Juergen Siepmann

Mathematical modeling of drug delivery.

Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design parameters of the dosage form on the resulting drug concentration time profiles at the site of action and the pharmacodynamic effects will become predictable.

Gastroretentive drug delivery systems

A controlled drug delivery system with prolonged residence time in the stomach is of particular interest for drugs that i) are locally active in the stomach, ii) have an absorption window in the stomach or in the upper small intestine, iii) are unstable in the intestinal or colonic environment, or iv) exhibit low solubility at high pH values. This article gives an overview of the parameters affecting gastric emptying in humans as well as on the main concepts used to design pharmaceutical dosage forms with prolonged gastric residence times. In particular, bioadhesive, size-increasing and floating drug delivery systems are presented and their major advantages and shortcomings are discussed. Both single- and multiple-unit dosage forms are reviewed and, if available, results from in vivo trials are reported.

Diffusion-controlled drug delivery systems: calculation of the required composition to achieve desired release profiles

The aim of this study was to investigate the effect of the composition of diffusion-controlled release devices (type and amount of plasticizer, type of polymer) on the drug diffusivity and the resulting release kinetics in a quantitative way. Diltiazem hydrochloride and theophylline were investigated in ethyl cellulose (EC) and Eudragit((R)) RS 100, plasticized with various amounts of acetyltributyl citrate (ATBC), acetyltriethyl citrate (ATEC), dibutyl phthalate (DBP), dibutyl sebacate (DBS), diethyl phthalate (DEP), and tributyl citrate (TBC). Thin drug-containing films (monolithic solutions) were used to determine the diffusion coefficients experimentally. The effect of the type and amount of plasticizer on the drug diffusivity was found to be significant, whereas the chain length of the polymer only played a minor rule in the investigated systems. Interestingly, a quantitative relationship between the diffusion coefficient of the drug and the plasticizer level could be established. Based on these results, the release kinetics of diffusion-controlled drug delivery systems could be predicted. In this study, the release patterns from microparticles were calculated and the significant effect of the composition of the device on the resulting release rate was simulated. The latter could be effectively modified by varying the type and amount of plasticizer. Independent experiments verified the theoretical predictions. The practical benefit of the presented method is to calculate the required composition of diffusion-controlled drug delivery systems (monolithic solutions) to achieve desired release profiles.

Mathematical modeling of drug dissolution

The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particles surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role.

A New Mathematical Model Quantifying Drug Release from Bioerodible Microparticles Using Monte Carlo Simulations

AbstractPurpose. The major objectives of this study were to 1) develop a new mathematical model describing all phases of drug release from bioerodible microparticles; 2) evaluate the validity of the theory with experimental data; and 3) use the model to elucidate the release mechanisms in poly(lactide-co-glycolide acid)-based microspheres. Methods. 5-Fluorouracil-loaded microparticles were prepared with an oil-in-water solvent extraction technique and characterized in vitro. Monte Carlo simulations and sets of partial differential equations were used to describe the occurring chemical reactions and physical mass transport phenomena during drug release. Results. The new mathematical model considers drug dissolution, diffusion with nonconstant diffusivities and moving boundary conditions, polymer degradation/erosion, time-dependent system porosities, and the three-dimensional geometry of the devices. In contrast with previous theories, this model is able to describe the observed drug release kinetics accurately over the entire period of time, including 1) initial “burst” effects; 2) subsequent, approximately zero-order drug release phases; and 3) second rapid drug release phases. Important information, such as the evolution of the drug concentration profiles within the microparticles, can be calculated. Conclusions. A new, mechanistic mathematical model was developed that allows further insight into the release mechanisms in bioerodible microparticles.

Blends of enteric and GIT-insoluble polymers used for film coating: physicochemical characterization and drug release patterns

THE OBJECTIVES OF THIS STUDY WERE: (i). to use blends of gastrointestinal tract (GIT)-insoluble and enteric polymers (ethyl cellulose and Eudragit L) as coating materials for multiparticulate controlled release dosage forms; (ii). to investigate the effects of the polymer blend ratio and coating level on the resulting drug release patterns; and (iii). to explain the observed phenomena based on the physicochemical properties of the systems. Propranolol HCl-loaded pellets were coated in a fluidized bed coater with organic polymer solutions; thin, drug-containing and drug-free, polymeric films were prepared using a casting knife. In vitro drug release, water uptake and dry weight loss studies were performed in 0.1 M HCl and phosphate buffer pH 7.4, respectively. The apparent drug diffusion coefficients within the polymeric systems were determined using different experimental and theoretical techniques (side-by-side diffusion cells, in vitro drug release from thin films; exact and approximate solutions of Ficks second law of diffusion). A broad range of drug release patterns from coated pellets could be achieved by varying the GIT-insoluble:enteric polymer blend ratio. With increasing relative amounts of Eudragit L, the release rates in both media significantly increased. The increase at low pH could be attributed to an increase in water uptake, as observed with thin films. Interestingly, only partial Eudragit L leaching occurred in phosphate buffer pH 7.4 even at high enteric polymer contents, indicating that the GIT-insoluble polymer effectively hindered the dissolution of the entrapped Eudragit L. At high pH, both polymer leaching and polymer swelling contributed to the control of drug release. The determined apparent drug diffusion coefficients take the two effects adequately into account.

Polymer Blends Used for the Coating of Multiparticulates: Comparison of Aqueous and Organic Coating Techniques

AbstractPurpose. The purpose of this study was to use polymer blends for the coating of pellets and to study the effects of the type of coating technique (aqueous vs. organic) on drug release. Methods. Propranolol HCl-loaded pellets were coated with blends of a water-insoluble and an enteric polymer (ethyl cellulose and Eudragit L). Drug release from the pellets as well as the mechanical properties, water uptake, and dry weight loss behavior of thin polymeric films were determined in 0.1 M HCl and phosphate buffer, pH 7.4. Results. Drug release strongly depended on the type of coating technique. Interestingly, not only the slope, but also the shape of the release curves was affected, indicating changes in the underlying drug release mechanisms. The observed effects could be explained by the higher mobility of the macromolecules in organic solutions compared to aqueous dispersions, resulting in higher degrees of polymer-polymer interpenetration and, thus, tougher and less permeable film coatings. The physicochemical properties of the latter were of major importance for the control of drug release, which was governed by diffusion through the intact polymeric films and/or water-filled cracks. Conclusions. The type of coating technique strongly affects the film microstructure and, thus, the release mechanism and rate from pellets coated with polymer blends.

Drug release from MCC- and carrageenan-based pellets: Experiment and theory

Microcrystalline cellulose (MCC) is a well-established pelletisation aid. However, MCC pellets generally do not disintegrate, resulting in prolonged drug release, especially in the case of drugs with poor/low aqueous solubility. The major objectives of this study were (i) to modify the prolonged matrix-type drug release from MCC pellets by addition of a disintegrant (croscarmellose Na) or pore former (PEG 6000), (ii) to evaluate carrageenan as potential alternative pelletisation aid for manufacturing high-dose immediate release pellets, and (iii) to better understand the underlying drug release mechanisms. Pellets containing 77-90% drug with poor/low aqueous solubility (vatalanib succinate, SAG/ZK, or theophylline) were prepared by extrusion-spheronisation. All batches showed acceptable yields, aspect ratios, tensile strengths, and porosities. Drug release from MCC pellets was predominantly controlled by pure diffusion and limited drug solubility and could be quantitatively described using Ficks law. Importantly, the apparent drug diffusivity could effectively be adjusted by adding small amounts of a disintegrant or pore former, allowing for release periods ranging from a few minutes to several hours. The drug diffusion coefficients varied between 0.36 and 29 x 10(-6)cm(2)/s. In contrast, carrageenan-based pellets very rapidly disintegrated upon contact with aqueous media and released high doses of drugs with poor/low aqueous solubility within a few minutes.

Development of injection moulded matrix tablets based on mixtures of ethylcellulose and low-substituted hydroxypropylcellulose

The objective of this study was to produce sustained-release matrix tablets by means of injection moulding and to evaluate the influence of matrix composition, process temperature and viscosity grade of ethylcellulose on processability and drug release by means of a statistical design. The matrix tablets were physico-chemically characterized and the drug release mechanism and kinetics were studied. Formulations containing metoprolol tartrate (30%, model drug), ethylcellulose with dibutylsebacate (matrix former and plasticizer) and L-HPC were extruded and subsequently injection moulded into tablets (375mg, 10mm diameter, convex-shaped) at different temperatures (110, 120 and 130 degrees C). Dissolution tests were performed and tablets were characterized by means of DSC, X-ray powder diffraction studies, X-ray tomography, porosity and hardness. Tablets containing 30% metoprolol and 70% ethylcellulose (EC 4cps) showed an incomplete drug release within 24h (<50%). Formulations containing L-HPC and EC in a ratio of 20/50 and 27.5/42.5 resulted in nearly zero-order drug release, while the drug release rate was not constant when 35% L-HPC was included. Processing of these formulations was possible at all temperatures, but at higher processing temperatures the drug release rate decreased and tablet hardness increased. Higher viscosity grades of EC resulted in a faster drug release and a higher tablet hardness. The statistical design confirmed a significant influence of the EC and L-HPC concentration on drug release, while the processing temperature and EC viscosity grade did not affect drug release. Tablet porosity was low (<5%), independent of the formulation and process conditions. DSC and XRD demonstrated the formation of a solid dispersion. The hydration front in the tablets during dissolution was visualized by dynamic X-ray tomography, this technique also revealed an anisotropic pore structure through the tablet.

Modeling drug release from PVAc/PVP matrix tablets

Kollidon SR-based matrix tablets containing various amounts of diprophylline were prepared and thoroughly characterized in vitro. This includes drug release measurements in 0.1M HCl and phosphate buffer pH 7.4, monitoring of changes in the tablets height and diameter, morphology as well as dry mass upon exposure to the release media. Based on these experimental results, a mechanistic realistic mathematical theory is proposed, taking into account the given initial and boundary conditions as well as radial and axial mass transport in cylinders. Importantly, good agreement between theory and experiment was obtained in all cases, indicating that drug diffusion with constant diffusivity is the dominant mass transport mechanism in these systems. Furthermore, the proposed theory was used to quantitatively predict the effects of the initial tablet height and diameter on the resulting drug release patterns. These theoretical predictions were compared with independently measured drug release kinetics. Good agreement was observed in all cases, proving the validity of the mathematical theory and illustrating the latters practical benefit: The model can help to significantly facilitate the recipe optimization of this type of advanced drug delivery systems in order to achieve a desired release profile.