On the Validation of a Fractional Order Model for Pharmacokinetics Using Clinical Data
Abstract
:1. Introduction
2. Preliminaries
2.1. Fractional Calculus
2.2. Fractional Order Compartment Model
2.3. Sensitivity Analysis
3. Methodology
3.1. Model 1: Intravenous Bolus
3.2. Numerical Algorithm
3.2.1. The Grunwald–Letnikov
3.2.2. L1 Approximation
4. Model 2: Oral Absorption
Implementation: The Grunwald–Letnikov and L1 Approximations
- The GL Approximate Formula
- The L1 Approximation
5. Method of Manufactured Solution
- A solution is manufactured.
- The manufactured solution is passed through the governing equation to produce the new source term.
- The source term undergoes verification by being added to the governing equation.
- The code is run and compares the numerical solution to the solution manufactured in step 1 [21].
6. Results
7. Sensitivity Analysis
Clinical Data
8. Discussion
9. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Mtshali, S.; Jacobs, B.A. On the Validation of a Fractional Order Model for Pharmacokinetics Using Clinical Data. Fractal Fract. 2023, 7, 84. https://doi.org/10.3390/fractalfract7010084
Mtshali S, Jacobs BA. On the Validation of a Fractional Order Model for Pharmacokinetics Using Clinical Data. Fractal and Fractional. 2023; 7(1):84. https://doi.org/10.3390/fractalfract7010084
Chicago/Turabian StyleMtshali, Sinenhlanhla, and Byron A. Jacobs. 2023. "On the Validation of a Fractional Order Model for Pharmacokinetics Using Clinical Data" Fractal and Fractional 7, no. 1: 84. https://doi.org/10.3390/fractalfract7010084