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Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sources. (English) Zbl 1436.76064
Summary: We present a new method for modeling tissue perfusion on the capillary scale. The microvasculature is represented by a network of one-dimensional vessel segments embedded in the extra-vascular space. Vascular and extra-vascular space exchange fluid over the vessel walls. This exchange is modeled by distributed sources using smooth kernel functions for the extra-vascular domain. It is shown that the proposed method may significantly improve the approximation of the exchange flux, in comparison with existing methods for mixed-dimension embedded problems. Furthermore, the method exhibits better convergence rates of the relevant quantities due to the increased regularity of the extra-vascular pressure solution. Numerical experiments with a vascular network from the rat cortex show that the error in the approximation of the exchange flux for coarse grid resolutions may be decreased by a factor of 3. This may open the way for computing on larger network domains, where a fine grid resolution cannot be achieved in practical simulations due to constraints in computational resources, for example in the context of uncertainty quantification.
Reviewer: Reviewer (Berlin)

MSC:
76Z05 Physiological flows
76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
92C35 Physiological flow
Software:
DuMuX; ISTL
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