Emerging Leaders in Mathematical Oncology: The MathOnco Subgroup Minisymposium

Maximilian Strobl

Cleveland Clinic (Department for Translational Hematology and Oncology Research, Lerner Research Institute)

"Using mathematical modeling to design protocols for preclinical testing of evolutionary therapies"

Over the past two decades it has become clear that cancers are complex and evolving diseases. Genetic and non-genetic processes generate diverse subpopulations of tumor cells which can thrive under a variety of conditions and stressors. This provides a rich pool of variation that by means of natural selection and continued evolution enables adaptation to even the most modern treatments, especially in advanced cancers. Based on this novel understanding, so-called “evolutionary therapy” or “evolution-informed treatment strategies” have emerged which try to leverage, and potentially even steer, tumour evolution by strategically and dynamically sequencing and combining existing therapies and adjusting dose levels. In particular, adaptive therapy, which dynamically changes treatment levels to maintain drug-sensitive cells in order to competitively suppress emerging drug resistance, has produced a number of promising theoretical, preclinical and also clinical results. However, unlike for new drugs for which there are clear established frameworks for translation from bench to bedside, the design of preclinical protocols to ensure efficacy and safety of evolutionary therapies is an open question. In this study, we use mathematical modeling to develop and interpret in vitro experimental protocols and apply them towards the development of an adaptive therapy for Osimertinib for the treatment of Non-Small Cell Lung Cancer. In the first step, we consider the question of how to measure ecological interactions between tumor subpopulations. To do so, we build on the “Game Assay” previously developed by our group, in which cells are co-cultured at different frequencies to measure how a population’s fitness depends on its frequency in the environment. Using an agent-based model of our in vitro experiments, we study how different aspects of the design (number of replicates, number of proportions) and analysis (regression technique, regression window) impact the accuracy and precision of the assay. Subsequently, we use our optimized protocol to quantify the frequency-dependent interactions between Osimertinib sensitive and resistant PC9 cells under different drug levels. In the next step, we use our model to explore whether and how so-obtained fitness differences translate to the ability to steer the composition of the tumor in long-term in vitro experiments, in which cells are co-cultured and passaged at regular intervals. In particular, we explore the role of the population size, passaging frequency, and passage fraction (proportion of cells carried forward to next passage). To conclude, we will present preliminary data in which we use this assay to trial a potential adaptive Osimertinib therapy protocol in vitro. Overall, we demonstrate how mathematical models can help to understand and improve experimental assays, and we contribute towards the important discussion as to how to translate evolutionary therapies from the blackboard to the bedside.
Additional authors: Dagim Tadele; Rowan Barker-Clarke; Mina Dinh; Jeffrey Maltas; Jacob Scott

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Rebecca A. Bekker

H. Lee Moffitt Cancer Center & Research Institute (Department of Integrated Mathematical Oncology)

"The Immunological Consequences of Spatially Fractionated Radiotherapy"

Radiotherapy (RT) is the single most frequently used cancer treatment, with approximately 60% of patients undergoing RT alone or in conjunction with other therapeutics. However, many patients develop RT-induced lymphopenia, which has been associated with decreased overall survival in head and neck cancer patients. Thus, it is conceivable that sparing select immune populations may improve patient outcomes. One potential method of minimizing the adverse effects of RT on the immune response is the use of spatially fractionated radiotherapy (SFRT), administered through GRID blocks to create areas of low and high dose exposure. We hypothesize that the regions receiving low dose may act as immune reservoirs wherein the anti-tumor immune population is protected from RT-induced death. We develop and calibrate a mechanistic agent-based model of tumor-immune interactions to investigate the therapeutic utility of SFRT. Initializing the model with the multiplex immunohistochemistry / immunofluorescence slides of 30 patients with head and neck cancer, we identify specific GRID block architectures and treatment schedules that are better suited, with respect to anti-tumor immune infiltration and patient outcome, for specific pre-treatment tumor immune microenvironment states.
Additional authors: Nina Obertopp, Department of Immunology at H. Lee Moffitt Cancer Center & Research Institute, and Cancer Biology Ph.D. Program, University of South Florida, Tampa, Florida, USA; José Penagaricano, Department of Radiation Oncology at H. Lee Moffitt Cancer Center & Research Institute; Kosj Yamoah, Department of Radiation Oncology at H. Lee Moffitt Cancer Center & Research Institute; Shari Pilon-Thomas, Department of Immunology at H. Lee Moffitt Cancer Center & Research Institute; Heiko Enderling, Departments of Integrated Mathematical Oncology at H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, 33612, USA;

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Ibrahim Chamseddine

Massachusetts General Hospital, Harvard Medical School (Radiation Oncology)

"Towards Personalized Oncology: Machine Learning-Driven Radiotherapy Across Multiple Disease Sites"

Radiotherapy (RT) is a prominent modality in cancer treatments, utilized in over half of the patients, either as a standalone therapy or in combination with other treatments. However, current RT planning predominantly focuses on dose prescription, neglecting patient-specific properties and leading to variable responses between patients. This highlights the need for personalized strategies to enhance treatment outcomes. To advance towards personalized RT, we employed machine learning (ML) techniques across hepatocellular carcinoma (HCC), prostate cancer, and brain and head and neck cancers. By leveraging ML feature selection on clinical data, we identified predictors of tumor control, survival, and toxicity. We incorporated medical images in prostate and brain cancers using deep learning to further enhance the predictive models. These models facilitated the stratification of patients into low- and high-risk groups, enabling treatment modifications for those in need. We refined our approach by generating an ML-based decision map for personalized treatment selection in HCC and integrating ML techniques with treatment planning systems to optimize patient-specific therapies. We aimed through ML to identify risk groups in multiple disease sites and adapt therapies accordingly, with the future goal of introducing a paradigm shift towards fully personalized RT.

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Alexander B. Brummer

College of Charleston (Department of Physics and Astronomy)

"Data-driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables"

In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.
Additional authors: Agata Xella, Beckman Research Institute, City of Hope National Medical Center; Ryan Woodall, Beckman Research Institute, City of Hope National Medical Center; Vikram Adhikarla, Beckman Research Institute, City of Hope National Medical Center; Heyrim Cho, University of California, Riverside; Margarita Gutova, Beckman Research Institute, City of Hope National Medical Center; Christine Brown, Beckman Research Institute, City of Hope National Medical Center; Russell Rockne, Beckman Research Institute, City of Hope National Medical Center

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