Parameter Estimation in Cellular Radiation Effects Using PSO-SQP and GA-SQP Hybrid Methods.

Despite the current developments in mathematical modelling of biological process, some phenomena such as those encountered with the aspects of cell populations remain poorly understood. Fractional differential equations (FDEs) recently have received a significant amount of attention and demonstrated its rigor in representing real-world problems as opposed to traditional differential equations. In the present work, a systematic investigation using a mathematical approach dealing with the effects of ionizing radiation and using FDEs is proposed to illuminate some biological properties of the cell populations. For this purpose, the theoretical revelation of the cells population memory was treated within the context of FDEs, where the Mittag-Leffler function and Caputo derivatives are used to consider genetic potentials and memory traces. The model verification based on the parameter estimation algorithms is then accomplished by the implementation of two evolutionary hybrid optimization methods, namely the genetic algorithm-sequential quadratic programming (GA-SQP) and the particle swarm optimization-sequential quadratic programming (PSO-SQP). These algorithms have recently gained prominence as they present a practical approach to managing cell populations as well as their ability to effectively estimate the quality of the proposed solution by achieving the optimal solution. Insights and knowledge derived from the optimization of the objective function used in these two algorithms, whether through maximization or minimization, significantly contribute to the enhancement of evolutionary computation within the same cell population. The performance of these two algorithms is illustrated by determining the difference between the optimal results determined from GA-SQP and PSO-SQP algorithms. Both Control data and Bismuth Oxide Nanoparticles (BIONPS) survival experimental data are used. The reliability of the algorithms is elucidated based on the number of iterations, the computational time as well as the sum of squared error values. The linear quadratic method is used for treating the evolutionary computation of the cell population. By contrasting the theoretical findings with experimental results, it turns out that both PSO-SQP and GA-SQP optimization methods provide a correlation value close to experimental data and the estimated survival data. This emerging methodology reliably demonstrates the capability of the model to accurately fit the experimental data. Interestingly, a greater efficiency and effectiveness of the proposed PSO-SQP algorithm than the GA-SQP algorithm is observed suggesting hence the superiority of the PSO-SQP algorithm for determining the most realistic estimates of all the six model parameters studied herein.