## Abstract

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.

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# Imperfect drug penetration leads to spatial monotherapy and rapid evolution of multi-drug resistance

## Abstract

Infections with rapidly evolving pathogens are often treated using combinations of drugs with different mechanisms of action. One of the major goals of combination therapy is to reduce the risk of drug resistance emerging during a patient's treatment. While this strategy generally has significant benefits over monotherapy, it may also select for multi-drug resistant strains, which present an important clinical and public health problem. For many antimicrobial treatment regimes, individual drugs have imperfect penetration throughout the body, so there may be regions where only one drug reaches an effective concentration. Here we propose that mismatched drug coverage can greatly speed up the evolution of multi-drug resistance by allowing mutations to accumulate in a stepwise fashion. We develop a mathematical model of within-host pathogen evolution under spatially heterogeneous drug coverage and demonstrate that even very small single-drug compartments lead to dramatically higher resistance risk. We find that it is often better to use drug combinations with matched penetration profiles, although there may be a trade-off between preventing eventual treatment failure due to resistance in this way, and temporarily reducing pathogen levels systemically. Our results show that drugs with the most extensive distribution are likely to be the most vulnerable to resistance. We conclude that optimal combination treatments should be designed to prevent this spatial effective monotherapy. These results are widely applicable to diverse microbial infections including viruses, bacteria and parasites.

# Statistical interpretations and new findings on Variation in Cancer Risk Among Tissues

Tomasetti and Vogelstein (2015a) find that the incidence of a set of cancer types is correlated with the total number of normal stem cell divisions. Here, we separate the effects of standing stem cell number (i.e., organ or tissue size) and per stem cell lifetime replication rate. We show that each has a statistically significant and independent effect on explaining variation in cancer incidence over the 31 cases considered by Tomasetti and Vogelstein. When considering the total number of stem cell divisions and when removing cases associated with disease or carcinogens, we find that cancer incidence attains a plateau of approximately 0.6% incidence for the cases considered by these authors. We further demonstrate that grouping by anatomical site explains most of the remaining variation in risk between cancer types. This new analysis suggests that cancer risk depends not only on the number of stem cell divisions but varies enormously ($\sim$10,000 times) depending on the stem cell's environment. Future research should investigate how tissue characteristics (anatomical site, type, size, stem cell divisions) explain cancer incidence over a wider range of cancers, to what extent different tissues express specific protective mechanisms, and whether any differential protection can be attributed to natural selection.