Related papers: The cardiac bidomain model and homogenization
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…
An electrocardiogram (EKG) is a common, non-invasive test that measures the electrical activity of a patient's heart. EKGs contain useful diagnostic information about patient health that may be absent from other electronic health record…
It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates…
We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials…
There exists a large body of research on the lens of mammalian eye over the past several decades. The objective of the current work is to provide a link between the most recent computational models to some of the pioneering work in the…
An important paradigm in smart health is developing diagnosis tools and monitoring a patient's heart activity through processing Electrocardiogram (ECG) signals is a key example, sue to high mortality rate of heart-related disease. However,…
Rhythmogenesis, which is critical for many biological functions, involves a transition to coherent activity through cell-cell communication. In the absence of centralized coordination by specialized cells (pacemakers), competing oscillating…
Cell membranes are out of thermodynamic equilibrium notably because of membrane recycling, i.e. active exchange of material with the cytosol. We propose an analytically tractable model of biomembrane predicting the effects of recycling on…
Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as \textit{pacemaker dynamics}. In this article we address…
Heteroclinic connections between two distinct hyperbolic periodic orbits in conservative systems are important in a wide range of applications. On the other hand, it is theoretically challenging to find large amplitude connections from…
Reentrant waves propagating in a ring or annulus of excitable media model is the basic mechanism underlying a major class of irregular cardiac rhythms known as anatomical reentry. Such reentrant waves are terminated by rapid electrical…
Electrocardiographic imaging (ECGI) seeks to reconstruct cardiac electrical activity from body-surface potentials noninvasively. However, the associated inverse problem is severely ill-posed and requires robust regularization. While…
We propose a novel approach to generate samples from the conditional distribution of patient-specific cardiovascular models given a clinically aquired image volume. A convolutional neural network architecture with dropout layers is first…
This note gives a brief and `crash' introduction to the method of Homogenization with the use of wave equation and diffusion equation with periodic in space coefficients as instructive examples. We expose the method with the use of an…
The present work studies the robustness of certain basic homoclinic motions in an equilateral restricted four body problem. The problem can be viewed as a two parameter family of conservative autonomous vector fields. The main tools are…
In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we…
We propose a model addressing the coupling mechanism between two spatially modulated monolayers. We obtain the mean-field phase diagrams of coupled bilayers when the two monolayers have the same preferred modulation wavelength. Various…
This paper presents an extension of the unfolding operator technique, initially applied to two-dimensional domains, to the realm of three-dimensional thin domains. The advancement of this methodology is pivotal, as it enhances our…
Circadian rhythms are archetypical examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…