arXiv subjects

Lia Gander

Publications and source records attributed to Lia Gander.

4 recordsLinked to original sources

arXiv2024

An eikonal model with re-excitability for fast simulations in cardiac electrophysiology

Precision cardiology based on cardiac digital twins requires accurate simulations of cardiac arrhythmias. However, detailed models, such as the monodomain model, are computationally costly and have limited applicability in practice. Thus, it desirable to have fast models that can still represent the main physiological features presented during cardiac arrhythmias. The eikonal model is an approximation of the monodomain model that is widely used to describe the arrival times of the electrical wave. However, the standard eikonal model does not generalize to the complex re-entrant dynamics that characterize the cardiac arrhythmias. In this work, we propose an eikonal model that includes the tissue re-excitability, which allows to describe re-entries. The re-excitability properties are inferred from the monodomain model. Our eikonal model also handles the tissue anisotropy and heterogeneity. We compare the eikonal model to the monodomain model in various numerical experiments in the atria and the ventricles. The eikonal model is qualitatively accurate in the simulation of re-entries and can be potentially ran in real-time, opening the door to its clinical applicability.

cs.CE↗

arXiv2021

Fast characterization of inducible regions of atrial fibrillation models with multi-fidelity Gaussian process classification

Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites. A critical step to assess the effect of an ablation pattern is to pace the model from different, potentially random, locations to determine whether arrhythmias can be induced in the atria. In this work, we propose to use multi-fidelity Gaussian process classification on Riemannian manifolds to efficiently determine the regions in the atria where arrhythmias are inducible. We build a probabilistic classifier that operates directly on the atrial surface. We take advantage of lower resolution models to explore the atrial surface and combine seamlessly with high-resolution models to identify regions of inducibility. When trained with 40 samples, our multi-fidelity classifier shows a balanced accuracy that is 10% higher than a nearest neighbor classifier used as a baseline atrial fibrillation model, and 9% higher in presence of atrial fibrillation with ablations. We hope that this new technique will allow faster and more precise clinical applications of computational models for atrial fibrillation.

cs.LG↗

arXiv2021

Space-time shape uncertainties in the forward and inverse problem of electrocardiography

In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic-in-time covariance kernel for the random field and approximate the Karhunen-Loève expansion using low-rank techniques for fast sampling. The space-time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi-Monte Carlo method. We present several numerical experiments on a simplified but physiologically grounded 2-dimensional geometry to illustrate the validity of the approach. The tested parametric dimension ranged from 100 up to 600. For the forward problem the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi-Monte Carlo method perform as expected, except for the total variation regularisation, where convergence is limited by lack of regularity. We finally investigate an $H^{1/2}$ regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.

math.NA↗

arXiv2021

Optimal explicit stabilized postprocessed $τ$-leap method for the simulation of chemical kinetics

The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this paper we propose a new discrete stochastic simulation algorithm: the postprocessed second kind stabilized orthogonal $τ$-leap Runge-Kutta method (PSK-$τ$-ROCK). In the context of chemical kinetics this method can be seen as a stabilization of Gillespie's explicit $τ$-leap combined with a postprocessor. The stabilized procedure allows to simulate problems with multiple scales (stiff), while the postprocessing procedure allows to approximate the invariant measure (e.g. mean and variance) of ergodic stochastic dynamical systems. We prove stability and accuracy of the PSK-$τ$-ROCK. Numerical experiments illustrate the high reliability and efficiency of the scheme when compared to other $τ$-leap methods.

math.NA↗