One-compartment stochastic pharmacokinetic model

In this work, we consider a pharmacokinetic (PK) model with first-order drug absorption and first-order elimination that represent the concentration of drugs in the body, including both the absorption and elimination parts, and we also add a random factor to describe the variability between patients...

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Bibliographic Details
Published inUniversitas scientiarum Vol. 28; no. 1; pp. 23 - 41
Main Authors Cano Macias, Ricardo, Jiménez Moscoso, José Alfredo, Ruiz Vera, Jorge Mauricio
Format Journal Article
LanguageEnglish
Published Bogotá Editorial Pontificia Universidad Javeriana 01.07.2023
Pontificia Universidad Javeriana
Subjects
Absorption
analytic solutions
Differential equations
Drug dosages
Expected values
itô’s lemma
Laplace transforms
Mathematical models
Numerical methods
Parameter estimation
Pharmacokinetics
pk model
Statistical analysis
stochastic differential equations
Stochasticity
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Summary:In this work, we consider a pharmacokinetic (PK) model with first-order drug absorption and first-order elimination that represent the concentration of drugs in the body, including both the absorption and elimination parts, and we also add a random factor to describe the variability between patients and the environment. Using Itô’s lemma and the Laplace transform, we obtain the solutions in integral form for a single and constant dosage regimen in time. Moreover, formulas for the expected value and the variance for each case of study are presented, which allows the statistical assessment of the proposed models, as well as predicting the ideal path of drug concentration and its uncertainty. These results are important in the long-term analysis of drug concentration and the persistence of therapeutic level. Further, a numerical method for the solution of the stochastic differential equation (SDE) is introducedand developed.
ISSN:0122-7483
2027-1352
DOI:10.11144/Javeriana.SC281.ocsp