MS03 - ONCO-02

Advances in Optimal Control Methods for Diverse Modeling Frameworks

Tuesday, July 15 at 10:20am

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Hannah Anderson (Moffitt Cancer Center), Kasia Rejniak, Moffitt Cancer Center

Description:

Optimal control is an optimization method that has largely been applied to ordinary differential equation models. However, biological systems are often modelled with other modeling frameworks, such as partial differential equations or agent-based models, to examine spatial aspects of the system. This mini-symposium will bring speakers addressing the application of optimal control methods for biological models in the context of each of these diverse modeling frameworks. We will specifically focus on the use of optimal control in treatment optimization, where a range of treatments and diseases will be considered. Optimization aims vary but include addressing drug efficacy, drug toxicity, administrative costs, and spatial constraints of disease growth. We will also evaluate the role of optimal control in the context of digital twins. Thus, this mini-symposium will highlight various modeling frameworks and a broad range of applications in mathematical biology.

Hannah Anderson

Moffitt Cancer Center

"Evaluating robustness of an optimized regimen in a virtual murine cohort of bladder cancer"

Virtual cohorts can capture the heterogeneity across patient populations and thus different responses to treatment. In this talk, we develop an ODE model of a combination therapy for mice implanted with bladder cancer. Using a murine data set, we develop a virtual cohort using a framework that consists of 1) structural identifiability, 2) modifying data use, 3) estimating parameters, 4) determining practically identifiable parameters, 5) obtaining parameter distributions, and then 6) simulating the virtual cohort alongside data. Using the parameter set that represents an average mouse from data, we perform optimal control to optimize a regimen for adoptive cell therapy in combination with gemcitabine. Then, we evaluate the robustness of this regimen by determining its efficacy when applied to the virtual murine cohort.

Christian Parkinson

Michigan State University

"Optimal control of a reaction-diffusion epidemic model with noncompliance"

We consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a portion of the population does not comply with them, and this noncompliance affects the spread of the disease. Drawing from social contagion theory, our model allows for the spread of noncompliance parallel to the spread of the disease. Control variables affect the infection rate among the compliant population, the rate of spread of noncompliance, and the rate at which non-compliant individuals return to a compliant state. We prove the existence of global-in-time solutions for fixed controls and study the regularity properties of the resulting control-to-state map. We establish the existence of optimal controls for a fairly general class of objective functions and present a first-order stationary system which is necessary for optimality. Finally, we present simulations with various parameters values to demonstrate the behavior of the model.

Xinyue Zhao

University of Tennessee Knoxville

"Optimal control of free boundary models for tumor growth"

In this talk, we will investigate the optimal control of treatment in free boundary PDE models for tumor growth. The optimal control strategy is designed to inhibit tumor growth while minimizing side effects. In order to characterize it, the optimality system is derived, and a necessary condition is obtained. Numerical simulations will be presented to illustrate the theoretical findings and assess the impact of the optimal control strategy on tumor growth dynamics.

Luis Maria Lopes da Fonseca

University of Florida

"Surrogate modeling and control of medical digital twins"

The vision of personalized medicine is to identify interventions that maintain or restore a person's health based on their individual biology. Medical digital twins, computational models that integrate a wide range of health-related data about a person and can be dynamically updated, are a key technology that can help guide medical decisions. Such medical digital twin models can be high-dimensional, multi-scale, and stochastic. To be practical for healthcare applications, they often need to be simplified into low-dimensional surrogate models that can be used for the optimal design of interventions. Here, we introduce surrogate modeling algorithms for optimal control applications. As a use case, we focus on agent-based models (ABMs), a common model type in biomedicine for which there are no readily available optimal control algorithms. By deriving surrogate models based on systems of ordinary differential equations, we show how optimal control methods can be employed to compute effective interventions, which can then be lifted back to a given ABM. The relevance of the methods introduced here extends beyond medical digital twins to other complex dynamical systems.

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Annual Meeting for the Society for Mathematical Biology, 2025.