Stochastic electromechanical bidomain model
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913366088351744 |
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| author | Bendahmane, Mostafa Karlsen, Kenneth H. Mroue, Fatima |
| author_facet | Bendahmane, Mostafa Karlsen, Kenneth H. Mroue, Fatima |
| contents | We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs the dynamics of ionic quantities, intra and extra-cellular potentials, and linearized elasticity equations. We introduce a framework called the active strain decomposition, which factors the material gradient of deformation into an active (electrophysiology-dependent) part and an elastic (passive) part, to capture the coupling between muscle contraction, biochemical reactions, and electric activity. Under the assumption of linearized elastic behavior and a truncation of the nonlinear diffusivities, we propose a stochastic electromechanical bidomain model, and establish the existence of weak solutions for this model. To prove existence through the convergence of approximate solutions, we employ a stochastic compactness method in tandem with an auxiliary non-degenerate system and the Faedo--Galerkin method. We utilize a stochastic adaptation of de Rham's theorem to deduce the weak convergence of the pressure approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13455 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic electromechanical bidomain model Bendahmane, Mostafa Karlsen, Kenneth H. Mroue, Fatima Analysis of PDEs Probability 60H15, 35K57, 35M10, 92C30, 92C10 We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs the dynamics of ionic quantities, intra and extra-cellular potentials, and linearized elasticity equations. We introduce a framework called the active strain decomposition, which factors the material gradient of deformation into an active (electrophysiology-dependent) part and an elastic (passive) part, to capture the coupling between muscle contraction, biochemical reactions, and electric activity. Under the assumption of linearized elastic behavior and a truncation of the nonlinear diffusivities, we propose a stochastic electromechanical bidomain model, and establish the existence of weak solutions for this model. To prove existence through the convergence of approximate solutions, we employ a stochastic compactness method in tandem with an auxiliary non-degenerate system and the Faedo--Galerkin method. We utilize a stochastic adaptation of de Rham's theorem to deduce the weak convergence of the pressure approximations. |
| title | Stochastic electromechanical bidomain model |
| topic | Analysis of PDEs Probability 60H15, 35K57, 35M10, 92C30, 92C10 |
| url | https://arxiv.org/abs/2309.13455 |