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A novel mathematical model for hepatocytes and surrounding volume is presented here; in addition to tracking ion transport and diffusion the new model allows for changing cell volume. Using temporally and spatially varying temperature as an input, this paper shows how differences between diffusion coefficients directly influence increases in cell volume. The multiscale nature of the model presents...
A domain decomposition approach is proposed for finite element modeling of small features and fine details in large homogeneous or composite media. The proposed approach addresses the issue of preconditioning when electrically small details are discretized in an otherwise smooth computational domain. Specifically, we propose a fully overlapping domain decomposition method that decouples the discretization...
A model is presented that is an alternative approach to the bio-heat equation for use in radio frequency heating of the liver. The model comprises both a tissue subvolume and a blood subvolume. Separate bio-heat equations are determined for each subvolume, but with an additional term exchanging heat between them, thus creating a coupled system. The derivation for the two coupled differential equations...
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