Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling
In this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusio...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/13/2171 |
| _version_ | 1797408659690487808 |
|---|---|
| author | Rosaura Hernandez-Montelongo Javiera Salazar-Araya Jacobo Hernandez-Montelongo Juan Paulo Garcia-Sandoval |
| author_facet | Rosaura Hernandez-Montelongo Javiera Salazar-Araya Jacobo Hernandez-Montelongo Juan Paulo Garcia-Sandoval |
| author_sort | Rosaura Hernandez-Montelongo |
| collection | DOAJ |
| description | In this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusion process which follows Fick’s second law while considering the convective phenomena from the polymer matrix to the liquid where the drug is delivered and the polymer–liquid drug distribution equilibrium. The resulting model is solved using Laplace transformation for two scenarios: (1) a constant initial condition for a single drug delivery experiment; and (2) a recursive delivery process where the liquid medium is replaced with fresh liquid after a fixed period of time, causing a stepped delivery rate. Finally, the proposed model is validated with experimental data. |
| first_indexed | 2024-03-09T04:02:31Z |
| format | Article |
| id | doaj.art-6ebe01a68a534d80ab5a7d29cb426328 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:02:31Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6ebe01a68a534d80ab5a7d29cb4263282023-12-03T14:11:33ZengMDPI AGMathematics2227-73902022-06-011013217110.3390/math10132171Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection CouplingRosaura Hernandez-Montelongo0Javiera Salazar-Araya1Jacobo Hernandez-Montelongo2Juan Paulo Garcia-Sandoval3Department of Translational Bioengineering, University of Guadalajara, Guadalajara 44430, MexicoDepartment of Physical and Mathematical Sciences, Catholic University of Temuco, Temuco 4813302, ChileDepartment of Physical and Mathematical Sciences, Catholic University of Temuco, Temuco 4813302, ChileDepartment of Chemical Engineering, University of Guadalajara, Guadalajara 44430, MexicoIn this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusion process which follows Fick’s second law while considering the convective phenomena from the polymer matrix to the liquid where the drug is delivered and the polymer–liquid drug distribution equilibrium. The resulting model is solved using Laplace transformation for two scenarios: (1) a constant initial condition for a single drug delivery experiment; and (2) a recursive delivery process where the liquid medium is replaced with fresh liquid after a fixed period of time, causing a stepped delivery rate. Finally, the proposed model is validated with experimental data.https://www.mdpi.com/2227-7390/10/13/2171drug deliverymathematical modeldiffusionconvectioninterface equilibriumFourier series |
| spellingShingle | Rosaura Hernandez-Montelongo Javiera Salazar-Araya Jacobo Hernandez-Montelongo Juan Paulo Garcia-Sandoval Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling Mathematics drug delivery mathematical model diffusion convection interface equilibrium Fourier series |
| title | Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling |
| title_full | Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling |
| title_fullStr | Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling |
| title_full_unstemmed | Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling |
| title_short | Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling |
| title_sort | mathematical modeling of recursive drug delivery with diffusion equilibrium and convection coupling |
| topic | drug delivery mathematical model diffusion convection interface equilibrium Fourier series |
| url | https://www.mdpi.com/2227-7390/10/13/2171 |
| work_keys_str_mv | AT rosaurahernandezmontelongo mathematicalmodelingofrecursivedrugdeliverywithdiffusionequilibriumandconvectioncoupling AT javierasalazararaya mathematicalmodelingofrecursivedrugdeliverywithdiffusionequilibriumandconvectioncoupling AT jacobohernandezmontelongo mathematicalmodelingofrecursivedrugdeliverywithdiffusionequilibriumandconvectioncoupling AT juanpaulogarciasandoval mathematicalmodelingofrecursivedrugdeliverywithdiffusionequilibriumandconvectioncoupling |