Multiphase porous media models for mechanics in medicine: Applications to transport oncophysics and diabetic foot

Physical phenomena in biological systems constitute an intricate framework, which develops on multiple scales and usually entails several interconnected feedbacks. Computational modeling provides the physical scientists with a set of tools for the deconvolution of such complexities. The field of application of this approach is extraordinarily large, including models for cardiovascular diseases, bone injuries, locomotion, and recently tumor progression. In this work, we present different multiphase models based upon porous media theory. We focus on two major applications, namely the growth of a solid tumor and the case of diabetic foot. The tumor model accounts for cancer cell proliferation, cell necrosis induced by the lack of nutrients, and migration of cells through an extracellular matrix. It allows also to consider the effects of cortical tensions between distinct cell species, and tumor angiogenesis. In the second part of this article, we show results for a biphasic model developed for the diabetic foot. In this case, the computational framework can predict the occurrence of high interstitial pressures and the possible appearance of ulcers. Such models, adequately extended and fed with patient-specific data, could be used in the future to stimulate novel therapeutic strategies.