Related papers: The cardiac bidomain model and homogenization
Simultaneous electrocardiography (ECG) and phonocardiogram (PCG) provide a comprehensive, multimodal perspective on cardiac function by capturing the heart's electrical and mechanical activities, respectively. However, the distinct and…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing…
Objective: The bidomain model and the finite element method are an established standard to mathematically describe cardiac electrophysiology, but are both suboptimal choices for fast and large-scale simulations due to high computational…
We develop a minimal whole-heart model that describes cardiac electrical conduction and simulate a basic three-lead electrocardiogram (ECG). We compare our 3-lead ECG model with clinical data from a Norwegian athlete database. The results…
Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- and two-dimensional homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue.…
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure…
The forward problem in electrocardiology, computing body surface potentials from cardiac electrical activity, is traditionally solved using physics-based models such as the bidomain or monodomain equations. While accurate, these approaches…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the…
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the…
Some mechanisms of cardiac arrhythmias can be presented as a composition of elementary acts of block and reflection on the contacts of homogeneous areas of the conducting tissue. For study this phenomena we use an axiomatic one-dimensional…
Our evolving understanding of the heterocellular cardiac environment demands innovative tools for its study. While murine models are lauded for their versatility and accessibility, they are constrained by scale; tools designed for larger…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
The bidomain model is the standard model for cardiac electrophysiology. In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of the bidomain Allen-Cahn equation and the bidomain…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
In this work we develop a homogenisation methodology to upscale mathematical descriptions of microcirculatory blood flow from the microscale (where individual vessels are resolved) to the macroscopic (or tissue) scale. Due to the assumed…
Electrocardiogram (ECG)-based models have achieved strong performance in diagnostic tasks, yet they remain limited in modeling how cardiac dynamics evolve under external interventions. In particular, existing approaches focus primarily on…
Human heart is a complex system that can be studied using its electrical activity recorded as Electrocardiogram (ECG). Any variations or anomalies in the ECG can indicate abnormalities in the cardiac dynamics. In this work, we present a…