Evolution of Resistance to Targeted Anti-Cancer Therapies during Continuous and Pulsed Administration Strategies

The discovery of small molecules targeted to specific oncogenic pathways has revolutionized anti-cancer therapy. However, such therapy often fails due to the evolution of acquired resistance. One long-standing question in clinical cancer research is the identification of optimum therapeutic administration strategies so that the risk of resistance is minimized. In this paper, we investigate optimal drug dosing schedules to prevent, or at least delay, the emergence of resistance. We design and analyze a stochastic mathematical model describing the evolutionary dynamics of a tumor cell population during therapy. We consider drug resistance emerging due to a single (epi)genetic alteration and calculate the probability of resistance arising during specific dosing strategies. We then optimize treatment protocols such that the risk of resistance is minimal while considering drug toxicity and side effects as constraints. Our methodology can be used to identify optimum drug administration schedules to avoid resistance conferred by one (epi)genetic alteration for any cancer and treatment type

Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton-Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose

Multi Drug Resistance on Cancer Cell Lines

This document can be treated as Final Thesis Report for the project titled "Multi-Drug Resistance on Cancer Cell Lines". Drug is said to be resistant on cancer site if it doesn't bind the specified cancer tumor target or site. Drug Resistant mutant is a major obstacle in cancer treatment and a lot of research have been done to overcome this phenomenon with the present technology and also with limited success. My interests lies in understanding drug resistance or more specifically multi-drug resistance with the help of mathematical modeling through the lens of system biology. The processes and underlying experimental research is much applied than the simple mathematics which explains it here. You may find some experimental quotations and results which I have to believe to be true in order to address the problem. The central theme of this project is two-fold. First, we look at a stochastic processes describing cancer growth, mutant formation and treatment success or failure based on whether resistant mutants are created prior-to/after treatment or based on the rate of growth of cancer cells under simultaneous treatment with single/multiple drugs. Further refinement in the existing model is necessary to include biological complexity and realism. So, we incorporate cross-resistance effects of drugs which happens when multiple drugs are used for treatment. Result shows that cross-resistant two drugs are superior than single drug in use as most of the mutation confers resistant to that single drug in first line therapy. Adding second drug in combination with the first drug, despite of cross-resistance effect, improves the treatment success. We will also look into the aspects of quiescence effects and its relation to drug resistance. Finally, at the end we will review an optimal drug dozing regimen based on continuous and pulsed dosing scheme to delay the resistance formation to a maximum extent that arises due to single (epi) genetic alteration only. The stochastic process described here is multi-type branching process. We will calculate the resistance generation probability based on initial cancer tumor load and growth or death rate of cell colony. We will also find an average population size of resistant cells over time scale and other useful parameters defining the multi-type branching process

Engaging the Immune Response to Normalize the Tumor Microenvironment

Solid tumors exist as heterogeneous populations comprised not only of malignant cells, but various other cell types, including cells that make up the vasculature, that can strongly influence tumorgenicity. Many forms of solid cancers are highly vascularized due to dysregulated angiogenesis. The tumor vasculature is classified by leaky, chaotic blood vessels consisting of several components including vascular endothelial cells and pericytes, as well vascular progenitors, resulting in vascular permeability and high interstitial pressure. As a result, the tumor vasculature limits the access of immune effector cells to the tumor, and may in part be responsible for the modest success observed in many current anti-cancer immunotherapies. Current first-line therapeutics in the advanced stage disease setting include anti-angiogenic small molecule drugs that have yielded high objective clinical response rates, however these responses tend to be transient in nature, with most patients becoming drug-refractory. Anti-tumor vasculature vaccines may promote the reconditioning of the tumor microenvironment by coordinately promoting a pro-inflammatory environment and the specific immune targeting of tumor-associated stromal cell populations that contribute to vasculature destabilization. Implementing a vaccine with these therapeutic effects is a promising treatment option that may extend disease-free intervals and overall patient survival. I show that vaccines specifically targeting tumor vasculature populations can “normalize” the tumor microenvironment, as shown by upregulation of proinflammatory molecules within the tumor as well as vascular remodeling promoting enhanced recruitment of CD8+ T cells, resulting in superior anti-tumor efficacy

Minimizing Metastatic Risk in Radiotherapy Fractionation Schedules

Metastasis is the process by which cells from a primary tumor disperse and form new tumors at distant anatomical locations. The treatment and prevention of metastatic cancer remains an extremely challenging problem. This work introduces a novel biologically motivated objective function to the radiation optimization community that takes into account metastatic risk instead of the status of the primary tumor. In this work, we consider the problem of developing fractionated irradiation schedules that minimize production of metastatic cancer cells while keeping normal tissue damage below an acceptable level. A dynamic programming framework is utilized to determine the optimal fractionation scheme. We evaluated our approach on a breast cancer case using the heart and the lung as organs-at-risk (OAR). For small tumor $\alpha/\beta$ values, hypo-fractionated schedules were optimal, which is consistent with standard models. However, for relatively larger $\alpha/\beta$ values, we found the type of schedule depended on various parameters such as the time when metastatic risk was evaluated, the $\alpha/\beta$ values of the OARs, and the normal tissue sparing factors. Interestingly, in contrast to standard models, hypo-fractionated and semi-hypo-fractionated schedules (large initial doses with doses tapering off with time) were suggested even with large tumor $\alpha$/$\beta$ values. Numerical results indicate potential for significant reduction in metastatic risk.Comment: 12 pages, 3 figures, 2 table