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Ectopic heartbeats can trigger reentrant arrhythmias, leading to ventricular fibrillation and sudden cardiac death. Such events have been attributed to perturbed Ca2+ handling in cardiac myocytes leading to spontaneous Ca2+ release and delayed afterdepolarizations (DADs). However, the ways in which perturbation of specific molecular mechanisms alters the probability of ectopic beats is not understood. We present a multiscale model of cardiac tissue incorporating a biophysically detailed three-dimensional model of the ventricular myocyte. This model reproduces realistic Ca2+ waves and DADs driven by stochastic Ca2+ release channel (RyR) gating and is used to study mechanisms of DAD variability. In agreement with previous experimental and modeling studies, key factors influencing the distribution of DAD amplitude and timing include cytosolic and sarcoplasmic reticulum Ca2+ concentrations, inwardly rectifying potassium current (IK1) density, and gap junction conductance. The cardiac tissue model is used to investigate how random RyR gating gives rise to probabilistic triggered activity in a one-dimensional myocyte tissue model. A novel spatial-average filtering method for estimating the probability of extreme (i.e. rare, high-amplitude) stochastic events from a limited set of spontaneous Ca2+ release profiles is presented. These events occur when randomly organized clusters of cells exhibit synchronized, high amplitude Ca2+ release flux. It is shown how reduced IK1 density and gap junction coupling, as observed in heart failure, increase the probability of extreme DADs by multiple orders of magnitude. This method enables prediction of arrhythmia likelihood and its modulation by alterations of other cellular mechanisms.

Modeling of the heart ventricles is one of the most challenging tasks in soft tissue mechanics because cardiac tissue is a strongly anisotropic incompressible material with an active component of stress. In most current approaches with active force, the number of degrees of freedom (DOF) is limited by the direct method of solution of linear systems of equations. We develop a new approach for high-resolution heart models with large numbers of DOF by: (1) developing a hex-dominant finite element mixed formulation and (2) developing a Krylov subspace iterative method that is able to solve the system of linearized equations for saddle-point problems with active stress. In our approach, passive cardiac tissue is modeled as a hyperelastic, incompressible material with orthotropic properties, and mixed pressure-displacement finite elements are used to enforce incompressibility. Active stress is generated by a model with force dependence on length and velocity of muscle shortening. The ventricles are coupled to a lumped circulatory model. For efficient solution of linear systems, we use Flexible GMRES with a nonlinear preconditioner based on block matrix decomposition involving the Schur complement. Three methods for approximating the inverse of the Schur complement are evaluated: inverse of the pressure mass matrix; least squares commutators; and sparse approximate inverse. The sub-matrix corresponding to the displacement variables is preconditioned by a V-cycle of hybrid geometric-algebraic multigrid followed by correction with several iterations of GMRES preconditioned by sparse approximate inverse. The overall solver is demonstrated on a high-resolution two ventricle mesh based on a human anatomy with roughly 130 K elements and 1.7 M displacement DOF. Effectiveness of the numerical method for active contraction is shown. To the best of our knowledge, this solver is the first to efficiently model ventricular contraction using an iterative linear solver for the mesh size demonstrated and therefore opens the possibility for future very high-resolution models. In addition, several relatively simple benchmark problems are designed for a verification exercise to show that the solver is functioning properly and correctly solves the underlying mathematical model. Here, the output of the newly designed solver is compared to that of the mechanics component of Chaste ('Cancer, Heart and Soft Tissue Environment'). These benchmark tests may be used by other researchers to verify their newly developed methods and codes.

We have developed the capability to rapidly simulate cardiac electrophysiological phenomena in a human heart discretised at a resolution comparable with the length of a cardiac myocyte. Previous scientific investigation has generally invoked simplified geometries or coarse-resolution hearts, with simulation duration limited to 10s of heartbeats. Using state-of-the-art high-performance computing techniques coupled with one of the most powerful computers available (the 20 PFlop/s IBM BlueGene/Q at Lawrence Livermore National Laboratory), high-resolution simulation of the human heart can now be carried out over 1200 times faster compared with published results in the field. We demonstrate the utility of this capability by simulating, for the first time, the formation of transmural re-entrant waves in a 3D human heart. Such wave patterns are thought to underlie Torsades de Pointes, an arrhythmia that indicates a high risk of sudden cardiac death. Our new simulation capability has the potential to impact a multitude of applications in medicine, pharmaceuticals and implantable devices.

Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.

One of the most important components of mechanoelectric coupling is stretch-activated channels, sarcolemmal channels that open upon mechanical stimuli. Uncovering the mechanisms by which stretch-activated channels contribute to ventricular arrhythmogenesis under a variety of pathologic conditions is hampered by the lack of experimental methodologies that can record the 3-dimensional electromechanical activity simultaneously at high spatiotemporal resolution. Computer modeling provides such an opportunity. The goal of this review is to illustrate the utility of sophisticated, physiologically realistic, whole heart computer simulations in determining the role of mechanoelectric coupling in ventricular arrhythmogenesis. We first present the various ways by which stretch-activated channels have been modeled and demonstrate how these channels affect cardiac electrophysiologic properties. Next, we use an electrophysiologic model of the rabbit ventricles to understand how so-called commotio cordis, the mechanical impact to the precordial region of the heart, can initiate ventricular tachycardia via the recruitment of stretch-activated channels. Using the same model, we also provide mechanistic insight into the termination of arrhythmias by precordial thump under normal and globally ischemic conditions. Lastly, we use a novel anatomically realistic dynamic 3-dimensional coupled electromechanical model of the rabbit ventricles to gain insight into the role of electromechanical dysfunction in arrhythmogenesis during acute regional ischemia., (Copyright © 2010 Elsevier Inc. All rights reserved.)