scholarly journals Modelling far field pacing for terminating spiral waves pinned to ischaemic heterogeneities in cardiac tissue

2017 ◽  
Vol 375 (2096) ◽  
pp. 20160289 ◽  
Author(s):  
E. Boccia ◽  
S. Luther ◽  
U. Parlitz
Keyword(s):  
Cardiac Tissue ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Far Field ◽  
Mathematical Methods ◽  
Successful Termination ◽  
Anisotropic Substrate ◽  
Isotropic Media ◽  
Intensive Investigation ◽  
The Impact

In cardiac tissue, electrical spiral waves pinned to a heterogeneity can be unpinned (and eventually terminated) using electric far field pulses and recruiting the heterogeneity as a virtual electrode. While for isotropic media the process of unpinning is much better understood, the case of an anisotropic substrate with different conductivities in different directions still needs intensive investigation. To study the impact of anisotropy on the unpinning process, we present numerical simulations based on the bidomain formulation of the phase I of the Luo and Rudy action potential model modified due to the occurrence of acute myocardial ischaemia. Simulating a rotating spiral wave pinned to an ischaemic heterogeneity, we compare the success of sequences of far field pulses in the isotropic and the anisotropic case for spirals still in transient or in steady rotation states. Our results clearly indicate that the range of pacing parameters resulting in successful termination of pinned spiral waves is larger in anisotropic tissue than in an isotropic medium. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

VULNERABILITY TO REENTRY, AND DRIFT, STABILITY AND BREAKDOWN OF SPIRAL WAVES IN A LINEAR GRADIENT OF GK IN A LUO–RUDY 1 VIRTUAL VENTRICULAR TISSUE

2003 ◽  
Vol 13 (12) ◽  
pp. 3865-3871 ◽  
Author(s):  
O. V. ASLANIDI ◽  
R. H. CLAYTON ◽  
A. V. HOLDEN ◽  
H. K. PHILLIPS ◽  
R. J. WARD
Keyword(s):  
Action Potential ◽  
Velocity Component ◽  
Action Potential Duration ◽  
Cardiac Tissue ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Linear Gradient ◽  
Wave Solutions ◽  
Ventricular Tissue ◽  
Vulnerable Window

The vulnerable window in a heterogeneous virtual LRl cardiac tissue, with a linear gradient in GK, is wider when following propagation down the gradient, towards tissue with longer action potential duration, than when following propagation up the gradient. Spiral wave solutions in a uniform linear gradient in GK drift, with a velocity component along the gradient of the order of mm/s, towards tissue with a longer APD.

scholarly journals The impact of cardiac tissue anisotropy on spiral wave superseding: A simulation study using ionic cell models

2018 ◽  
Vol 136 ◽  
pp. 359-369 ◽  
Author(s):  
Timofei I. Epanchintsev ◽  
Sergei F. Pravdin ◽  
Alexander V. Panfilov
Keyword(s):  
Simulation Study ◽  
Cardiac Tissue ◽  
Spiral Wave ◽  
Cell Models ◽  
Tissue Anisotropy ◽  
The Impact

scholarly journals Interaction between spiral and paced waves in cardiac tissue

2007 ◽  
Vol 293 (1) ◽  
pp. H503-H513 ◽  
Author(s):  
Konstantin Agladze ◽  
Matthew W. Kay ◽  
Valentin Krinsky ◽  
Narine Sarvazyan
Keyword(s):  
High Frequency ◽  
Cardiac Tissue ◽  
Spiral Wave ◽  
Neonatal Rat ◽  
Implantable Cardioverter Defibrillators ◽  
Antitachycardia Pacing ◽  
Rotating Waves ◽  
Rat Cardiomyocytes ◽  
Successful Termination ◽  
Patients At Risk

For prevention of lethal arrhythmias, patients at risk receive implantable cardioverter-defibrillators, which use high-frequency antitachycardia pacing (ATP) to convert tachycardias to a normal rhythm. One of the suggested ATP mechanisms involves paced-induced drift of rotating waves followed by their collision with the boundary of excitable tissue. This study provides direct experimental evidence of this mechanism. In monolayers of neonatal rat cardiomyocytes in which rotating waves of activity were initiated by premature stimuli, we used the Ca2+-sensitive indicator fluo 4 to observe propagating wave patterns. The interaction of the spiral tip with a paced wave was then monitored at a high spatial resolution. In the course of the experiments, we observed spiral wave pinning to local heterogeneities within the myocyte layer. High-frequency pacing led, in a majority of cases, to successful termination of spiral activity. Our data show that 1) stable spiral waves in cardiac monolayers tend to be pinned to local heterogeneities or areas of altered conduction, 2) overdrive pacing can shift a rotating wave from its original site, and 3) the wave break, formed as a result of interaction between the spiral tip and a paced wave front, moves by a paced-induced drift mechanism to an area where it may become unstable or collide with a boundary. The data were complemented by numerical simulations, which was used to further analyze experimentally observed behavior.

Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study

1999 ◽  
Vol 276 (1) ◽  
pp. H269-H283 ◽  
Author(s):  
Zhilin Qu ◽  
James N. Weiss ◽  
Alan Garfinkel
Keyword(s):  
Action Potential ◽  
Antiarrhythmic Drugs ◽  
Cardiac Tissue ◽  
Potential Model ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Recovery From Inactivation ◽  
Main Determinants ◽  
The Stability

Spiral wave breakup is a proposed mechanism underlying the transition from ventricular tachycardia to fibrillation. We examined the importance of the restitution of action potential duration (APD) and of conduction velocity (CV) to the stability of spiral wave reentry in a two-dimensional sheet of simulated cardiac tissue. The Luo-Rudy ventricular action potential model was modified to eliminate its restitution properties, which are caused by deactivation or recovery from inactivation of K+, Ca2+, and Na+ currents ( I K, I Ca, and I Na, respectively). In this model, we find that 1) restitution of I Ca and I Na are the main determinants of the steepness of APD restitution; 2) for promoting spiral breakup, the range of diastolic intervals over which the APD restitution slope is steep is more important than the maximum steepness; 3) CV restitution promotes spiral wave breakup independently of APD restitution; and 4) “defibrillation” of multiple spiral wave reentry is most effectively achieved by combining an antifibrillatory intervention based on altering restitution with an antitachycardia intervention. These findings suggest a novel paradigm for developing effective antiarrhythmic drugs.

Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model

2003 ◽  
Vol 284 (2) ◽  
pp. H542-H548 ◽  
Author(s):  
K. H. W. J. Ten Tusscher ◽  
A. V. Panfilov
Keyword(s):  
Action Potential ◽  
Cardiac Tissue ◽  
Potential Model ◽  
Phase 1 ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Local Current ◽  
Gradient Component ◽  
Reentrant Excitation ◽  
Ventricular Action Potential

Heterogeneity of cardiac tissue is an important factor determining the initiation and dynamics of cardiac arrhythmias. In this paper, we studied the effects of gradients of electrophysiological heterogeneity on reentrant excitation patterns using computer simulations. We investigated the dynamics of spiral waves in a two-dimensional sheet of cardiac tissue described by the Luo-Rudy phase 1 (LR1) ventricular action potential model. A gradient of action potential duration (APD) was imposed by gradually varying the local current density of K+ current or inward rectifying K+ current along one axis of the tissue sheet. We show that a gradient of APD resulted in spiral wave drift. This drift consisted of two components. The longitudinal (along the gradient) component was always directed toward regions of longer spiral wave period. The transverse (perpendicular to the gradient) component had a direction dependent on the direction of rotation of the spiral wave. We estimated the velocity of the drift as a function of the magnitude of the gradient and discuss its implications.

scholarly journals Drift and termination of spiral waves in optogenetically modified cardiac tissue at sub-threshold illumination

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Sayedeh Hussaini ◽  
Vishalini Venkatesan ◽  
Valentina Biasci ◽  
José M Romero Sepúlveda ◽  
Raul A Quiñonez Uribe ◽  
...  
Keyword(s):  
Cardiac Tissue ◽  
Dynamic Control ◽  
Spiral Wave ◽  
Deep Understanding ◽  
Spiral Waves ◽  
Mouse Heart ◽  
Cell Coupling ◽  
Wave Dynamics ◽  
Systematic Exploration ◽  
Voltage Gradients

The development of new approaches to control cardiac arrhythmias requires a deep understanding of spiral wave dynamics. Optogenetics offers new possibilities for this. Preliminary experiments show that sub-threshold illumination affects electrical wave propagation in the mouse heart. However, a systematic exploration of these effects is technically challenging. Here, we use state-of-the-art computer models to study the dynamic control of spiral waves in a two-dimensional model of the adult mouse ventricle, using stationary and non-stationary patterns of sub-threshold illumination. Our results indicate a light-intensity-dependent increase in cellular resting membrane potentials, which together with diffusive cell-cell coupling leads to the development of spatial voltage gradients over differently illuminated areas. A spiral wave drifts along the positive gradient. These gradients can be strategically applied to ensure drift-induced termination of a spiral wave, both in optogenetics and in conventional methods of electrical defibrillation.

scholarly journals Drift and termination of spiral waves in optogenetically modified cardiac tissue at sub-threshold illumination

2020 ◽  
Author(s):  
Sayedeh Hussaini ◽  
Vishalini Venkatesan ◽  
Valentina Biasci ◽  
José M. Romero Sepúlveda ◽  
Raúl A. Quiñonez Uribe ◽  
...  
Keyword(s):  
Cardiac Tissue ◽  
Dynamic Control ◽  
Spiral Wave ◽  
Deep Understanding ◽  
Spiral Waves ◽  
Mouse Heart ◽  
Cell Coupling ◽  
Wave Dynamics ◽  
Systematic Exploration ◽  
Voltage Gradients

AbstractThe development of new approaches to control cardiac arrhythmias requires a deep understanding of spiral wave dynamics. Optogenetics offers new possibilities for this. Preliminary experiments show that sub-threshold illumination affects electrical wave propagation in the mouse heart. However, a systematic exploration of these effects is technically challenging. Here, we use state-of-the-art computer models to study the dynamic control of spiral waves in a two-dimensional model of the adult mouse ventricle, using stationary and non-stationary patterns of sub-threshold illumination. Our results indicate a light intensity-dependent increase in cellular resting membrane potentials, which together with diffusive cell-cell coupling leads to the development of spatial voltage gradients over differently illuminated areas. A spiral wave drifts along the positive gradient. These gradients can be strategically applied to ensure drift-induced termination of a spiral wave, both in optogenetics and in conventional methods of electrical defibrillation.

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

2014 ◽  
Vol 307 (7) ◽  
pp. H1024-H1035 ◽  
Author(s):  
Rupamanjari Majumder ◽  
Rahul Pandit ◽  
A. V. Panfilov
Keyword(s):  
Wave Propagation ◽  
Cardiac Tissue ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Delayed Rectifier ◽  
High Frequency Stimulation ◽  
Secondary Importance ◽  
Ionic Model ◽  
Delayed Rectifier Current ◽  
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 Ca2+ 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.

scholarly journals Phase-resolved analysis of the susceptibility of pinned spiral waves to far-field pacing in a two-dimensional model of excitable media

2010 ◽  
Vol 368 (1918) ◽  
pp. 2221-2236 ◽  
Author(s):  
Philip Bittihn ◽  
Amgad Squires ◽  
Gisa Luther ◽  
Eberhard Bodenschatz ◽  
Valentin Krinsky ◽  
...  
Keyword(s):  
Local Control ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Media ◽  
Excitation Threshold ◽  
Far Field ◽  
Life Threatening ◽  
Discontinuous Phase ◽  
Rotating Wave ◽  
Spatio Temporal

Life-threatening cardiac arrhythmias are associated with the existence of stable and unstable spiral waves. Termination of such complex spatio-temporal patterns by local control is substantially limited by anchoring of spiral waves at natural heterogeneities. Far-field pacing (FFP) is a new local control strategy that has been shown to be capable of unpinning waves from obstacles. In this article, we investigate in detail the FFP unpinning mechanism for a single rotating wave pinned to a heterogeneity. We identify qualitatively different phase regimes of the rotating wave showing that the concept of vulnerability is important but not sufficient to explain the failure of unpinning in all cases. Specifically, we find that a reduced excitation threshold can lead to the failure of unpinning, even inside the vulnerable window. The critical value of the excitation threshold (below which no unpinning is possible) decreases for higher electric field strengths and larger obstacles. In contrast, for a high excitation threshold, the success of unpinning is determined solely by vulnerability, allowing for a convenient estimation of the unpinning success rate. In some cases, we also observe phase resetting in discontinuous phase intervals of the spiral wave. This effect is important for the application of multiple stimuli in experiments.

Using distributed lag models to predict regional budget revenues

2020 ◽  
Vol 19 (6) ◽  
pp. 1154-1172
Author(s):  
Yu.V. Granitsa
Keyword(s):  
Unemployment Rate ◽  
Consumer Price Index ◽  
Mathematical Methods ◽  
Distributed Lag ◽  
Key Indicator ◽  
Distributed Lag Models ◽  
Regional Budget ◽  
The Impact ◽  
Financial Result

Subject. The article addresses projections of regional budget revenues, using distributed lag models. Objectives. The purpose is to review economic and statistical tools that are suitable for the analysis of relationship between the revenues of the regional budget system and regional macroeconomic predictors. Methods. The study draws on statistical, constructive, economic and mathematical methods of analysis. Results. In models with quantitative variables obtained under the Almon method, the significant predictors in the forecasting of regional budget revenues are determined mainly by the balanced financial result, the consumer price index, which characterizes inflation processes in the region, and the unemployment rate being the key indicator of the labor market. Models with quantitative variables obtained through the Koyck transformation are characterized by a wider range of predictors, the composition of which is determined by the peculiarities of economic situation in regions. The two-year forecast provides the average lag obtained during the evaluation of the models. The exception is the impact of unemployment rate, which is characterized as long-term. Conclusions. To generate forecasts of budget parameters, the results of both the Koyck method and the Almon method should be considered, though the former is more promising.

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