Rupamanjari Majumder

Nonequilibrium Arrhythmic States and Transitions in a Mathematical Model for Diffuse Fibrosis in Human Cardiac Tissue

We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to fibroblasts via a gap-junctional conductance , reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.

Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.

Islands of spatially discordant APD alternans underlie arrhythmogenesis by promoting electrotonic dyssynchrony in models of fibrotic rat ventricular myocardium.

Fibrosis and altered gap junctional coupling are key features of ventricular remodelling and are associated with abnormal electrical impulse generation and propagation. Such abnormalities predispose to reentrant electrical activity in the heart. In the absence of tissue heterogeneity, high-frequency impulse generation can also induce dynamic electrical instabilities leading to reentrant arrhythmias. However, because of the complexity and stochastic nature of such arrhythmias, the combined effects of tissue heterogeneity and dynamical instabilities in these arrhythmias have not been explored in detail. Here, arrhythmogenesis was studied using in vitro and in silico monolayer models of neonatal rat ventricular tissue with 30% randomly distributed cardiac myofibroblasts and systematically lowered intercellular coupling achieved in vitro through graded knockdown of connexin43 expression. Arrhythmia incidence and complexity increased with decreasing intercellular coupling efficiency. This coincided with the onset of a specialized type of spatially discordant action potential duration alternans characterized by island-like areas of opposite alternans phase, which positively correlated with the degree of connexinx43 knockdown and arrhythmia complexity. At higher myofibroblast densities, more of these islands were formed and reentrant arrhythmias were more easily induced. This is the first study exploring the combinatorial effects of myocardial fibrosis and dynamic electrical instabilities on reentrant arrhythmia initiation and complexity.

Localized Optogenetic Targeting of Rotors in Atrial Cardiomyocyte Monolayers

Background: Recently, a new ablation strategy for atrial fibrillation has emerged, which involves the identification of rotors (ie, local drivers) followed by the localized targeting of their core region by ablation. However, this concept has been subject to debate because the mode of arrhythmia termination remains poorly understood, as dedicated models and research tools are lacking. We took a unique optogenetic approach to induce and locally target a rotor in atrial monolayers. Methods and Results: Neonatal rat atrial cardiomyocyte monolayers expressing a depolarizing light-gated ion channel (Ca2+-translocating channelrhodopsin) were subjected to patterned illumination to induce single, stable, and centralized rotors by optical S1-S2 cross-field stimulation. Next, the core region of these rotors was specifically and precisely targeted by light to induce local conduction blocks of circular or linear shapes. Conduction blocks crossing the core region, but not reaching any unexcitable boundary, did not lead to termination. Instead, electric waves started to propagate along the circumference of block, thereby maintaining reentrant activity, although of lower frequency. If, however, core-spanning lines of block reached at least 1 unexcitable boundary, reentrant activity was consistently terminated by wave collision. Lines of block away from the core region resulted merely in rotor destabilization (ie, drifting). Conclusions: Localized optogenetic targeting of rotors in atrial monolayers could lead to both stabilization and destabilization of reentrant activity. For termination, however, a line of block is required reaching from the core region to at least 1 unexcitable boundary. These findings may improve our understanding of the mechanisms involved in rotor-guided ablation.

Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue

Wave propagation around various geometric expansions, structures, and obstacles in cardiac tissue may result in the formation of unidirectional block of wave propagation and the onset of reentrant arrhythmias in the heart. Therefore, we investigated the conditions under which reentrant spiral waves can be generated by high-frequency stimulation at sharp-edged obstacles in the ten Tusscher-Noble-Noble-Panfilov (TNNP) ionic model for human cardiac tissue. We show that, in a large range of parameters that account for the conductance of major inward and outward ionic currents of the model [fast inward Na(+) current (INa), L-type slow inward Ca(2+) current (ICaL), slow delayed-rectifier current (IKs), rapid delayed-rectifier current (IKr), inward rectifier K(+) current (IK1)], the critical period necessary for spiral formation is close to the period of a spiral wave rotating in the same tissue. We also show that there is a minimal size of the obstacle for which formation of spirals is possible; this size is ∼2.5 cm and decreases with a decrease in the excitability of cardiac tissue. We show that other factors, such as the obstacle thickness and direction of wave propagation in relation to the obstacle, are of secondary importance and affect the conditions for spiral wave initiation only slightly. We also perform studies for obstacle shapes derived from experimental measurements of infarction scars and show that the formation of spiral waves there is facilitated by tissue remodeling around it. Overall, we demonstrate that the formation of reentrant sources around inexcitable obstacles is a potential mechanism for the onset of cardiac arrhythmias in the presence of a fast heart rate.

Optogenetic manipulation of anatomical re-entry by light-guided generation of a reversible local conduction block

Aims Anatomical re-entry is an important mechanism of ventricular tachycardia, characterized by circular electrical propagation in a fixed pathway. It’s current investigative and therapeutic approaches are non-biological, rather unspecific (drugs), traumatizing (electrical shocks), or irreversible (ablation). Optogenetics is a new biological technique that allows reversible modulation of electrical function with unmatched spatiotemporal precision using light-gated ion channels. We therefore investigated optogenetic manipulation of anatomical re-entry in ventricular cardiac tissue. Methods and results Transverse, 150-&mgr;m-thick ventricular slices, obtained from neonatal rat hearts, were genetically modified with lentiviral vectors encoding Ca2+-translocating channelrhodopsin (CatCh), a light-gated depolarizing ion channel, or enhanced yellow fluorescent protein (eYFP) as control. Stable anatomical re-entry was induced in both experimental groups. Activation of CatCh was precisely controlled by 470-nm patterned illumination, while the effects on anatomical re-entry were studied by optical voltage mapping. Regional illumination in the pathway of anatomical re-entry resulted in termination of arrhythmic activity only in CatCh-expressing slices by establishing a local and reversible, depolarization-induced conduction block in the illuminated area. Systematic adjustment of the size of the light-exposed area in the re-entrant pathway revealed that re-entry could be terminated by either wave collision or extinction, depending on the depth (transmurality) of illumination. In silico studies implicated source–sink mismatches at the site of subtransmural conduction block as an important factor in re-entry termination. Conclusions Anatomical re-entry in ventricular tissue can be manipulated by optogenetic induction of a local and reversible conduction block in the re-entrant pathway, allowing effective re-entry termination. These results provide distinctively new mechanistic insight into re-entry termination and a novel perspective for cardiac arrhythmia management.

An Overview of Spiral- and Scroll-Wave Dynamics in Mathematical Models for Cardiac Tissue

We provide a brief overview of recent numerical studies of spiral- and scroll-wave dynamics in mathematical models of cardiac tissue. These waves are believed to be important in developing an understanding of life-threatening cardiac arrhythmias like ventricular tachycardia and ventricular fibrillation. In addition to giving a description of how spiral and scroll waves can be initiated in such models, how they evolve, how they interact with conduction and ionic inhomogeneities, and how they may be controlled, we also discuss the relevance of such studies to defibrillation.

A Mathematical Model of Neonatal Rat Atrial Monolayers with Constitutively Active Acetylcholine-Mediated K+ Current.

Atrial fibrillation (AF) is the most frequent form of arrhythmia occurring in the industrialized world. Because of its complex nature, each identified form of AF requires specialized treatment. Thus, an in-depth understanding of the bases of these arrhythmias is essential for therapeutic development. A variety of experimental studies aimed at understanding the mechanisms of AF are performed using primary cultures of neonatal rat atrial cardiomyocytes (NRAMs). Previously, we have shown that the distinct advantage of NRAM cultures is that they allow standardized, systematic, robust re-entry induction in the presence of a constitutively-active acetylcholine-mediated K+ current (IKACh-c). Experimental studies dedicated to mechanistic explorations of AF, using these cultures, often use computer models for detailed electrophysiological investigations. However, currently, no mathematical model for NRAMs is available. Therefore, in the present study we propose the first model for the action potential (AP) of a NRAM with constitutively-active acetylcholine-mediated K+ current (IKACh-c). The descriptions of the ionic currents were based on patch-clamp data obtained from neonatal rats. Our monolayer model closely mimics the action potential duration (APD) restitution and conduction velocity (CV) restitution curves presented in our previous in vitro studies. In addition, the model reproduces the experimentally observed dynamics of spiral wave rotation, in the absence and in the presence of drug interventions, and in the presence of localized myofibroblast heterogeneities.

Forced fusion of human ventricular scar cells with cardiomyocytes suppresses arrhythmogenicity in a co-culture model

AIMS Fibrosis increases arrhythmogenicity in myocardial tissue by causing structural and functional disruptions in the cardiac syncytium. Forced fusion of fibroblastic cells with adjacent cardiomyocytes may theoretically resolve these disruptions. Therefore, the electrophysiological effects of such electrical and structural integration of fibroblastic cells into a cardiac syncytium were studied. METHODS AND RESULTS Human ventricular scar cells (hVSCs) were transduced with lentiviral vectors encoding enhanced green fluorescent protein alone (eGFP↑-hVSCs) or together with the fusogenic vesicular stomatitis virus G protein (VSV-G/eGFP↑-hVSCs) and subsequently co-cultured (1:4 ratio) with neonatal rat ventricular cardiomyocytes (NRVMs) in confluent monolayers yielding eGFP↑- and VSV-G/eGFP↑-co-cultures, respectively. Cellular fusion was induced by brief exposure to pH = 6.0 medium. Optical mapping experiments showed eGFP↑-co-cultures to be highly arrhythmogenic [43.3% early afterdepolarization (EAD) incidence vs. 7.7% in control NRVM cultures, P < 0.0001], with heterogeneous prolongation of action potential (AP) duration (APD). Fused VSV-G/eGFP↑-co-cultures displayed markedly lower EAD incidence (4.6%, P < 0.001) than unfused co-cultures, associated with decreases in APD, APD dispersion, and decay time of cytosolic Ca(2+) waves. Heterokaryons strongly expressed connexin43 (Cx43). Also, maximum diastolic potential in co-cultures was more negative after fusion, while heterokaryons exhibited diverse mixed NRVM/hVSC whole-cell current profiles, but consistently showed increased outward Kv currents compared with NRVMs or hVSCs. Inhibition of Kv channels by tetraethylammonium chloride abrogated the anti-arrhythmic effects of fusion in VSV-G/eGFP↑-co-cultures raising EAD incidence from 7.9 to 34.2% (P < 0.001). CONCLUSION Forced fusion of cultured hVSCs with NRVMs yields electrically functional heterokaryons and reduces arrhythmogenicity by preventing EADs, which is, at least partly, attributable to increased repolarization force.

Optogenetics enables real-time spatiotemporal control over spiral wave dynamics in an excitable cardiac system

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the aforementioned hypothesis in silico, with subsequent in vitro validation in optogenetically modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system.