Efficient termination of cardiac arrhythmias using optogenetic resonant feedback pacing.

Malignant cardiac tachyarrhythmias are associated with complex spatiotemporal excitation of the heart. The termination of these life-threatening arrhythmias requires high-energy electrical shocks that have significant side effects, including tissue damage, excruciating pain, and worsening prognosis. This significant medical need has motivated the search for alternative approaches that mitigate the side effects, based on a comprehensive understanding of the nonlinear dynamics of the heart.

Predicting critical ignition in slow-fast excitable models.

Linearization around unstable traveling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family of spatially confined perturbations to the rest state. This theory relies on the knowledge of the unstable traveling wave solution as well as the leading left and right eigenfunctions of its linearization. We investigate the asymptotics of these ingredients, and utility of the resulting approximations of the strength-extent curves, in the slow-fast limit in two-component excitable systems of FitzHugh-Nagumo type and test those on four illustrative models.

Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves.

In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.

Filament Tension and Phase Locking of Meandering Scroll Waves.

Meandering spiral waves are often observed in excitable media such as the Belousov-Zhabotinsky reaction and cardiac tissue. We derive a theory for drift dynamics of meandering rotors in general reaction-diffusion systems and apply it to two types of external disturbances: an external field and curvature-induced drift in three dimensions. We find two distinct regimes: with small filament curvature, meandering scroll waves exhibit filament tension, whose sign determines the stability and drift direction.

The competitive nature of signal transducer and activator of transcription complex formation drives phenotype switching of T cells.

Signal transducers and activators of transcription (STATs) are key molecular determinants of T-cell fate and effector function. Several inflammatory diseases are characterized by an altered balance of T-cell phenotypes and cytokine secretion. STATs, therefore, represent viable therapeutic targets in numerous pathologies.

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system.

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor and the threshold in the activator's kinetics.

Fast-slow asymptotics for a Markov chain model of fast sodium current.

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology.

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc.

Mechanisms of vortices termination in the cardiac muscle.

We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex.

Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law.

Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, "excitable" systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only.

A Computer Simulation Study of Anatomy Induced Drift of Spiral Waves in the Human Atrium.

The interaction of spiral waves of excitation with atrial anatomy remains unclear. This simulation study isolates the role of atrial anatomical structures on spiral wave spontaneous drift in the human atrium. We implemented realistic and idealised 3D human atria models to investigate the functional impact of anatomical structures on the long-term (∼40 s) behaviour of spiral waves.

Semianalytical approach to criteria for ignition of excitation waves.

We consider the problem of ignition of propagating waves in one-dimensional bistable or excitable systems by an instantaneous spatially extended stimulus. Earlier we proposed a method [I. Idris and V.

Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations.

A scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behavior is affected by the layer geometry. We identify the effect of sharp variations of the layer thickness, which is separate from filament tension and curvature-induced drifts described earlier. We outline a two-step asymptotic theory describing this effect, including asymptotics in the layer thickness and calculation of the drift of so-perturbed spiral waves using response functions.

Classification of wave regimes in excitable systems with linear cross diffusion.

We consider principal properties of various wave regimes in two selected excitable systems with linear cross diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope waves, multienvelope waves, and intermediate regimes appearing as waves propagating at a fixed shape most of the time but undergoing restructuring from time to time. Depending on parameters, most of these regimes can be with and without the "quasisoliton" property of reflection of boundaries and penetration through each other.

Exponential integrators for a Markov chain model of the fast sodium channel of cardiomyocytes.

The modern Markov chain models of ionic channels in excitable membranes are numerically stiff. The popular numerical methods for these models require very small time steps to ensure stability. Our objective is to formulate and test two methods addressing this issue, so that the timestep can be chosen based on accuracy rather than stability.

Analysis of anchor-size effects on pinned scroll waves and measurement of filament rigidity.

Inert, spherical heterogeneities can pin three-dimensional scroll waves in the excitable Belousov-Zhabotinsky reaction. Three pinning sites cause initially circular rotation backbones to approach equilateral triangles. The resulting stationary shapes show convex deviations that increase with decreasing anchor radii.

A method of ‘speed coefficients’ for biochemical model reduction applied to the NF-κB system.

The relationship between components of biochemical network and the resulting dynamics of the overall system is a key focus of computational biology. However, as these networks and resulting mathematical models are inherently complex and non-linear, the understanding of this relationship becomes challenging. Among many approaches, model reduction methods provide an avenue to extract components responsible for the key dynamical features of the system.

Simulating cell apoptosis induced sinus node dysfunction.

Sinus node dysfunction (SND) is correlated to the pacemaker sinoatrial node (SAN) cell apoptosis. This study explores the effect of such a dysfunctional SAN on electrical propagation into neighboring atrial tissue. The Fenton Karma model was extended to simulate mouse SAN and atrial cell action potentials.

Simulating the role of anisotropy in human atrial cardioversion.

This computational study quantifies the effectiveness of feedback controlled low energy cardioversion in the anisotropic human atria. An established biophysical human cell model was adopted to reproduce Control and chronic atrial fibrillation (CAF) action potentials. The cell model was combined with a detailed human atrial geometry to construct a 3D realistic human atrial model.

A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient.

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.

Buckling of scroll waves.

A scroll wave in a sufficiently thin layer of an excitable medium with negative filament tension can be stable nevertheless due to filament rigidity. Above a certain critical thickness of the medium, such a scroll wave will have a tendency to deform into a buckled, precessing state. Experimentally this will be seen as meandering of the spiral wave on the surface, the amplitude of which grows with the thickness of the layer, until a breakup to scroll wave turbulence happens.

Envelope quasisolitons in dissipative systems with cross-diffusion.

We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasisoliton" pulses, which have a fixed stable structure but can reflect from boundaries and penetrate each other. Herein we demonstrate a different type of quasisolitons, with a phenomenology resembling that of the envelope solitons in the nonlinear Schrödinger equation: spatiotemporal oscillations with a smooth envelope, with the velocity of the oscillations different from the velocity of the envelope.

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone.

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells.

Alternative stable scroll waves and conversion of autowave turbulence.

Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh-Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods. Response functions are used to predict the filament tension of the alternative scrolls and it is shown that the slow-period scroll has negative filament tension, while the filament tension of the fast-period scroll changes sign within a hysteresis loop.

Computation of the drift velocity of spiral waves using response functions.

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave's center of rotation and fiducial phase may change over time, i.e.