Makarand Deo

Towards predictive modelling of the electrophysiology of the heart

The simulation of cardiac electrical function is an example of a successful integrative multiscale modelling approach that is directly relevant to human disease. Today we stand at the threshold of a new era, in which anatomically detailed, tomographically reconstructed models are being developed that integrate from the ion channel to the electromechanical interactions in the intact heart. Such models hold high promise for interpretation of clinical and physiological measurements, for improving the basic understanding of the mechanisms of dysfunction in disease, such as arrhythmias, myocardial ischaemia and heart failure, and for the development and performance optimization of medical devices. The goal of this article is to present an overview of current state‐of‐art advances towards predictive computational modelling of the heart as developed recently by the authors of this article. We first outline the methodology for constructing electrophysiological models of the heart. We then provide three examples that demonstrate the use of these models, focusing specifically on the mechanisms for arrhythmogenesis and defibrillation in the heart. These include: (1) uncovering the role of ventricular structure in defibrillation; (2) examining the contribution of Purkinje fibres to the failure of the shock; and (3) using magnetic resonance imaging reconstructed heart models to investigate the re‐entrant circuits formed in the presence of an infarct scar.

Arrhythmogenesis by single ectopic beats originating in the Purkinje system

Cells in the Purkinje system (PS) are known to be more vulnerable than ventricular myocytes to secondary excitations during the action potential (AP) plateau or repolarization phases, known as early afterdepolarizations (EADs). Since myocytes have a lower intrinsic AP duration than the PS cells to which they are coupled, EADs occurring in distal branches of the PS are more likely to result in propagating ectopic beats. In this study, we use a computer model of the rabbit ventricles and PS to investigate the consequences of EADs occurring at different times and places in the cardiac conduction system. We quantify the role of tissue conductivity and excitability, as well as interaction with sinus excitation, in determining whether an EAD-induced ectopic beat will establish reentrant activity. We demonstrate how a single ectopic beat arising from an EAD in the distal PS can give rise to reentrant arrhythmia; in contrast, EADs in the proximal PS were unable to initiate reentry. Clinical studies have established the PS as a potential substrate for reentry, but the underlying mechanisms of these types of disorder are not well understood, nor are conditions leading to their development clearly defined; this work provides new insights into the role of the PS in such circumstances. Our findings indicate that simulated EADs in the distal PS can induce premature beats, which can lead to the tachycardias involving the conduction system due to interactions with sinus activity or impaired myocardial conduction velocity.

Arrhythmogenic mechanisms of the Purkinje system during electric shocks: A modeling study

BACKGROUND The function of the Purkinje system (PS) is to ensure fast and uniform activation of the heart. Although this vital role during sinus rhythm is well understood, this is not the case when shocks are applied to the heart, especially in the case of failed defibrillation. The PS activates differently from the myocardium, has different electrophysiological properties, and provides alternate propagation pathways; thus, there are many ways in which it can contribute to postshock behavior. OBJECTIVE The purpose of this study was to elucidate the role of the PS in the initiation and maintenance of postshock arrhythmias. METHODS A computer model of the ventricles including the PS was subjected to different reentry induction protocols. RESULTS The PS facilitated reentry induction at relatively weaker shocks. Disconnecting the PS from the ventricles during the postshock interval revealed that the PS helps stabilize early-stage reentry by providing focal breakthroughs. During later stages, the PS contributed to reentry by leading to higher frequency rotors. The PS also promoted wave front splitting during reentry due to electrotonic coupling, which prolongs action potential durations at PS-myocyte junctions. The presence of a PS results in the anchoring of reentrant activations that propagate through the pathways provided by the PS. CONCLUSIONS The PS is proarrhythmic in that it provides pathways that prolong activity, and it plays a supplementary role in maintaining the later stages of reentry (>800 ms).

Purkinje-mediated Effects in the Response of Quiescent Ventricles to Defibrillation Shocks

In normal cardiac function, orderly activation of the heart is facilitated by the Purkinje system (PS), a specialized network of fast-conducting fibers that lines the ventricles. Its role during ventricular defibrillation remains unelucidated. Physical characteristics of the PS make it a poor candidate for direct electrical observation using contemporary experimental techniques. This study uses a computer modeling approach to assess contributions by the PS to the response to electrical stimulation. Normal sinus rhythm was simulated and epicardial breakthrough sites were distributed in a manner consistent with experimental results. Defibrillation shocks of several strengths and orientations were applied to quiescent ventricles, with and without PS, and electrical activation was analyzed. All shocks induced local polarizations in PS branches parallel to the field, which led to the rapid spread of excitation through the network. This produced early activations at myocardial sites where tissue was unexcited by the shock and coupled to the PS. Shocks along the apico-basal axis of the heart resulted in a significant abbreviation of activation time when the PS was present; these shocks are of particular interest because the fields generated by internal cardioverter defibrillators tend to have a strong component in the same direction. The extent of PS-induced changes, both temporal and spatial, was constrained by the amount of shock-activated myocardium. Increasing field strength decreased the transmission delay between PS and ventricular tissue at Purkinje-myocardial junctions (PMJs), but this did not have a major effect on the organ-level response. Weaker shocks directly affect a smaller volume of myocardial tissue but easily excite the PS, which makes the PS contribution to far field excitation more substantial than for stronger shocks.

Behaviour of the Purkinje System During Defibrillation-Strength Shocks

During normal sinus rhythm, orderly activation of the heart is facilitated by a specialized network of fibres lining the ventricles called the Purkinje system (PS). Characteristic features of the PS encourage coordinated depolarization of spatially disparate endocardial sites. Although the basic role of the PS is well understood, many questions regarding its behaviour, especially during the process of defibrillation, remain unanswered. Purkinje fibres react differently during large electrical shocks than the myocardium on which they run because they are oriented in different directions than the endocardial fibres, they possess distinct electrophysiology, and they are part of a system that is one-dimensional in nature. Because of the small size of Purkinje fibres and their positioning on the endocardium, in vivo observation of PS-related phenomena remains problematic. Therefore, computer modelling offers a unique opportunity to investigate the role of the PS during defibrillation. In this paper, the effects of defibrillation-strength shocks on a finite element model of the ventricles coupled to a distinct PS are ascertained. Results indicate that the presence of the PS has a profound impact on the course of activation in the ventricles. During shocks, depolarizations are elicited at bends and bifurcations in the PS. Subsequently, this activity spreads throughout the PS in all directions, creating numerous regions of myocardial depolarization and accelerating the excitation of the whole structure. These excitations are explained by the cable-like nature of Purkinje fibres, which exposes them to vastly different electrical field effects than bulk myocardium due to abrupt conductivity tensor changes. Depending on electrode orientation and the depth of fibre penetration into the endocardium, this phenomenon can bring about a significant abbreviation of the total activation time for a particular shock when compared to simulations where the PS is not included. For a medium-strength shock oriented along the main axis of the heart, the PS produced a 30% reduction in activation time. In conclusion, the PS is of fundamental importance for determining defibrillation shock response.

Reduced-Order Preconditioning for Bidomain Simulations

Simulations of the bidomain equations involve solving large, sparse, linear systems of the form Ax=b. Being an initial value problems, it is solved at every time step. Therefore, efficient solvers are essential to keep simulations tractable. Iterative solvers, especially the preconditioned conjugate gradient (PCG) method, are attractive since memory demands are minimized compared to direct methods, albeit at the cost of solution speed. However, a proper preconditioner can drastically speed up the solution process by reducing the number of iterations. In this paper, a novel preconditioner for the PCG method based on system order reduction using the Arnoldi method (A-PCG) is proposed. Large order systems, generated during cardiac bidomain simulations employing a finite element method formulation, are solved with the A-PCG method. Its performance is compared with incomplete LU (ILU) preconditioning. Results indicate that the A-PCG estimates an approximate solution considerably faster than the ILU, often within a single iteration. To reduce the computational demands in terms of memory and run time, the use of a cascaded preconditioner was suggested. The A-PCG was applied to quickly obtain an approximate solution, and subsequently a cheap iterative method such as successive overrelaxation (SOR) is applied to further refine the solution to arrive at a desired accuracy. The memory requirements are less than those of direct LU but more than ILU method. The proposed scheme is shown to yield significant speedups when solving time evolving systems

The Role of the Purkinje System in Defibrillation

Only relatively recently have we begun to understand how defibrillation shocks work on the mechanistic level (Cheng et al., 1999; Trayanova & Skouibine, 1998). Virtual electrode polarization has offered a plausible mechanism for explaining far field effects of defibrillation shocks. However, this body of work has not considered the role of the specialized cardiac conduction system, the Purkinje System (PS), in the defibrillation process. Despite its crucial role in activation, relatively little is known about the role of the PS in defibrillation. This is due to several factors which make recording from it challenging: The PS is a fine structure lying on the endocardium which makes it difficult to see and impale with microelectrodes. While Langendorf preparations allow easy access to the epicardium for optical recordings, the PS lies on the endocardium and is, therefore, much harder to access while maintaining the integrity of the ventricles. Depending on species, the PS penetrates various depths into the myocardium, masking midmyocardial activation. Plunge electrodes are one option for recording from the midmyocardium, but amplifier saturation immediately following large shocks would lose important information. Since the PS fibres are fine, the signals produced by them are very small and get easily swamped by signals from the myocardium. This is true for both electrical and optical recordings. Computer modelling, therefore, offers an attractive platform for studying the role of the PS in defibrillation, since the electrical activity everywhere in the system is known and can be visualized.

Role of Purkinje system in cardiac arrhythmias

The mechanisms responsible for postshock behavior of the heart are poorly understood. Below threshold shocks may induce arrhythmias that are difficult to contain. Cardiac vulnerability to shocks and defibrillation efficacy are largely determined by the postshock activity during the occurrence of a brief electrically quiescent period, known as the isoelectric window (IW) and activations following the IW period. This paper presents a detailed computer simulation study that underlines the role of the Purkinje system (PS) in postshock arrhythmogenesis. Reentry was induced in an anatomically realistic rabbit heart model using three different shocking protocols. Regions of vulnerability were determined for each protocol with and without PS. The role of PS during reentry was studied by isolating the PS from myocardium at various instances. The earliest post-shock activations were observed originating from the PS which initiated the reentry. The PS was shown to facilitate the reentry induction at weaker shocks. The PS also helped to stabilize the reentry in the early stages but did not play any significant role in the later stages. This research provides valuable insights into the postshock arrhythmogenesis and maintenance, and extends the discussion on the occurrence of IW as observed during clinical and experimental studies.

Accelerating Large Cardiac Bidomain Simulations by Arnoldi Preconditioning

Bidomain simulations of cardiac systems often in volve solving large, sparse, linear systems of the form Ax=b. These simulations are computationally very expensive in terms of run time and memory requirements. Therefore, efficient solvers are essential to keep simulations tractable. In this paper, an efficient preconditioner for the conjugate gradient (CG) method based on system order reduction using the Arnoldi method (A-PCG) is explained. Large order systems generated during cardiac bidomain simulations using a finite element method formulation, are solved using the A-PCG method. Its performance is compared with incomplete LU (ILU) preconditioning. Results indicate that the A-PCG estimates an approximate solution considerably faster than the ILU, often within a single iteration. To reduce the computational demands in terms of memory and run time, the use of a cascaded preconditioner is suggested. The A-PCG can be applied to quickly obtain an approximate solution, subsequently a cheap iterative method such as successive overrelaxation (SOR) is applied to further refine the solution to arrive at a desired accuracy. The memory requirements are less than direct LU but more than ILU method. The proposed scheme is shown to yield significant speedups when solving time evolving systems

Arnoldi Preconditioning for Solving Large Linear Biomedical Systems

Simulations of biomedical systems often involve solving large, sparse, linear systems of the form Ax = b. In initial value problems, this system is solved at every time step, so a quick solution is essential for tractability. Iterative solvers, especially preconditioned conjugate gradient, are attractive since memory demands are minimized compared to direct methods, albeit at a cost of solution speed. A proper preconditioner can drastically reduce computation and remains an area of active research. In this paper, we propose a novel preconditioner based on system order reduction using the Arnoldi method. Systems of orders up to a million, generated from a finite element method formulation of the elliptic portion of the bidomain equations, are solved with the new preconditioner and performance is compared with that of other preconditioners. Results indicate that the new method converges considerably faster, often within a single iteration. It also uses less memory than an incomplete LU decomposition (ILU). For solving a system repeatedly, the Arnoldi transformation must be continually recomputed, unlike ILU, but this can be done quickly. In conclusion, for solving a system once, the Arnoldi preconditioner offers a greatly reduced solution time, and for repeated solves, will still be faster than an ILU preconditioner