Simulation of Microcirculation in Solid Tumors

In this paper, a numerical method is developed to investigate the microcirculation in solid tumors based on the mathematical models of tumor angiogenesis and tumor micro-circulation. The 2D9P (2-dimensional 9-point) model of tumor angiogenesis used in this paper is an improvement on the 2D5P (2-dimensional 5-point) one of Anderson and Chaplain [1, 2]. The model of tumor microcirculation provides the link between the microvasculature and interstitial space perfusion through a matrix describing the local vascular density, and accordingly couples the intravascular and interstitial flow by vascular leaky terms. The intravascular, transvascular and interstitial flow are governed by the flux conservation equation, Starling's law and Darcy's law, respectively; compliance of tumor vessels is specified by the empirical equation from Netti et al. [3], and blood rheology follows the formula proposed by Pries et al. [4] with an extension of distribution rules of haematocrit at branches on the basis of Fung's conclusions [5]. We simulate the flows numerically. The results not only present the basic features and characteristics of tumor microcirculation, consisting with the corresponding experimental observations reported, but also predict an intimate relationship between the tumor intravascular and interstitial flow, among which the vascular leakiness is one key factor to govern the systemic flowing pattern, influence the tumor internal environment and contribute to the metastasis of tumor cells.