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MATHEMATICAL ANALYSIS OF AN IN VIVO MODEL OF MITOCHONDRIAL SWELLING

机译:线粒体肿胀的体内模型的数学分析

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摘要

We analyze the effect of Robin boundary conditions in a mathematical model for a mitochondria swelling in a living organism. This is a coupled PDE/ODE model for the dependent variables calcium ion contration and three fractions of mitochondria that are distinguished by their state of swelling activity. The model assumes that the boundary is a permeable 'membrane', through which calcium ions can both enter or leave the cell. Under biologically relevant assumptions on the data, we prove the well-posedness of solutions of the model and study the asymptotic behavior of its solutions. We augment the analysis of the model with computer simulations that illustrate the theoretically obtained results.
机译:我们分析了在生物体内线粒体肿胀的数学模型中罗宾边界条件的影响。这是耦合因数PDE / ODE模型,用于因变量钙离子对立和线粒体的三个部分,它们的溶胀活性状态是不同的。该模型假定边界是可渗透的“膜”,钙离子可通过该膜进入或离开细胞。在数据的生物学相关假设下,我们证明了模型解的适定性,并研究了其解的渐近行为。我们通过计算机仿真来扩大对模型的分析,这些仿真说明了理论上获得的结果。

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