Mathematical Biology Tumor Growth
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Abstract
Abstract
Designing combination cancer therapies requires choosing not only which agents to combine but also their relative doses and timing decisions that critically shape the trade-off between efficacy and toxicity. High-fidelity mechanistic models of tumor growth, formulated as systems of coupled PDEs, can in principle resolve how these scheduling choices interact with the tumor microenvironment, but each evaluation is computationally expensive, rendering brute-force exploration of the design space intractable. We present a Bayesian Optimization framework that treats a multiphase, vascularized, two-dimensional PDE tumor simulator as a black box and uses a Gaussian-process surrogate to find schedules that maximize therapeutic outcomes within a small budget of expensive simulations. We orchestrate the COMSOL Multiphysics solver from Python, producing a fully automated optimization loop in which a single simulation of ~650 days of tumor evolution requires roughly 80 hours of wall time. The framework is applied to three clinically relevant scenarios: (i) a two-agent regimen (docetaxel + bevacizumab), (ii) a three-agent regimen (docetaxel + bevacizumab + radiation) under reduced and full intensity, and (iii) a single-agent dose-fractionation problem in which efficacy is balanced against healthy-tissue toxicity through a weighted multi-objective formulation. The BO loop converges to clinically plausible optima with one to two orders of magnitude fewer simulations than an equivalent grid search, identifies docetaxel-induced radiosensitization as a decisive factor in the triple-therapy optimum, and recovers a fractionation regime consistent with clinical protocols when both efficacy and toxicity are considered. The framework is agnostic to the specifics of the underlying PDE model and provides a transferable methodology for design optimization of expensive engineered or biological simulators.
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@article{Lampropoulos2026Bayesian,
title = {A Bayesian-optimization framework coupling a multiphase PDE tumor model to efficiently design combination therapy schedules},
author = {Ioannis Lampropoulos and Yorgos Psarellis and Michail Kavousanakis},
journal = {arXiv (Cornell University)},
year = {2026},
doi = {10.48550/arxiv.2607.20782},
url = {https://doi.org/10.48550/arxiv.2607.20782}
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