A mechanistic approach to modelling the formation of a drug reservoir in the skin

It has been shown that prolonged systemic presence of a drug can cause a build-up of that drug in the skin. This drug ‘reservoir’, if properly understood, could provide useful information about recent drug-taking history of the patient. We create a pair of coupled mathematical models which combine to explore the potential for a drug reservoir to establish based on the kinetic properties of the drug. The first compartmental model is used to characterise time-dependent drug concentrations in plasma and tissue following a customisable drug regimen. Outputs from this model provide boundary conditions for the second, spatio-temporal model of drug build-up in the skin. We focus on drugs that are highly bound as this will restrict their potential to move freely into the skin but which are lipophilic so that, in the unbound form, they would demonstrate an affinity to the outer layers of the skin. Buprenorphine, a drug used to treat opiate addiction, is one example of a drug satisfying these properties. In the discussion we highlight how our study might be used to inform future experimental design and data collection to provide relevant parameter estimates for reservoir formation and its potential to contribute to enhanced drug monitoring techniques.