| Summary: | This work deals with numerical computation of the interstitial fluid pressure distribution for various synthetic tumor configurations in two spatial dimensions. In order to attend a reasonable degree of realism, we also consider asymmetric configurations and use unstructured triangular grids to accurately discretize the computational domains. A multi point flux approximation method, previously used for porous medium flow simulations, is utilized for solving the corresponding Poisson equation for the pressure. We are particularly interested in the effects of spatial variation of the hydraulic conductivity as well as vessel hydraulic conductivities on the interstitial fluid pressure. Spatially varying hydraulic conductivity was first studied by Liu and Schlesinger [17] in some special situations using analytical methods. Here we complement their work by performing a set of relatively comprehensive numerical investigations. A considerable difference in the computed pressure profiles is found when comparing the results with the more classical approach using piecewise constant hydraulic conductivities. We also explore the response of the numerical model when varying i.e. size of necrotic core and vessel hydraulic conductivities. The pressure profiles display a striking dependence on the arterial hydraulic conductivity in the peripheral region. A strong dependence on the arterial hydraulic conductivity is also observed when introducing so called “vascular hot-spots” in the model as well as looking at non-symmetric geometries. Finally, we discuss our numerical results in light of other numerical studies of TIFP distribution and experimental studies of tumor biology. It is concluded that the computed results are in accordance with the general understanding of TIFP. Although we have worked on a simplified system, our results highlight the importance of describing hydraulic conductivity as a spatially varying parameter. Keywords: Interstitial fluid pressure, Tumor, Hydraulic conductivity, Microvascular density, Vessel hydraulic conductivity
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