Alexander V. Panfilov

A Simple Two-variable Model of Cardiac Excitation*

We modified the FitzHugh-Nagumo model of an excitable medium so that it describes adequately the dymanics of pulse propagation in the canine myocardium. The modified model is simple enough to be used for intensive 3-dimensional (3D) computations of the whole heart. It simulates the pulse shape and the restitution property of the canine myocardium with good precision.

Models of cardiac tissue electrophysiology: Progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions

In this paper, we formulate a model for human ventricular cells that is efficient enough for whole organ arrhythmia simulations yet detailed enough to capture the effects of cell level processes such as current blocks and channelopathies. The model is obtained from our detailed human ventricular cell model by using mathematical techniques to reduce the number of variables from 19 to nine. We carefully compare our full and reduced model at the single cell, cable and 2D tissue level and show that the reduced model has a very similar behaviour. Importantly, the new model correctly produces the effects of current blocks and channelopathies on AP and spiral wave behaviour, processes at the core of current day arrhythmia research. The new model is well over four times more efficient than the full model. We conclude that the new model can be used for efficient simulations of the effects of current changes on arrhythmias in the human heart.

Organization of Ventricular Fibrillation in the Human Heart

Sudden cardiac death is a major cause of death in the industrialized world, claiming approximately 300 000 victims annually in the United States alone. In most cases, sudden cardiac death is caused by ventricular fibrillation (VF). Experimental studies in large animal hearts have shown that the uncoordinated contractions during VF are caused by large numbers of chaotically wandering reentrant waves of electrical activity. However, recent clinical data on VF in the human heart seem to suggest that human VF may have a markedly different organization. Here, we use a detailed model of the human ventricles, including a detailed description of cell electrophysiology, ventricular anatomy, and fiber direction anisotropy, to study the organization of human VF. We show that characteristics of our simulated VF are qualitatively similar to the clinical data. Furthermore, we find that human VF is driven by only approximately 10 reentrant sources and thus is much more organized than VF in animal hearts of comparable size, where VF is driven by approximately 50 sources. We investigate the influence of anisotropy ratio, tissue excitability, and restitution properties on the number of reentrant sources driving VF. We find that the number of rotors depends strongest on minimum action potential duration, a property that differs significantly between human and large animal hearts. Based on these findings, we suggest that the simpler spatial organization of human VF relative to VF in large animal hearts may be caused by differences in minimum action potential duration. Both the simpler spatial organization of human VF and its suggested cause may have important implications for treating and preventing this dangerous arrhythmia in humans.

Rotating Spiral Waves Created by Geometry

The Belousov-Zhabotinsky reagent and numerical simulations were used to show that under high-frequency stimuli, rotating spiral waves can be initiated in a homogeneous excitable medium in the vicinity of domain boundaries or inexcitable barriers with sharp corners.

Electromechanical wavebreak in a model of the human left ventricle

In the present report, we introduce an integrative three-dimensional electromechanical model of the left ventricle of the human heart. Electrical activity is represented by the ionic TP06 model for human cardiac cells, and mechanical activity is represented by the Niederer-Hunter-Smith active contractile tension model and the exponential Guccione passive elasticity model. These models were embedded into an anatomic model of the left ventricle that contains a detailed description of cardiac geometry and the fiber orientation field. We demonstrated that fiber shortening and wall thickening during normal excitation were qualitatively similar to experimental recordings. We used this model to study the effect of mechanoelectrical feedback via stretch-activated channels on the stability of reentrant wave excitation. We found that mechanoelectrical feedback can induce the deterioration of an otherwise stable spiral wave into turbulent wave patterns similar to that of ventricular fibrillation. We identified the mechanisms of this transition and studied the three-dimensional organization of this mechanically induced ventricular fibrillation.

Drift and breakup of spiral waves in reaction–diffusion–mechanics systems

Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction–diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD–mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD–mechanics systems for mathematics applied to life sciences.

Re-entry in three-dimensional Fitzhugh-Nagumo medium with rotational anisotropy

We study numerically the dynamics of re-entry in a three-dimensional Fitzhugh-Nagumo-type model of myocardial tissue with rotational anisotropy. We find that rotational anisotropy can induce the breakdown of re-entry from a stable scroll wave into a complicated pattern having a surface electrogram similar to that from ventricular fibrillation.

Organization of ventricular fibrillation in the human heart: experiments and models.

Sudden cardiac death is a major health problem in the industrialized world. The lethal event is typically ventricular fibrillation (VF), during which the co‐ordinated regular contraction of the heart is overthrown by a state of mechanical and electrical anarchy. Understanding the excitation patterns that sustain VF is important in order to identify potential therapeutic targets. In this paper, we studied the organization of human VF by combining clinical recordings of electrical excitation patterns on the epicardial surface during in vivo human VF with simulations of VF in an anatomically and electrophysiologically detailed computational model of the human ventricles. We find both in the computational studies and in the clinical recordings that epicardial surface excitation patterns during VF contain around six rotors. Based on results from the simulated three‐dimensional excitation patterns during VF, which show that the total number of electrical sources is 1.4 ± 0.12 times greater than the number of epicardial rotors, we estimate that the total number of sources present during clinically recorded VF is 9.0 ± 2.6. This number is approximately fivefold fewer compared with that observed during VF in dog and pig hearts, which are of comparable size to human hearts. We explain this difference by considering differences in action potential duration dynamics across these species. The simpler spatial organization of human VF has important implications for treatment and prevention of this dangerous arrhythmia. Moreover, our findings underline the need for integrated research, in which human‐based clinical and computational studies complement animal research.

Light-induced termination of spiral wave arrhythmias by optogenetic engineering of atrial cardiomyocytes

AIMS Atrial fibrillation (AF) is the most common cardiac arrhythmia and often involves reentrant electrical activation (e.g. spiral waves). Drug therapy for AF can have serious side effects including proarrhythmia, while electrical shock therapy is associated with discomfort and tissue damage. Hypothetically, forced expression and subsequent activation of light-gated cation channels in cardiomyocytes might deliver a depolarizing force sufficient for defibrillation, thereby circumventing the aforementioned drawbacks. We therefore investigated the feasibility of light-induced spiral wave termination through cardiac optogenetics. METHODS AND RESULTS Neonatal rat atrial cardiomyocyte monolayers were transduced with lentiviral vectors encoding light-activated Ca(2+)-translocating channelrhodopsin (CatCh; LV.CatCh∼eYFP↑) or eYFP (LV.eYFP↑) as control, and burst-paced to induce spiral waves rotating around functional cores. Effects of CatCh activation on reentry were investigated by optical and multi-electrode array (MEA) mapping. Western blot analyses and immunocytology confirmed transgene expression. Brief blue light pulses (10 ms/470 nm) triggered action potentials only in LV.CatCh∼eYFP↑-transduced cultures, confirming functional CatCh-mediated current. Prolonged light pulses (500 ms) resulted in reentry termination in 100% of LV.CatCh∼eYFP↑-transduced cultures (n = 31) vs. 0% of LV.eYFP↑-transduced cultures (n = 11). Here, CatCh activation caused uniform depolarization, thereby decreasing overall excitability (MEA peak-to-peak amplitude decreased 251.3 ± 217.1 vs. 9.2 ± 9.5 μV in controls). Consequently, functional coresize increased and phase singularities (PSs) drifted, leading to reentry termination by PS-PS or PS-boundary collisions. CONCLUSION This study shows that spiral waves in atrial cardiomyocyte monolayers can be terminated effectively by a light-induced depolarizing current, produced by the arrhythmogenic substrate itself, upon optogenetic engineering. These results provide proof-of-concept for shockless defibrillation.