Optimal policies of non-cross-resistant chemotherapy on Goldie and Coldman's cancer model

Preventing evolutionary rescue in cancer

First-line cancer treatment frequently fails due to initially rare therapeutic resistance. An important clinical question is then how to schedule subsequent treatments to maximize the probability of tumour eradication. Here, we provide a theoretical solution to this problem by using mathematical analysis and extensive stochastic simulations within the framework of evolutionary rescue theory to determine how best to exploit the vulnerability of small tumours to stochastic extinction. Whereas standard clinical practice is to wait for evidence of relapse, we confirm a recent hypothesis that the optimal time to switch to a second treatment is when the tumour is close to its minimum size before relapse, when it is likely undetectable. This optimum can lie slightly before or slightly after the nadir, depending on tumour parameters. Given that this exact time point may be difficult to determine in practice, we study windows of high extinction probability that lie around the optimal switching point, showing that switching after the relapse has begun is typically better than switching too early. We further reveal how treatment dose and tumour demographic and evolutionary parameters influence the predicted clinical outcome, and we determine how best to schedule drugs of unequal efficacy. Our work establishes a foundation for further experimental and clinical investigation of this evolutionarily-informed "extinction therapy" strategy.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

Biphasic drug release from electrospun polyblend nanofibers for optimized local cancer treatment

We report the first attempt to apply biphasic drug release from electrospun polyblend nanofibers for optimized local cancer treatment.

Pharmacokinetics and Drug Interactions Determine Optimum Combination Strategies in Computational Models of Cancer Evolution

The identification of optimal drug administration schedules to battle the emergence of resistance is a major challenge in cancer research. The existence of a multitude of resistance mechanisms necessitates administering drugs in combination, significantly complicating the endeavor of predicting the evolutionary dynamics of cancers and optimal intervention strategies. A thorough understanding of the important determinants of cancer evolution under combination therapies is therefore crucial for correctly predicting treatment outcomes. Here we developed the first computational strategy to explore pharmacokinetic and drug interaction effects in evolutionary models of cancer progression, a crucial step towards making clinically relevant predictions. We found that incorporating these phenomena into our multiscale stochastic modeling framework significantly changes the optimum drug administration schedules identified, often predicting nonintuitive strategies for combination therapies. We applied our approach to an ongoing phase Ib clinical trial (TATTON) administering AZD9291 and selumetinib to EGFR-mutant lung cancer patients. Our results suggest that the schedules used in the three trial arms have almost identical efficacies, but slight modifications in the dosing frequencies of the two drugs can significantly increase tumor cell eradication. Interestingly, we also predict that drug concentrations lower than the MTD are as efficacious, suggesting that lowering the total amount of drug administered could lower toxicities while not compromising on the effectiveness of the drugs. Our approach highlights the fact that quantitative knowledge of pharmacokinetic, drug interaction, and evolutionary processes is essential for identifying best intervention strategies. Our method is applicable to diverse cancer and treatment types and allows for a rational design of clinical trials. Cancer Res; 77(14); 3908-21. ©2017 AACR.

Optimal treatment and stochastic modeling of heterogeneous tumors

In this work we review past articles that have mathematically studied cancer heterogeneity and the impact of this heterogeneity on the structure of optimal therapy. We look at past works on modeling how heterogeneous tumors respond to radiotherapy, and take a particularly close look at how the optimal radiotherapy schedule is modified by the presence of heterogeneity. In addition, we review past works on the study of optimal chemotherapy when dealing with heterogeneous tumors.

REVIEWERS

This article was reviewed by Thomas McDonald, David Axelrod, and Leonid Hanin.