Fractional modeling of drug diffusion from cylindrical tablets based on Fickian and relaxed approaches with in vivo validation

Abstract

Mathematical simulation of drug diffusion is a significant tool for predicting the bio‐transport process. Moreover, the reported models in the literature are based on Fick's approach, which leads to an infinite propagation speed. Consequently, it is essential to construct a mathematical model to represent the diffusion processes for estimating drug concentrations at different sites and throughout the circulation. Thus, in this article, the diffusion process is employed to propose three models for estimating the drug release from multi‐layer cylindrical tablets. A fractional model is presented based on Fick's approach, while classical and fractional Cattaneo models are presented using the relaxed principle. Various numerical methods are used to solve the specified problem. The numerical scheme's stability and convergence are demonstrated. Drug concentration and mass profiles are presented for the tablet and the external medium and compared with the in vivo plasma profiles. The results show the efficiency and precision of the proposed fractional models based on the fourth‐order weighted‐shifted Grünwald–Letnikov difference operator approximation. These models are compatible with the in vivo data compared with the classical Fick's one.

Non-differentiable kernel-based approximation of memory-dependent derivative for drug delivery applications

“…The physical issue of drug release from a cylindrical tablet with multiple layers is reliant on several variables. To facilitate our study, consider table 6, which concludes the used parameters values [5]. The release distances were approximated with R s ≈ 18R 0 and Z s ≈ 4Z 0 to ensure thorough depletion of the drug content in the tablet and achieve a complete release and absorption period of about 70 hours for Valsartan and 140 hours for Amlodipine, respectively.…”

“…The concentration in the tablet and the release media is dropping Table 6. Numerical values of the parameters for the simulation [5].…”

“…The time-fractional model for simulating the drug diffusion is now described as an extension of the model in [5] as mentioned below:…”

“…It has also been utilized in the laser drilling process [4], where it is necessary to consider the previously measured temperatures of each particle to accurately mimic such a complicated process. FC has also been used in biology [5,6], biochemistry [7], and quantum mechanics [8] to precisely model dynamical processes compared with integer-order calculus. Riemann-Liouville and Caputo fractional derivatives have been frequently employed in problem formulation using the memory effect [9].…”

“…It has aided in predicting and controlling the drug release and diffusion from multi-layer capsules and tablets and reaching the targeted biological tissue [22]. Various mathematical models have been proposed over the last 50 years to simulate the release and diffusion from microcapsules [23,24], capsules/tablets [5,21,25], and other drug delivery devices [6,26,27].…”