A new ecologically inspired paradigm in cancer treatment known as “adaptive therapy” capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent “cycles” of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary “absorbing region” reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy. Significance: Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.

Adaptive therapy seeks to exploit intratumoral competition to avoid, or at least delay, the emergence of therapy resistance in cancer. Motivated by promising results in prostate cancer, there is growing interest in extending this approach to other neoplasms. As such, it is urgent to understand the characteristics of a cancer that determine whether or not it will respond well to adaptive therapy. A plausible candidate for such a selection criterion is the fitness cost of resistance. In this article, we study a general, but simple, mathematical model to investigate whether the presence of a cost is necessary for adaptive therapy to extend the time to progression beyond that of a standard-of-care continuous therapy. Tumor cells were divided into sensitive and resistant populations and we model their competition using a system of two ordinary differential equations based on the Lotka–Volterra model. For tumors close to their environmental carrying capacity, a cost was not required. However, for tumors growing far from carrying capacity, a cost may be required to see meaningful gains. Notably, it is important to consider cell turnover in the tumor, and we discuss its role in modulating the impact of a resistance cost. To conclude, we present evidence for the predicted cost–turnover interplay in data from 67 patients with prostate cancer undergoing intermittent androgen deprivation therapy. Our work helps to clarify under which circumstances adaptive therapy may be beneficial and suggests that turnover may play an unexpectedly important role in the decision-making process. Significance: Tumor cell turnover modulates the speed of selection against drug resistance by amplifying the effects of competition and resistance costs; as such, turnover is an important factor in resistance management via adaptive therapy. See related commentary by Strobl et al., p. 811

Significance: Glucose is converted to energy through “fermentation” or “oxidation.” Generally, if oxygen is available, cells will oxidize glucose to CO ₂ because it is more efficient than fermentation, which produces lactic acid. But Warburg noted that cancers ferment glucose at a “remarkable” rate even if O ₂ is available! This “Warburg Effect” is still misunderstood because it doesn’t make sense that a cell would ferment glucose when it could get much more energy by oxidizing it. The current paper goes to the heart of this problem by defining the microenvironmental conditions that exist in early cancers that would select for a Warburg Effect. This is important because such cells are much more aggressive and like to lead to cancers that are lethal.

Purpose: Integration of evolutionary dynamics into systemic therapy for metastatic cancers can prolong tumor control compared with standard maximum tolerated dose (MTD) strategies. Prior investigations have focused on monotherapy, but many clinical cancer treatments combine two or more drugs. Optimizing the evolutionary dynamics in multidrug therapy is challenging because of the complex cellular interactions and the large parameter space of potential variations in drugs, doses, and treatment schedules. However, multidrug therapy also represents an opportunity to further improve outcomes using evolution-based strategies. Experimental Design: We examine evolution-based strategies for two-drug therapy and identify an approach that divides the treatment drugs into primary and secondary roles. The primary drug has the greatest efficacy and/or lowest toxicity. The secondary drug is applied solely to reduce the resistant population to the primary drug. Results: Simulations from the mathematical model demonstrate that the primary–secondary approach increases time to progression (TTP) compared with conventional strategies in which drugs are administered without regard to evolutionary dynamics. We apply our model to an ongoing adaptive therapy clinical trial of evolution-based administration of abiraterone to treat metastatic castrate-resistant prostate cancer. Model simulations, parameterized with data from individual patients who progressed, demonstrate that strategic application of docetaxel during abiraterone therapy would have significantly increased their TTP. Conclusions: Mathematical models can integrate evolutionary dynamics into multidrug cancer clinical trials. This has the potential to improve outcomes and to develop clinical trials in which these mathematical models are also used to estimate the mechanism(s) of treatment failure and explore alternative strategies to improve outcomes in future trials.

The Hybrid Automata Library (HAL) is a Java Library developed for use in mathematical oncology modeling. It is made of simple, efficient, generic components that can be used to model complex spatial systems. HAL’s components can broadly be classified into: on- and off-lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and data collection. These components are designed to operate independently and are standardized to make them easy to interface with one another. As a demonstration of how modeling can be simplified using our approach, we have included a complete example of a hybrid model (a spatial model with interacting agent-based and PDE components). HAL is a useful asset for researchers who wish to build performant 1D, 2D and 3D hybrid models in Java, while not starting entirely from scratch. It is available on GitHub at https://github.com/MathOnco/HAL under the MIT License. HAL requires the Java JDK version 1.8 or later to compile and run the source code. In this paper we introduce the Hybrid Automata Library (HAL) with the purpose of simplifying the implementation and sharing of hybrid models for use in mathematical oncology. Hybrid modeling is used in oncology to create spatial models of tissue, typically by modeling cells using agent-based techniques, and by modeling diffusible chemicals using partial differential equations (PDEs). HAL’s key components are designed to run agent-based models, PDEs, and visualization. The components are standardized and are completely decoupled, so models can be built with any combination of them. We first explore the philosophy behind HAL, then summarize the components. Lastly we demonstrate how the components work together with an example of a hybrid model, and a walk-through of the code used to construct it. HAL is open-source and will produce identical results on any machine that supports Java 8 and above, making it highly portable. We recommend HAL to modelers interested in spatial dynamics, even those outside of mathematical oncology, as the components are general enough to facilitate a variety of model types. A community page that provides a download link and online documentation can be found at https://halloworld.org.