Abstract
The use of enhancers to increase drug release from medical devices and drug transport through tissues has been largely investigated. Researchers from different fields like polymer chemistry, materials science, pharmaceutics, bioengineering, and chemical engineering have addressed efforts to combine materials, stimuli and drugs to design effective drug delivery platforms. For instance heat has been used to increase transdermal drug delivery. Patches with iron batteries are today in the market where heat generated by the batteries increases the drug release from the patches and the permeability of the skin, increasing drug absorption. Heat has been also used to increase drug availability in the target tissue in other contexts like in chemotherapy. In this case, to avoid the side effects of the systemic chemotherapy administration, drugs are encapsulated in thermosensitive carriers that transport the drug to the target where the cargo release is enhanced by heat. The aim of the present work is to study a system of partial differential equations (PDEs), from a numerical point of view, that can been used to describe the drug transport through tissues enhanced by heat. The system is composed by nonlinear PDEs for the temperature and for the drug concentration where the drug diffusion coefficient depends on the temperature. A finite difference method is studied and the qualitative behaviour of the temperature and concentration is numerically illustrated.
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Acknowledgements
This work was supported by Centro de Matemática da Universidade de Coimbra UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. The first and the second authors were also supported by the project NEXT.parts - Next- generation of advanced hybrid parts, funded by EU’s Horizon 2020 science programme (Portugal 2020, COMPETE 2020).
Elisa Silveira was supported by the FCT PhD grant PD/BD/128058/2016 funded by the Portuguese Government through FCT/MCTES.
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Ferreira, J.A., de Oliveira, P., Silveira, E. (2020). Coupling Temperature with Drug Diffusion: A Second Order Approximation. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_33
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