Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling

Hernández-Montelongo, Rosaura; Salazar-Araya, Javiera; Hernández‐Montelongo, Jacobo; García-Sandoval, J.P.

doi:10.3390/math10132171

Cited by 4 publications

(6 citation statements)

References 8 publications

(13 reference statements)

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“…The model used in the present study is based on the work of R. Hernandez-Montelongo et al (2022) [ 27 ] and describes the drug delivery process as a unidirectional diffusion, governed by Fick’s second law. The model accounts for convective phenomena from the polymer matrix to the liquid where the drug is delivered, as well as the polymer–liquid drug distribution equilibrium.…”

Section: Mathematical Modelmentioning

confidence: 99%

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Unraveling Drug Delivery from Cyclodextrin Polymer-Coated Breast Implants: Integrating a Unidirectional Diffusion Mathematical Model with COMSOL Simulations

Hernandez-Montelongo,

Salazar-Araya,

Mas-Hernández

et al. 2024

Pharmaceutics

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Breast cancer ranks among the most commonly diagnosed cancers worldwide and bears the highest mortality rate. As an integral component of cancer treatment, mastectomy entails the complete removal of the affected breast. Typically, breast reconstruction, involving the use of silicone implants (augmentation mammaplasty), is employed to address the aftermath of mastectomy. To mitigate postoperative risks associated with mammaplasty, such as capsular contracture or bacterial infections, the functionalization of breast implants with coatings of cyclodextrin polymers as drug delivery systems represents an excellent alternative. In this context, our work focuses on the application of a mathematical model for simulating drug release from breast implants coated with cyclodextrin polymers. The proposed model considers a unidirectional diffusion process following Fick’s second law, which was solved using the orthogonal collocation method, a numerical technique employed to approximate solutions for ordinary and partial differential equations. We conducted simulations to obtain release profiles for three therapeutic molecules: pirfenidone, used for preventing capsular contracture; rose Bengal, an anticancer agent; and the antimicrobial peptide KR-12. Furthermore, we calculated the diffusion profiles of these drugs through the cyclodextrin polymers, determining parameters related to diffusivity, solute solid–liquid partition coefficients, and the Sherwood number. Finally, integrating these parameters in COMSOL multiphysics simulations, the unidirectional diffusion mathematical model was validated.

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Section: Mathematical Modelmentioning

confidence: 99%

“…The model has been solved analytically via a Laplace transformation method [ 27 ]. Conversely, in this study, we use numerical methods to solve this model and compare results to the experimental data.…”

Section: Mathematical Modelmentioning

confidence: 99%

Unraveling Drug Delivery from Cyclodextrin Polymer-Coated Breast Implants: Integrating a Unidirectional Diffusion Mathematical Model with COMSOL Simulations

Hernandez-Montelongo,

Salazar-Araya,

Mas-Hernández

et al. 2024

Pharmaceutics

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“…The proposed model also contemplates a unidirectional recursive diffusion process which follows Fick’s second law while considering the convective phenomena from the polymer matrix to the PBS, where the drug is delivered, and the equilibrium of the polymer–liquid drug distribution. Results indicated that diffusion controls the delivery rate; however, as RB concentration increases, the equilibrium plays an increasing role, becoming the controlling mechanism for a longer time [ 14 ]. These sophisticated mathematical models also allow for determining the drug-concentration profile in the polymer matrix ( Figure 8 ).…”

Section: Mechanisms Of Release Of Cd/ctr-based Biopolymersmentioning

confidence: 99%

“…( B ) Prediction of the drug concentration profile in the HP-

-CD/CTR matrix. Adapted from [ 14 ], with permission from MDPI.…”

Section: Figurementioning

confidence: 99%

“…Usually, this phenomenon in CD/CTR systems is modeled by the semiempirical mathematical model of Korsmeyer–Peppas [ 12 , 13 ]. Although this tool is very useful for predicting the release kinetics before the release systems are realized, they must be used with criteria because they do not provide further insights into complex systems [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

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Coatings of Cyclodextrin/Citric-Acid Biopolymer as Drug Delivery Systems: A Review

et al. 2023

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In the early 2000s, a method for cross-linking cyclodextrins (CDs) with citric acid (CTR) was developed. This method was nontoxic, environmentally friendly, and inexpensive compared to the others previously proposed in the literature. Since then, the CD/CTR biopolymers have been widely used as a coating on implants and other materials for biomedical applications. The present review aims to cover the chemical properties of CDs, the synthesis routes of CD/CTR, and their applications as drug-delivery systems when coated on different substrates. Likewise, the molecules released and other pharmaceutical aspects involved are addressed. Moreover, the different methods of pretreatment applied on the substrates before the in situ polymerization of CD/CTR are also reviewed as a key element in the final functionality. This process is not trivial because it depends on the surface chemistry, geometry, and physical properties of the material to be coated. The biocompatibility of the polymer was also highlighted. Finally, the mechanisms of release generated in the CD/CTR coatings were analyzed, including the mathematical model of Korsmeyer–Peppas, which has been dominantly used to explain the release kinetics of drug-delivery systems based on these biopolymers. The flexibility of CD/CTR to host a wide variety of drugs, of the in situ polymerization to integrate with diverse implantable materials, and the controllable release kinetics provide a set of advantages, thereby ensuring a wide range of future uses.

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Synthesis of Zn2(BDC)2(DABCO) Metal–Organic Framework and Its Polyethylene Glycol Composite for Acetaminophen Delivery

Rahmani,

Jafariazar,

Mousavi

et al. 2024

Iran J Sci

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Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling

Cited by 4 publications

References 8 publications

Unraveling Drug Delivery from Cyclodextrin Polymer-Coated Breast Implants: Integrating a Unidirectional Diffusion Mathematical Model with COMSOL Simulations

Unraveling Drug Delivery from Cyclodextrin Polymer-Coated Breast Implants: Integrating a Unidirectional Diffusion Mathematical Model with COMSOL Simulations

Coatings of Cyclodextrin/Citric-Acid Biopolymer as Drug Delivery Systems: A Review

Synthesis of Zn2(BDC)2(DABCO) Metal–Organic Framework and Its Polyethylene Glycol Composite for Acetaminophen Delivery

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