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arXiv · 2503.17049

Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage

Giulia Cavalleri·Alain Miranville
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Abstract

In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca, On a Brain Tumor Growth Model with Lactate Metabolism, Viscoelastic Effects, and Tissue Damage (2025)], couples a Fisher-Kolmogorov type equation for tumor cell density with a reaction-diffusion equation for the lactate, a quasi-static force balance governing the displacement, and a nonlinear differential inclusion for tissue damage. The control variables, representing chemotherapy and a lactate-targeting drug, influence tumor progression and treatment response. Starting from well-posedness, regularity, and continuous dependence results already established, we define a suitable cost functional and prove the existence of optimal controls. Then, we analyze the differentiability of the control-to-state operator and establish a necessary first-order condition for treatment optimality.

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Giulia Cavalleri, Alain Miranville. 2025-03-21. Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage. https://arxiv.org/abs/2503.17049

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