Optimal control problem with state constraints in cancer chemotherapy and treatment optimization


 The success of chemotherapy depends on the effectiveness of the drug delivery strategy and its ability to destroy cancer cells while minimizing damage to healthy tissues. This research aims to develop optimal strategies for personalized treatment of tumor invasion by chemotherapy while minimizing drug damage to healthy tissues. 
We introduce an optimal control problem with state constraints to reduce tumor cell progression while minimizing damage to normal cells. We use a nonlinear deterministic and stochastic reaction-diffusion equations system to describe the drug's effect on cancer cells.
 After conducting a mathematical analysis of the problem, we perform several numerical simulations of optimal solutions using realistic and random data to eradicate breast and lung cancer. These simulations highlight the importance of incorporating state constraints in modern cancer treatment strategies.
First, the 2D breast mesh domain; second, the tumor density on the 20th day without treatment; third, the optimal drug concentration on the 20th day of treatment; and finally, the optimal tumor density on the 20th day.
First, the 2D lung mesh; second, the tumor density on the 20th day without treatment; third, the optimal drug concentration on the 20th day of treatment; and finally, the optimal tumor density on the 20th day.

Publications


Optimal control problem with mixed control and state constraints for cancer chemotherapy and treatment optimization


David Lassounon, Aziz Belmiloudi, Mounir Haddou

2025, Preprint (Very soon available online).


A Penalization Approach in Breast Cancer Chemotherapy: Preliminary Numerical Simulations


David Lassounon, Aziz Belmiloudi, Mounir Haddou

In. Proceedings of the 10th IEEE International Conference on Optimization and Applications (ICOA), 2024, pp. 1-6


Optimal control problem in treatment strategies for breast tumors


David Lassounon, Aziz Belmiloudi, Mounir Haddou

In. Proceedings of Optimization and Applications, Lecture Notes in Computer Science (LNCS, vol 15218), Springer, 2024, pp. 293--307


Share

Tools
Translate to