Göran Frenning

Theoretical investigation of drug release from planar matrix systems: effects of a finite dissolution rate

Drug release from planar matrix systems has been investigated with special emphasis on the influence of a finite dissolution rate on the drug release profile. A mathematical model of the drug dissolution and release processes was formulated in terms of two coupled nonlinear partial differential equations (PDEs). These were solved numerically by using well-established FORTRAN routines. An approximate analytical solution, valid during the early stages of the release process, was derived. The analytical solution was compared to the numerical one and to drug release models existing in the literature. From this comparison, it was established that the analytical approximation provided a good description of the major part of the release profile, irrespective of the dissolution rate. Existing literature models, based on instantaneous dissolution, were found to agree with the numerical solution only when drug dissolution proceeded very rapidly in comparison with the diffusion process. Consequently, the new analytical short-time approximation of the drug release complements the formulas existing in the literature, since it provides a superior description of the release of slowly dissolving drugs.

Modelling of drug release from coated granular pellets

A mathematical model of drug release from coated pellets with a granular core has been developed. The model includes a dynamic description of all three main processes contributing to drug release from such a system, i.e. liquid inflow, drug dissolution, and liquid efflux caused by diffusion across the coating. The cumulative fraction of released drug has been shown to be determined by three rate constants, one for each process mentioned above, together with two dimensionless parameters. These parameters are related to the porosity of the pellet core and the solubility of the drug in the dissolution medium. The model has been validated by comparison with experimentally determined release profiles for pellets consisting of a granular core of microcrystalline cellulose containing dispersed salicylic acid, coated by a thin layer of ethyl cellulose.

Drug release modeled by dissolution, diffusion, and immobilization

This article presents a novel drug release model that combines drug dissolution, diffusion, and immobilization caused by adsorption of the drug to the tablet constituents. Drug dissolution is described by the well-known Noyes-Whitney equation and drug adsorption by a Langmuir-Freundlich adsorption isotherm, and these two processes are included as source and sink terms in the diffusion equation. The model is applicable to tablets that disintegrate into a number of approximately spherical fragments. In order to simplify the analysis it is assumed that liquid absorption, matrix swelling, and tablet disintegration are much faster than drug dissolution and subsequent drug release. The resulting model is shown to yield release characteristics in good agreement with those observed experimentally.

Modelling drug release from inert matrix systems: From moving-boundary to continuous-field descriptions

The purpose of this review is to provide a comprehensive overview of mathematical procedures that can be used to describe the release of drugs from inert matrix systems. The review focuses on general principles rather than particular applications. The inherent multiscale nature of the drug-release process is pointed out and multiscale modelling is exemplified for inert porous matrices. Although effects of stagnant layers and finite volumes of release media are briefly discussed, the systematic analysis is restricted to systems under sink conditions. When the initial drug loading exceeds the drug solubility in the matrix, Higuchi-type moving-boundary descriptions continue to be highly valuable for obtaining approximate analytical solutions, especially when coupled with integral balance methods. Continuous-field descriptions have decisive advantages when numerical solutions are sought. This is because the mathematical formulation reduces to a diffusion equation with a nonlinear source term, valid over the entire matrix domain. Solutions can thus be effortlessly determined for arbitrary geometries using standard numerical packages.

Ionic motion in polypyrrole-cellulose composites: trap release mechanism during potentiostatic reduction.

This work investigates the movement of anions during potentiostatic controlled reduction of novel composite materials consisting of high surface area cellulose substrates, extracted from the Cladophora sp. algae, coated with thin ( approximately 50 nm) layers of the intrinsically conducting polymer (ICP) polypyrrole. The coating was achieved by chemical polymerization of pyrrole on the cellulose fibers with iron(III) chloride and phosphomolybdic acid, respectively. The composites are in the form of paper sheets and can be directly immersed into an electrolyte solution for ion absorption/desorption. The motion of glutamate and aspartate anions during cathodic polarization was investigated as a function of preceding anodic polarization at various potentials. The composite was found to exhibit memory effect as the response to a cathodic polarization of constant magnitude produced different responses depending on the magnitude of the preceding anodic potential. After the application of a cathodic potential to the composite, the reduction current curvesgenerated by anions leaving the compositewere found to initially increase in magnitude followed by a monotonic decay. A similar response has not been described and analyzed for electrochemical reduction of anion containing ICP materials earlier. A theoretical model was developed to aid the analysis of the experimental data. The model accounts for both freely mobile anions and anions that may be temporarily trapped in a contracting PPy network during cathodic polarization. By fitting the recorded reduction current curves to this model, detailed information about the ionic movement in the composite could be obtained, which may be used to further optimize the materials properties of conducting polymer systems aimed for specific electrochemical ion exchange processes.

A model describing the internal structure of core/shell hydrogels

We apply a theory to the constrained swelling of gel particles, explicitly accounting for the propagation of elastic forces through the particle. This approach, together with conventional thermodynamics of gel swelling, allows modelling of the equilibrium state of gels with properties that are spatially inhomogeneous. In our case we consider both a discrete inhomogeneity in the form of assigning different water solubilities to the core and shell domains of the particle, and a continuous inhomogeneity in allowing the density of chemical cross-links to vary gradually through the network. The model is used to understand the behaviour of temperature-sensitive poly(N-isopropyl acrylamide) core/poly(N-isopropyl methacrylamide) shell microgels investigated in an earlier experimental study. How the swelling of the core and shell is affected by the presence of each other at different temperatures is investigated and explained from a mechanical and thermodynamic perspective.

Modeling structure–function relationships for diffusive drug transport in inert porous geopolymer matrices

A unique structure-function relationship investigation of mechanically strong geopolymer drug delivery vehicles for sustained release of potent substances is presented. The effect of in-synthesis water content on geopolymer pore structure and diffusive drug transport is investigated. Scanning electron microscopy, N2 gas adsorption, mercury intrusion porosimetry, compression strength test, drug permeation, and release experiments are performed. Effective diffusion coefficients are measured and compared with corresponding theoretical values as derived from pore size distribution and connectivity via pore-network modeling. By solely varying the in-synthesis water content, mesoporous and mechanically strong geopolymers with porosities of 8%-45% are obtained. Effective diffusion coefficients of the model drugs Saccharin and Zolpidem are observed to span two orders of magnitude (∼1.6-120 × 10(-8) cm(2) /s), comparing very well to theoretical estimations. The ability to predict drug permeation and release from geopolymers, and materials alike, allows future formulations to be tailored on a structural and chemical level for specific applications such as controlled drug delivery of highly potent substances.

Factors Affecting Enzymatic Degradation of Microgel-Bound Peptides

Proteolytic degradation and release of microgel-bound peptides was investigated for trypsin, poly(acrylic acid-co-acrylamide) microgels (70-90 μm in diameter), and oppositely charged polylysine, using a method combination of confocal microscopy and micromanipulator-assisted light microscopy. Results show that trypsin-induced release of polylysine increased with increasing trypsin concentration, decreasing microgel charge density and decreasing peptide molecular weight. While the microgel offered good protection against enzymatic degradation at high microgel charge density, it was also observed that the cationic peptide enabled trypsin to bind throughout the peptide-loaded microgels, even when it did not bind to the peptide-void ones. With the exception of highly charged microgels, proteolytic degradation throughout the peptide-loaded microgel resulted in the generation of short and non-adsorbing peptide stretches, giving rise to the concentration and peptide length dependence observed. A simple random scission model was able to qualitatively capture these experimental findings. Collectively, the results demonstrate that microgel charge density, peptide molecular weight, and enzyme concentration greatly influence degradation/release of microgel-bound peptides and need to be considered in the use of microgels, e.g., as carriers for protein and peptide drugs.

Dielectric and Li transport properties of electron conducting and non-conducting sputtered amorphous Ta2O5 films

Two types of sputtered thin film amorphous tantalum oxide (Ta 2 O 5 ) were studied: one electron conducting Ta 2 O 5 (ec-Ta 2 O 5 ) and the other non-conducting Ta 2 O 5 (nc-Ta 2 O 5 ). The as-deposited films were characterized by impedance spectroscopy (IS) and isothermal transient ionic current (ITIC) measurements. From IS, the dc conductivity 2 × 10 -14 S/cm was obtained for the ec-Ta 2 O 5 film at an applied ac potential of 50 mV whereas a value ≤ 1 × 10 -17 S/cm was obtained for the nc-Ta 2 O 5 film. Li conducting properties were studied using the galvanostatic intermittent titration technique and ITIC measurements on the intercalated samples. Despite the very dissimilar dc conductivities of the as-deposited films, the two Ta 2 O 5 samples showed surprisingly similar Li ion conducting properties for small Li/Ta 2 O 5 ratios. The Li ion mobility was in the range 1.1 × 10 -9 3.0 × 10 -9 cm 2 /V s for both films. However, the Li storage behaviour as well as the chemical diffusion coefficient differed. For the nc-Ta 2 O 5 film a plateau was observed in the equilibrium potential vs. composition curve for Li/Ta 2 O 5 ratios between 7 × 10 -5 and 2 × 10 -3 . This plateau was likely to have been caused by attractive interactions between the intercalated ions, possibly large enough to cause phase separation. The attractive interactions were shown to suppress the chemical diffusion coefficient in this composition range.

The degree of compression of spherical granular solids controls the evolution of microstructure and bond probability during compaction

The effect of degree of compression on the evolution of tablet microstructure and bond probability during compression of granular solids has been studied. Microcrystalline cellulose pellets of low (about 11%) and of high (about 32%) porosity were used. Tablets were compacted at 50, 100 and 150 MPa applied pressures and the degree of compression and the tensile strength of the tablets determined. The tablets were subjected to mercury intrusion measurements and from the pore size distributions, a void diameter and the porosities of the voids and the intra-granular pores were calculated. The pore size distributions of the tablets had peaks associated with the voids and the intra-granular pores. The void and intra-granular porosities of the tablets were dependent on the original pellet porosity while the total tablet porosity was independent. The separation distance between pellets was generally lower for tablets formed from high porosity pellets and the void size related linearly to the degree of compression. Tensile strength of tablets was higher for tablets of high porosity pellets and a scaled tablet tensile strength related linearly to the degree of compression above a percolation threshold. In conclusion, the degree of compression controlled the separation distance and the probability of forming bonds between pellets in the tablet.