A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

Advancing cancer drug development with mechanistic mathematical modeling: bridging the gap between theory and practice

Quantitative predictive modeling of cancer growth, progression, and individual response to therapy is a rapidly growing field. Researchers from mathematical modeling, systems biology, pharmaceutical industry, and regulatory bodies, are collaboratively working on predictive models that could be applied for drug development and, ultimately, the clinical management of cancer patients. A plethora of modeling paradigms and approaches have emerged, making it challenging to compile a comprehensive review across all subdisciplines. It is therefore critical to gauge fundamental design aspects against requirements, and weigh opportunities and limitations of the different model types. In this review, we discuss three fundamental types of cancer models: space-structured models, ecological models, and immune system focused models. For each type, it is our goal to illustrate which mechanisms contribute to variability and heterogeneity in cancer growth and response, so that the appropriate architecture and complexity of a new model becomes clearer. We present the main features addressed by each of the three exemplary modeling types through a subjective collection of literature and illustrative exercises to facilitate inspiration and exchange, with a focus on providing a didactic rather than exhaustive overview. We close by imagining a future multi-scale model design to impact critical decisions in oncology drug development.

To modulate or to skip: De-escalating PARP inhibitor maintenance therapy in ovarian cancer using adaptive therapy

Toxicity and emerging drug resistance pose important challenges in poly-adenosine ribose polymerase inhibitor (PARPi) maintenance therapy of ovarian cancer. We propose that adaptive therapy, which dynamically reduces treatment based on the tumor dynamics, might alleviate both issues. Utilizing in vitro time-lapse microscopy and stepwise model selection, we calibrate and validate a differential equation mathematical model, which we leverage to test different plausible adaptive treatment schedules. Our model indicates that adjusting the dosage, rather than skipping treatments, is more effective at reducing drug use while maintaining efficacy due to a delay in cell kill and a diminishing dose-response relationship. In vivo pilot experiments confirm this conclusion. Although our focus is toxicity mitigation, reducing drug use may also delay resistance. This study enhances our understanding of PARPi treatment scheduling and illustrates the first steps in developing adaptive therapies for new treatment settings. A record of this paper's transparent peer review process is included in the supplemental information.

Leveraging Cancer Phenotypic Plasticity for Novel Treatment Strategies

Cancer cells, like all other organisms, are adept at switching their phenotype to adjust to the changes in their environment. Thus, phenotypic plasticity is a quantitative trait that confers a fitness advantage to the cancer cell by altering its phenotype to suit environmental circumstances. Until recently, new traits, especially in cancer, were thought to arise due to genetic factors; however, it is now amply evident that such traits could also emerge non-genetically due to phenotypic plasticity. Furthermore, phenotypic plasticity of cancer cells contributes to phenotypic heterogeneity in the population, which is a major impediment in treating the disease. Finally, plasticity also impacts the group behavior of cancer cells, since competition and cooperation among multiple clonal groups within the population and the interactions they have with the tumor microenvironment also contribute to the evolution of drug resistance. Thus, understanding the mechanisms that cancer cells exploit to tailor their phenotypes at a systems level can aid the development of novel cancer therapeutics and treatment strategies. Here, we present our perspective on a team medicine-based approach to gain a deeper understanding of the phenomenon to develop new therapeutic strategies.

Targeting PI3K/AKT/mTOR signaling to overcome drug resistance in cancer

This review comprehensively explores the challenge of drug resistance in cancer by focusing on the pivotal PI3K/AKT/mTOR pathway, elucidating its role in oncogenesis and resistance mechanisms across various cancer types. It meticulously examines the diverse mechanisms underlying resistance, including genetic mutations, feedback loops, and microenvironmental factors, while also discussing the associated resistance patterns. Evaluating current therapeutic strategies targeting this pathway, the article highlights the hurdles encountered in drug development and clinical trials. Innovative approaches to overcome resistance, such as combination therapies and precision medicine, are critically analyzed, alongside discussions on emerging therapies like immunotherapy and molecularly targeted agents. Overall, this comprehensive review not only sheds light on the complexities of resistance in cancer but also provides a roadmap for advancing cancer treatment.

A seven-step guide to spatial, agent-based modelling of tumour evolution

Spatial agent-based models are frequently used to investigate the evolution of solid tumours subject to localized cell-cell interactions and microenvironmental heterogeneity. As spatial genomic, transcriptomic and proteomic technologies gain traction, spatial computational models are predicted to become ever more necessary for making sense of complex clinical and experimental data sets, for predicting clinical outcomes, and for optimizing treatment strategies. Here we present a non-technical step by step guide to developing such a model from first principles. Stressing the importance of tailoring the model structure to that of the biological system, we describe methods of increasing complexity, from the basic Eden growth model up to off-lattice simulations with diffusible factors. We examine choices that unavoidably arise in model design, such as implementation, parameterization, visualization and reproducibility. Each topic is illustrated with examples drawn from recent research studies and state of the art modelling platforms. We emphasize the benefits of simpler models that aim to match the complexity of the phenomena of interest, rather than that of the entire biological system. Our guide is aimed at both aspiring modellers and other biologists and oncologists who wish to understand the assumptions and limitations of the models on which major cancer studies now so often depend.

Adaptive Control of Tumor Growth

Cancer treatment optimizations select the most optimum combinations of drugs, sequencing schedules, and appropriate doses that would limit toxicity and yield an improved patient quality of life. However, these optimizations often lack an adequate consideration of cancer's near-infinite potential for evolutionary adaptation to therapeutic interventions. Adapting cancer therapy based on monitored tumor burden and clonal composition is an intuitively sound approach to the treatment of cancer as an inherently complex and adaptive system. The adaptation would be driven by clinical outcome setpoints embodying the aims to thwart therapeutic resistance and maintain a long-term management of the disease or even a cure. However, given the nonlinear, stochastic dynamics of tumor response to therapeutic interventions, adaptive therapeutic strategies may at least need a one-step-ahead prediction of tumor burden to maintain their control over tumor growth dynamics. The article explores the feasibility of adaptive cancer treatment driven by tumor state feedback assuming cell adaptive fitness to be the underlying source of phenotypic plasticity and pathway entropy as a biomarker of tumor growth trajectory. The exploration is undertaken using deterministic and stochastic models of tumor growth dynamics.

Adaptive Cancer Therapy in the Age of Generative Artificial Intelligence

Therapeutic resistance is a major challenge facing the design of effective cancer treatments. Adaptive cancer therapy is in principle the most viable approach to manage cancer's adaptive dynamics through drug combinations with dose timing and modulation. However, there are numerous open issues facing the clinical success of adaptive therapy. Chief among these issues is the feasibility of real-time predictions of treatment response which represent a bedrock requirement of adaptive therapy. Generative artificial intelligence has the potential to learn prediction models of treatment response from clinical, molecular, and radiomics data about patients and their treatments. The article explores this potential through a proposed integration model of Generative Pre-Trained Transformers (GPTs) in a closed loop with adaptive treatments to predict the trajectories of disease progression. The conceptual model and the challenges facing its realization are discussed in the broader context of artificial intelligence integration in oncology.

A calibration and uncertainty quantification analysis of classical, fractional and multiscale logistic models of tumour growth

BACKGROUND AND OBJECTIVE

The validation of mathematical models of tumour growth is frequently hampered by the lack of sufficient experimental data, resulting in qualitative rather than quantitative studies. Recent approaches to this problem have attempted to extract information about tumour growth by integrating multiscale experimental measurements, such as longitudinal cell counts and gene expression data. In the present study, we investigated the performance of several mathematical models of tumour growth, including classical logistic, fractional and novel multiscale models, in terms of quantifying in-vitro tumour growth in the presence and absence of therapy. We further examined the effect of genes associated with changes in chemosensitivity in cell death rates.

METHODS

The multiscale expansion of logistic growth models was performed by coupling gene expression profiles to the cell death rates. State-of-the-art Bayesian inference, likelihood maximisation and uncertainty quantification techniques allowed a thorough evaluation of model performance.

RESULTS

The results suggest that the classical single-cell population model (SCPM) was the best fit for the untreated and low-dose treatment conditions, while the multiscale model with a cell death rate symmetric with the expression profile of OCT4 (Sym-SCPM) yielded the best fit for the high-dose treatment data. Further identifiability analysis showed that the multiscale model was both structurally and practically identifiable under the condition of known OCT4 expression profiles.

CONCLUSIONS

Overall, the present study demonstrates that model performance can be improved by incorporating multiscale measurements of tumour growth when high-dose treatment is involved.

Early Evolution in Cancer: A Mathematical Support for Pathological and Genomic Evidence in Clear Cell Renal Cell Carcinoma

Clear cell renal cell carcinoma (CCRCC) is an aggressive form of cancer and a paradigmatic example of intratumor heterogeneity (ITH). The hawk-dove game is a mathematical tool designed to analyze competition in biological systems. Using this game, the study reported here analyzes the early phase of CCRCC development, comparing clonal fitness in homogeneous (linear evolutionary) and highly heterogeneous (branching evolutionary) models. Fitness in the analysis is a measure of tumor aggressiveness. The results show that the fittest clone in a heterogeneous environment is fitter than the clone in a homogeneous context in the early phases of tumor evolution. Early and late periods of tumor evolution in CCRCC are also compared. The study shows the convergence of mathematical, histological, and genomics studies with respect to clonal aggressiveness in different periods of the natural history of CCRCC. Such convergence highlights the importance of multidisciplinary approaches for obtaining a better understanding of the intricacies of cancer.

Quenching thirst with poison? Paradoxical effect of anticancer drugs

Anticancer drugs have been developed with expectations to provide long-term or at least short-term survival benefits for patients with cancer. Unfortunately, drug therapy tends to provoke malignant biological and clinical behaviours of cancer cells relating not only to the evolution of resistance to specific drugs but also to the enhancement of their proliferation and metastasis abilities. Thus, drug therapy is suspected to impair long-term survival in treated patients under certain circumstances. The paradoxical therapeutic effects could be described as 'quenching thirst with poison', where temporary relief is sought regardless of the consequences. Understanding the underlying mechanisms by which tumours react on drug-induced stress to maintain viability is crucial to develop rational targeting approaches which may optimize survival in patients with cancer. In this review, we describe the paradoxical adverse effects of anticancer drugs, in particular how cancer cells complete resistance evolution, enhance proliferation, escape from immune surveillance and metastasize efficiently when encountered with drug therapy. We also describe an integrative therapeutic framework that may diminish such paradoxical effects, consisting of four main strategies: (1) targeting endogenous stress response pathways, (2) targeting new identities of cancer cells, (3) adaptive therapy- exploiting subclonal competition of cancer cells, and (4) targeting tumour microenvironment.

Overcoming chemotherapy resistance in low-grade gliomas: A computational approach

Low-grade gliomas are primary brain tumors that arise from glial cells and are usually treated with temozolomide (TMZ) as a chemotherapeutic option. They are often incurable, but patients have a prolonged survival. One of the shortcomings of the treatment is that patients eventually develop drug resistance. Recent findings show that persisters, cells that enter a dormancy state to resist treatment, play an important role in the development of resistance to TMZ. In this study we constructed a mathematical model of low-grade glioma response to TMZ incorporating a persister population. The model was able to describe the volumetric longitudinal dynamics, observed in routine FLAIR 3D sequences, of low-grade glioma patients acquiring TMZ resistance. We used the model to explore different TMZ administration protocols, first on virtual clones of real patients and afterwards on virtual patients preserving the relationships between parameters of real patients. In silico clinical trials showed that resistance development was deferred by protocols in which individual doses are administered after rest periods, rather than the 28-days cycle standard protocol. This led to median survival gains in virtual patients of more than 15 months when using resting periods between two and three weeks and agreed with recent experimental observations in animal models. Additionally, we tested adaptive variations of these new protocols, what showed a potential reduction in toxicity, but no survival gain. Our computational results highlight the need of further clinical trials that could obtain better results from treatment with TMZ in low grade gliomas.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Adaptive therapy achieves long-term control of chemotherapy resistance in high grade ovarian cancer

Drug resistance results in poor outcomes for most patients with metastatic cancer. Adaptive Therapy (AT) proposes to address this by exploiting presumed fitness costs incurred by drug-resistant cells when drug is absent, and prescribing dose reductions to allow fitter, sensitive cells to re-grow and re-sensitise the tumour. However, empirical evidence for treatment-induced fitness change is lacking. We show that fitness costs in chemotherapy-resistant ovarian cancer cause selective decline and apoptosis of resistant populations in low-resource conditions. Moreover, carboplatin AT caused fluctuations in sensitive/resistant tumour population size in vitro and significantly extended survival of tumour-bearing mice. In sequential blood-derived cell-free DNA and tumour samples obtained longitudinally from ovarian cancer patients during treatment, we inferred resistant cancer cell population size through therapy and observed it correlated strongly with disease burden. These data have enabled us to launch a multicentre, phase 2 randomised controlled trial (ACTOv) to evaluate AT in ovarian cancer.