Modeling of dissolution-diffusion controlled drug release from planar polymeric systems with finite dissolution rate and arbitrary drug loading

Boundary conditions at a thin membrane for the normal diffusion equation which generate subdiffusion

We consider a particle transport process in a one-dimensional system with a thin membrane, described by the normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators, with time-dependent kernels, which act on the functions and their spatial derivatives defined on both membrane surfaces. We show how boundary conditions at the membrane change the temporal evolution of the first and second moments of particle position distribution (the Green's function) which is a solution to the normal diffusion equation. As these moments define the kind of diffusion, an appropriate choice of boundary conditions generates the moments characteristic for subdiffusion. The interpretation of the process is based on a particle random walk model in which the subdiffusion effect is caused by anomalously long stays of the particle in the membrane.

Transient Diffusion in Bi-Layer Composites With Mass Transfer Resistance: Exact Solution and Time Lag Analysis

Exact analytical and closed-form solutions to the transient diffusion in bi-layer composites with external mass transfer resistance are reported. Expressions for the concentrations and the mass permeated are derived in both the Laplace and time domains through the use of the Laplace transform Inversion Theorem. The lead and lag times, which are often of importance in the characterization of membranes and arise from the analysis of the asymptotic behavior of the mass permeated through the bi-layer composite, were also derived. The presented solutions are also compared to previously derived limiting cases of the diffusion in a bi-layer with an impermeable wall and constant concentrations at the upstream and downstream boundaries. Analysis of the time lag shows that this membrane property is independent of the direction of flow. Finally, an outline is provided of how these transient solutions in response to a step function increase in concentration can be used to derive more complex input conditions. The importance of adequately handling boundary layer effects has a wide array of applications such as the study of bi-layers undergoing phenomena of heat convection, gas film resistance, and absorption/desorption.

Boundary conditions at a thin membrane that generate non-Markovian normal diffusion

We show that some boundary conditions assumed at a thin membrane may result in normal diffusion not being the stochastic Markov process. We consider boundary conditions defined in terms of the Laplace transform in which there is a linear combination of probabilities and probability fluxes defined on both membrane surfaces. The coefficients of the combination may depend on the Laplace transform parameter. Such boundary conditions are most commonly used when considering diffusion in a membrane system unless collective or nonlocal processes in particles diffusion occur. We find Bachelier-Smoluchowski-Chapmann-Kolmogorov (BSCK) equation in terms of the Laplace transform and we derive the criterion to check whether the boundary conditions lead to fundamental solutions of diffusion equation satisfying this equation. If the BSCK equation is not met, then the Markov property is broken. When a probability flux is continuous at the membrane, the general forms of the boundary conditions for which the fundamental solutions meet the BSCK equation are derived. A measure of broken of semi-group property is also proposed. The relation of this measure to the non-Markovian property measure is discussed.

Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs

Amending the neglect of finite dissolution in traditional release models, this study proposed a more generalized drug release model considering the simultaneous dissolution and diffusion procedure from a drug-loaded spherical matrix. How the shape factor (n = 0, 1/2, and 2/3 for the planar, cylindrical, and spherical geometry, respectively) of dispersed drug particles affected the release from the matrix was examined for the first time. Numerical solutions of this generalized model were validated by consensus with a short-time analytical solution for planar drugs and by the approach of the diffusion-controlled limits with Higuchi’s model. The drug release rate increases with the ratio of dissolution/diffusion rate (G) and the ratio of solubility/drug loading (K) but decreases with the shape factor of drug particles. A zero-order release profile is identified for planar drugs before starting the surface depletion layer, and also found for cylindrical and spherical dispersed drugs when K and G are small, i.e. the loaded drug is mainly un-dissolved and the drug release rate is dissolution-controlled. It is also shown that for the case of a small G value, the variation of drug release profile, due to the drug particle geometry, becomes prominent. Detailed comparison with the results of the traditional Higuchi’s model indicates that Higuchi’s model can be applied only when G is large because of the assumption of an instantaneous dissolution. For K = 1/101–1/2, the present analysis suggests an error of 33–85% for drug release predicted by Higuchi’s model for G = 10⁰, 14–44% error for G = 10¹, while a less than 5% error for G ≧ 10³.

Development and In Vitro-In Vivo Evaluation of a Novel Sustained-Release Loxoprofen Pellet with Double Coating Layer

This study aimed to develop a novel sustained release pellet of loxoprofen sodium (LXP) by coating a dissolution-rate controlling sub-layer containing hydroxypropyl methyl cellulose (HPMC) and citric acid, and a second diffusion-rate controlling layer containing aqueous dispersion of ethyl cellulose (ADEC) on the surface of a LXP conventional pellet, and to compare its performance in vivo with an immediate release tablet (Loxinon^®). A three-level, three-factor Box-Behnken design and the response surface model (RSM) were used to investigate and optimize the effects of the citric acid content in the sub-layer, the sub-layer coating level, and the outer ADEC coating level on the in vitro release profiles of LXP sustained release pellets. The pharmacokinetic studies of the optimal sustained release pellets were performed in fasted beagle dogs using an immediate release tablet as a reference. The results illustrated that both the citric acid (CA) and ADEC as the dissolution- and diffusion-rate controlling materials significantly decreased the drug release rate. The optimal formulation showed a pH-independent drug release in media at pH above 4.5 and a slightly slow release in acid medium. The pharmacokinetic studies revealed that a more stable and prolonged plasma drug concentration profile of the optimal pellets was achieved, with a relative bioavaibility of 87.16% compared with the conventional tablets. This article provided a novel concept of two-step control of the release rate of LXP, which showed a sustained release both in vitro and in vivo.

Model of anomalous diffusion-absorption process in a system consisting of two different media separated by a thin membrane

We present the model of a diffusion-absorption process in a system which consists of two media separated by a thin partially permeable membrane. The kind of diffusion as well as the parameters of the process may be different in both media. Based on a simple model of a particle's random walk in a membrane system we derive the Green's functions, then we find the boundary conditions at the membrane. One of the boundary conditions is rather complicated and takes a relatively simple form in terms of the Laplace transform. Assuming that particles diffuse independently of one another, the obtained boundary conditions can be used to solve differential or differential-integral equations describing the processes in multilayered systems for any initial condition. We consider normal diffusion, subdiffusion, and slow subdiffusion processes, and we also suggest how superdiffusion could be included in this model. The presented method provides the functions in terms of the Laplace transform and some useful methods of calculation of the inverse Laplace transform are shown.

Modified n-HA/PA66 scaffolds with chitosan coating for bone tissue engineering: cell stimulation and drug release

The dipping-drying procedure and cross-linking method were used to make drug-loaded chitosan (CS) coating on nano-hydroxyapatite/polyamide66 (nHA/PA66) composite porous scaffold, endowing the scaffold controlled drug release functionality. The prefabricated scaffold was immersed into an aqueous drug/CS solution in a vacuum condition and then crosslinked by vanillin. The structure, porosity, composition, compressive strength, swelling ratio, drug release and cytocompatibility of the pristine and coating scaffolds were investigated. After coating, the scaffold porosity and pore interconnection were slightly decreased. Cytocompatibility performance was observed through an in vitro experiment based on cell attachment and the MTT assay by MG63 cells which revealed positive cell viability and increasing proliferation over the 11-day period in vitro. The drug could effectively release from the coated scaffold in a controlled fashion and the release rate was sustained for a long period and highly dependent on coating swelling, suggesting the possibility of a controlled drug release. Our results demonstrate that the scaffold with drug-loaded crosslinked CS coating can be used as a simple technique to render the surfaces of synthetic scaffolds active, thus enabling them to be a promising high performance biomaterial in bone tissue engineering.

The behavior of hydrophobic-core/hydrophilic-shell structured microgels at an interface: from Mickering emulsion to colloidosomes with dual-level controlled permeability

The release of model drug FITC-Dex from colloidosomes was examined in selected media and the controllable release was achieved by adjusting the pH (coarse level) and the ratio of the shell to core in the microgels (fine level).

Random walk model of subdiffusion in a system with a thin membrane

We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the probabilities (Green's functions) P(x,t) describing a particle's random walk are found. The membrane, which can be asymmetrical, is characterized by the two probabilities of stopping a random walker by the membrane when it tries to pass through the membrane in both opposite directions. Green's functions are transformed to the system in which the variables are continuous, and then the membrane permeability coefficients are given by special formulas which involve the probabilities mentioned above. From the obtained Green's functions, we derive boundary conditions at the membrane. One of the conditions demands the continuity of a flux at the membrane, but the other one is rather unexpected and contains the Riemann-Liouville fractional time derivative P(x(N)(-),t)=λ(1)P(x(N)(+),t)+λ(2)∂(α/2)P(x(N)(+),t)/∂t(α/2), where λ(1),λ(2) depending on membrane permeability coefficients (λ(1)=1 for a symmetrical membrane), α is a subdiffusion parameter, and x(N) is the position of the membrane. This boundary condition shows that the additional "memory effect," represented by the fractional derivative, is created by the membrane. This effect is also created by the membrane for a normal diffusion case in which α=1.

Numerical modelling and experimental investigation of drug release from layered silicone matrix systems

Medical devices and polymeric matrix systems that release drugs or other bioactive compounds are of interest for a variety of applications. The release of the drug can be dependent on a number of factors such as the solubility, diffusivity, dissolution rate and distribution of the solid drug in the matrix. Achieving the goal of an optimal release profile can be challenging when relying solely on traditional experimental work. Accurate modelling complementing experimentation is therefore desirable. Numerical modelling is increasingly becoming an integral part of research and development due to the significant advances in computer simulation technology. This work focuses on numerical modelling and investigation of multi-layered silicone matrix systems. A numerical model that can be used to model multi-layered systems was constructed and validated by comparison with experimental data. The model could account for the limited dissolution rate and effect of the drug distribution on the release profiles. Parametric study showed how different factors affect the characteristics of drug release. Multi-layered medical silicone matrices were prepared in special moulds, where the quantity of drug in each layer could be varied, and release was investigated with Franz-diffusion cell setup. Data for long-term release was fitted to the model and the full depletion of the system predicted. The numerical model constructed for this study, whose input parameters are the diffusion, effective dissolution rate and dimensional solubility coefficients, does not require any type of steady-state approximation. These results indicate that numerical model can be used as a design tool for development of controlled release systems such as drug-loaded medical devices.

Development of a standardized dissolution test method for inhaled pharmaceutical formulations

The aim of this research was to investigate a potential standardized test method to characterize the dissolution properties of formulations intended for pulmonary delivery. A commercially available dissolution tester was adapted to be used as a testing apparatus by incorporation of a membrane containing cassette. The cassette was designed to enclose previously air-classified formulations, so that they could be uniformly tested in the dissolution apparatus. The influence of particle size, amount of drug loading, and the composition of a simulated lung fluid (SLF) dissolution media on the dissolution rate were studied. Dissolution rate was significantly affected by the uniformity of drug loading, and particle size. Diffusion coefficients, estimated using the Higuchi model, showed an increase from 2.28 to 9.60x10(-7) cm(2)/h as the particle size decreased. Addition of DPPC (0.02%, w/v) to the SLF dissolution media resulted also resulted in an increase in the diffusion coefficient value. This study demonstrated that the developed method was reproducible and may be used to evaluate the dissolution properties of pharmaceutical inhalation products following their aerodynamic particle classification.

Accelerated release of a sparingly soluble drug from an injectable hyaluronan-methylcellulose hydrogel

An injectable hydrogel, comprised of hyaluronan and methylcellulose (HAMC), shows promise for localized, sustained delivery of growth factors for treatment of spinal cord injury (SCI). To better understand its potential for the delivery of small molecules, the release of sparingly soluble neuroprotectant, nimodipine, was investigated experimentally and via continuum modeling. This revealed that the MC in HAMC increased the solubility of sparingly soluble drug by over an order of magnitude, and enabled highly tunable release rates to be achieved by varying the method by which the drug was introduced into the scaffold. When nimodipine was introduced into HAMC in solubilized form, it was rapidly released from the scaffold within 8 h. Conversely, when nimodipine was blended into HAMC in particulate form, the release rates were greatly reduced, giving rise to complete release over 2-3 days for small, sub-micron particles, and longer times for large, 100 mum particles. The nimodipine particle-loaded gels yielded particle size-dependent, biphasic release profiles, which reflected rapid release of the solubilized drug followed by the slow, dissolution-limited release of solid nimodipine. This suggests that injectable hydrogel matrices can act as polymeric excipients that accelerate the delivery of poorly soluble drugs and yield highly tunable release rates.