# A Mathematical Model for the Release of Peptide-Binding Drugs from Affinity Hydrogels

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## Abstract

A mathematical model for the release of peptide-binding drugs from affinity hydrogels is analyzed in detail. The model is not specific to any particular peptide/drug/gel system, and can describe drug release from a large class of affinity systems. In many cases, it is shown that the model can be reduced to a coupled pair of nonlinear partial differential equations for the total drug and peptide. Quantitative information relating the rate of drug release to the values of the model parameters is presented. Numerical solutions are displayed that illustrate the rich variety of release behaviors the system is capable of exhibiting. Theoretical release profiles generated by the model are compared with experimental release data from three different studies, and good agreement is found. The development of reliable mathematical models for affinity hydrogels will provide useful design tools for these systems.

## Keywords

Drug delivery Affinity-based delivery system Peptide-binding drug Mathematical model## Notes

### Acknowledgments

We gratefully acknowledge the support of the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland (SFI) Investigator Award 12/IA/1683. Dr Meere thanks NUI Galway for the award of a travel grant. We thank the referees for their helpful suggestions to improve the paper.

### Conflict of interest

Tuoi T. N. Vo and Martin G. Meere declare that they have no conflicts of interest.

### Ethical Standards

No human or animal studies were carried out by the authors for this article.

## Supplementary material

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