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IJMSI 2025, 20(2): 41-62 |
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Cano M R, Jiménez M. J A, Ruiz V. J M. Exact Solution of a Stochastic Differential Model for Repeated Dose Pharmacokinetics. IJMSI 2025; 20 (2) :41-62
URL: http://ijmsi.ir/article-1-2096-en.html
URL: http://ijmsi.ir/article-1-2096-en.html
Abstract:
This paper examines the dynamics of drug concentration in the body accounting for random factors like patient and environmental variability. We develop an explicit solution for drug concentration using a Stochastic Differential Equation (SDE) model. We calculate formulas for the expected value and variance, enabling statistical evaluation and prediction of the drug’s concentration trajectory and its uncertainty. The unknown parameters in the model are estimated using the method of moments. We apply our proposed methods to a real-world dataset, providing useful insights analysis of drug concentration and the determination of its therapeutic range.
Keywords: Stochastic differential equations, Brownian motion process, Analytic solutions, Stochastic simulation, Pharmacokinetics.
Type of Study: Research paper |
Subject:
General
References
1. A. Boeckmann, L. Sheiner, S. Beal, NONMEM Users Guide-Part V: Introductory Guide, NONMEM Project Group, University of California, San Francisco, 1994.
2. R. Cano, J. A. Jim'enez, J. M. Ruiz, One-Compartment Stochastic Pharmacokinetic Model, Universitas Scientiarum, 28(1), (2023), 23-41. [DOI:10.11144/Javeriana.SC281.ocsp]
3. S. Ditlevsen, A. De Gaetano, Stochastic vs. Deterministic Uptake of Dodecanedioic Acid by Isolated Rat Livers, Bull Math. Biol., 67(3), (2005b), 547-561. [DOI:10.1016/j.bulm.2004.09.005]
4. S. Donnet, A.Samson, A Review on Estimation of Stochastic Differential Equations for Pharmacokinetic/ Pharmacodynamic Models, Advanced Drug Delivery Reviews, 65(7), (2013), 929-939. [DOI:10.1016/j.addr.2013.03.005]
5. L. Ferrante, S. Bompadre, L. Leone, A Stochastic Compartmental Model with Long Lasting Infusion, Biometrical journal 45(2), (2003), 182-194. [DOI:10.1002/bimj.200390004]
6. M. Fisz, Probability Theory and Mathematical Statistics, Krieger Pub. Co, USA, 1980.
7. G. Karniadakis, Z. Zhang, Numerical Methods for Stochastic Partial Differential Equations with White Noise, Applied mathematical sciences (Springer-Verlag New York Inc.) 196, 2017.
8. H. Kitoh, M. Matsushita, K. Mishima, T. Nagata, Y. Kamiya, K. Ueda, Y. Kuwatsuka, H. Morikawa, Y. Nakai, N. Ishiguro, Pharmacokinetics and Safety After Once and Twice a Day Doses of Meclizine Hydrochloride Administered to Children with Achondroplasia, PLOS ONE 15(4), (2020), 1-13. [DOI:10.1371/journal.pone.0229639]
9. P. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, SpringerVerlag, Berlin, 1992. [DOI:10.1007/978-3-662-12616-5]
10. Z. Liu, Y. Yang, Pharmacokinetic Model Based on Multifactor Uncertain Differential Equation, Applied Mathematics and Computation, 392, (2021), 1-16. [DOI:10.1016/j.amc.2020.125722]
11. B. Oksendal, Stochastic Differential Equations: an Introduction with Applications, Springer-Verlag, Berlin-Heidelberg, 2007.
12. R. Overgaard, E. Jonsson, C. Tornoe, H. Madsen, Non-Linear Mixed Effects Models with Stochastic Differential Equations. Implementation of an Estimation Algorithm,Journal of Pharmacokinetics and Pharmacodynamics 32(1), (2005), 85-107. [DOI:10.1007/s10928-005-2104-x]
13. U. Picchini, S. Ditlevsen, A. De gaetano, Modeling the Euglycemic Hyperinsulinemic Clamp by Stochastic Differential Equations, J. Math. Biol., 53(5), (2006), 771-796. [DOI:10.1007/s00285-006-0032-z]
14. M. Ramanathan, An application of itˆo's Lemma in Population Pharmacokinetics and Pharmacodynamics, Pharm Res, 16(4), (1999a), 584-586. [DOI:10.1023/A:1011910800110]
15. M. Ramanathan, A Method for Estimating Pharmacokinetic Risks of ConcentrationDependent Drug Interactions from Preclinical Data, Drug Metabolism and Disposition, 27(12), (1999b), 1479-1487. [DOI:10.1016/S0090-9556(24)14959-8]
16. M. Rowland, T. Tozer, Clinical Pharmacokinetics: Concepts and Applications, Lippincott Williams & Wilkins, Baltimore, 1995.
17. M. Saqlain, M Alam, L R¨onneg˚ard, J. Westin, Investigating Stochastic Differential Equations Modelling for Levodopa Infusion in Patients with Parkinson's Disease European Journal of Drug Metabolism and Pharmacokinetics, 45, (2020), 41-49. [DOI:10.1007/s13318-019-00580-w]
18. T. W. Schnider, C. F. Minto, P. L. Gambus, C. Andresen, D. B. Goodale, S. L. Shafer, E. J. Youngs, The Influence of Method of Administration and Covariates on the Pharmacokinetics of Propofol in Adult Volunteers, Anesthesiology, 88(5), (1998), 1170-1182. [DOI:10.1097/00000542-199805000-00006]
19. C. Scholl, A. Lepper, T. Lehr, N. Hanke, K. L. Schneider, J. Brockm¨oller, T. Seufferlein, J. C. Stingl, Population Nutrikinetics of Green Tea Extract, PLOS ONE, 13(2), (2018), e0193074. [DOI:10.1371/journal.pone.0193074]
20. C. H. Skiadas, Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential, Methodology and Computing in Applied Probability, 12(2), (2010), 261-270. [DOI:10.1007/s11009-009-9145-3]
21. G. D. Sweeney, Variability in the Human Drug Response, Thrombosis Research, 29, (1983), 3-15. [DOI:10.1016/0049-3848(83)90353-5]
22. C. W. Tornoe, J. L. Jacobse, H. Madsen, Grey-box Pharmacokinetic/ Pharmacodynamic Modelling of a Euglycaemic Clamp Study, J. Math. Biol., 48(6), (2004), 591-604. [DOI:10.1007/s00285-003-0257-z]
23. O. Vasicek, An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5(2), (1977), 177-188. [DOI:10.1016/0304-405X(77)90016-2]
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