Enhancing Parameter Estimation Process for Pharmacokinetic-Pharmacodynamic Models with Meta-heuristic Optimization Approaches
Authors: Lee Dongjin , Lin Chih-Wei 
Published: February 2025

Objectives: In PK-PD modeling, the gradient-based parameter estimation methods it employs pose challenges, particularly regarding the requirement for reasonable initial estimates for all model parameters. This challenge escalates as models grow in complexity with increased number of parameters. As parameter estimation entails optimizing the objective function, alternative meta-heuristic approaches offer potential solutions that may enhance parameter estimation process. In this investigation, we employed the python package pyMetaheuristic, offering 53 continuous optimization algorithms, and examined the algorithms where most of them have not evaluated within the context of classical PK-PD models. Methods: Simulation datasets were generated from (1) a two-compartment PK model with linear and nonlinear Michaelis-Menten elimination, and (2) the Friberg semi-mechanistic myelosuppression PK-PD model. The true parameters were estimated using a variety of meta-heuristic algorithms. The focus was on trajectory-based algorithms (Simulated Annealing), nature-inspired algorithms including evolutionary algorithms (Genetic Algorithm, etc.), swarm-based algorithms (Particle Swarm Optimization Algorithm, etc.), bio-inspired (Grey Wolf Optimizer, etc.), and human-based algorithms (Teaching Learning based Optimization, etc.) while also considering non-evolutionary approaches like Random Search. All algorithms were executed using identical computational resources and were subject to consistent constraints, including a maximum limit on the number of objective function executions and minimum/maximum bounds for each parameter. The performance of these algorithms was assessed based on their objective function values, parameter estimates and execution time. Results: Our findings indicate that Symbiotic Organisms Search, Teaching Learning Based Optimization, Improved Whale Optimization Algorithm, Improved Grey Wolf Optimizer, Adaptive Chaotic Grey Wolf Optimizer, Grey Wolf Optimizer, and Memetic Algorithm showed the best performance to provide reasonable parameter estimates for the ODE-based models out of the 53 evaluated algorithms. The estimates are generally within 2-fold ranges of the true parameters. Of the 7 algorithms, Teaching Learning Based Optimization and Improved Whale Optimization Algorithm have faster run times than the others and these algorithms can be made even quicker with a suitable runtime environment such as Just-In-Time compiler in Python. Initial values are not required for these algorisms. Conclusions: As multiple nature-inspired meta-heuristics algorithms demonstrated promising results, further exploration of their efficiency and robustness is warranted, particularly when applied to different models such as physiologically based pharmacokinetic models and quantitative systems models. Additionally, the proposed approach holds potential to serve as a tool for providing robust initial values in automatic development of population PK-PD models.Citations: [1] V. Pereira, pyMetaheuristic 1.9.5 (2022), https://github.com/Valdecy/pyMetaheuristic