Multiscale modelling of fluid and drug transport in vascular tumours. (English) Zbl 1198.92028
Summary: A model for fluid and drug transport through the leaky neovasculature and porous interstitium of a solid tumour is developed. The transport problems are posed on a micro-scale characterized by the inter-capillary distance, and the method of multiple scales is used to derive the continuum equations describing fluid and drug transport on the length scale of the tumour (under the assumption of a spatially periodic microstructure). The fluid equations comprise a double porous medium, with coupled Darcy flow through the interstitium and vasculature, whereas the drug equations comprise advection-reaction equations; in each case the dependence of the transport coefficients on the vascular geometry is determined by solving micro-scale cell problems.
MSC:
| 92C50 | Medical applications (general) |
| 92C35 | Physiological flow |
| 76S05 | Flows in porous media; filtration; seepage |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
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