The role of the microvascular tortuosity in tumor transport phenomena.

The role of the microvascular network geometry in transport phenomena in solid tumors and its interplay with the leakage and pressure drop across the vessels is qualitatively and quantitatively discussed. Our starting point is a multiscale homogenization, suggested by the sharp length scale separation that exists between the characteristic vessels and the tumor tissue spatial scales, referred to as the microscale and the macroscale, respectively. The coupling between interstitial and capillary compartment is described by a double Darcy model on the macroscale, whereas the geometric information on the microvascular structure is encoded in the effective hydraulic conductivities, which are numerically computed by solving classical differential problems on the microscale representative cell. Then, microscale information is injected into the macroscopic model, which is analytically solved in a prototypical geometry and compared with previous experimentally validated, phenomenological models. In this way, we are able to capture the role of the standard blood flow determinants in the tumor, such as tumor radius, tissue hydraulic conductivity and vessels permeability, as well as influence of the vascular tortuosity on fluid convection. The results quantitatively confirm that transport of blood (and, as a consequence, of any advected anti-cancer drug) can be dramatically impaired by increasing the geometrical complexity of the microvasculature. Hence, our quantitative analysis supports the argument that geometric regularization of the capillary network improves blood transport and drug delivery in the tumor mass.