Blood circulation in capillaries occurs in a complex hierarchical network of capillaries. At this spatial scale the vessels deliver nutrients to the living tissues; tumor vessels characterized by a tortuous geometry, leaky walls and small transmural pressure gap are particularly ineffective in delivering drug to the malignant cells.
Numerical simulations at a single capillary level are difficult to carry out at a large scale. Homogenization techniques allow to extract from the geometrical characteristics of the capillary network the effective hydraulic properties that drive the blood flow and oxygen/drug exchanges in the tissue at an average level.
References
Penta R and Ambrosi D, “The role of the microvascular tortuosity in tumor transport phenomena” J. Theor. Biol., to appear.
R. Penta, D. Ambrosi and A. Quarteroni, “Multiscale homogenization for fluid and drug transport in vascularized malignant tissues”, Math. Models. Meth. Appl. Sciences, to appear.
R. Penta, D. Ambrosi and R. Shipley, “Effective governing equations for poroelastic growing media”, Quart. J. Mech. Appl. Math, 67(1):69–91 (2014).
