On a dissolution–diffusion model. Existence, uniqueness, regularity and simulations

Castillo, María Emilia Candela; Morín, Pedro

doi:10.1016/j.camwa.2015.08.004

Cited by 2 publications

(2 citation statements)

References 20 publications

(31 reference statements)

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“…In spite of these further refinements, the effect of a finite dissolution rate is still ignored in general. Nevertheless, quite often it is found that drug release is also controlled by the dissolution process of the dispersed drug particles in the matrices [ 9 , 10 ]. The effects of a finite dissolution rate have been observed for rather insoluble substances [ 11 , 12 ].…”

Section: Introductionmentioning

confidence: 99%

Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs

Lin

Tsay²

2020

Pharmaceutics

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Amending the neglect of finite dissolution in traditional release models, this study proposed a more generalized drug release model considering the simultaneous dissolution and diffusion procedure from a drug-loaded spherical matrix. How the shape factor (n = 0, 1/2, and 2/3 for the planar, cylindrical, and spherical geometry, respectively) of dispersed drug particles affected the release from the matrix was examined for the first time. Numerical solutions of this generalized model were validated by consensus with a short-time analytical solution for planar drugs and by the approach of the diffusion-controlled limits with Higuchi’s model. The drug release rate increases with the ratio of dissolution/diffusion rate (G) and the ratio of solubility/drug loading (K) but decreases with the shape factor of drug particles. A zero-order release profile is identified for planar drugs before starting the surface depletion layer, and also found for cylindrical and spherical dispersed drugs when K and G are small, i.e. the loaded drug is mainly un-dissolved and the drug release rate is dissolution-controlled. It is also shown that for the case of a small G value, the variation of drug release profile, due to the drug particle geometry, becomes prominent. Detailed comparison with the results of the traditional Higuchi’s model indicates that Higuchi’s model can be applied only when G is large because of the assumption of an instantaneous dissolution. For K = 1/101–1/2, the present analysis suggests an error of 33–85% for drug release predicted by Higuchi’s model for G = 100, 14–44% error for G = 101, while a less than 5% error for G ≧ 103.

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Section: Introductionmentioning

confidence: 99%

Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs

Lin

Tsay²

2020

Pharmaceutics

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“…Practical examples illustrate the usefulness of mathematical modeling of diffusion-controlled drug delivery. More recently, Castillo and Morin [42] have performed a mathematical model for drug dissolutiondiffusion in nonerodible nor swellable devices in order to analyze existence, uniqueness, and regularity properties of the system. e authors have obtained a coupled nonlinear system which contains a parabolic equation for the dissolved drug and an ordinary differential equation for the solid drug, which is assumed to be distributed in the whole domain into microspheres which can differ in size.…”

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confidence: 99%

On the Transient Atomic/Heat Diffusion in Cylinders and Spheres with Phase Change: A Method to Derive Closed-Form Solutions

Ferreira

Garcia

Moreira

2021

International Journal of Mathematics and Mathematical Sciences

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Analytical solutions for the transient single-phase and two-phase inward solid-state diffusion and solidification applied to the radial cylindrical and spherical geometries are proposed. Both solutions are developed from the differential equation that treats these phenomena in Cartesian coordinates, which are modified by geometric correlations and suitable changes of variables to achieve closed-form solutions. The modified differential equations are solved by using two well-known closed-form solutions based on the error function, and then equations are obtained to analyze the diffusion interface position as a function of time and position in cylinders and spheres. These exact correlations are inserted into the closed-form solutions for the slab and are used to update the roots for each radial position of the moving boundary interface. The predictions provided by the proposed analytical solutions are validated against the results of a numerical approach. Finally, a comparative study of diffusion in slabs, cylinders, and spheres is also presented for single-phase and two-phase solid-state diffusion and solidification, which shows the importance of the effects imposed by the radial cylindrical and spherical curvatures with respect to the Cartesian coordinate system in the process kinetics. The analytical model is proved to be general, as far as, a semi-infinite solution for diffusion problems with phase change exists in the form of the error function, which enables exact closed-form analytical solutions to be derived, by updating the root at each radial position the moving boundary interface.

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On a dissolution–diffusion model. Existence, uniqueness, regularity and simulations

Cited by 2 publications

References 20 publications

Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs

Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs

On the Transient Atomic/Heat Diffusion in Cylinders and Spheres with Phase Change: A Method to Derive Closed-Form Solutions

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