Key result
A finite element method for a 3D reaction-diffusion system of calcium dynamics established the existence of discrete solutions that converge to the corresponding weak solution.
Why the study?
The authors sought to model the interaction of calcium dynamics in a medium including the sarcolemma and sarcoplasmic reticulum.
Provides a validated mathematical framework and finite element method for simulating 3D calcium dynamics in cardiac cells.
Offers a numerical method for simulating cardiac calcium dynamics; leaves open experimental validation and clinical translation.
We are interested in modeling the interaction of calcium dynamics in a medium including sarcolemma and sarcoplasmic reticulum. The governing equations consist of a nonlinear reaction–diffusion system representing the various calcium fluxes and theirs buffers in the two media. We address the question of existence of weak solutions by using a fixed-point approach. We propose a finite element method for this system, we establish the existence of the discrete solution, and we show that the discrete solution generated by the given scheme converges to the corresponding weak solution for the model studied. Finally, we give some 2D and 3D numerical examples to our model.
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Bendahmane et al. (2019) studied Calcium dynamics in cardiac cell. 3D reaction-diffusion system modeling was evaluated on Existence of weak solutions and convergence of discrete solution. A finite element method for a 3D reaction-diffusion system of calcium dynamics established the existence of discrete solutions that converge to the corresponding weak solution.
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