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This paper reports a minimal model simulating the growth of a Lewy body (LB). To the best of our knowledge, this is the first model simulating LB growth. The LB is assumed to consist of a central spherical core, which is composed of membrane fragments and various dysfunctional intracellular organelles, and a halo, which is composed of alpha-synuclein (α-syn) fibrils. Membrane fragments and α-syn monomers are assumed to be produced in the soma at constant rates. The growth of the core and the halo are simulated by the Finke–Watzky model. Analytical (closed-form) solutions describing the growth of the core and the halo are obtained. A sensitivity analysis in terms of model parameters is performed. [ABSTRACT FROM AUTHOR]

Drug-eluting stents have significantly improved the treatment of coronary artery disease. They offer reduced rates of restenosis compared with their bare-metal predecessors and are the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been approved for use in humans since 2002 and yet, despite the intensive research activity over the past decade, the drug release mechanism(s) and the uptake into the arterial wall are still poorly understood. While stent manufacturers have focussed primarily on empirical methods, several mathematical models have appeared in the literature considering the release problem, the uptake problem and also the coupled problem. However, two significant challenges that remain are in understanding the drug release mechanism(s) and also the determination of the various parameters characterizing the system. These include drug diffusion coefficients and dissolution constants in the stent polymer coating as well as drug diffusion coefficients, binding/uptake rates and the magnitude of the transmural convection in the arterial wall. In this paper we attempt to address these problems. We provide analytical solutions which, when compared with appropriate experiments, may allow the various parameters of the system to be estimated via the inverse problem. The analytical solutions which we provide here for drug release in vitro may thus be used as a tool for providing insights into the mechanism(s) of release. [ABSTRACT FROM AUTHOR]