Coupled modeling of blood perfusion in intravascular, interstitial spaces in tumor microvasculature.

The coupling of intravascular and interstitial flow is a distinct feature of tumor microcirculation, due to the high vessel permeability, the low osmotic pressure gradient as well as the absence of functional lymphatic system inside tumors. In this paper, a coupled mathematical model of tumor microcirculation is developed, which provides the link between microvasculature and interstitial space perfusion through the matrices determining a neighbor point belonging to either connected vessel (matrix B) or interstitial space (matrix A), and combines the intravascular and interstitial flow by vascular leaky terms. In addition, the compliance of tumor vessels, blood rheology with hematocritic distribution at branches is also considered. The microvascular network, on which the microcirculation calculation is carried out, is generated from our two-dimensional 9-point (2D9P) model of tumor angiogenesis, improved from the previous 2D5P one. A specific coupling procedure is developed in the study to couple the intravascular and interstitial flow. It is based on the iteratively numerical simulation techniques, including local iterations at individual parameter level and one global loop to provide coupling and simulation convergence. The simulation results not only present the basic features and characteristics of tumor microcirculation, which agree with the corresponding experimental observations reported, but also predict an intimate relationship between the tumor intravascular and interstitial flow quantitatively. Among the parameters, the vascular leakiness is a key to govern the systemic flowing pattern, influence the tumor internal environment and contribute to the metastasis of tumor cells, which could not be presented by the previous uncoupled models.