Parameter Estimation for a Mechanistic Model of High Dose Irradiation Damage Using Nelder-Mead Simplex Method and Genetic Algorithm

Abstract

Radiation therapy is one of the cancer cells treatments that use high-energy radiation to shrink tumors and kill cancer cells. Radiation therapy kills cancer cells by damaging their DNA directly or creates charged particles within the cells that can in turn damage the DNA. As a side effect of the treatment, the radiation therapy can also damage the normal cell that located at parts of our body. The main goals of radiation therapy are to maximize the damaging of tumors cell and minimize the damage of normal tissue cell. Hence, in this study, we adopt an existing model of high dose irradiation damage. The purpose of this study is to estimate the six parameters of the model which are involved. Two optimization algorithms are used in order to estimate the parameters: Nelder-Mead (NM) simplex method and Genetic Algorithm (GA). Both methods have to achieve the objective function which is to minimize the sum of square error (SSE) between the experimental data and the simulation data. The performances of both algorithms are compared based on the computational time, number of iteration and value of sum of square error. The optimization process is carried out using MATLAB programming built-in functions. The parameters estimation results shown that Nelder-Mead simplex method is more superior compare to Genetic Algorithm for this problem.

Simulation and Sensitivity Analysis on the Parameter of Non-Targeted Irradiation Effects Model

“…The result on the elasticity analysis of the model illustrates that the major control response to the survival fraction of non-targeted cells is regulated by the DSBs induction coefficient among bystander cells, ϑ and successful repair probability of nontargeted cells, p. For further development, the mathematical model developed in this work should be continued with parameter fitting procedure. Parameter fitting procedure is a method which requires an experimental data in order to prove the accuracy of a mathematical model [37]. It also can be suggested that the bystander factors concentration released by the targeted cells into the medium follow a saturating Michaelis-Menten saturating function so that, the possible value of maximum signal concentration released could be analyzed.…”

Comparison of parameter fitting on the model of irradiation effects on bystander cells between Nelder-Mead simplex and particle swarm optimization

“…In [7] used NMS optimization in estimating the value of parameters in the case of high dose effects of irradiation on the targeted cells. Then in [10] showed that NMS optimization is much superior to the Genetic Algorithm in inding the least SEE between the model simulation data and the experimental data. In [11] studied the distance to the Galactic cen-ter determined by G, K, and M stars.…”