Mathematical medicine and biology : a journal of the IMA, 2013
We consider a mathematical model that describes the leakage of heparin-binding growth factors fro... more We consider a mathematical model that describes the leakage of heparin-binding growth factors from an affinity-based delivery system. In the delivery system, heparin binds to a peptide which has been covalently cross-linked to a fibrin matrix. Growth factor in turn binds to the heparin, and growth factor release is governed by both binding and diffusion mechanisms, the purpose of the binding being to slow growth factor release. The governing mathematical model, which in its original formulation consists of six partial differential equations, is reduced to a system of just two equations. It is usually desirable that there be no passive release of growth factor from a device, with all of the growth factor being held in place via binding until such time as it is actively released by invading cells. However, there will inevitably be some passive release, and so it is of interest to identify conditions that will make this release as slow as possible. In this paper, we identify a paramete...
Journal of Thermal Science and Engineering Applications, 2014
A mathematical model is developed to evaluate the feasibility of an in vivo implanted drug delive... more A mathematical model is developed to evaluate the feasibility of an in vivo implanted drug delivery system. The delivery device consists of a cooling material coated by a drug-loaded * Corresponding author. † These authors contributed equally to this work. thermoresponsive polymeric film. Drug release is initiated by remotely dropping the temperature of the cooling material sufficiently for the temperature throughout the polymer coating to drop below its volume phase transition temperature (VPTT), causing the polymer to swell and release the drug. Drug release switches off again when heat conduction from an external fluid medium raises the polymer temperature to above the VPTT causing the polymer to collapse. Candidate cooling mechanisms based on endothermic chemical reactions, the Peltier effect, and the magnetocaloric effect are considered. In the thin polymer film limit, the model provides an upper bound for the temperature the cooling material must be lowered for drug release to be initiated. Significantly, the model predicts that the duration a thin polymer will continue to release drug in a single cycle is proportional to the square of the thickness of the cooling material. It is found that the system may be realised for realistic parameter values and materials. A simple illustrative calculation incorporating the presence of a heat source is presented, and the results suggest that conduction due to the initial temperature difference between the water and the cooling material can make the dominant contribution to heat transfer in the polymer as it reheats to its VPTT.
We consider a model for local drug re-distribution in a tissue that incorporates the effects of d... more We consider a model for local drug re-distribution in a tissue that incorporates the effects of diffusion and reversible binding with immobile sites within the tissue. The model tracks the evolution of the concentration in the tissue of free drug, specifically and non-specifically bound drug, and specific binding sites. We reduce the model to a scalar nonlinear diffusion equation for the total drug. The model is used to investigate tissue residence time for strongly bound drugs by considering a problem with uniform initial drug concentration and perfect sink boundary conditions. The behaviour predicted by the model has potential implications for the design of local drug delivery systems if the drug is strongly bound.
In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting ... more In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting stents. The generalised model is capable of predicting drug release from a number of polymer-free systems including those that exhibit nanoporous, nanotubular and smooth surfaces. We derive analytical solutions which allow us to easily determine the important parameters that control drug release. Drug release profiles are provided, and we offer design recommendations so that the release profile may be tailored to achieve the desired outcome. The models presented here are not specific to drug-eluting stents and may also be applied to other biomedical implants that use nanoporous surfaces to release a drug.
Mathematical medicine and biology : a journal of the IMA, 2013
We consider a mathematical model that describes the leakage of heparin-binding growth factors fro... more We consider a mathematical model that describes the leakage of heparin-binding growth factors from an affinity-based delivery system. In the delivery system, heparin binds to a peptide which has been covalently cross-linked to a fibrin matrix. Growth factor in turn binds to the heparin, and growth factor release is governed by both binding and diffusion mechanisms, the purpose of the binding being to slow growth factor release. The governing mathematical model, which in its original formulation consists of six partial differential equations, is reduced to a system of just two equations. It is usually desirable that there be no passive release of growth factor from a device, with all of the growth factor being held in place via binding until such time as it is actively released by invading cells. However, there will inevitably be some passive release, and so it is of interest to identify conditions that will make this release as slow as possible. In this paper, we identify a paramete...
Journal of Thermal Science and Engineering Applications, 2014
A mathematical model is developed to evaluate the feasibility of an in vivo implanted drug delive... more A mathematical model is developed to evaluate the feasibility of an in vivo implanted drug delivery system. The delivery device consists of a cooling material coated by a drug-loaded * Corresponding author. † These authors contributed equally to this work. thermoresponsive polymeric film. Drug release is initiated by remotely dropping the temperature of the cooling material sufficiently for the temperature throughout the polymer coating to drop below its volume phase transition temperature (VPTT), causing the polymer to swell and release the drug. Drug release switches off again when heat conduction from an external fluid medium raises the polymer temperature to above the VPTT causing the polymer to collapse. Candidate cooling mechanisms based on endothermic chemical reactions, the Peltier effect, and the magnetocaloric effect are considered. In the thin polymer film limit, the model provides an upper bound for the temperature the cooling material must be lowered for drug release to be initiated. Significantly, the model predicts that the duration a thin polymer will continue to release drug in a single cycle is proportional to the square of the thickness of the cooling material. It is found that the system may be realised for realistic parameter values and materials. A simple illustrative calculation incorporating the presence of a heat source is presented, and the results suggest that conduction due to the initial temperature difference between the water and the cooling material can make the dominant contribution to heat transfer in the polymer as it reheats to its VPTT.
We consider a model for local drug re-distribution in a tissue that incorporates the effects of d... more We consider a model for local drug re-distribution in a tissue that incorporates the effects of diffusion and reversible binding with immobile sites within the tissue. The model tracks the evolution of the concentration in the tissue of free drug, specifically and non-specifically bound drug, and specific binding sites. We reduce the model to a scalar nonlinear diffusion equation for the total drug. The model is used to investigate tissue residence time for strongly bound drugs by considering a problem with uniform initial drug concentration and perfect sink boundary conditions. The behaviour predicted by the model has potential implications for the design of local drug delivery systems if the drug is strongly bound.
In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting ... more In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting stents. The generalised model is capable of predicting drug release from a number of polymer-free systems including those that exhibit nanoporous, nanotubular and smooth surfaces. We derive analytical solutions which allow us to easily determine the important parameters that control drug release. Drug release profiles are provided, and we offer design recommendations so that the release profile may be tailored to achieve the desired outcome. The models presented here are not specific to drug-eluting stents and may also be applied to other biomedical implants that use nanoporous surfaces to release a drug.
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