Wednesday, February 25, 2015

A Hydrodynamic Approach To Cancer


This is the pre-print version of a paper submitted to Technische Mechanik (ISSN 0232-3869) Hydrodynamic analysis suggests that the injection of drag-reducing agents (DRA) in nanomolar concentrations may hinder metastasizing of circulating tumor cells and serve this way as a complementary post-operative treatment for cancer patients. Our conclusion is based on the following considerations: - Tumor cells need an extra nutrient supply in order to survive and grow. - The attachment of circulating tumor cells therefore tends to occur at sites in the human circulatory system characterized by localized turbulence, which enhances the mass transfer of nutrients, e.g., at sites of vessel branching and bending with plasma skimming. - Also obstacles to blood flow, such as plaques (atherosclerosis), tumors, and red blood cell (RBC) rouleaux, produce local vortices that increase mass transfer, i.e., food supply. - DRA have the ability to smooth (laminarise) localized turbulence in the circulatory system and to reduce mass transfer. - Depriving tumor cells of their required nutrient levels will reduce the probability of creating metastatic tumors, and may lead to their starvation-induced death. In the first part of our essay we demonstrate how flow constrictions decrease mean blood flow velocity, wall shear rates, and Reynolds numbers respectively, and increase the friction factor. Experimentally derived apparent viscosity data from literature will be used to determine the probability of RBC rouleaux formation. This is of importance since RBC rouleaux are typically associated with turbulent blood flow patterns. An increase in apparent viscosity at low flow rates will be attributed to the formation of RBC rouleaux. In part two we discuss the application of the Lockhart/Martinelli method to determine the pressure drop in blood vessels. The objective is to determine a mass transfer coefficient characterizing the mass transfer between the center and the wall of both healthy and cancerous blood vessels. This coefficient indicates the nutrient supply available to tumor cells under different flow conditions and shows the effect of DRA. Our hydrodynamic approach contrasts with previous studies of the possible benefits of DRA injection, which were focused on improving blood supply. We emphasize the reduction of the mass transfer rate as a tool to withhold turbulence induced supplementary food supply to tumor cells. Due to the possibility of unexpected side effects when using DRA (including their mechanical degradation products) animal models are indispensable before clinical trials.