Vadim Biktashev | University of Exeter (original) (raw)

Papers by Vadim Biktashev

Research paper thumbnail of Autowave principles for parallel image processing

Physica D: Nonlinear Phenomena, 1991

A highly parallel autowave method for pattern analysis and topological feature detection is prese... more A highly parallel autowave method for pattern analysis and topological feature detection is presented. It is invariant against translations, rotations and scalings of the input pattern. The method yields an increase in computational speed of 3 to 6 orders of magnitude in comparison with a sequential (von Neumann) computer. The method can be realized in principle using only one chip with simple uniform connections of elements.

Research paper thumbnail of The role of fibre orientation in cardioversion of chronic atrial fibrillation: a simulation study

Research paper thumbnail of Simulating cell apoptosis induced sinus node dysfunction

Sinus node dysfunction (SND) is correlated to the pacemaker sinoatrial node (SAN) cell apoptosis.... more 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. The cell models were incorporated into a 2D model consisting of a central SAN region surrounded by atrial tissue. The intercellular gap junctional coupling, as quantified by the diffusion constant, was estimated to give conduction speeds as observed in mouse atrial tissue. The size of mouse SAN pacemaking region was estimated using the 2D model. In multiple simulations, the effects of an increasing proportion of apoptotic pacemaker cells on atrial tissue pacing were simulated and quantified. The SAN size that gave a basal mouse atrial cycle length (ACL) of 295 ms was found to be 0.6 mm in radius. At low pacemaker cell apoptosis proportion, there was a drastic increase of ACL. At modest increase in the number of apoptotic cells, bradycardia was observed. The incidence of sinus arrest was also found to be high. When the number of apoptotic cells were 10% of the total number of pacemaking cells, all pacemaking was arrested. Phenomenological models have been developed to study mouse atrial electrophysiology and confirm experimental findings. The results show the significance of cell apoptosis as a major mechanism of SND.

Research paper thumbnail of Asymptotic properties of mathematical models of excitability

Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences, 2006

Research paper thumbnail of Control of re-entrant activity in a model of mammalian atrial tissue

Proceedings of the Royal Society of London. Series B: Biological Sciences, 1995

We evaluate the feasibility of using resonant drift under feedback driven stimulation to control ... more We evaluate the feasibility of using resonant drift under feedback driven stimulation to control re-entrant excitation in atrial muscle. We simulate a two-dimensional sheet of atrial tissue, where the local kinetics are described by the Earm-Hilgemann-Noble equations for a rabbit atrial cell, and the effects of small amplitude spatially uniform forcing of the whole sheet are computed. Repetitive forcing can induce a drift of a spiral wave in the two-dimensional model, with a drift velocity of up to 10 cm s-1. For a 4 cm x 4 cm atrial surface this resonant drift can move the re-entrant spiral to the inexcitable boundaries, eliminating re-entry in less than 10 s when the amplitude of the repetitive stimulation is 10% that of the single shock defibrillation threshold.

Research paper thumbnail of Design Principles of a Low Voltage Cardiac Defibrillator Based on the Effect of Feedback Resonant Drift

Journal of Theoretical Biology, 1994

We explore the possibility of exploiting the phenomenon of the resonant drift of autowave vortice... more We explore the possibility of exploiting the phenomenon of the resonant drift of autowave vortices in the design of low-voltage cardiac defibrillators. The problem of reflection of resonantly drifting vortices by inexcitable boundaries is overcome by using feedback. Numerical studies show that the voltage needed for defibrillation by this method may be substantially less (by an order of magnitude) than that used in conventional single-shock defibrillation.

Research paper thumbnail of On Two Mechanisms of the Domain Structure of Ventricular Fibrillation

International Journal of Bifurcation and Chaos, 2001

Analysis of optically recorded irregular electrical wave activity on the surface of the heart dur... more Analysis of optically recorded irregular electrical wave activity on the surface of the heart during experimentally induced fibrillation reveals a strong local temporal periodicity. The spatial distribution of the dominant temporal frequencies of excitation has a domain organization. The domains are large (≈1 cm 2) and they persist for minutes. We demonstrate that these data can be reproduced in a two-dimensional excitable medium governed by the FitzHugh–Nagumo equations with a spatial inhomogeneity. We identified two potential mechanisms that may contribute to the observed experimental dynamics: coexistence of stable spiral waves with noncommensurate frequencies of rotation, and Wenckebach-like frequency division from a single spiral source due to inhomogeneity. The number of domains is not an index of the number of wave sources. Both mechanisms reproduce the uniformity of the dominant frequency within individual domains and sharp boundaries between domains. The possibility of dist...

Research paper thumbnail of Three-dimensional organisation of re-entrant propagation during experimental ventricular fibrillation

Chaos, Solitons & Fractals, 2002

... Some qualitative results can be obtained for simpler models, which caricature the excitation ... more ... Some qualitative results can be obtained for simpler models, which caricature the excitation and propagation properties of ... As a single spiral wave would only produce a periodic (monomorphic) pattern, some modification is ... W”: There is essentially only one re-entry vortex, but its ...

Research paper thumbnail of Computational biology of propagation in excitable media models of cardiac tissue

Chaos, Solitons & Fractals, 2002

Research paper thumbnail of Characterization of patterned irregularity in locally interacting, spatially extended systems: Ventricular fibrillation

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2001

The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation ar... more The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation are produced by abnormal spatio-temporal patterns of propagation in the ventricular myocardium. These behaviors can be described by solutions of reaction-diffusion equation excitable medium models. The direct comparison of such solutions with existing experimental observations is virtually impossible as there are too many factors to be taken into account, including not only the complicated dynamics of the re-entrant waves of excitation in the tissue, but also the way the appearance of these waves on the surface is modified by the inhomogeneity, anisotropy and three-dimensional nature of heart tissue. One way of indirect comparison is to compare characteristics of the complexity of the model and the real data, that are invariant under these modifications of the signal. Karhunen–Loéve decomposition is a standard tool for evaluating the complexity of multidimensional signals. A comparison of ...

Research paper thumbnail of On the Movement of Excitation Wave Breaks

Chaos, Solitons & Fractals, 1998

ABSTRACT

Research paper thumbnail of Spiral Wave Motion Models Studied General Comments

Spiral Wave Solutions in the Comoving Frame of Reference

Research paper thumbnail of Drift and Meander of Spiral Waves

arXiv: Pattern Formation and Solitons, 2009

In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion ... more In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of meandering (quasiperiodic spiral wave solutions) spiral waves which are drifting due to symmetry breaking perturbations. This theory is based on earlier theories: the 1995 Biktashev et al theory of drift of rigidly rotating spirals, and the 1996 Biktashev et al theory of meander of spirals in unperturbed systems. We combine the two theories by first rewriting the 1995 drift theory using the symmetry quotient system method of the 1996 meander theory, and then go on to extend the approach to meandering spirals by considering Floquet theory and using a singular perturbation method. We demonstrate the work of the newly developed theory on simple examples. We also develop a numerical implementation of the quotient system method, demonstrate its numerical c...

Research paper thumbnail of Characterisation of Patterned Irregularity in Locally Interacting, Spatially Extended Systems: Ventricular Fibrillation

Research paper thumbnail of Resonant Drift of Autowave Vortices in 2D and the E8ects of Boundaries and Inhomogeneities

Research paper thumbnail of Resonant drift of an autowave vortex in a bounded medium

Physics Letters A, 1993

... References [1] AV Holden, M. Markus and HG Othmer, eds., Nonlinear wave processes in excitabl... more ... References [1] AV Holden, M. Markus and HG Othmer, eds., Nonlinear wave processes in excitable media (Plenum, New York, 1991). ... 224. References. 1. AV Holden, M. Markus and HG Othmer, Editors, Nonlinear wave processes in excitable media, Plenum, New York (1991). ...

Research paper thumbnail of Exponential integrators for a markov chain model of the fast sodium channel of cardiomyocytes

IEEE transactions on bio-medical engineering, 2015

The modern Markov chain models of ionic channels in excitable membranes are numerically stiff. Th... more 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. Both proposed methods extend Rush-Larsen technique, which was originally developed to Hogdkin-Huxley type gate models. One method, "matrix Rush-Larsen" (MRL) uses a matrix reformulation of the Rush-Larsen scheme, where the matrix exponentials are calculated using precomputed tables of eigenvalues and eigenvectors. The other, "hybrid operator splitting" (HOS) method exploits asymptotic properties of a particular Markov chain model, allowing explicit analytical expressions for the substeps. We test both methods on the Clancy and Rudy (2002) [Formula: see text] Markov chain model. With precomputed tables for functions of the tran...

Research paper thumbnail of Reentrant arrhythmias and their control in models of mammalian cardiac tissue

Journal of electrocardiology, 1999

We use detailed biophysical and simplified models of excitation propagation in heart muscle to st... more We use detailed biophysical and simplified models of excitation propagation in heart muscle to study the properties of reentrant arrhythmias. Using a detailed model of excitation combined with a bidomain description of propagation and action of electric current, we have obtained a theoretical estimation for the defibrillation threshold consistent with experimental data. Reentry acts as a spiral wave, propagating around a region of block, the core. A series of properly timed low-voltage stimuli can cause directed "resonant" drift of this block and act as a low-voltage defibrillation strategy. Experimentally observed activation patterns in fibrillating tissue are more complicated than the simplest spiral wave patterns. This is due to complicated geometry, the 3-dimensional nature of the tissue, and its anisotropy and inhomogeneity. However, some fibrillation patterns can be produced by a single reentrant wave, modulated by inhomogeneous tissue properties and Wenckebach frequ...

Research paper thumbnail of Conduction Block in Virtiual Cardiac Tissue by Dissipation of Propagation Fronts

Research paper thumbnail of Simulating the role of anisotropy in human atrial cardioversion

This computational study quantifies the effectiveness of feedback controlled low energy cardiover... more 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. Scroll waves were simulated under Control and CAF conditions and the cardioversion parameters of stimulation strength and pacing duration were evaluated for scroll wave termination. Scroll waves were initiated at two locations in the atria to elicit the effects of scroll wave location. The role of anisotropy was highlighted by comparison to results from the isotropic case. Under Control conditions, scroll wave self-termination was rapid in the anisotropic case. Under CAF conditions, anisotropy caused the initiated scroll wave to degenerate into multiple scrolls with each evolving erratically or pinning to anatomical defects. The cardioversion successfully terminated scroll waves within 10 s, but the stimulus strength had a strong correlation to the location of the scroll wave. The low energy stimulation strength was always lower than the threshold stimulus. Anisotropy plays an important role in atrial electrical properties. Anisotropy aggravates CAF and leads to high frequency atrial pacing. The efficacy of cardioversion is significantly affected by anisotropy.

Research paper thumbnail of Autowave principles for parallel image processing

Physica D: Nonlinear Phenomena, 1991

A highly parallel autowave method for pattern analysis and topological feature detection is prese... more A highly parallel autowave method for pattern analysis and topological feature detection is presented. It is invariant against translations, rotations and scalings of the input pattern. The method yields an increase in computational speed of 3 to 6 orders of magnitude in comparison with a sequential (von Neumann) computer. The method can be realized in principle using only one chip with simple uniform connections of elements.

Research paper thumbnail of The role of fibre orientation in cardioversion of chronic atrial fibrillation: a simulation study

Research paper thumbnail of Simulating cell apoptosis induced sinus node dysfunction

Sinus node dysfunction (SND) is correlated to the pacemaker sinoatrial node (SAN) cell apoptosis.... more 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. The cell models were incorporated into a 2D model consisting of a central SAN region surrounded by atrial tissue. The intercellular gap junctional coupling, as quantified by the diffusion constant, was estimated to give conduction speeds as observed in mouse atrial tissue. The size of mouse SAN pacemaking region was estimated using the 2D model. In multiple simulations, the effects of an increasing proportion of apoptotic pacemaker cells on atrial tissue pacing were simulated and quantified. The SAN size that gave a basal mouse atrial cycle length (ACL) of 295 ms was found to be 0.6 mm in radius. At low pacemaker cell apoptosis proportion, there was a drastic increase of ACL. At modest increase in the number of apoptotic cells, bradycardia was observed. The incidence of sinus arrest was also found to be high. When the number of apoptotic cells were 10% of the total number of pacemaking cells, all pacemaking was arrested. Phenomenological models have been developed to study mouse atrial electrophysiology and confirm experimental findings. The results show the significance of cell apoptosis as a major mechanism of SND.

Research paper thumbnail of Asymptotic properties of mathematical models of excitability

Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences, 2006

Research paper thumbnail of Control of re-entrant activity in a model of mammalian atrial tissue

Proceedings of the Royal Society of London. Series B: Biological Sciences, 1995

We evaluate the feasibility of using resonant drift under feedback driven stimulation to control ... more We evaluate the feasibility of using resonant drift under feedback driven stimulation to control re-entrant excitation in atrial muscle. We simulate a two-dimensional sheet of atrial tissue, where the local kinetics are described by the Earm-Hilgemann-Noble equations for a rabbit atrial cell, and the effects of small amplitude spatially uniform forcing of the whole sheet are computed. Repetitive forcing can induce a drift of a spiral wave in the two-dimensional model, with a drift velocity of up to 10 cm s-1. For a 4 cm x 4 cm atrial surface this resonant drift can move the re-entrant spiral to the inexcitable boundaries, eliminating re-entry in less than 10 s when the amplitude of the repetitive stimulation is 10% that of the single shock defibrillation threshold.

Research paper thumbnail of Design Principles of a Low Voltage Cardiac Defibrillator Based on the Effect of Feedback Resonant Drift

Journal of Theoretical Biology, 1994

We explore the possibility of exploiting the phenomenon of the resonant drift of autowave vortice... more We explore the possibility of exploiting the phenomenon of the resonant drift of autowave vortices in the design of low-voltage cardiac defibrillators. The problem of reflection of resonantly drifting vortices by inexcitable boundaries is overcome by using feedback. Numerical studies show that the voltage needed for defibrillation by this method may be substantially less (by an order of magnitude) than that used in conventional single-shock defibrillation.

Research paper thumbnail of On Two Mechanisms of the Domain Structure of Ventricular Fibrillation

International Journal of Bifurcation and Chaos, 2001

Analysis of optically recorded irregular electrical wave activity on the surface of the heart dur... more Analysis of optically recorded irregular electrical wave activity on the surface of the heart during experimentally induced fibrillation reveals a strong local temporal periodicity. The spatial distribution of the dominant temporal frequencies of excitation has a domain organization. The domains are large (≈1 cm 2) and they persist for minutes. We demonstrate that these data can be reproduced in a two-dimensional excitable medium governed by the FitzHugh–Nagumo equations with a spatial inhomogeneity. We identified two potential mechanisms that may contribute to the observed experimental dynamics: coexistence of stable spiral waves with noncommensurate frequencies of rotation, and Wenckebach-like frequency division from a single spiral source due to inhomogeneity. The number of domains is not an index of the number of wave sources. Both mechanisms reproduce the uniformity of the dominant frequency within individual domains and sharp boundaries between domains. The possibility of dist...

Research paper thumbnail of Three-dimensional organisation of re-entrant propagation during experimental ventricular fibrillation

Chaos, Solitons & Fractals, 2002

... Some qualitative results can be obtained for simpler models, which caricature the excitation ... more ... Some qualitative results can be obtained for simpler models, which caricature the excitation and propagation properties of ... As a single spiral wave would only produce a periodic (monomorphic) pattern, some modification is ... W”: There is essentially only one re-entry vortex, but its ...

Research paper thumbnail of Computational biology of propagation in excitable media models of cardiac tissue

Chaos, Solitons & Fractals, 2002

Research paper thumbnail of Characterization of patterned irregularity in locally interacting, spatially extended systems: Ventricular fibrillation

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2001

The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation ar... more The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation are produced by abnormal spatio-temporal patterns of propagation in the ventricular myocardium. These behaviors can be described by solutions of reaction-diffusion equation excitable medium models. The direct comparison of such solutions with existing experimental observations is virtually impossible as there are too many factors to be taken into account, including not only the complicated dynamics of the re-entrant waves of excitation in the tissue, but also the way the appearance of these waves on the surface is modified by the inhomogeneity, anisotropy and three-dimensional nature of heart tissue. One way of indirect comparison is to compare characteristics of the complexity of the model and the real data, that are invariant under these modifications of the signal. Karhunen–Loéve decomposition is a standard tool for evaluating the complexity of multidimensional signals. A comparison of ...

Research paper thumbnail of On the Movement of Excitation Wave Breaks

Chaos, Solitons & Fractals, 1998

ABSTRACT

Research paper thumbnail of Spiral Wave Motion Models Studied General Comments

Spiral Wave Solutions in the Comoving Frame of Reference

Research paper thumbnail of Drift and Meander of Spiral Waves

arXiv: Pattern Formation and Solitons, 2009

In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion ... more In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of meandering (quasiperiodic spiral wave solutions) spiral waves which are drifting due to symmetry breaking perturbations. This theory is based on earlier theories: the 1995 Biktashev et al theory of drift of rigidly rotating spirals, and the 1996 Biktashev et al theory of meander of spirals in unperturbed systems. We combine the two theories by first rewriting the 1995 drift theory using the symmetry quotient system method of the 1996 meander theory, and then go on to extend the approach to meandering spirals by considering Floquet theory and using a singular perturbation method. We demonstrate the work of the newly developed theory on simple examples. We also develop a numerical implementation of the quotient system method, demonstrate its numerical c...

Research paper thumbnail of Characterisation of Patterned Irregularity in Locally Interacting, Spatially Extended Systems: Ventricular Fibrillation

Research paper thumbnail of Resonant Drift of Autowave Vortices in 2D and the E8ects of Boundaries and Inhomogeneities

Research paper thumbnail of Resonant drift of an autowave vortex in a bounded medium

Physics Letters A, 1993

... References [1] AV Holden, M. Markus and HG Othmer, eds., Nonlinear wave processes in excitabl... more ... References [1] AV Holden, M. Markus and HG Othmer, eds., Nonlinear wave processes in excitable media (Plenum, New York, 1991). ... 224. References. 1. AV Holden, M. Markus and HG Othmer, Editors, Nonlinear wave processes in excitable media, Plenum, New York (1991). ...

Research paper thumbnail of Exponential integrators for a markov chain model of the fast sodium channel of cardiomyocytes

IEEE transactions on bio-medical engineering, 2015

The modern Markov chain models of ionic channels in excitable membranes are numerically stiff. Th... more 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. Both proposed methods extend Rush-Larsen technique, which was originally developed to Hogdkin-Huxley type gate models. One method, "matrix Rush-Larsen" (MRL) uses a matrix reformulation of the Rush-Larsen scheme, where the matrix exponentials are calculated using precomputed tables of eigenvalues and eigenvectors. The other, "hybrid operator splitting" (HOS) method exploits asymptotic properties of a particular Markov chain model, allowing explicit analytical expressions for the substeps. We test both methods on the Clancy and Rudy (2002) [Formula: see text] Markov chain model. With precomputed tables for functions of the tran...

Research paper thumbnail of Reentrant arrhythmias and their control in models of mammalian cardiac tissue

Journal of electrocardiology, 1999

We use detailed biophysical and simplified models of excitation propagation in heart muscle to st... more We use detailed biophysical and simplified models of excitation propagation in heart muscle to study the properties of reentrant arrhythmias. Using a detailed model of excitation combined with a bidomain description of propagation and action of electric current, we have obtained a theoretical estimation for the defibrillation threshold consistent with experimental data. Reentry acts as a spiral wave, propagating around a region of block, the core. A series of properly timed low-voltage stimuli can cause directed "resonant" drift of this block and act as a low-voltage defibrillation strategy. Experimentally observed activation patterns in fibrillating tissue are more complicated than the simplest spiral wave patterns. This is due to complicated geometry, the 3-dimensional nature of the tissue, and its anisotropy and inhomogeneity. However, some fibrillation patterns can be produced by a single reentrant wave, modulated by inhomogeneous tissue properties and Wenckebach frequ...

Research paper thumbnail of Conduction Block in Virtiual Cardiac Tissue by Dissipation of Propagation Fronts

Research paper thumbnail of Simulating the role of anisotropy in human atrial cardioversion

This computational study quantifies the effectiveness of feedback controlled low energy cardiover... more 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. Scroll waves were simulated under Control and CAF conditions and the cardioversion parameters of stimulation strength and pacing duration were evaluated for scroll wave termination. Scroll waves were initiated at two locations in the atria to elicit the effects of scroll wave location. The role of anisotropy was highlighted by comparison to results from the isotropic case. Under Control conditions, scroll wave self-termination was rapid in the anisotropic case. Under CAF conditions, anisotropy caused the initiated scroll wave to degenerate into multiple scrolls with each evolving erratically or pinning to anatomical defects. The cardioversion successfully terminated scroll waves within 10 s, but the stimulus strength had a strong correlation to the location of the scroll wave. The low energy stimulation strength was always lower than the threshold stimulus. Anisotropy plays an important role in atrial electrical properties. Anisotropy aggravates CAF and leads to high frequency atrial pacing. The efficacy of cardioversion is significantly affected by anisotropy.