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<https://discovery.ucl.ac.uk/id/eprint/1306876> <http://purl.org/dc/terms/title> "Numerical simulation of blood flow through permeable vascular network embedded in tumour porous interstitium"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/1306876> <http://purl.org/ontology/bibo/abstract> "Tumour blood flow plays a critical role in tumour growth and cancer therapies.\r\nComputational fluid dynamics is an efficient method to study blood behaviour\r\nby modelling fluid flow through numerical simulations. A mathematical model\r\nis developed to study the blood flow through a three-dimensional permeable\r\nvascular network embedded in a solid tumour, and its transvascular movement\r\nand spread within tumour interior in context with cancer therapies. The\r\nvasculature is described by the parametric equations in terms of vessel centre\r\nlines. The flow through each tumour vessel is approximated with the leading\r\ncomponent in the longitudinal direction of the vessel, and its governing\r\nequation becomes an ordinary differential equation based on the parameter\r\nof the parametric equation for the vessel centre line. The pressure continuity\r\nand mass conservation conditions are imposed at every junction within tumour\r\nvascular network. The interstitial flow is described by the Darcy’s law which\r\nis converted into the Laplace equation. The coupling effect between the flows\r\nthrough tumour vasculature and within tumour interstitial due to the vascular\r\npermeability is described by the Starling’s law. A coupling mathematical\r\nmodel is then developed. Based on mass conservation, a differential equation\r\nfor pressures on both sides of vascular surface is obtained. Transforming the\r\nLaplace equation into the boundary-integral form by using the Green’s function\r\noffers another equation linking the pressures inside and outside vessels. The numerical procedure is developed, and the discretised differential and integral\r\nequations are solved by finite difference method and boundary element\r\nmethod respectively. The model is applied to investigate how different types of\r\nphysical parameters and special characters of tumour vasculature affect tumour\r\nblood flow. Finally, an approximation model by ignoring the term with small\r\nvalue of the fully coupling model is developed, and its validity and simulation\r\nefficiency are examined."^^<http://www.w3.org/2001/XMLSchema#string> .
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