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The tremendous advancement of cardiac imaging methods, the substantial progress in predictive modelling, along with the amount of new investigative multimodalities, challenge the current technologies in the cardiology field. Innovative, robust and multimodal tools need to be created in order to fuse imaging data (e.g., MR, CT) with mapped electrical activity and to integrate those into 3D biophysical models. In the past years, several cross-platform toolkits have been developed to provide image analysis tools to help build such software. The aim of this study is to introduce a novel multimodality software platform dedicated to cardiovascular diagnosis and therapy guidance: MUSIC. This platform was created to improve the image-guided cardiovascular interventional procedures and is a robust platform for AI/Deep Learning, image analysis and modelling in a newly created consortium with international hospitals. It also helps our researchers develop new techniques and have a better understanding of the cardiac tissue properties and physiological signals. Thus, this extraction of quantitative information from medical data leads to more repeatable and reliable medical diagnoses. [ABSTRACT FROM AUTHOR]

Mathematical modelling and numerical simulation in cardiac electrophysiology have already been studied extensively. However, there is a clear lack of techniques and methodologies for studying the propagation of action potential in a heart with structural defects. In this article, we present a modified version of the bidomain model, derived using homogenisation techniques with the assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, for example, fat, fibrosis, and so forth. We present an application of this model to a rat heart. Starting from high‐resolution MRI, the geometry of the heart is built and meshed using image processing techniques. We perform a study of the effects of tissue heterogeneities induced by diffusive inclusions on the velocity and shape of the depolarisation wavefront. We present several test cases with different geometries of diffusive inclusions. We reach the conclusion that the conduction velocity is not affected in the best cases, while it is affected by up to 76% in the worst case scenario. Additionally, the shape of the wavefront was affected in some cases. [ABSTRACT FROM AUTHOR]

In this paper we study how mesoscopic heterogeneities affect electrical signal propagation in cardiac tissue. The standard model used in cardiac electrophysiology is a bidomain model - a system of degenerate parabolic PDEs, coupled with a set of ODEs, representing the ionic behviour of the cardiac cells. We assume that the heterogeneities in the tissue are periodically distributed diffusive regions, that are significantly larger than a cardiac cell. These regions represent the fibrotic tissue, collagen or fat, that is electrically passive. We give a mathematical setting of the model. Using semigroup theory we prove that such model has a uniformly bounded solution. Finally, we use two–scale convergence to find the limit problem that represents the average behviour of the electrical signal in this setting. [ABSTRACT FROM AUTHOR]

The electrocardiographic imaging (ECGI) inverse problem highly relies on adding constraints, a process called regularization, as the problem is ill-posed. When there are no prior information provided about the unknown epicardial potentials, the Tikhonov regularization method seems to be the most commonly used technique. In the Tikhonov approach the weight of the constraints is determined by the regularization parameter. However, the regularization parameter is problem and data dependent, meaning that different numerical models or different clinical data may require different regularization parameters. Then, we need to have as many regularization parameter-choice methods as techniques to validate them. In this work, we addressed this issue by showing that the Discrete Picard Condition (DPC) can guide a good regularization parameter choice for the two-norm Tikhonov method. We also studied the feasibility of two techniques: The U-curve method (not yet used in the cardiac field) and a novel automatic method, called ADPC due its basis on the DPC. Both techniques were tested with simulated and experimental data when using the method of fundamental solutions as a numerical model. Their efficacy was compared with the efficacy of two widely used techniques in the literature, the L-curve and the CRESO methods. These solutions showed the feasibility of the new techniques in the cardiac setting, an improvement of the morphology of the reconstructed epicardial potentials, and in most of the cases of their amplitude. [ABSTRACT FROM AUTHOR]

Background: Non-invasive electrocardiographic imaging (ECGI) is a promising tool to provide high-resolution panoramic imaging of cardiac electrical activity noninvasively from body surface potential measurements. Current experimental methods for ECGI validation are limited to comparison with unipolar electrograms and the relatively low spatial resolution of cardiac mapping arrays. We aim to develop a novel experimental set up combining a human shaped torso tank with high-resolution optical mapping allowing the validation of ECGI reconstructions. Methods: Langendorff-perfused pig hearts (n = 3) were suspended in a human torso-shaped tank, with the left anterior descending artery (LAD) cannulated on a separate perfusion. Electrical signals were recorded from an 108-electrode epicardial sock and 128 electrodes embedded in the tank surface. Simultaneously, optical mapping of the heart was performed through the anterior surface of the tank. Recordings were made in sinus rhythm and ventricular pacing (n = 55), with activation and repolarization heterogeneities induced by perfusion of hot and cold solutions as well as Sotalol through the LAD. Fluoroscopy provided 3D cardiac and electrode geometries in the tank that were transformed to the 2D optical mapping window using an optimization algorithm. Epicardial unipolar electrograms were reconstructed from torso potentials using ECGI and validated using optical activation and repolarization maps. Results: The transformation and alignment of the 3D geometries onto the 2D optical mapping window was good with an average correlation of 0.87 ± 0.10 and error of 7.7 ± 3.1 ms with activation derived from the sock. The difference in repolarization times were more substantial (error = 17.4 ± 3.7 ms) although the sock and optical repolarization patterns themselves were very similar (correlation = 0.83 ± 0.13). Validation of ECGI reconstructions revealed ECGI accurately captures the pattern of activation (correlation = 0.79 ± 0.11) and identified regions of late and/or early repolarization during different perfusions through LAD. ECGI also correctly demonstrated gradients in both activation and repolarization, although in some cases these were under or over-estimated or shifted slightly in space. Conclusion: A novel experimental setup has been developed, combining a human-shaped torso tank with optical mapping, which can be effectively used in the validation of ECGI techniques; including the reconstruction of activation and repolarization patterns and gradients. [ABSTRACT FROM AUTHOR]

Electrocardiographic imaging aims at reconstructing cardiac electrical events from electrical signals measured on the body surface. The most common approach relies on the inverse solution of the Laplace equation in the torso to reconstruct epicardial potential maps from body surface potential maps. Here we apply a method based on a parameter identification problem to reconstruct both activation and repolarization times. From an ansatz of action potential, based on the Mitchell-Schaeffer ionic model, we compute body surface potential signals. The inverse problem is reduced to the identification of the parameters of the Mitchell-Schaeffer model. We investigate whether solving the inverse problem with the endocardium improves the results or not. We solved the parameter identification problem on two different meshes: one with only the epicardium, and one with both the epicardium and the endocardium. We compared the results on both the heart (activation and repolarization times) and the torso. The comparison was done on validation data of sinus rhythm and ventricular pacing. We found similar results with both meshes in 6 cases out of 7: the presence of the endocardium slightly improved the activation times. This was the most visible on a sinus beat, leading to the conclusion that inclusion of the endocardium would be useful in situations where endo-epicardial gradients in activation or repolarization times play an important role. [ABSTRACT FROM AUTHOR]

Numerical simulations of the cardiac electrophysiology in the atria are often based on the standard bidomain or monodomain equations stated on a two-dimensional manifold. These simulations take advantage of the thinness of the atrial tissue, and their computational cost is reduced, as compared to three-dimensional simulations. However, these models do not take into account the heterogeneities located in the thickness of the tissue, like discontinuities of the fiber direction, although they can be a substrate for atrial arrhythmia (Hocini et al., Circulation 105(20):2442-2448, ; Ho et al., Cardiovasc Res 54(2):325-336, ; Nattel, Nature 415(6868):219-226, ). We investigate a two-dimensional model with two coupled, superimposed layers that allows to introduce three-dimensional heterogeneities, but retains a reasonable computational cost. We introduce the mathematical derivation of this model and error estimates with respect to the three-dimensional model. We give some numerical illustrations of its interest: we numerically show its convergence for vanishing thickness, introduce an optimization process of the coupling coefficient and assess its validity on physiologically relevant geometries. Our model would be an efficient tool to test the influence of three-dimensional fiber direction heterogeneities in reentries or atrial arrhythmia without using three-dimensional models. [ABSTRACT FROM AUTHOR]

The bidomain model is the current most sophisticated model used in cardiac electrophysiology. The monodomain model is a simplification of the bidomain model that is less computationally intensive but only valid under equal conductivity ratio. We propose in this paper optimal monodomain approximations of the bidomain model. We first prove that the error between the bidomain and monodomain solutions is bounded by the error |B - A| between the bidomain and monodomain conductivity operators. Optimal monodomain approximations are defined by minimizing the distance |B - A|, which reduces for solutions over all ℝd to minimize the Lp norm of the difference between the operator symbols. Similarly, comparing the symbols pointwise amounts to compare the propagation of planar waves in the bidomain and monodomain models. We prove that any monodomain model properly propagates at least d planar waves in ℝd. We next consider and solve the optimal problem in the L∞ and L2 norms, the former providing minimal propagation error uniformly over all directions. The quality of these optimal monodomain approximations is compared among themselves and with other published approximations using two sets of test cases. The first one uses periodic boundary conditions to mimic propagation in ℝd while the second is based on a square domain with common Neumann boundary conditions. For the first test cases, we show that the error on the propagation speed is highly correlated with the error on the symbols. The second test cases show that domain boundaries control propagation directions, with only partial impact from the conductivity operator used. [ABSTRACT FROM AUTHOR]

We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation procedure to enforce the required robustness property. Indeed, the invariant region is usually preserved at the expense of a more restrictive CFL condition. Here, we try to optimize this condition in order to reduce the computational cost. [ABSTRACT FROM AUTHOR]

This paper is devoted to the introduction of a numerical scheme for a bone healing model and simulation of skull fractures. The mathematical model describes the evolution of mesenchymal stem cells, osteoblasts, bone matrix and osteogenic growth factor. We propose a numerical scheme based on an implicit finite volume method constructed on an orthogonal mesh. The efficiency and robustness of the scheme are shown in simulating a skull fracture in rats. [ABSTRACT FROM AUTHOR]

Discrete duality finite volume (DDFV) schemes have recently been developed in two dimensions to approximate nonlinear diffusion problems on general meshes. In this paper, a three-dimensional extension of these schemes is proposed. The construction of this extension is detailed and its main properties are proved: a priori bounds, well-posedness, and error estimates. The practical implementation of this scheme is easy. Numerical experiments are presented to illustrate its good behavior. [ABSTRACT FROM AUTHOR]