A comment on pulsatile pipe flow

This article is concerned with analytic solutions of flows in cylindrical and annular pipes subject to an arbitrary time dependent pressure gradient and arbitrary initial flow

Mathematical Modelling of Variable Porosity Coatings for Dual Drug Delivery

In this paper we describe a theoretical mathematical model of dual drug delivery from a durable polymer coated medical device. We demonstrate how the release rate of each drug may in principle be controlled by altering the initial loading configuration of the two drugs. By varying the underlying microstructure of polymer coating, further control may be obtained, providing the opportunity to tailor the release profile of each drug for the given application

A general model of coupled drug release and tissue absorption for drug delivery devices

In this paper we present a general model of drug release from a drug delivery device and the subsequent transport in biological tissue. The model incorporates drug diffusion, dissolution and solubility in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue. Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations. One of the novelties is the generality of the model in each layer. Within the drug coating, our model includes diffusion as well as three different models of dissolution. We show that the model may also be used in cases where dissolution is rapid or not relevant, and additionally when drug release is not limited by its solubility. Within the biological tissue, the model can account for nonlinear saturable reversible binding, with linear reversible binding and linear irreversible binding being recovered as special cases. The generality of our model will allow the simulation of the release from a wide range of drug delivery devices encompassing many different applications. To demonstrate the efficacy of our model we simulate results for the particular application of drug release from arterial stents

A general model of coupled drug release and tissue absorption for drug delivery devices

In this paper we present a general model of drug release from a drug delivery device and the subsequent transport in biological tissue. The model incorporates drug diffusion, dissolution and solubility in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue. Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations. One of the novelties is the generality of the model in each layer. Within the drug coating, our model includes diffusion as well as three different models of dissolution. We show that the model may also be used in cases where dissolution is rapid or not relevant, and additionally when drug release is not limited by its solubility. Within the biological tissue, the model can account for non-linear saturable reversible binding, with linear reversible binding and linear irreversible binding being recovered as special cases. The generality of our model will allow the simulation of the release from a wide range of drug delivery devices encompassing many different applications. To demonstrate the efficacy of our model we simulate results for the particular application of drug release from arterial stents

Simulating Drug-Eluting Stents: Progress Made and the Way Forward

Drug-eluting stents have significantly improved the treatment of coronary artery disease. Compared with their bare metal predecessors, they offer reduced rates of restenosis and thus represent the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been around for over a decade, and while progress is continually being made, they are not suitable in all patients and lesion types. Furthermore there are still real concerns over incomplete healing and late stent thrombosis. In this paper, some modelling approaches are reviewed and the future of modelling and simulation in this field is discussed

A mathematical model of sonoporation using a liquid-crystalline shelled microbubble

In recent years there has been a great deal of interest in using thin shelled microbubbles as a transportation mechanism for localised drug delivery, particularly for the treatment of various types of cancer. The technique used for such site-specific drug delivery is sonoporation. Despite there being numerous experimental studies on sonoporation, the mathematical modelling of this technique has still not been extensively researched. Presently there exists a very small body of work that models both hemispherical and spherical shelled microbubbles sonoporating due to acoustic microstreaming. Acoustic microstreaming is believed to be the dominant mechanism for sonoporation via shelled microbubbles. Rather than considering the shell of the microbubble to be composed of a thin protein, which is typical in the literature, in this paper we consider the shell to be a liquid-crystalline material. Up until now there have been no studies reported in the literature pertaining to sonoporation of a liquid-crystalline shelled microbubble. A mathematical expression is derived for the maximum wall shear stress, illustrating its dependency on the shell’s various material parameters. A sensitivity analysis is performed for the wall shear stress considering the shell’s thickness; its local density; the elastic constant of the liquid-crystalline material; the interfacial surface tension and; the shell’s viscoelastic properties. In some cases, our results indicate that a liquid-crystalline shelled microbubble may yield a maximum wall shear stress that is two orders of magnitude greater than the stress generated by commercial shelled microbubbles that are currently in use within the scientific community. In conclusion, our preliminary analysis suggests that using liquid-crystalline shelled microbubbles may significantly enhance the efficiency of site-specific drug delivery

Modelling phase separation in amorphous solid dispersions

Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space are lacking. Hence theoretical predictions for the timescale over which phase separation occurs in a solid dispersion are not available. In this paper, we address some of these deficiencies by (i) constructing a general multicomponent diffusion model for a dissolving solid dispersion; (ii) specializing the model to a binary drug/polymer system in storage; (iii) deriving an effective concentration dependent drug diffusion coefficient for the binary system, thereby obtaining a theoretical prediction for the timescale over which phase separation occurs; and (iv) presenting a detailed numerical investigation of the HPMCAS/Felodipine system assuming a Flory-Huggins activity coefficient. The numerical simulations exhibit numerous interesting phenomena, such as the formation of polymer droplets and strings, Ostwald ripening/coarsening, phase inversion, and droplet-to-string transitions

Mathematically Modelling The Dissolution Of Solid Dispersions

summary:A solid dispersion is a dosage form in which an active ingredient (a drug) is mixed with at least one inert solid component. The purpose of the inert component is usually to improve the bioavailability of the drug. In particular, the inert component is frequently chosen to improve the dissolution rate of a drug that is poorly soluble in water. The construction of reliable mathematical models that accurately describe the dissolution of solid dispersions would clearly assist with their rational design. However, the development of such models is challenging since a dissolving solid dispersion constitutes a non-ideal mixture, and the selection of appropriate forms for the activity coefficients that describe the interaction between the drug, the inert matrix, and the dissolution medium is delicate. In this paper, we present some preliminary ideas for modelling the dissolution of solid dispersions

Asymptotic analysis of drug dissolution in two layers having widely differing diffusivities

This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusivity is many orders of magnitude smaller. The classical Neumann similarity solution holds while the front is passing through the first layer, but this breaks down in the second layer. Asymptotic methods are used to understand what is happening in the second layer. Although this necessitates numerical computation, one interesting outcome is that only one calculation is required, no matter what the diffusivity is for the second laye

Does anisotropy promote spatial uniformity of stent-delivered drug distribution in arterial tissue?

In this article we investigate the role of anisotropic diffusion on the resulting arterial wall drug distribution following stent-based delivery. The arterial wall is known to exhibit anisotropic diffusive properties, yet many authors neglect this, and it is unclear what effect this simplification has on the resulting arterial wall drug concentrations. Firstly, we explore the justification for neglecting the curvature of the cylindrical arterial wall in favour of using a Cartesian coordinate system. We then proceed to consider three separate transport regimes (convection dominated, diffusion dominated, reaction dominated) based on the range of parameter values available in the literature. By comparing the results of a simple one-dimensional model with those of a fully three-dimensional numerical model, we demonstrate, perhaps surprisingly, that the anisotropic diffusion can promote the spatial uniformity of drug concentrations, and furthermore, that the simple analytical one-dimensional model is an excellent predictor of the three-dimensional numerical results. However, the level of uniformity and the time taken to reach a uniform concentration profile depends on the particular regime considered. Furthermore, the more uniform the profile, the better the agreement between the one-dimensional and three-dimensional models. We discuss the potential implications in clinical practice and in stent design