Mathematical Optimization of Combination Drug Regimens

Mahya Aghaee, Helen Moore

When developing a new therapy or optimizing the dose of an established therapy, preclinical and clinical testing can provide a dose-response relationship that is used to determine the dose. However, when multiple therapies are being combined, it is challenging to test enough different combinations to find a regimen that gives the best results. Mathematical modeling can help in this and other settings. We start with a mechanistic model of a disease that incorporates therapeutic effects. This model can be validated with data. Then we apply constrained optimization methods to the model and predict a regimen that maximizes efficacy while simultaneously minimizing toxicity. The final validation is to test this predicted optimal regimen against others that are being considered. We use these techniques in a variety of disease and therapy settings to achieve better patient outcomes while also saving time and resources.

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Publications

Aghaee M, Ledzewicz U, Robbins M, Bezman N, Cho HJ, Moore H. Determining Optimal Combination Regimens for Patients with Multiple Myeloma. 2022 Nov 17, https://arxiv.org/abs/2211.09280.

Helen Moore (2018) How to mathematically optimize drug regimens using optimal control. Journal of Pharmacokinetics and Pharmacodynamics, Vol 45: 127, https://rd.springer.com/content/pdf/10.1007/s10928-018-9568-y.

Helen Moore, Lewis Strauss, and Urszula Ledzewicz (2018) Optimization of combination therapy for chronic myeloid leukemia with dosing constraints. Journal of Mathematical Biology, https://doi.org/10.1007/s00285-018-1262-6.

Urszula Ledzewicz and Helen Moore (2018) Optimal control applied to a generalized Michaelis-Menten model of CML therapy. Discrete and Continuous Dynamical Systems Series B, Vol. 23, No. 1, 331-346, doi: 10.3934/dcdsb.2018022, http://www.aimsciences.org/article/doi/10.3934/dcdsb.2018022.

Seema Nanda, Helen Moore, and Suzanne Lenhart (2007) Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Mathematical Biosciences, Vol. 210, No. 1, 143-156, https://www.sciencedirect.com/science/article/abs/pii/S0025556407000831?via%3Dihub.

Weiqing Gu and Helen Moore (2006) Optimal therapy regimens for treatment-resistant mutations of HIV. Contemporary Mathematics, Vol. 410, 139-152, https://www.ams.org/books/conm/410/conm410-endmatter.pdf