputs. In such modes, our approach takes advantage of the analytical solution of the modes' linear differential equations to eliminate all integration steps, and therefore to dramatically reduce the amount of computation required. We first present a simple simulation framework for EHA based on a time-step integration method that follows naturally from our EHA models. We then present our event-driven simulation framework, where each cell has an associated event specifying both the type of processing next required for the cell and a time at which the processing must occur. A priority queue, specifically designed to reduce queueing overhead, maintains the correct ordering among events. This approach allows us to avoid handling certain cells for extended periods of time. Through a mode-by-mode case analysis, we demonstrate that our event-driven simulation procedure is at least as accurate as the time-step one. As experimental validation of the efficacy of the event-driven approach, we demonstrate a five-fold improvement in the simulation time required to produce spiral waves in a 400-x-400 cell array.

Background: Previous studies that have examined genetic influences on suicidal behaviour were confounded by genetic vulnerability for psychiatric risk factors. The present study examines genetic influences on suicidality (i.e. suicidal ideation and/or suicide attempt) after controlling for the inheritance of psychiatric disorders., Methods: Sociodemographics, combat exposure, lifetime DSM-III-R major depression, bipolar disorder, childhood conduct disorder, adult antisocial personality disorder, panic disorder, post-traumatic stress disorder, drug dependence, alcohol dependence and lifetime suicidal ideation and attempt were assessed in 3372 twin pairs from the Vietnam Era Twin Registry who were assessed in 1987 and 1992. Genetic risk factors for suicidality were examined in a multinomial logistic regression model. Additive genetic, shared environmental and non-shared environmental effects on suicidality were estimated using structural equation modelling, controlling for other risk factors., Results: The prevalence of suicidal ideation and suicide attempt were 16.1% and 2.4% respectively. In a multinomial regression model, co-twin's suicidality, being white, unemployment, being other than married, medium combat exposure and psychiatric disorders were significant predictors for suicidal ideation. Co-twin's suicidality, unemployment, marital disruption, low education attainment and psychiatric disorders (except childhood conduct disorder) were significant predictors for suicide attempt. Model-fitting suggested that suicidal ideation was influenced by additive genetic (36%) and non-shared environmental (64%) effects, while suicide attempt was affected by additive genetic (17%), shared environmental (19%) and non-shared environmental (64%) effects., Conclusions: There may be a genetic susceptibility specific to both suicidal ideation and suicide attempt in men, which is not explained by the inheritance of common psychiatric disorders.