Numerical Modeling of Fluid Flow in Solid Tumors

M Soltani,P Chen,Ioannis P Androulakis

doi:10.1371/journal.pone.0020344

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.

Highlights

Cancer is the second leading cause of death, causing one of every four deaths in North America [1]
The transport of the drug 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, as the maximum interstitial fluid pressure (IFP) is much lower than effective pressure, Pe
Numerical solutions for the simplest case of a homogeneous and alymphatic tumor demonstrate that, in a uniformly perfused tumor, high interstitial pressure is the main cause of heterogeneous drug distribution

Summary

Introduction

Cancer is the second leading cause of death, causing one of every four deaths in North America [1]. The most important treatment is surgical removal of the tumor, the key to a successful cure is often an efficient delivery of anticancer drugs after the surgery. Many new drugs have been developed to eradicate cancer but are ineffective when used in humans for lack of efficient delivery. All drugs have possible side effects, such as toxicity to normal cells and the development of drug resistance [2]. The two considerations in effective cancer treatment, from an engineering point of view, are drug transport and drug conversion or reaction at the tumor site [3,4]. Many drugs cannot be delivered to their targets because of transport limitations. Other drugs induce biochemical reactions in the body that produce toxicity

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