The Analysis of Fixed Final State Optimal Control in Bilinear System Applied to Bone Marrow by Cell-Cycle Specific (CCS) Chemotherapy

3rd International Conference on Mathematics, Science and Education 2016

数学;自然科学;教育

Rainarli, E.^1 ; Dewi, K.E.^1

Universitas Komputer Indonesia, Bandung, Indonesia^1

关键词: Bone marrow cells;    Cell cycle specific chemotherapy;    Fixed final state;    Fixed-final-state optimal control;    Optimal conditions;    Optimal control model;    Short time frames;    Treatment conditions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/824/1/012029/pdf
DOI  :  10.1088/1742-6596/824/1/012029

来源: IOP

【 摘 要 】

The research conducted by Fister & Panetta shown an optimal control model of bone marrow cells against Cell Cycle Specific chemotherapy drugs. The model used was a bilinear system model. Fister & Panetta research has proved existence, uniqueness, and characteristics of optimal control (the chemotherapy effect). However, by using this model, the amount of bone marrow at the final time could achieve less than 50 percent from the amount of bone marrow before given treatment. This could harm patients because the lack of bone marrow cells made the number of leukocytes declining and patients will experience leukemia. This research would examine the optimal control of a bilinear system that applied to fixed final state. It will be used to determine the length of optimal time in administering chemotherapy and kept bone marrow cells on the allowed level at the same time. Before simulation conducted, this paper shows that the system could be controlled by using a theory of Lie Algebra. Afterward, it shows the characteristics of optimal control. Based on the simulation, it indicates that strong chemotherapy drug given in a short time frame is the most optimal condition to keep bone marrow cells spine on the allowed level but still could put playing an effective treatment. It gives preference of the weight of treatment for keeping bone marrow cells. The result of chemotherapy's effect (u) is not able to reach the maximum value. On the other words, it needs to make adjustments of medicine's dosage to satisfy the final treatment condition e.g. the number of bone marrow cells should be at the allowed level.