From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales

BY GERNOT PLANK 1 2 LUFANG ZHOU 0 3 JOSEPH L. GREENSTEIN 1 3 SONIA CORTASSA 0 3 RAIMOND L. WINSLOW 1 3 BRIAN O'ROURKE 0 NATALIA A. TRAYANOVA 1 3 0 Institute of Molecular Cardiobiology, Johns Hopkins School of Medicine 1 Institute for Computational Medicine, Johns Hopkins University , Baltimore, MD 21218 , USA 2 Institute of Biophysics, Medical University Graz , 8010 Graz , Austria 3 Department of Biomedical Engineering, Johns Hopkins University , Baltimore, MD 21205 , USA Computer simulations of electrical behaviour in the whole ventricles have become commonplace during the last few years. The goals of this article are (i) to review the techniques that are currently employed to model cardiac electrical activity in the heart, discussing the strengths and weaknesses of the various approaches, and (ii) to implement a novel modelling approach, based on physiological reasoning, that lifts some of the restrictions imposed by current state-of-the-art ionic models. To illustrate the latter approach, the present study uses a recently developed ionic model of the ventricular myocyte that incorporates an excitation-contraction coupling and mitochondrial energetics model. A paradigm to bridge the vastly disparate spatial and temporal scales, from subcellular processes to the entire organ, and from submicroseconds to minutes, is presented. Achieving sufficient computational efficiency is the key to success in the quest to develop multiscale realistic models that are expected to lead to better understanding of the mechanisms of arrhythmia induction following failure at the organelle level, and ultimately to the development of novel therapeutic applications. * Author and address for correspondence: 216 CSEB, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA (). One contribution of 11 to a Theme Issue 'The virtual physiological human: building a framework for computational biomedicine II'. 1. Introduction Computer simulations of electrical behaviour in the whole ventricles ( Xie et al. 2004; Rodriguez et al. 2005; Potse et al. 2006; Ten Tusscher et al. 2007; Ashihara et al. 2008) or atria (Harrild & Henriquez 2000; Vigmond et al. 2001; Virag et al. 2002; Seemann et al. 2006) have become commonplace during the last few years. However, even when powerful state-of-the-art computational resources are used, attempts to integrate behaviour from the protein scale of ion channels to the organ scale of cardiac arrhythmias remain enormously challenging, and typically include significant trade-offs between representations of different types of complexities (subcellular processes versus structural complexities). To arrive at a computational efficiency in modelling the (patho)physiological processes in the heart, such that it permits the exploration of the parameter space of interest, the simplifications typically made are as follows. The geometry of the organ is represented in a stylized fashion (one heart geometry fits all approach; Xie et al. 2004; Rodriguez et al. 2005; Ashihara et al. 2008); only parts of the heart are modelled, such as slices across the ventricles (Meunier et al. 2002; Trayanova & Eason 2002; Hillebrenner et al. 2004) or wedges (Burton et al. 2006; Plank et al. 2008); and idealized geometries, such as myocardial slabs ( Vigmond & Leon 1999; Cherry et al. 2003; Plank et al. 2005), sheets (Beaumont et al. 1998; Skouibine et al. 1999; Anderson & Trayanova 2001; Samie et al. 2001; Kneller et al. 2002; Weiss et al. 2005) or strands ( Thomas et al. 2003; Qu et al. 2006), are used. In constraining the degrees of freedom, the choice of the computational mesh discretization often leads to (i) under-representation of (to the degree of fully ignoring) the finer details of the cardiac anatomy, such as endocardial trabeculations or papillary muscles, and (ii) the necessity to adjust ad hoc the tissue conductivity tensors in order to avoid the artificial scaling of the wavelength, thus compensating for the dependence of conduction velocities on grid granularity. That is, as the grid is coarsened with all other model parameters remaining unchanged, conduction velocity becomes reduced and thus the wavelength is diminished, with conduction block occurring above a certain spatial discretization limit. The myocardial mass is treated as a homogeneous continuum, without representing intramyocardial discontinuities such as vascularization, cleavage planes, or patches of fat or collagen. The specialized cardiac conduction system, i.e. the sinuatrial (SA) and atrioventricular (AV ) nodes and the Purkinje network, is typically not represented in the whole-organ simulations, although a few exceptions exist (Berenfeld & Jalife 1998; Vigmond & Clements 2007; Ten Tusscher & Panfilov 2008). Myocardial membrane ion transport kinetics are modelled in a simplified fashion (Rogers & McCulloch 1994; Ten Tusscher & Panfilov 2006a). Reduced models preserve salient features such as excitability, refractoriness, electrical restitution, etc.; these are usually represented phenomenologically at the scale of the cell (so that they can be easily manipulated). Such approaches have led to important insights into the mechanisms by which action potential characteristics control the stability of electrical propagation ( Weiss et al. 2006). Their limitation is, however, that phenomenologically represented parameters do not directly correspond to actual molecular structures or processes, and are thus incapable of accounting for many potentially arrhythmogenic mechanisms, such as propagation instabilities induced by instabilities in calcium cycling or by the altered metabolic state of the cell. Clearly, the ultimate goal of modelling is to accurately represent the interplay between the subsystems responsible for the primary functions of the heart, including the electrophysiological, Ca2C handling, contractile and energetic components. This necessitates a significant level of complexity of the cell models, often achieved by implementing highly nonlinear control systems. Moreover, the ability to use simulations to gain a better understanding of cardiac pathophysiology requires a representation of the bidirectional feedback loops connecting the various subsystems. This presents additional computational concerns with respect to the coupling of processes that span very different temporal and spatial scales, described by equations with varying numerical stiffness. A case in point is a recently described cell model, which combines mitochondrial bioenergetics with previously developed electrophysiological, Ca2C handling and contractile models, referred to as the excitationcontraction coupling and mitochondrial energetics (ECME) model (Cortassa et al. 2006). This cell model was developed as a framework for studying how the failure of the mitochondrial network of the cardiomyocyte can lead to action potential shortening or complete electrical inexcitability as a result of the depletion of the hi (...truncated)