A multi-scale FE model for convective-diffusive transport within tumor and vascular networks

Mass transport within an organ occurs through networks of blood vessels and surrounding tissue. This convective-diffusive transport is a very complex process which spans several different scales, from nano- to micro- to macro-scale. The blood vessel network is usually very intricate and irregular with respect to size and geometry, with mass transport being directly coupled to the neighboring tissue. Due to such complexity, development of a comprehensive transport model remains a challenge. The primary focus of this study is on solid tumors which are extremely complex autonomous systems with regard to mass transport. Additionally, tumors develop various biological barriers which hinder effective delivery of drug molecules into cancer tissue. We introduce a multi-scale tumor transport model where larger tumor vessels are modeled by simple 1D finite elements, whereas the capillary bed is replaced by equivalent 3D continuum finite elements. The model couples convective-diffusive transport within capillaries (fluid domain) and tissue (solid domain). These fluid and solid domains are connected by fictitious 1D elements. The proposed tumor model incorporates the imaged inhomogeneous tumor tissue and blood vessel network - from larger vessels to the smallest capillary bed. The tumor model is also applicable to transport within organs, such as the mouse brain, which is presented here as an example.