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.
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