Related papers: The cardiac bidomain model and homogenization
This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…
Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
In this work, we study the convergence and performance of nonlinear solvers for the Bidomain equations after decoupling the ordinary and partial differential equations of the cardiac system. Firstly, we provide a rigorous proof of the…
In this work, we prove a two-scale homogenization result for a set of diffusion-coagulation Smoluchowski-type equations with transmission boundary conditions. This system is meant to describe the aggregation and diffusion of pathological…
The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard…
A major challenge in computational models of cardiac electromechanics is the reconstruction of myocardial fiber architecture, as direct in vivo measurements of fiber orientation are not feasible. Consequently, rule-based methods are…
The work concerns the multiscale modeling of a nerve fascicle of myelinated axons. We present a rigorous derivation of a macroscopic bidomain model describing the behavior of the electric potential in the fascicle based on the…
A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
To provide a unified theoretical framework ranging from a cellular-level excitation mechanism to organic-level geometric propagation, a new theory inspired by quantum electrodynamic theory for light propagation is proposed by describing the…
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…
We consider a thin heterogeneous layer consisted of the thin beams (of radius $r$) and we study the limit behaviour of this problem as the periodicity $\varepsilon$, the thickness $\delta$ and the radius $r$ of the beams tend to zero. The…
We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory…
In this paper we will address the problem of developing mathematical models for the numerical simulation of the human circulatory system. In particular, we will focus our attention on the problem of haemodynamics in large human arteries.
A coupled map is suggested to investigate various spatial or temporal designs in biology: Several cells (or tissues) in an organ are considered as connected to each other in terms of some molecular diffusions or electrical potential…
Developing new methods for predicting electromagnetic instabilities in cardiac activity is of primary importance. However, we still need a comprehensive view of the heart's magnetic activity at the tissue scale. To fill this gap, we present…
Classical theory of crystals states that a medium to be considered homogeneous must satisfy the following requirements: a) the dimension of the elementary cell must be much smaller than the incident wavelength; b) the sample must contain a…
Deformation modeling of cardiac muscle is an important issue in the field of cardiac analysis. Many approaches have been developed to better estimate the cardiac muscle deformation, and to obtain a practical model to be used in diagnostic…