MS09 - ONCO-03

MathOnco Subgroup Mini-Symposium: At the Interface of Modeling and Machine Learning (Part 2)

Friday, July 18 at 4:00pm

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Note: this minisymposia has multiple sessions. The other session is: and Part-1.

Jana Gevertz (The College of New Jersey), Thomas Hillen (University of Alberta), Linh Huynh (Dartmouth College)

Description:

Mathematical oncology models describe cancer dynamics using biologically motivated equations that are validated using experimental data. Machine learning models, on the other hand, leverage vast amounts of data to make predictions without necessarily including any a-priori biological knowledge. Mathematical models result in biologically interpretable predictions, whereas machine learning models excel at handling complex, high-dimensional datasets. Thus, work at the interface of modeling and machine learning holds the promise of realizing the advantages of both methods. In this mini-symposium, we will showcase how cancer research benefits from a combined approach of mathematical modeling and machine learning.

John Metzcar

University of Minnesota

"Evaluation of mechanistic and machine learning modeling approaches for glioblastoma recurrence prediction using white blood cell dynamics"

Glioblastoma (GBM) is the most aggressive primary brain tumor, with median recurrence times of approximately 9–11 months following surgery, despite intensive standard-of-care interventions. Early detection of recurrence is crucial for timely enrollment in clinical trials, potentially improving patient outcomes. The significant impact of GBM and its associated therapies on the immune system suggests clinically obtained white blood cell (WBC) counts with differential as possible biomarkers for recurrence prediction. We explore how mechanistic ODE modeling, capturing tumor-immune interactions and treatment impacts, compares with data-driven techniques (GPR and CPH) in predicting GBM recurrence. We apply methods individually and in hybrid combinations to patient-specific WBC trajectories spanning the perioperative period through recurrence. This comparative analysis evaluates predictive accuracy, interpretability, and clinical relevance across methodologies. Our aim is to share preliminary insights from applying multiple modeling strategies to a common clinical problem. By evaluating how each technique performs in the context of GBM recurrence, we hope to better understand their respective advantages and limitations. This work serves as a step toward assessing whether integrating mechanistic with data-driven models enables improved recurrence prediction through a clinically determined, dynamic biomarker.

Lena Podina

University of Waterloo

"Universal Physics-Informed Neural Networks and Their Applications"

Differential equations are widely used to model systems such as predator-prey interactions, and the effect of chemotherapy on cancer cells. However, in order to construct these models, assumptions must be made about the behaviour of these systems, which may require significant manual distillation of the literature if the model is large. In this talk, I will discuss Universal Physics-Informed Neural Networks (UPINNs), and show how UPINNs can be used to learn unknown terms in ordinary and partial differential equations from sparse and noisy data. This approach allows one to use machine learning to identify the best way to model a system, rather than relying on prior assumptions. Physics Informed Neural Networks (PINNs) have been very successful in a sparse data regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). The Universal PINN approach (UPINN) adds a neural network that learns a representation of unknown hidden terms in the differential equation. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In our work, we demonstrate strong performance of UPINNs even when provided with very few measurements of noisy data in both the ODE and PDE regime. We apply UPINNs to learning predator-prey interaction in the Lotka-Volterra model, chemotherapy drug action terms in a model of cancer cell growth, and terms in Burgers’ PDE. UPINNs could be instrumental to paving the way to allow machine learning to help applied mathematicians model systems in a more automatic, data-driven way even when observations are sparse.

Kit Gallagher

University of Oxford, Moffitt Cancer Center

"Predicting Treatment Outcomes from Adaptive Therapy — A New Mathematical Biomarker"

Adaptive Therapy dynamically adjusts drug treatment to control, rather than minimize, the tumor burden of metastatic cancer, thus suppressing the growth of treatment-resistant cell populations and delaying patient relapse. Promising clinical results in prostate cancer indicate the potential of adaptive treatment protocols, but demonstrate broad heterogeneity in patient response. This naturally leads to the question: why does this heterogeneity occur, and is a ‘one-size-fits-all' protocol best for patients across this spectrum of responses? Using deep reinforcement learning, we obtain personalized and clinically-feasible treatment protocols based on individual patient dynamics, and present a framework to generate these treatment schedules based on the patient's response to the first treatment cycle. From a Lotka–Volterra tumor model, we also obtain a predictive expression for the expected benefit from Adaptive Therapy and propose new mathematical biomarkers that can identify the best responders from a clinical dataset after only the first treatment cycle. Overall, the proposed strategies offer personalized treatment schedules that consistently outperform clinical standard-of-care protocols.

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Annual Meeting for the Society for Mathematical Biology, 2025.