Comparative Study of Parameter Estimation Methods in Pharmacokinetic Model with Oral Administration: Simulations of Theophylline Drug Concentration


Diny Zulkarnaen(1*)

(1) UIN Sunan Gunung Djati Bandung, Indonesia
(*) Corresponding Author

Abstract


Parameter estimation for the elimination and absorption rate constants is performed in a pharmacokinetic model, where a drug is administered orally. Some methods have been introduced to estimate these parameters but without comparison which one gives better estimates. Here, two different methods are used for comparison in estimating the absorption rate constant: the Wagner-Nelson and residual methods. The Wagner-Nelson method requiring fewer data sets while the residual method uses all available data sets for estimation. For the elimination rate constant estimate, we use only the least square error method. Simulations are conducted using sample data points of Theophylline drug concentration that varies over time to estimate the parameters. These parameter values are then utilized to approximate the drug concentration over time, using both methods. These approximations are then compared with the actual data sets to see and calculate the error values so that the best method can be determined. The comparison shows that the residual method provides better approximation since this method utilizes the entire sample data points, while the Wagner-Nelson uses only the data in the beginning time, that is when the absorption process is dominant.

Keywords


Pharmacokinetic Model, Parameter Estimation, Wagner-Nelson, Residual

Full Text:

PDF

References


N. S. Al-Mumtazah, Widodo, and Indarsih, "Drug elimination in two-compartment phar macokinetic model with nonstandard finite difference approach," Int. J. Appl. Math. vol. 50, 2020.

C. N. Angstmann, B. I. Henry, B. A. Jacobs, and A. V. McGann, "An explicit numerical scheme for solving fractional order compartment models from the master equations of a stochastic process," Commun. Nonlinear Sci. Numer. Simul. vol. 68, pp. 188–202, 2019.

C. N. Angstmann et al., "Fractional order compartment models," SIAM J. Appl. Math. vol. 77, pp. 430–446, 2017.

W. E. Boyce, and R. C. DiPrima, "Elementary Differential Equations and Boundary Value Problems," John Wiley & Sons, 2012.

O. Egbelowo, “Nonlinear elimination of drug in one-compartment pharmacokinetic models: Nonstandard finite difference approach for various routes of administration,” Math. Comput. Appl., vol.23 (2018).

O. Egbelowo, C. Harley, and B. Jacobs, “Nonstandard finite difference method applied to a linear pharmacokinetics model,” Bioeng., vol. 4, 2017.

A. T. Florence, and E. G. Salole, “Routes of Drug Administration,” Wright, 1980.

M. Gibaldi, and D. Perrier, “Pharmacokinetics” Informa, 2007.

F. R. Giordano, W. P. Fox, and S. B. Horton, “A First Course in Mathematical Modeling,” Brooks/Cole, 2014.

M. A. Hedaya, “Basic Pharmacokinetics,” CRC Press, 2012.

M. Khanday, A. Rafiq, and K. Nazir, “Mathematical models for drug diffusion through the compartments of blood and tissue medium,” Alexandria J. Med., vol. 53, pp. 245–249, 2017.

J. Kim, and O. De Jesus, “Medication Routes of Administration,” StatPearls Publishing, 2024.

E. Kreyszig, “Advanced Engineering Mathematics,” John Wiley & Sons, 2011.

S. Mtshali, and B. A. Jacobs, “On the validation of a fractional order model for pharmacokinetics using clinical data,” Fractal Frac., vol 7, no. 84, 2023.

V. S. R. K. Reddy, and K. L. Narayah, “The concentration of digoxin after intravenous and oral administration studied by a two-compartment model,” Lett. Biomath., vol. 6, 2019.

W. A. Ritschel, “Handbook of Pharmacokinetics,” Drug Intelligence Publication, 1976.

M. A. Rodrigo, “Laplace transform approach to direct and inverse problems for multicompartment models,” Eur. J. Appl. Math., vol. 33, pp. 1–15, 2022.

M. Savva, “A Mathematical treatment of multiple intermittent intravenous infusion in a one-Compartment Model,” Comput. Methods and Programs in Biomed., vol. 205, 2021.

M. Savva, “Real-time analytical solutions as series formulas and heaviside off/on switch functions for multiple intermittent intravenous oinfusions in One and two-compartment models,” J. Biosci. Med., vol. 10, 2022.

L. Shargel, and A. B. C. Yu, “Applied Biopharmaceutics and Pharmacokinetics,” McGraw-Hill, 2005.

P. Sopasakis, H. Sarimveis, P. Macheras, and A. Dokoumetzidis, “Fractional calculus in pharmacokinetics,” J. Pharmacokinet. Pharmacodyn., vol. 45, pp. 107–125, 2018.

J. G. Wagner, and E. Nelson, “Percent absorbed time plots derived from blood level and/or urinary excretion data,” J. Pharm. Sci., vol. 52, pp. 610–611, 1963.

J. G. Wagner, “Pharmacokinetics for the Pharmaceutical Scientist,” CRC Press, 2019.

D. Zulkarnaen, M. S. Irfani, and E. S. Erianto, “Drug-drug interactions pharmacokinetic models with extravascular administration: estimation of elimination and absorption rate constants,” Jur. Teori Apl. Mat., vol. 7, pp. 1077–1093, 2023.




DOI: https://doi.org/10.15575/kubik.v9i1.31233

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Diny Zulkarnaen

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.


Journal KUBIK: Jurnal Publikasi Ilmiah Matematika has indexed by:

SINTA DOAJ Dimensions Google Scholar Garuda Moraref DOI Crossref

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.