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Gels
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Mathematical Modeling of Hydrogels: Gelation, Physical Properties, and Drug Delivery
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Mathematical Modeling of Hydrogels: Gelation, Physical Properties, and Drug Delivery

A special issue of Gels (ISSN 2310-2861).

Deadline for manuscript submissions: closed (15 January 2019) | Viewed by 14389

Special Issue Editors

Dr. Mark W. Tibbitt

E-Mail Website
Guest Editor
Macromolecular Engineering Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland
Interests: hydrogels; tissue engineering; drug delivery; nanoparticles; macromolecular engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Filippo Rossi

E-Mail Website
Guest Editor
Department of Chemistry, Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Via Mancinelli 7, 20131 Milan, Italy
Interests: colloids; drug delivery; nanogels; tissue engineering; transport phenomena
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical modeling has played a key role in the engineering and design of hydrogels for controlled drug delivery.

Mathematical models enable understanding of the critical physical phenomena involved in drug delivery systems and, once their predictive capability has been established, they can be used for the rational design of the device according to the desired performances.

Since the initial contributions of Prof. Takeru Higuchi in 1961, mathematical modeling of drug delivery systems has become a well-established and ever-expanding field. The development of new methods and software optimization as well as increasing computational power have contributed to a refinement of precision in drug delivery modeling. Now complex simulations can accommodate moving boundary conditions or the integration of disparate physical models. In addition, drug delivery modeling benefits not only from standard approaches based on fundamental mass, energy and momentum conservation equations, but also from methods focused on the molecular scale that act as a “computational microscope” and provide valuable insights not always accessible from an experimental point of view.

The present Special Issue is dedicated to an overview of the most relevant applications of mathematical models on the design of hydrogels for controlled drug delivery with special emphasis on gelation, physical properties, and final applications.

Dr. Mark W. Tibbitt
Dr. Filippo Rossi
Guest Editors

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. Gels 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 2600 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

  • diffusion
  • drug delivery
  • gelation
  • mathematical modeling

Related Special Issue

Published Papers (3 papers)

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Research

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15 pages, 2612 KiB  
Article
Theoretical Importance of PVP-Alginate Hydrogels Structure on Drug Release Kinetics
by Michela Abrami, Paolo Marizza, Francesca Zecchin, Paolo Bertoncin, Domenico Marson, Romano Lapasin, Filomena de Riso, Paola Posocco, Gabriele Grassi and Mario Grassi
Gels 2019, 5(2), 22; https://doi.org/10.3390/gels5020022 - 18 Apr 2019
Cited by 9 | Viewed by 3711
Abstract
Background: The new concepts of personalized and precision medicine require the design of more and more refined delivery systems. In this frame, hydrogels can play a very important role as they represent the best surrogate of soft living tissues for what concerns rheological [...] Read more.
Background: The new concepts of personalized and precision medicine require the design of more and more refined delivery systems. In this frame, hydrogels can play a very important role as they represent the best surrogate of soft living tissues for what concerns rheological properties. Thus, this paper focusses on a global theoretical approach able to describe how hydrogel polymeric networks can affect the release kinetics of drugs characterized by different sizes. The attention is focused on a case study dealing with an interpenetrated hydrogel made up by alginate and poly(N-vinyl-2-pyrrolidone). Methods: Information about polymeric network characteristics (mesh size distribution and polymer volume fraction) is deduced from the theoretical interpretation of the rheological and the low field Nuclear Magnetic Resonance (NMR) characterization of hydrogels. This information is then, embodied in the mass balance equation whose resolution provides the release kinetics. Results: Our simulations indicate the influence of network characteristics on release kinetics. In addition, the reliability of the proposed approach is supported by the comparison of the model outcome with experimental release data. Conclusions: This study underlines the necessity of a global theoretical approach in order to design reliable delivery systems based on hydrogels. Full article
(This article belongs to the Special Issue Mathematical Modeling of Hydrogels: Gelation, Physical Properties, and Drug Delivery)
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16 pages, 3532 KiB  
Article
A Diffusion-Reaction Model for Predicting Enzyme-Mediated Dynamic Hydrogel Stiffening
by Hung-Yi Liu and Chien-Chi Lin
Gels 2019, 5(1), 17; https://doi.org/10.3390/gels5010017 - 13 Mar 2019
Cited by 11 | Viewed by 4888
Abstract
Hydrogels with spatiotemporally tunable mechanical properties have been increasingly employed for studying the impact of tissue mechanics on cell fate processes. These dynamic hydrogels are particularly suitable for recapitulating the temporal stiffening of a tumor microenvironment. To this end, we have reported an [...] Read more.
Hydrogels with spatiotemporally tunable mechanical properties have been increasingly employed for studying the impact of tissue mechanics on cell fate processes. These dynamic hydrogels are particularly suitable for recapitulating the temporal stiffening of a tumor microenvironment. To this end, we have reported an enzyme-mediated stiffening hydrogel system where tyrosinase (Tyrase) was used to stiffen orthogonally crosslinked cell-laden hydrogels. Herein, a mathematical model was proposed to describe enzyme diffusion and reaction within a highly swollen gel network, and to elucidate the critical factors affecting the degree of gel stiffening. Briefly, Fick’s second law of diffusion was used to predict enzyme diffusion in a swollen poly(ethylene glycol) (PEG)-peptide hydrogel, whereas the Michaelis–Menten model was employed for estimating the extent of enzyme-mediated secondary crosslinking. To experimentally validate model predictions, we designed a hydrogel system composed of 8-arm PEG-norbornene (PEG8NB) and bis-cysteine containing peptide crosslinker. Hydrogel was crosslinked in a channel slide that permitted one-dimensional diffusion of Tyrase. Model predictions and experimental results suggested that an increasing network crosslinking during stiffening process did not significantly affect enzyme diffusion. Rather, diffusion path length and the time of enzyme incubation were more critical in determining the distribution of Tyrase and the formation of additional crosslinks in the hydrogel network. Finally, we demonstrated that the enzyme-stiffened hydrogels exhibited elastic properties similar to other chemically crosslinked hydrogels. This study provides a better mechanistic understanding regarding the process of enzyme-mediated dynamic stiffening of hydrogels. Full article
(This article belongs to the Special Issue Mathematical Modeling of Hydrogels: Gelation, Physical Properties, and Drug Delivery)
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Review

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42 pages, 2333 KiB  
Review
From Microscale to Macroscale: Nine Orders of Magnitude for a Comprehensive Modeling of Hydrogels for Controlled Drug Delivery
by Tommaso Casalini and Giuseppe Perale
Gels 2019, 5(2), 28; https://doi.org/10.3390/gels5020028 - 15 May 2019
Cited by 28 | Viewed by 4979
Abstract
Because of their inherent biocompatibility and tailorable network design, hydrogels meet an increasing interest as biomaterials for the fabrication of controlled drug delivery devices. In this regard, mathematical modeling can highlight release mechanisms and governing phenomena, thus gaining a key role as complementary [...] Read more.
Because of their inherent biocompatibility and tailorable network design, hydrogels meet an increasing interest as biomaterials for the fabrication of controlled drug delivery devices. In this regard, mathematical modeling can highlight release mechanisms and governing phenomena, thus gaining a key role as complementary tool for experimental activity. Starting from the seminal contribution given by Flory–Rehner equation back in 1943 for the determination of matrix structural properties, over more than 70 years, hydrogel modeling has not only taken advantage of new theories and the increasing computational power, but also of the methods offered by computational chemistry, which provide details at the fundamental molecular level. Simulation techniques such as molecular dynamics act as a “computational microscope” and allow for obtaining a new and deeper understanding of the specific interactions between the solute and the polymer, opening new exciting possibilities for an in silico network design at the molecular scale. Moreover, system modeling constitutes an essential step within the “safety by design” paradigm that is becoming one of the new regulatory standard requirements also in the field-controlled release devices. This review aims at providing a summary of the most frequently used modeling approaches (molecular dynamics, coarse-grained models, Brownian dynamics, dissipative particle dynamics, Monte Carlo simulations, and mass conservation equations), which are here classified according to the characteristic length scale. The outcomes and the opportunities of each approach are compared and discussed with selected examples from literature. Full article
(This article belongs to the Special Issue Mathematical Modeling of Hydrogels: Gelation, Physical Properties, and Drug Delivery)
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