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

Area of Science:

• Mathematical Biology
• Computational Biology
• Radiation Biology

Background:

• Understanding cell population dynamics, especially under ionizing radiation, remains a challenge.
• Traditional differential equations have limitations in modeling complex biological phenomena like cell memory.
• Fractional differential equations (FDEs) offer a more robust framework for real-world biological problems.

Purpose of the Study:

• To investigate the effects of ionizing radiation on cell populations using FDEs.
• To model cell population memory and genetic potentials within the FDE framework.
• To compare the efficacy of two hybrid optimization algorithms for parameter estimation in the proposed model.

Main Methods:

• Utilized fractional differential equations with Mittag-Leffler functions and Caputo derivatives to model cell memory.
• Implemented two hybrid optimization algorithms: Genetic Algorithm-Sequential Quadratic Programming (GA-SQP) and Particle Swarm Optimization-Sequential Quadratic Programming (PSO-SQP).
• Validated the model using experimental data from control groups and Bismuth Oxide Nanoparticles (BIONPS) treated cells.

Main Results:

• Both GA-SQP and PSO-SQP algorithms demonstrated a strong correlation between the model's predictions and experimental survival data.
• The PSO-SQP algorithm exhibited greater efficiency and effectiveness compared to the GA-SQP algorithm.
• Reliability was assessed through iterations, computational time, and sum of squared errors, favoring PSO-SQP.

Conclusions:

• The proposed FDE model, incorporating cell memory, accurately fits experimental data for radiation effects.
• PSO-SQP is a superior optimization method for estimating model parameters in cell population dynamics.
• This methodology enhances evolutionary computation and provides realistic estimates for biological model parameters.