Integrating Python optimization algorithms inside PhysPK® (PK/PD/PBPK) software for improving PK estimation methods.
Sergio Sánchez-Herrero (1,2), Marina Cuquerella-Gilabert (1,3), Serna, Jenifer (1), Rueda-Ferreiro, Almudena (1), Diego García-Álvarez (4)
(1) Simulation Department, Empresarios Agrupados Internacional S.A., Madrid, Spain; (2) Computer Science, Multimedia and Telecommunication Department, Universitat Oberta de Catalunya. Barcelona (Spain); (3) Department of Pharmacy and Pharmaceutical Technology and Parasitology, School of Pharmacy, University of Valencia, Valencia, Spain; (4) Department of Computer Science, University of Valladolid, Valladolid, Spain.
Introduction/Objectives:
Characterization of the pharmacokinetics (PK) and pharmacodynamics (PD) of a drug product through mathematical modelling approaches of the relationships between exposure, safety, and efficacy is vital for pharmacological experts and pharmaceutical companies. In addition, regulatory agencies are taken into account the importance of new innovative M&S technologies (FDA Modernization Act 2.0) [1]. Computer engineering areas have taken into account how programming languages software like Python, Julia, R, or MATLAB could enrich PK/PD models by providing better predictions and optimizations algorithmic capabilities. The main aims of this project are: (i) to lay/export automatically PhysPK® PK models inside Python environment. (ii) we will explore python minimize optimization methods, in a proof-of-concept, for a one-compartment PK model to analyse optimization methods like Nelder-Mead, BFGS, COBYLA, Newton-CG, SLSQP, among others in comparison with classical SQPS y Genetic methods usually used in PhysPK® PK/PD analysis.
Methods:
PhysPK® v.2.4.1 platform is a software based on first-principles modelling of complex systems with continuous and discrete time equations. PhysPK® has a set of methods and functions defined to estimate parameters and validate the final model a sequential quadratic programming (SQP) method and a genetic algorithm linked to First-order conditional estimation (FOCE-i) methods [2]. Any PK/PD model can be exported in the form of a black-box to python to manage and run models. To analyse python optimization methods were used scipy.optimize.minimize function. SciPy optimize provides functions for minimizing objective functions. It includes solvers for nonlinear problems, linear programming, constrained and nonlinear least-squares, root finding, and curve fitting. These optimization methods were used to estimate CL and Vc in a one-compartment PK model based on real data patient from plasma concentrations in µg/mL of Cefepime for intravenous administration [4].
Results:
Python optimization method to estimate CL and Vc in one patient for a one-compartment intra-venous PK model obtained better final J_Cost function than PhysPK® optimization methods. COBYLA and Nelder-Mead presented better results with Cl= 26.74 l/h and Vc= 60.94 L and final J_Cost= 0.042. PhysPK® solutions were Cl= 10 l/h and Vc=50 L and final J_Cost=16.41. Despite the differences, PhysPK® obtained better Cmax prediction. Both estimation results showed ratios between 0.8-1.25 for all the parameters. However, the Nelder–Mead and COBYLA techniques are heuristic search methods that can converge to non-stationary points, so PhysPK® methods should be compared with other complex Python alternative methods [5].
Conclusions:
PhysPK® could open a large promising research umbrella to integrate success optimization methods and algorithms widely used by python in other areas inside pharmacokinetic environment. PhysPK® biosimulation software is useful for estimating pharmacokinetic parameters, however, integrating innovative Python algorithms and methods could improve notoriously the tool. However, further research is needed to fully analyse the python integration methods. For example, restrictions based on pharmacokinetics approaches and future FOCE, Bayesian and SAEM analysis should be taken into account.
References:
[1] J. J. Han, Fda modernization act 2.0 allows for alternatives to animal testing (2023).
[2] Reig-Lopez J. et al. Comput Methods Programs Biomed, 189, 2020.
[3] Virtanen, Pauli, et al. "Scipy/Scipy: Scipy 1.1. 0." Zenodo (2018).
[4] Rodvold, Keith A., et al. Antimicrobial Agents and Chemotherapy 62.8 (2018): e00682-18.
[5] Lewis et al., SIAM Journal on Scientific Computing 29.6 (2007): 2507-2530.
