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Pharmaceutics
Special Issues
Mathematical Modeling in Drug Delivery
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Mathematical Modeling in Drug Delivery

A special issue of Pharmaceutics (ISSN 1999-4923). This special issue belongs to the section "Drug Delivery and Controlled Release".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 4139

Special Issue Editor

Prof. Dr. Fjóla Jónsdóttir

E-Mail Website1 Website2
Guest Editor
Mechanical Engineering, School of Engineering and Natural Sciences, University of Iceland, Hjardarhaga 2-6, 107 Reykjavik, Iceland
Interests: trandermal drug delivery; finite element modeling; diffusive transport; controlled drug release; prosthetics

Special Issue Information

Dear Colleagues,

Medical devices that release drugs in a controlled manner provide targeted drug delivery and can reduce adverse side effects. Mathematical modeling plays an important role in the design process as it can be used to study various design parameters and, hence, significantly reduce the expensive experimentation required for the optimization of such devices. Mathematical modeling relies on the careful representation of the physical situation and requires a thorough understanding of drug release kinetics, as well as mathematical expressions and modeling tools. Numerious mathematical models have been described in the literature in the past and solved either analytically or numerically; however, there are still many challenges that need to be overcome in order for a mathematical model to be an accurate and easy-to-use tool in the design of medical devices.

This Special Issue serves as a forum to bring together scientists in the field of the mathematical modeling of drug delivery. Both review and original articles are invited.

Prof. Dr. Fjóla Jónsdóttir
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Pharmaceutics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2900 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical modeling
  • drug delivery
  • controlled release system
  • drug release mechanism
  • numerical model
  • mass transport
  • diffusion
  • dissolution
  • mass transfer coefficient
  • partition coefficient

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Published Papers (3 papers)

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Research

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18 pages, 2665 KiB  
Article
The Key Role of Wettability and Boundary Layer in Dissolution Rate Test
by Alice Biasin, Federico Pribac, Erica Franceschinis, Angelo Cortesi, Lucia Grassi, Dario Voinovich, Italo Colombo, Gabriele Grassi, Gesmi Milcovich, Mario Grassi and Michela Abrami
Pharmaceutics 2024, 16(10), 1335; https://doi.org/10.3390/pharmaceutics16101335 - 18 Oct 2024
Viewed by 660
Abstract
Background/Objectives: The present work proposes a mathematical model able to describe the dissolution of poly-disperse drug spherical particles in a solution (Dissolution Rate Test—DRT). DRT is a pivotal test performed in the pharmaceutical field to qualitatively assess drug bioavailability. Methods: The proposed mathematical [...] Read more.
Background/Objectives: The present work proposes a mathematical model able to describe the dissolution of poly-disperse drug spherical particles in a solution (Dissolution Rate Test—DRT). DRT is a pivotal test performed in the pharmaceutical field to qualitatively assess drug bioavailability. Methods: The proposed mathematical model relies on the key hallmarks of DRT, such as particle size distribution, solubility, wettability, hydrodynamic conditions in the dissolving liquid of finite dimensions, and possible re-crystallization during the dissolution process. The spherical shape of the drug particles was the only cue simplification applied. Two model drugs were considered to check model robustness: theophylline (both soluble and wettable) and praziquantel (both poorly soluble and wettable). Results: The DRT data analysis within the proposed model allows us to understand that for theophylline, the main resistance to dissolution is due to the boundary layer surrounding drug particles, whereas wettability plays a negligible role. Conversely, the effect of low wettability cannot be neglected for praziquantel. These results are validated by the determination of drug wettability performed while measuring the solid–liquid contact angle on four liquids with decreasing polarities. Moreover, the percentage of drug polarity was determined. Conclusions: The proposed mathematical model confirms the importance of the different physical phenomena leading the dissolution of poly-disperse solid drug particles in a solution. Although a comprehensive mathematical model was proposed and applied, the DRT data of theophylline and praziquantel was successfully fitted by means of just two fitting parameters. Full article
(This article belongs to the Special Issue Mathematical Modeling in Drug Delivery)
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20 pages, 5222 KiB  
Article
Unraveling Drug Delivery from Cyclodextrin Polymer-Coated Breast Implants: Integrating a Unidirectional Diffusion Mathematical Model with COMSOL Simulations
by Jacobo Hernandez-Montelongo, Javiera Salazar-Araya, Elizabeth Mas-Hernández, Douglas Soares Oliveira and Juan Paulo Garcia-Sandoval
Pharmaceutics 2024, 16(4), 486; https://doi.org/10.3390/pharmaceutics16040486 - 2 Apr 2024
Viewed by 1559
Abstract
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), [...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematical Modeling in Drug Delivery)
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Review

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30 pages, 3291 KiB  
Review
Advances in Modeling Approaches for Oral Drug Delivery: Artificial Intelligence, Physiologically-Based Pharmacokinetics, and First-Principles Models
by Yehuda Arav
Pharmaceutics 2024, 16(8), 978; https://doi.org/10.3390/pharmaceutics16080978 - 24 Jul 2024
Cited by 1 | Viewed by 957
Abstract
Oral drug absorption is the primary route for drug administration. However, this process hinges on multiple factors, including the drug’s physicochemical properties, formulation characteristics, and gastrointestinal physiology. Given its intricacy and the exorbitant costs associated with experimentation, the trial-and-error method proves prohibitively expensive. [...] Read more.
Oral drug absorption is the primary route for drug administration. However, this process hinges on multiple factors, including the drug’s physicochemical properties, formulation characteristics, and gastrointestinal physiology. Given its intricacy and the exorbitant costs associated with experimentation, the trial-and-error method proves prohibitively expensive. Theoretical models have emerged as a cost-effective alternative by assimilating data from diverse experiments and theoretical considerations. These models fall into three categories: (i) data-driven models, encompassing classical pharmacokinetics, quantitative-structure models (QSAR), and machine/deep learning; (ii) mechanism-based models, which include quasi-equilibrium, steady-state, and physiologically-based pharmacokinetics models; and (iii) first principles models, including molecular dynamics and continuum models. This review provides an overview of recent modeling endeavors across these categories while evaluating their respective advantages and limitations. Additionally, a primer on partial differential equations and their numerical solutions is included in the appendix, recognizing their utility in modeling physiological systems despite their mathematical complexity limiting widespread application in this field. Full article
(This article belongs to the Special Issue Mathematical Modeling in Drug Delivery)
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