Speaker
Description
Acute myeloid leukemia (AML) is one of the most aggressive forms of leukemia, driven by uncontrolled proliferation of abnormal stem cells in the bone marrow, which disrupts normal blood cell production.
Through mathematical modeling and analysis, we aim to better understand the dynamical behaviors underlying leukemia progression and to derive insights for optimal treatment design. Starting from the AML model in~\cite{Kumar}, we extend the framework by incorporating chemotherapy dosage as a control variable~\cite{Mazel}. We study the system dynamics and formulate an optimal control problem balancing leukemic cell reduction with toxicity. Our analysis reveals a turnpike phenomenon: the optimal therapy maintains a constant intermediate dose over most of the treatment horizon. This turnpike behavior occurs near a bifurcation point linked to a manifold of equilibria.
However, prolonged dosing at specific levels may favor clonal heterogeneity and drug resistance. To address this, we introduce a refined framework incorporating sensitive and resistant subpopulations. In this setting, the turnpike behavior persists, but with a richer structure featuring two manifolds of equilibria and a turnpike value shifted to the lowest bifurcation threshold.
Finally, we propose a Model Predictive Control approach that adapts dynamically to observed cell evolution, ensuring effective regulation even when resistance mechanisms are partially unknown, thereby enhancing therapeutic success.
Bibliography
@article{Kumar,
title = {Understanding the Impact of Feedback Regulations on Blood Cell Production and Leukemia Dynamics Using Model Analysis and Simulation of Clinically Relevant Scenarios},
author = {Kumar, Rohit and Shah, Sapna Ratan and Stiehl, Thomas},
year = {2024},
journal = {Applied Mathematical Modelling},
volume = {129},
pages = {340--389},
publisher = {Elsevier},
doi = {10.1016/j.apm.2024.01.048},
langid = {american}
}
@article{Mazel,
author = {Mazel, Pauline and Grognard, Frédéric and Stiehl, Thomas and Djema, Walid},
title = {Modeling, Analysis, and Optimal Control of Leukemic Cell Population Dynamics under Therapy},
journal = {Bulletin of Mathematical Biology},
year = {2026},
note = {Under review}
}
