Controlled Drug Release Asymptotics

The solution of Higushi's model for controlled release of drugs is examined when the solubility of the drug in the polymer matrix is a prescribed function of time. A time-dependent solubility results either from an external control or from a change in pH due to the activation of pH immobilized enzymes. The model is described as a one-phase moving boundary problem which cannot be solved exactly. We consider two limits of our problem. The first limit considers a solubility much smaller than the initial loading of the drug. This limit leads to a pseudo-steady-state approximation of the diffusion equation and has been widely used when the solubility is constant. The second limit considers a solubility close to the initial loading of the drug. It requires a boundary layer analysis and has never been explored before. We obtain simple analytical expressions for the release rate which exhibits the effect of the time-dependent solubility

Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found

Modelling arterial wall drug concentrations following the insertion of a drug-eluting stent

A mathematical model of a drug-eluting stent is proposed. The model considers a polymer region, containing the drug initially, and a porous region consisting of smooth muscle cells embedded in an extracellular matrix. An analytical solution is obtained for the drug concentration both in the target cells and the interstitial region of the tissue in terms of the drug release concentration at the interface between the polymer and the tissue. When the polymer region and the tissue region are considered as a coupled system it can be shown, under certain assumptions, that the drug release concentration satisfies a Volterra integral equation which must be solved numerically in general. The drug concentrations, both in the cellular and extracellular regions, are then determined from the solution of this integral equation and used in deriving the mass of drug in the cells and extracellular space

High performance simulation of drug release model and mass transport model by using hybrid platform

The controlled drug delivery in drug eluting stents exerts an important influence in decreasing restenosis in intravascular stenting. These stents are coated with drug to avoid the re-narrowing of the arterial wall. The drug is directly associated with the original bare metal stents. Drug eluting stents have plus point of a flexible time delivery of a curative drug to the neighboring arterial tissue. It treats the required injuries efficiently having negligible systemic drug interaction. This thesis aims to develop a mathematical model for describing the procedure of drug distribution from stent coating and from arterial wall. For this purpose, a mathematical model of two phase is presented to simulate the transportation of drug between coating and arterial tissue. This two-phase model explores the impact of non-dimensional parameters such as solid liquid mass transfer rate , ratio of accessible void volume to solid volume and Peclet number on drug release and mass concentrations from coating and tissue layers. For better understanding a 2D mathematical model of biodurable stent coating is developed, where the intravascular distribution of drug from an implanted drug eluting stent in arterial wall is simulated. The model integrates reversible drug binding and diffusion of drug in the stent coating. The arterial wall and coating drug diffusivities are examined for the impact of arterial drug uptake and drug release in the coating. The diffusion coefficient of drug , the diffusion coefficients of wall , , and strut embedment play an important role to regulate the drug release. Moreover, a 3D model of mass concentrations and drug release from the cross section of artery is investigated. The impact of advective and diffusive velocities is explored and these forces can be used to control the mass concentrations of drug. FEM and FDM is used for spatial and temporal discretization of model equations. The sequential and parallel algorithms are developed for numerical simulations. Furthermore, the motivation for using GPU accelerators with CUDA is explained to handle computational complexities. A hybrid CPU/GPU algorithm for the proposed models is designed and satisfactory results for parallel performance indicators such as; speedups Sp, temporal performance Tp, efficiency Ep and effectiveness Fp are obtained. The CN method gives better sequential results because it has less RMSE than GD and BD methods. However, the BD method gives good results for parallel indicators because it involves less computation than GD and CN methods. The sequential and parallel performance of BM method is better as compared to NM and PM methods. The BM method has least RMSE for both sequential and parallel algorithms. The parallel performance indicators Sp, Tp, Ep and Fp for BM method gives better performance than the other methods. Therefore, it is a superior method than the NM and PM methods. Hybrid algorithms are more efficient in large-scale problem simulations as shown in parallel performance results. The governing models in this research provide the basis of a design tool for studying and calculating drug distribution in coating and arterial wall in the application of stent-based drug delivery. The models propose in this research are used for monitoring purpose and to determine drug release, mass transport, visualization and observation. The simulations support to offer a good perception into the potential effects of different parameters such as γ1, e1, Pe, Dc, Dw, Dwx, Dwy and strut embedment can affect the efficiency of drug release

Liquid Crystal Microdroplets from Complex Binary Liquid Mixtures

Liquid crystals and binary fluid mixtures are fields of soft matter, which individually offer unique properties for applications in displays, drug delivery, sensors and optoelectronics. They are both responsive to external stimuli and may take part in self-assembly processes. When a liquid crystal becomes a component of a binary fluid mixture, one can envisage that the complex interplay presents interesting phenomena. In this work, the thermotropic liquid crystal, 4-cyano-4’-pentylbiphenyl (5CB) was combined with methanol (MeOH) to form a partially miscible liquid mixture with an upper critical solution temperature (UCST). The research presented herein is in four parts. First, the formation of liquid crystal-rich droplets by temperature-induced phase separation was investigated. The tuning of early-stage isotropic and nematic liquid crystal-rich droplet size and number through manipulation of nucleation and growth conditions was studied by exposure to simple temperature protocols in the range of 35 C to -5 C. Second, the dynamics of late-stage phase separation was investigated. This isotropic liquid-liquid crystal binary system presented a unique advantage, wherein the interactions of a binary liquid reaching equilibrium could be visualised through the optical properties of the liquid crystal,enabling a comparative study of bulk and microscale phase separation. Thirdly, the effect of surfactants and particles on this binary liquid system was investigated. Block co-polymers were found to increase nucleation points, and silica nanoparticles were found to lead to porous structures. Finally, the reversibility of the binary system was exploited for the production of microparticles. Reactive mesogens were incorporated into the liquid crystal 5CB, and photopolymerisation was employed to create temperature-responsive porous microparticles, which could be tuned in its size and ability to shrink and swell. Furthermore, the binary liquid could be separated from the microparticle by heating. The results achieved through this work offer a potential for the development of finely tuned liquid crystal droplets and microparticle production by simple temperature control, and offer novel insights into liquid-liquid phase separation, and the optical manipulation of liquid crystals