Related papers: Analytically Solvable Asymptotic Model of Atrial E…

Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for asymptotic reduction…

We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial cells. Some of…

We describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of…

Contemporary realistic mathematical models of single-cell cardiac electrical excitation are immensely detailed. Model complexity leads to parameter uncertainty, high computational cost and barriers to mechanistic understanding. There is a…

Mathematical models of a cellular action potential in cardiac modelling have become increasingly complex, particularly in gating kinetics which control the opening and closing of individual ion channel currents. As cardiac models advance…

An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in $\ln S$ and analytically continuing its divergent power series solution such that…

We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law…

Models of electrical excitation and recovery in the heart have become increasingly detailed, but have yet to be used routinely in the clinical setting to guide personalized intervention in patients. One of the main challenges is calibrating…

This work presents a novel approach for characterizing the mechanical behavior of atrial tissue using constitutive neural networks. Based on experimental biaxial tensile test data of healthy human atria, we automatically discover the most…

We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…

We propose a stochastic individual-based model of the progression of atrial fibrillation (AF). The model operates at patient level over a lifetime and is based on elements of the physiology and biophysics of AF, making contact with existing…

Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles of macrophages in atherosclerosis, is proposed. Using technic…

This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…

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 (Idris and Biktashev, PRL, vol 101, 2008, 244101) for…

While ventricular electromechanics is extensively studied, four-chamber heart models have only been addressed recently; most of these works however neglect atrial contraction. Indeed, as atria are characterized by a complex physiology…

We present an effective method to model empirical action potentials of specific patients in the human atria based on the minimal model of Bueno-Orovio, Cherry and Fenton adapted to atrial electrophysiology. In this model, three ionic are…

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of…

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…

In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic…

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about the heart diagnostic. Even though it is one of the major problems in biomedical research, an efficient mathematical…