Coupling fluid and solid domains in modeling drug transport within tumor

Development of a feasible model for transport within complex vasculature network and tissue remains a challenge. Such a model is particularly important when considering drug transport within tumor environment. A drug used to cure the cancer is first transported through blood vessels, then it attaches to the vessel endothelium and faces biological barriers in the vessel wall to reach cancerous cells. We have developed a model for convective-diffusive drug transport which is simple and computationally efficient. One of the challenges was to couple fluid domain within blood vessels and solid domain of the tumor microenvironment. We have introduced fictitious 1D finite elements which appropriately take into account transport characteristics of the vessel walls. These characteristics include leakage and permeability of the walls. In evaluating wall permeability of a drug, we implemented our hierarchical multiscale methodology which couples molecular dynamics (MD) and continuum FE model. A numerical homogenization procedure was employed to obtain equivalent continuum transport parameters which account for interaction on molecular level between drug and solid components of the wall microstructure. Also, a possibility of using equivalent continuum transport models for capillary beds is investigated in order to further simplify and increase efficiency for the overall model of tumor. As a numerical example, we calculate transport through a capillary bed to illustrate applicability of our methodology.