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Noninvasive reconstruction of cardiac electrical activity from surface electrocardiograms (ECG) involves solving an ill-posed inverse problem. Cardiac electrophysiological (EP) models have been used as important a priori knowledge to…
Electroanatomical mapping, a keystone diagnostic tool in cardiac electrophysiology studies, can provide high-density maps of the local electric properties of the tissue. It is therefore tempting to use such data to better individualize…
The inverse mechano-electrical problem in cardiac electrophysiology is the attempt to reconstruct electrical excitation or action potential wave patterns from the heart's mechanical deformation that occurs in response to electrical…
Personalized cardiac mechanics modeling is a powerful tool for understanding the biomechanics of cardiac function in health and disease and assisting in treatment planning. However, current models are limited to using medical images…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…
Noninvasive reconstruction of cardiac transmembrane potential (TMP) from surface electrocardiograms (ECG) involves an ill-posed inverse problem. Model-constrained regularization is powerful for incorporating rich physiological knowledge…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…
Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated…
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…
This paper proposes a data-driven model for solving the inverse problem of electrocardiography, the mathematical problem that forms the basis of electrocardiographic imaging (ECGI). We present a conditional diffusion framework that learns a…
Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of…
The article considers the nonlinear inverse problem of identifying the material parameters in viscoelastic structures based on a generalized Maxwell model. The aim is to reconstruct the model parameters from stress data acquired from a…
Solving inverse problems in cardiac electrophysiology consists in the recovery of physiological parameters from surface electrocardiogram (ECG) measurements, a task which is often computationally unfeasible due to the severe ill-posedness…
Cardiac arrhythmogenesis is governed by complex electromechanical interactions that are not directly observable in vivo, motivating the development of non-invasive computational approaches for reconstructing three-dimensional activation…
Patient-specific computational models of the heart are powerful tools for cardiovascular research and medicine, with demonstrated applications in treatment planning, device evaluation, and surgical decision-making. Yet constructing such…
We propose FiberNet, a method to estimate \emph{in-vivo} the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electro-mechanical function…
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…
Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…
The study of pathological cardiac conditions such as arrhythmias, a major cause of mortality in heart failure, is becoming increasingly informed by computational simulation, numerically modelling the governing equations. This can provide…