Modeling of diffusion and crystal dissolution in controlled release systems

Defining drug and target protein distributions after stent-based drug release: Durable versus deployable coatings

BACKGROUND

Innovations in drug eluting stent designs make it increasingly important to develop models for differentiating performance through spatial definition of drug, receptor binding and cell state.

METHODS

Two designs of sirolimus analog eluting stents were implanted into porcine coronary arteries for 28, 60 or 90 days (n = 9/time point), durable coating (Xience) and deployable absorbable coating (MiStent). Explanted arteries were evaluated for drug content (n = 3/time point) by LC-MS/MS and for drug and target protein (mTOR) distributions by immunofluorescence (IF, n = 6/time point). A computational model was developed to predict drug release and arterial distribution maps.

RESULTS

Both stents released the majority of drug load by 28 days, with different tissue retention efficiencies (91.4 ± 4.9% MiStent versus 21.5 ± 1.9% Xience, P < 0.001). Computational modeling of MiStent coating deployment and microcrystal dissolution recapitulated in vivo drug release and net tissue content and predicted that >98.5% of deployed drug remains crystalline through 90 days. Immunofluorescence and computational modeling showed peristrut drug localization for both stents, with similar peaks, but high interstrut levels only at sites of coating deployment from the absorbable coating. Co-localization of mTOR-IF with drug-IF for both devices showed persistent drug effects, though with differential drug-receptor pharmacokinetics.

CONCLUSIONS

Immunofluorescence and computational modeling provide insights into drug distribution and binding status that can help differentiate drug delivery technologies. Herein we found that tissue deployment of slow dissolving crystalline drug particles results in temporally and spatially more uniform drug delivery to interstrut zones that might otherwise be under-dosed without excess peristrut drug.

Mathematical models for dermal drug absorption

INTRODUCTION

Mathematical models of dermal transport offer the advantages of being much faster and less expensive than in vitro or in vivo studies. The number of methods used to create such models has been increasing rapidly, probably due to the steady rise in computational power. Although each of the various approaches has its own virtues and limitations, it may be difficult to decide which approach is best suited to address a given problem.

AREAS COVERED

Here we outline the basic ideas, drawbacks and advantages of compartmental and quantitative structure-activity relationship models, as well as of analytical and numerical approaches for solving the diffusion equation. Examples of special applications of the different approaches are given.

EXPERT OPINION

Although some models are sophisticated and might be used in future to predict transport through damaged or diseased skin, the comparatively low availability of suitable and accurate experimental data limits extensive usage of these models and their predictive accuracy. Due to the lack of experimental data, the possibility of validating mathematical models is limited.

Application of numerical methods for diffusion-based modeling of skin permeation

The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions.

Elaborations on the Higuchi model for drug delivery

The Higuchi model for the rate of drug release from matrix devices where the drug loading exceeds the solubility in the matrix medium, whose 50-year anniversary is celebrated in this issue, has proven to be a robust framework and an invaluable tool in developing a significant part of the modern controlled drug delivery industry. This paper reviews the conceptual and mathematical bases for this model and some consequences of its inherent assumptions. In addition, selected extensions of the model that have proven useful over the years are summarized. These include the effects of external mass transfer resistance and spatial variations of drug loading.

Development and evaluation of ethyl cellulose-based transdermal films of furosemide for improved in vitro skin permeation

Transdermal films of the furosemide were developed employing ethyl cellulose and hydroxypropyl methylcellulose as film formers. The effect of binary mixture of polymers and penetration enhancers on physicochemical parameters including thickness, moisture content, moisture uptake, drug content, drug-polymer interaction, and in vitro permeation was evaluated. In vitro permeation study was conducted using human cadaver skin as penetration barrier in modified Keshary-Chein diffusion cell. In vitro skin permeation study showed that binary mixture, ethyl cellulose (EC)/hydroxypropyl methylcellulose (HPMC), at 8.5:1.5 ratio provided highest flux and also penetration enhancers further enhanced the permeation of drug, while propylene glycol showing higher enhancing effect compared to dimethyl sulfoxide and isopropyl myristate. Different kinetic models, used to interpret the release kinetics and mechanism, indicated that release from all formulations followed apparent zero-order kinetics and non-Fickian diffusion transport except formulation without HPMC which followed Fickian diffusion transport. Stability studies conducted as per International Conference on Harmonization guidelines did not show any degradation of drug. Based on the above observations, it can be reasonably concluded that blend of EC-HPMC polymers and propylene glycol are better suited for the development of transdermal delivery system of furosemide.

Supercritical antisolvent production of biodegradable micro- and nanoparticles for controlled delivery of paclitaxel

Paclitaxel and poly (L-Lactic acid) (PLA) were co-precipitated to form micro and submicron particles in a manner similar to that used in the supercritical antisolvent with enhanced mass transfer (SAS-EM) process. As compared with conventional processes, a major advantage of supercritical CO(2) as an antisolvent in the SAS-EM process is the effective removal of residual organic solvents. In this work, the organic phase was sprayed into supercritical CO(2) (for CO(2), Tc=31.1 degrees C, Pc=73.8 bar) from a 500 microm ID capillary nozzle. Ultrasonic vibration with an amplitude of 0 to 120 microm (from a 3/8'' tip diameter titanium probe) was employed in the high pressure vessel during the antisolvent process to provide enhanced mixing between the solvent and antisolvent phases. The role and effects of ultrasonication on the properties of the resulting particles were studied. When no ultrasonication was applied, micrometer-sized particles were obtained. When ultrasonication was applied, more uniform particles in the submicron size range were obtained. The size of the particles was found to vary with the ultrasonic vibration amplitude. Encapsulation efficiencies up to 83.5% and controlled release of paclitaxel for more than 30 days were achieved with the particles fabricated in this study.

A mechanistic model of controlled drug release from polymer millirods: Effects of excipients and complex binding

The incorporation of different cyclodextrin (CD) excipients such as HPbeta-CD, beta-CD, gamma-CD or alpha-CD into polymer millirods for complexing beta-lapachone (beta-lap), a potent anti-cancer drug, significantly improved the drug release kinetics with various drug release patterns. However, such a complex system requires a mechanistically based model in order to provide a quantitative understanding of the many molecular events and processes that are essential for the rational development of millirod implants. This study focuses on mathematical modeling of drug release from PLGA cylindrical millirods. This millirod system incorporates multiple components: a PLGA matrix; excipient in free and complex forms; drug in free, bound, and crystalline forms. The model characterizes many dynamic transport and complexation processes that include radial diffusion, excipient complexation and crystalline drug dissolution. Optimal estimates of the model parameters were obtained by minimizing the difference between model simulation and experimentally measured drug release kinetics. The effects of different drug loadings on the drug release rate were simulated and compared with other data to validate this model. Whereas our model can simulate all the experimental data, the Higuchi model can simulate only some of them. Furthermore, our model incorporates mechanisms by which the processes underlying drug release from a polymer matrix can be quantitatively analyzed. These processes include drug entrapment/dissolution in the matrix, drug recrysallization, and supersaturation. This modeling study shows that complex binding capacity, which affects drug initial conditions, drug-polymer interactions, and bound drug behavior in aqueous solution, is crucial in controlling drug release kinetics.

Acyclovir permeation through rat skin: mathematical modelling and in vitro experiments

The aim of this work is to characterise the skin permeation properties of a male rat by means of a purely diffusive mathematical model based on Fick's second law. Additionally, in the attempt of proposing a reliable tool allowing the skin permeability (or resistance) determination on the basis of experimental data, the model automatically accounts also for two typical experimental conditions. In particular, drug dissolution in the donor environment and receiver sampling technique (part of the receiver volume is withdrawn and immediately replaced by fresh solvent) are considered. The results of this characterisation are then compared with those coming from a common simplified approach. Acyclovir is chosen as model drug and a thermostatic (37 degrees C) Franz cell apparatus is used to perform permeation experiments. This study suggests that Acyclovir permeation through the rat skin can be well described by the proposed model and that some differences arise in the evaluation of the full-skin resistance performed by means of our model or the usual simpler approach.

Drug release from an ensemble of swellable crosslinked polymer particles

This paper presents a new model suitable to describe the drug release from drug delivery systems constituted by an ensemble of drug loaded crosslinked polymer particles. The model accounts for the main factors affecting the drug release such as the particle size distribution, the physical state and the concentration profile of the drug inside the polymeric particles, the viscoelastic properties of the polymer-penetrant system and the dissolution-diffusion properties of the loaded drug. In order to check the validity of the model, release experiments were performed by using crosslinked polyvinyl-pyrrolidone (PVP) particles and two different model drugs, MAP (medroxyprogesterone acetate) and TEM (Temazepam). MAP and TEM were chosen because of their completely different dissolution behaviours in water. In particular, TEM undergoes a phase transition to the crystalline state upon dissolution when it is loaded in the polymeric network in the amorphous state. The comparison with the experimental results confirms that the most important factors determining the drug release kinetics can be properly accounted for.

Lidocaine loaded biodegradable nanospheres. II. Modelling of drug release

The mechanism of the release of encapsulated lidocaine from spherical nanoparticles based on poly(D,L-lactic acid) polymer carrier (PLA) was studied through mathematical modelling. The drug was incorporated in the PLA matrix with particle sizes from approximately 250 to 820 nm and corresponding loadings varying from about 7 to 32% (w/w). The rate of release correlated with the particle drug loading and was fastest at small particles with a low drug content. It was about four times slower at large particles with a high loading when the process of release took up to 100 h. Two simple models, diffusion and dissolution, were applied for the description of the experimental data of lidocaine release and for the identification of the release mechanisms for the nanoparticles of different drug loading. The modelling results showed that in the case of high drug loadings (about 30% w/w), where the whole drug or a large part of it was in the crystallised form, the crystal dissolution could be the step determining the release rate. On the other hand, the drug release was diffusion-controlled at low loadings (less than 10% w/w) where the solid drug was randomly dispersed in the matrix. The estimated values of the diffusion coefficient of lidocaine in these particles were in the range of 5-7x10(-20) m(2)/s. A significant influence of both crystal dissolution and drug diffusion on the overall rate of release was assumed at PLA nanoparticles with medium lidocaine loadings.

Mathematical modelling of drug permeation through a swollen membrane

This work proposes two different mathematical models (linear and numerical) able to simulate the drug permeation through a swollen membrane sandwiched by two external layers (trilaminate system). Moreover, a solid drug dissolution phenomenon in the donor compartment may be accounted for. Indeed, this is a situation that may often occur in permeation experiments. An insufficient stirring of the donor and of the receiver volume may give rise to two sandwiching layers and the target of a constant drug concentration in the donor compartment may be accomplished by putting a solid drug amount in the saturated donor solution. The linear model shows the advantage of having an analytical expression which extremely simplifies the calculation of the drug diffusion coefficient D inside the membrane. Its main drawback lies in the fact that it works only for thin trilaminate systems. The numerical model is more general than the linear one, as it works for all kind of trilaminate thickness and it may account for a solid powder dissolution in the donor compartment. Of course, it does not have an analytical solution and, thus, the D determination is less easy to perform as the numerical model is more time consuming than the linear one. These two models are then compared with the classical approach developed by Flynn and Barrie in order to better define its validity limits.