HAL (Le Centre pour la Communication Scientifique Directe), Mar 12, 2015
Computational modeling and simulation is extensively used to investigate diseases in cardiac elec... more Computational modeling and simulation is extensively used to investigate diseases in cardiac electrophysiological activity and also drug effects, side effects and interactions. Human embryonic stem cell-derived cardiomyocytes (hESC-CMs) have been recently considered as a promising tool in regenerative medicine: their major role in repairing damaged tissue is due to pluripotency and ability to differentiate. These pluripotent cells are also used in early stages of drugs development. Pharmaceutical companies use the MultiElectrode Array (MEA) device in order to perform many in vitro experiments on hESC-CMs. The goal of our study is to derive a mathematical model and to simulate these in vitro experiments.
In this paper, we consider an inverse problem of determining two space dependent ionic parameters... more In this paper, we consider an inverse problem of determining two space dependent ionic parameters of a strongly coupled parabolic-elliptic reaction–diffusion system arising in cardiac electrophysiology modeling when simulating drugs action with multi-electrode array/human induced pluripotent stem cells-cardiomyocytes assays. We use the bidomain model coupled to an ordinary differential equation and we consider the classical phenomenological model in cardiac electrophysiology of FitzHugh–Nagumo to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate for two ionic parameters ( k , γ ) of the model using sub-boundary observations over an interval of time. The key ingredients are a global Carleman-type estimates with a suitable observations acting on a part of the boundary.
One of the essential diagnostic tools of cardiac arrhythmia is activation mapping. Noninvasive cu... more One of the essential diagnostic tools of cardiac arrhythmia is activation mapping. Noninvasive current mapping procedures include electrocardiographic imaging. It allows reconstructing heart surface potentials from measured body surface potentials. Then, activation maps are generated using the heart surface potentials. Recently, a study suggests to deploy artificial neural networks to estimate activation maps directly from body surface potential measurements. Here we carry out a comparative study between the data-driven approach DirectMap and noninvasive classic technique based on reconstructed heart surface potentials using both Finite element method combined with L1-norm regularization (FEM-L1) and the spatial adaptation of Time-delay neural networks (SATDNN-AT). In this work, we assess the performance of the three approaches using a synthetic single paced-rhythm dataset generated on the atria surface. The results show that data-driven approach DirectMap quantitatively outperforms...
The tremendous advancement of cardiac imaging methods, the substantial progress in predictive mod... more 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 unders...
Inverse Problem in Electrocardiography via Factorization Method of Boundary Value Problems Julien... more Inverse Problem in Electrocardiography via Factorization Method of Boundary Value Problems Julien Bouyssier, Nejib Zemzemi, Jacques Henry, CARMEN team, Inria Bordeaux Sud-Ouest 200 avenue de la vieille tour, 33405 Talence Cedex Electrocardiographic Imaging (ECGI) is a new imaging technique that noninvasively images cardiac electrical activity on the heart surface. In ECGI, a multi-electrode vest records body-surface potential maps (BSPMs); then, using geometrical information from CT-scans and a mathematical al- gorithm, electrical potentials, electrograms and isochrones are reconstructed on the heart surface. The reconstruction of cardiac activity from BSPMs is an ill-posed inverse problem. In this work, we present an approach based on an invariant embedding method: the factorization method of boundary values problems [1, 2]. The idea is to embed the initial problem into a family of similar problems on subdomains bounded by a moving boundary from the torso skin to the epicardium sur...
Radio-frequency ablation is one of the most efficient treatments of atrial fibrillation. The idea... more Radio-frequency ablation is one of the most efficient treatments of atrial fibrillation. The idea behind it is to stop the propagation of ectopic beats coming from the pulmonary vein and the abnormal conduction pathways. Medical doctors need to use invasive catheters to localize the position of the triggers and they have to decide where to ablate during the intervention. ElectroCardioGraphy Imaging (ECGI) provides the opportunity to reconstruct the electrical potential and activation maps on the heart surface and analyze data prior to the intervention. The mathematical problem behind the reconstruction of heart potential is known to be ill posed. In this study we pro- pose to regularize the inverse problem with a statistically reconstructed heart potential, and we test the method on synthetically data produced using an ECG simulator.
In this work, we present an optimal control formulation for the bidomain model in order to estima... more In this work, we present an optimal control formulation for the bidomain model in order to estimate maximal conductance parameters in cardiac electrophysiology multiscale modelling. We consider a general Hodgkin-Huxley formalism to describe the ionic exchanges at the microscopic level. We treat the desired parameters as control variables in a cost function minimizing the gap between the measured and the computed transmembrane potentials. First, we establish the existence of an optimal control solution and we formally derive the optimality system. Second, we propose a strategy for solving the estimation problem for both single and multiple parameters cases. Our algorithm is based on a gradient descent method, where the gradient is obtained by solving an adjoint problem. Both the state and the adjoint problems are solved using the finite element method. Numerical simulations for single and multiple conductances estimations show the capability of this approach to identify the values of...
The method of fundamental solutions (MFS) has been extensively used for the electrocardiographic ... more The method of fundamental solutions (MFS) has been extensively used for the electrocardiographic imaging (ECGI) inverse problem. One of its advantages is that it is a meshless method. We remarked that the using cm instead of mm as a space unit has a high impact on the reconstructed inverse solution. Our purpose is to refine this observation, by introducing a rescaling coefficient in space and study its effect on the MFS inverse solution. Results are provided using simulated test data prepared using a reaction-diffusion model. We then computed the ECGI inverse solution for rescaling coefficient values varying from 1 to 100, and computed the relative error (RE) and correlation coefficient (CC). This approach improved the RE and CC by at least 10 % but can go up to 40 % independently of the pacing site. We concluded that the optimal coefficient depends on the heterogeneity and anisotropy of the torso and does not depend on the stimulation site. This suggests that it is related to an op...
HAL (Le Centre pour la Communication Scientifique Directe), Mar 12, 2015
Computational modeling and simulation is extensively used to investigate diseases in cardiac elec... more Computational modeling and simulation is extensively used to investigate diseases in cardiac electrophysiological activity and also drug effects, side effects and interactions. Human embryonic stem cell-derived cardiomyocytes (hESC-CMs) have been recently considered as a promising tool in regenerative medicine: their major role in repairing damaged tissue is due to pluripotency and ability to differentiate. These pluripotent cells are also used in early stages of drugs development. Pharmaceutical companies use the MultiElectrode Array (MEA) device in order to perform many in vitro experiments on hESC-CMs. The goal of our study is to derive a mathematical model and to simulate these in vitro experiments.
In this paper, we consider an inverse problem of determining two space dependent ionic parameters... more In this paper, we consider an inverse problem of determining two space dependent ionic parameters of a strongly coupled parabolic-elliptic reaction–diffusion system arising in cardiac electrophysiology modeling when simulating drugs action with multi-electrode array/human induced pluripotent stem cells-cardiomyocytes assays. We use the bidomain model coupled to an ordinary differential equation and we consider the classical phenomenological model in cardiac electrophysiology of FitzHugh–Nagumo to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate for two ionic parameters ( k , γ ) of the model using sub-boundary observations over an interval of time. The key ingredients are a global Carleman-type estimates with a suitable observations acting on a part of the boundary.
One of the essential diagnostic tools of cardiac arrhythmia is activation mapping. Noninvasive cu... more One of the essential diagnostic tools of cardiac arrhythmia is activation mapping. Noninvasive current mapping procedures include electrocardiographic imaging. It allows reconstructing heart surface potentials from measured body surface potentials. Then, activation maps are generated using the heart surface potentials. Recently, a study suggests to deploy artificial neural networks to estimate activation maps directly from body surface potential measurements. Here we carry out a comparative study between the data-driven approach DirectMap and noninvasive classic technique based on reconstructed heart surface potentials using both Finite element method combined with L1-norm regularization (FEM-L1) and the spatial adaptation of Time-delay neural networks (SATDNN-AT). In this work, we assess the performance of the three approaches using a synthetic single paced-rhythm dataset generated on the atria surface. The results show that data-driven approach DirectMap quantitatively outperforms...
The tremendous advancement of cardiac imaging methods, the substantial progress in predictive mod... more 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 unders...
Inverse Problem in Electrocardiography via Factorization Method of Boundary Value Problems Julien... more Inverse Problem in Electrocardiography via Factorization Method of Boundary Value Problems Julien Bouyssier, Nejib Zemzemi, Jacques Henry, CARMEN team, Inria Bordeaux Sud-Ouest 200 avenue de la vieille tour, 33405 Talence Cedex Electrocardiographic Imaging (ECGI) is a new imaging technique that noninvasively images cardiac electrical activity on the heart surface. In ECGI, a multi-electrode vest records body-surface potential maps (BSPMs); then, using geometrical information from CT-scans and a mathematical al- gorithm, electrical potentials, electrograms and isochrones are reconstructed on the heart surface. The reconstruction of cardiac activity from BSPMs is an ill-posed inverse problem. In this work, we present an approach based on an invariant embedding method: the factorization method of boundary values problems [1, 2]. The idea is to embed the initial problem into a family of similar problems on subdomains bounded by a moving boundary from the torso skin to the epicardium sur...
Radio-frequency ablation is one of the most efficient treatments of atrial fibrillation. The idea... more Radio-frequency ablation is one of the most efficient treatments of atrial fibrillation. The idea behind it is to stop the propagation of ectopic beats coming from the pulmonary vein and the abnormal conduction pathways. Medical doctors need to use invasive catheters to localize the position of the triggers and they have to decide where to ablate during the intervention. ElectroCardioGraphy Imaging (ECGI) provides the opportunity to reconstruct the electrical potential and activation maps on the heart surface and analyze data prior to the intervention. The mathematical problem behind the reconstruction of heart potential is known to be ill posed. In this study we pro- pose to regularize the inverse problem with a statistically reconstructed heart potential, and we test the method on synthetically data produced using an ECG simulator.
In this work, we present an optimal control formulation for the bidomain model in order to estima... more In this work, we present an optimal control formulation for the bidomain model in order to estimate maximal conductance parameters in cardiac electrophysiology multiscale modelling. We consider a general Hodgkin-Huxley formalism to describe the ionic exchanges at the microscopic level. We treat the desired parameters as control variables in a cost function minimizing the gap between the measured and the computed transmembrane potentials. First, we establish the existence of an optimal control solution and we formally derive the optimality system. Second, we propose a strategy for solving the estimation problem for both single and multiple parameters cases. Our algorithm is based on a gradient descent method, where the gradient is obtained by solving an adjoint problem. Both the state and the adjoint problems are solved using the finite element method. Numerical simulations for single and multiple conductances estimations show the capability of this approach to identify the values of...
The method of fundamental solutions (MFS) has been extensively used for the electrocardiographic ... more The method of fundamental solutions (MFS) has been extensively used for the electrocardiographic imaging (ECGI) inverse problem. One of its advantages is that it is a meshless method. We remarked that the using cm instead of mm as a space unit has a high impact on the reconstructed inverse solution. Our purpose is to refine this observation, by introducing a rescaling coefficient in space and study its effect on the MFS inverse solution. Results are provided using simulated test data prepared using a reaction-diffusion model. We then computed the ECGI inverse solution for rescaling coefficient values varying from 1 to 100, and computed the relative error (RE) and correlation coefficient (CC). This approach improved the RE and CC by at least 10 % but can go up to 40 % independently of the pacing site. We concluded that the optimal coefficient depends on the heterogeneity and anisotropy of the torso and does not depend on the stimulation site. This suggests that it is related to an op...
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