Numerical Modeling of Fluid Flow in Solid Tumors

Abstract

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges.

Effect of microvascular distribution and its density on interstitial fluid pressure in solid tumors: A computational model

“…10 for three cases shows that there is a high correlation between the IFP distribution and the tumor vasculature distribution and that the maximum IFP is close to the region with the highest density of vasculature. This finding adds to the finding of the previous studies (Baxter and Jain, 1989;Jain et al, 2007a;Soltani and Chen, 2011) that have stated that the maximum IFP occurs at the tumor center. Furthermore, the maximum interstitial pressure is 0.9 when MVD is close to 1 (Fig.…”

<b>Characteristics of interstitial fluid flow along with blood flow inside a cylindrical tumor: a numerical simulation

“…In order to validate the numerical method, the results of the paper are compared with Soltani and Chen (2011). In their work, the tumor is assumed as a sphere and blood flow in vessels has a constant pressure.…”

“…Table 1. Material properties used in numerical simulations (Soltani & Chen, 2011 For R = 1 cm in spherical tumor and properties in Table 1, IFP in tumor tissue is shown in Figure 2. For this paper, the tumor is assumed as a cylinder with constant radius and variable necrotic core and also variable intercapillary distance.…”

“…In this study they considered a potential source of nonuniformity in the blood flow: the enhanced fluid exchange between the vascular and interstitial space mediated by the high leakiness of tumor vessels which could lead to a coupling between vascular, transvascular and interstitial fluid flow. Soltani & Chen (2011), Sefidgar et al (2014 developed a mathematical model of interstitial fluid flow using a numerical element-based finite volume method for modeling the continuity equation in the porous media of spherical tumors. They introduced two new parameters: the critical tumor radius and the critical necrotic radius.…”

The Impact of Computational Fluid Mechanics on Cancer Research

“…Modifications of this equation for a deformable porous medium and for mass exchange between the constituents are given in De Angelis and Preziosi (2000) and Chaplain et al (2003). Darcy models have been considered by several authors in simulations of tumour growth (Cristini et al 2003), of fluid flow in solid tumours (Soltani and Chen 2011), and more recently for describing cancer-therapeutic transport in the lung (Erbertseder et al 2012). The former models have predicted interstitial velocities in very good agreement with experimental results, while the latter has described the flow, transport, and reaction processes of a therapeutic agent in the pulmonary circulation in healthy and cancerous pulmonary tissue.…”