Diffusion Erosion Research Articles

Simulation of Drug Release from Biodegradable Polymeric Microspheres with Bulk and Surface Erosions

New models are developed to account for the kinetics of drug release from porous, biodegradable polymeric microspheres under the schemes of bulk erosion and surface erosion of the polymer matrix, respectively. Three mechanisms of drug release, namely, drug diffusion, drug dissolution, and polymer erosion jointly govern the overall release process. For bulk erosion, the model incorporates an erosion term into the dissolution and diffusion equation and is solved numerically for various boundary conditions. Dissolution and erosion are defined in the model by introducing three equations which take into account the drug concentration in the liquid phase, virtual solid phase, and effective solid phase. For surface erosion, drug concentrations in liquid and solid phases are defined and a substitution is introduced to convert the moving‐boundary problem to a fixed‐boundary problem. The resulting differential equations are solved simultaneously to obtain the concentration profile in the liquid and solid phases, respectively. Numerical solutions are provided to illustrate the effects of drug dissolution constant, drug diffusion coefficient, and erosion rate constant. In general, increasing erosion rate, diffusivity, dissolution, and decreasing particle radius enhance the drug release rate. Predictions from the models are also compared with experimental data to verify their validity and possible improvements are proposed. © 2003 Wiley‐Liss, Inc. and the American Pharmacists Association J Pharm Sci 92:2040–2056, 2003

Erosion of high- Z metals with typical impurity ions

This paper reviews the erosion properties of high- Z plasma facing materials due to the bombardment with typical impurity ions. The different impurity species present in today’s fusion experiments are compared in terms of their importance for erosion of high- Z metals, showing that C is the main source of erosion. As example results are presented here from controlled ion beam experiments on the temperature dependent erosion and deposition processes occurring during bombardment of W by keV C-ions. It is shown that radiation enhanced sublimation (RES) and diffusion are responsible for the observed temperature dependence. A new code was developed to simulate the influence of thermally activated processes on the complex temperature dependence of protective C layer growth on W during simultaneous bombardment by keV C and eV hydrogen isotopes. To model RES, diffusion and chemical erosion of C the Monte Carlo program TRIDYN was coupled with a newly developed diffusion code DIFFUSEDC and a chemical erosion module YCEHM. This combination was validated by comparing calculated W erosion yields in D plasma with C as main impurity to spectroscopically measured values from ASDEX Upgrade as well as ion beam experiments using CH 3 +.

A smoothed-particle hydrodynamic automaton of landform degradation by overland flow

A novel model for calculating hillslope degradation by overland flow is based on a coupling of the cellular automaton and smoothed-particle hydrodynamics theories.Simulated debris-laden floods were initiated on digital elevation models (DEMs). The flows were created by solving equations for diffusion routing, and erosion and deposition. We separated advection and diffusion terms using operator splitting, then solved the advection term via automaton and the diffusion term via smoothed-particle hydrodynamics.The technique was tested on geometrically simple synthetic slopes, against data for erosion and deposition by debris-laden flows in a gully developing on a scoria cone (Arizona), and against data on a recent moderate-sized debris-laden flood generated by possible partial glacier melting at Popocatépetl volcano (Mexico). The flow and erosion/deposition patterns on the simple synthetic slopes appear intuitively reasonable. On the synthetic scoria-cone slope, the model reproduced some of the observed spatial patterns of event-scale erosion and deposition. Reasonable flow speeds, runup heights, and runout lengths were produced for the debris-laden flood at Popocatépetl.The coupled cellular automaton–smoothed-particle hydrodynamics technique represents some advance in the modeling of landform degradation and channel development by cellular automata (CA). Use of the technique may aid our understanding of the link between hillslope-scale and landform-scale degradation patterns.

Floating matrix tablets based on low density foam powder: effects of formulation and processing parameters on drug release

The aim of this study was to develop and physicochemically characterize single unit, floating controlled drug delivery systems consisting of (i) polypropylene foam powder, (ii) matrix-forming polymer(s), (iii) drug, and (iv) filler (optional). The highly porous foam powder provided low density and, thus, excellent in vitro floating behavior of the tablets. All foam powder-containing tablets remained floating for at least 8 h in 0.1 N HCl at 37 °C. Different types of matrix-forming polymers were studied: hydroxypropyl methylcellulose (HPMC), polyacrylates, sodium alginate, corn starch, carrageenan, gum guar and gum arabic. The tablets eroded upon contact with the release medium, and the relative importance of drug diffusion, polymer swelling and tablet erosion for the resulting release patterns varied significantly with the type of matrix former. The release rate could effectively be modified by varying the “matrix-forming polymer/foam powder” ratio, the initial drug loading, the tablet geometry (radius and height), the type of matrix-forming polymer, the use of polymer blends and the addition of water-soluble or water-insoluble fillers (such as lactose or microcrystalline cellulose). The floating behavior of the low density drug delivery systems could successfully be combined with accurate control of the drug release patterns.

Dissolution behaviour of hydrophilic matrix tablets containing two different polyethylene oxides (PEOs) for the controlled release of a water-soluble drug. Dimensionality study

Hydrophilic matrix tablets containing polyethylene oxides as the retarding polymer have been successfully employed in the controlled release of drugs. To evaluate the relative influence of drug diffusion and polymer erosion mechanisms in the drug delivery process, we studied the hydration behaviour of matrix tablets containing a water-soluble drug and PEOs of two different molecular weights: Polyox WSRN 1105 ( M w=0.9×10 6) and Polyox WSRN 301 ( M w=4×10 6). The hydration rate, the extent of swelling, and the erosion rate of matrices containing the polymer, the drug and tableting excipients were evaluated in comparison to tablets made of pure polymer. The results of these studies on function of the release behaviour were then discussed. The results show that the higher molecular weight PEO swells to a greater extent and tends to form, upon hydration, a stronger gel, which is therefore less liable to erosion, if compared to the lower molecular weight PEO. This difference in the erosion behaviour can explain the different efficiencies of the two polymeric products in modulating the delivery rate of the water-soluble drug. Moreover, the presence of other soluble components (drug and excipients) in the dosage form enhances the erosion trend of the tablets with a consequent reduction of the efficiency of the polymer in drug release control.

Quaternary faulting history along the Deep Springs fault, California

New geologic mapping, structural studies, geochronology, and diffusion erosion modeling along the Deep Springs fault, California, shed light on its Quaternary faulting history. The Deep Springs fault, a 26km-long, predominantly north-northeaststriking, west-northwestdipping normal fault bounding the eastern side of Deep Springs Valley, cuts Jurassic batholithic rocks nonconformably overlain by middle Miocene to Pleistocene stream gravels, coarse-grained sand, tuffaceous sand, unwelded to partially welded tuff, and Bishop ash, as well as Quaternary coarse- to finegrained alluvial fan deposits. The 40 Ar/ 39 Ar geochronology yields ages of 3.09 0.08 Ma for the unwelded tuff and 753 4k a for the Bishop ash. Holocene debris flows, a landslide, and recent alluvium bury the youngest fault scarp. The Deep Springs fault is characterized by multiple fault planes and fault scarps that become progressively younger toward the basin. The dip of the fault plane varies from 20 to 87 and fault-plane and striation measurements indicate an average orientation of N23E, 47NW, and N77E, 49SW, respectively. The offset of Bishop ash and underlying tuff across the Deep Springs fault indicates horizontal extension and vertical slip rates of 0.7 and 0.9 mm/yr, respectively, since the eruption of the Bishop Tuff, and 0.2 and 0.2 mm/yr, respectively, since the eruption of the unwelded tuff. If the vertical slip rate since the eruption of the Bishop Tuff has remained constant through time, then slip along the Deep Springs fault began ca. 1.7 Ma. Younger fault scarps to the west of the bedrock fault cut Quaternary deposits; scarp offset ranges from 0.8 to 17.5 m and scarp slope angle ranges from 8 to 37. Topographic profiling of the smallest, least eroded fault scarps, with an average surface offset of 2.7 m, indicates that these scarps developed as the result of a single earthquake and ruptured an 20km-long segment of the fault. Radiocarbon analyses on detrital charcoal, located in the footwall block of one of these scarps, yield an age of 1.960 0.055 ka. Diffusion erosion modeling of these fault scarps yields an elapsed time of 1.7 0.5 k.y. since these fault scarps formed. Making reasonable assumptions about the depth of this earthquake and shear modulus, we estimate a moment magnitude, MW 7.0, for this earthquake. The Deep Springs fault is one of several displacement-transfer normal faults that define a zone of distributed deformation between subparallel right-lateral strike-slip faults east of the Sierra Nevada that make up the northern part of the eastern California shear zone. The young age and recent earthquake activity along the Deep Springs fault are consistent with a model proposed for the kinematic evolution of this part of the eastern California shear zone.

Drug volume fraction profile in the gel phase and drug release kinetics in hydroxypropylmethyl cellulose matrices containing a soluble drug

In the present work, the drug volume fraction profiles of a colored and very soluble drug, buflomedil pyridoxal phosphate, in the gel layer of initially glassy hydroxypropylmethyl cellulose matrices were studied, using image analysis of pictures of the matrices during swelling and release. The goal was to correlate the drug release kinetics with the dynamic behavior of the drug gradient in the gel layer. An inert (nonswellable) matrix, manufactured by substituting hydroxypropylmethyl cellulose with an inert polymer and containing the same amount of buflomedil pyridoxal phosphate, was prepared as well. The drug color gradient in the partially extracted region and the flux of this matrix were compared to the swellable matrix. The drug gradient in the dissolved drug gel layer of swellable matrices was observed. It was demonstrated that drug release kinetics does not only depend on drug diffusion and matrix erosion, but also on drug dissolution in the gel and on polymer relaxation.

The effect of the aqueous solubility of xanthine derivatives on the release mechanism from ethylcellulose matrix tablets

Release data from ethylcellulose (EC) matrix tablets was analyzed to determine which release equation provides the best fit to the data and to observe the effect of drug solubility on the release mechanism(s). Tablets were prepared by direct compression of drug, EC, and lubricant in an appropriate mass ratio to achieve a high and a low drug loading. Theophylline, caffeine, and dyphylline were selected as non-electrolyte xanthine derivatives with solubilities from 8.3 to 330 mg/ml at 25°C. Drug release studies were conducted in 37°C water with UV detection at 272 nm. Several equations to characterize release mechanisms were tested with respect to the release data. Drug diffusion, polymer relaxation, and tablet erosion were the mechanisms considered. Parameters were generated and ANOVA data presented by WinNonlin Pro® software. The Akaike Information Criterion was also considered to ascertain the best fit equation. At high drug loading, drug was released by a diffusion mechanism with a rate constant that increased with an increase in aqueous solubility. At low drug loading, polymer relaxation also became a component of the release mechanism. However, its contribution to drug release was less pronounced as solubility decreases, becoming negligible in the case of theophylline.

Relationship between swelling, erosion and drug release in hydrophillic natural gum mini-matrix formulations

The swelling, erosion and solvent front penetration properties of mini-matrices containing xanthan (X), locust bean (LB) and karaya (K) gums were examined, analysed and related to the overall in vitro release kinetics of diclofenac sodium, used as a model drug. Mini-matrices were produced with drug:gum ratios of 1:1 as well as formulations of drug and X in combinations of 2:1, 2:3 and 1:2. The rank order of decreasing swelling index (SI) in both axial and radial dimensions was X>K>LB and each gum showed almost Fickian swelling behaviour. The solvent front penetration rates were consistent with the rates of swelling. However, the order of decreasing drug release and erosion rates was LB>X>K and all formulations demonstrated anomalous (non-Fickian) drug release kinetics. Therefore Fickian drug diffusion and polymer erosion were both occurring simultaneously. The dominant mechanism depended on the nature and content of the gum, as well as the stage in the dissolution time period. There was a loss of matrix integrity in formulations containing a high drug:gum ratio.

Controlled release of tobramycin sulfate from poly(ortho esters) implantable discs for the treatment of osteomyelitis

This study was designed to investigate a new biodegradable implantable disc system based upon poly(ortho esters) (POE) which could release tobramycin sulfate (TS) over a 21-day period at a rate of 2 mg TS/day/g of implant (usual clinical requirement) for the treatment of osteomyelitis. The device was formulated in the form of discs (diameter, 1 cm) cast from methylene chloride and in vitro release was investigated in phosphate buffered saline, pH 7.4 at 37°C. The POE-TS discs without any adjuvants released 20%–60% TS in 24 h and an additional 10% in subsequent 20 days with about 3% loss in polymer weight, irrespective of the drug loading (4, 8, 12% w/w) and disc thickness (148, 244, 433 μm). In order to achieve uniform and complete TS release over 21 days, lactic acid (LA), sorbic acid (SA), oleic acid (OA) and palmitoleic acids (PA), in varying concentrations, were incorporated in the 244 μm-discs containing 8% TS. The release of TS was near-zero order after an initial burst in the presence of lactic acid. In the presence of SA, OA and PA, the TS release was multi-phasic. The rate of polymer degradation was found to be acid concentration-dependent for all acids. The TS release from these discs could be attributed to burst effect, diffusion, and acid-catalyzed bulk erosion of POE polymer. Among these formulations, discs with 0.2% LA and 0.9% OA demonstrated release rates close to 2 mg TS/day/g of implant with significant and simultaneous POE degradation. No physical or chemical interactions between the drug and the polymer were detected by DSC, NMR and IR.

Development of biodegradable polymeric paste formulations for taxol: An in vitro and in vivo study

Biodegradable polymeric paste formulations (‘surgical pastes’) for local delivery of taxol were developed and characterized. Taxol was mixed into melted poly(D,L-lactide)- block-poly(ethylene glycol)- block-poly(D,L-lactide) (PDLLA-PEG-PDLLA) copolymers and blends of low molecular weight poly(D,L-lactic acid) and poly-ϵ-caprolactone (PDLLA:PCL) to obtain the paste formulations. The release of taxol into PBS albumin buffer was measured by HPLC. The polymers and pastes were characterized by gel permeation chromatography (GPC), differential scanning calorimetry (DSC), nuclear magnetic resonance (NMR) and scanning electron microscopy (SEM). Taxol was released in a sustained manner from the PDLLA-PEG-PDLLA paste over a period of 2 months by diffusion and polymer erosion. The release from the blend was mainly erosion controlled and consisted of a burst followed by a period of slow release. Efficacy of the pastes in inhibiting tumor growth in mice was evaluated. Molten, taxol loaded paste formulations were placed at subcutaneous tumor sites in mice (pastes harden at 37°C). After 16 days, the reduction in tumor weight was measured. Both the taxol loaded copolymer and 90:10 PDLLA:PCL blend formulations significantly inhibited tumor growth in mice. The pastes with faster in vitro release rates resulted in greater efficacy in inhibiting tumor growth. The results showed that biodegradable polymeric surgical pastes are promising formulations for the local delivery of taxol to inhibit tumor growth.

Hillslope development in areas of active tectonics

Tectonic and geomorphic displacements of the Earth's surface control topographic profile development; therefore, their analysis should be combined. In the model presented here, transient finite difference solutions to the continuity equation for material transport determine geomorphic displacements. The material transport rate is a function of distance from the divide to the power m, local slope to the power n, and a rate constant. Values of m and n may be adjusted to simulate processes varying from rainsplash and soil creep (i.e., diffusive; m = 0, n = 1) to slope wash and river flow (m > 0, n > 0). The actual geomorphic displacements may be transport or weathering‐limited, depending on soil profile development. Superimposed edge dislocations in an elastic half‐plane are used to model tectonic displacements. Slip along a normal or reverse fault of any dip, depth and down‐dip length may be incremental (earthquake) or continuous (aseismic creep). Considering climate and material properties constant, the ratio of the transport capacity rate constant to the fault slip rate roughly determines form. This model extends existing morphologic diffusion erosion analyses to include other geomorphic conditions and processes (transport‐ or weathering‐limited conditions, material flux boundary conditions, and the development of gullies and knickpoints) and more heterogeneous spatial and temporal distributions of tectonic displacement (such as those due to slip along buried thrust faults). We advocate calibration of these parameters and processes to provide a quantitative approach to modeling landform development, determining deformation rates, and inferring earthquake hazards.

Original forms and initial modifications of the Galway Lake Road scarp formed along the Emerson fault during the 28 June 1992 Landers, California, earthquake

A remarkable scarp formed southeast of the Galway Lake Road during the Mw 7.3 Landers, California earthquake. Over the first 11 months following the earthquake, we repeated topographic surveys and ground stereoscopic photography, and interpreted the observations of original forms and initial modifications of the faulted landforms. The complexity of the surface rupture influenced the geomorphic responses. The principal shear zone consisted of en-echelon right- and left-lateral, generally left-stepping, fault segments with cumulative offsets of 5 m right-lateral and 2.5 m vertical. Typical fault scarp profiles have different slope angles above and below the surface rupture and a small free face. The surface rupture formed steep, irregular knickpoints in channels crossing the scarp. The original channel surfaces were warped as they stepped down over tilted and rotated fracture-bounded blocks. The landforms were modified measurably by the above-average winter 1992-1993 rainfall. Over surfaces controlled by hillslope processes only, fault scarp erosion was controlled by rainsplash and slumping. Originally sharp corners were rounded and loose sediment collected in colluvial wedges. Surface flows over simple ramp steps in channel profiles caused incision that drove knick-points back by as much as 50 cm. Over more complex portions of the principal shear zone, flow was diverted into open fractures and little modification of the scarp occurred. The pre-earthquake topography at the site provided no clear evidence of the last similar slip event. Simple diffusion erosion models of the time required to bring the new scarp to its pre-Landers event configuration indicate that the last major rupture may have been several thousand years ago.

ERFUS 6—a FORTRAN program for calculating the response of alluvial channels to baselevel lowering

Under certain hydraulic and sedimentological conditions the process of degradation of alluvial streams due to baselevel lowering can be approximated reasonably by a diffusion equation. The rate of degradation, which changes in time and place along the stream, then is determined by a diffusion—erosion coefficient, K. A numerical solution of the diffusion equation is the basis of FORTRAN Program ERFUS 6, which permits the analysis of the development of longitudinal profiles of streams after baselevel lowering. The program operates in two modes: (1) K is not known and it is to be determined—the program fits a simulated longitudinal profile to the final actual profile and K is calculated. (2) K known—the program calculates different stages of degradation of the longitudinal profile. The program is applicable to a situation in which a gully is entrenched into homogenous, cohesive sediments and the amount of degradation is not too great, so that erosion by bank sloughing is not excessive.

Influence of device fabrication parameters on gradual degradation of (AlGa)As cw laser diodes

Several factors not previously associated with cw laser degradation are shown to influence the life and reliability of (AlGa)As cw injection laser diodes. They include zinc diffusion, sawing damage, and facet erosion. When proper attention is paid to these factors, lasers showing no significant degradation for at least 2000 h can be made.

Depth distributions of implanted atoms under the influence of surface erosion and diffusion

Abstract Shallow range distributions are altered significantly by diffusion and surface erosion. It will be shown here that the simultaneous processes of implantation, diffusion, and surface erosion can be described by a second order differential equation which is mathematically tractable and yields general results in terms of analytical functions. The resulting depth distributions depend on one parameter only which is a combination of the mean particle range, the diffusion coefficient, and the velocity of surface erosion (e.g. sputtering). The theory is applied to practical cases, e.g. implantation of plasma particles in the wall of fusion reactors, or solar wind ions in the surface of meteorite materials.

Energy relationships and the coefficient of energy conversion in the electrodynamic acceleration of a plasma, with consideration of the processes of mass transfer

We examine the effect of mass-transfer produced by the physical phenomena of plasma recombination, ambipolar diffusion, and electrode erosion, as well as the effect of the resistance forces on the energy relationships and the coefficient of energy conversion in the electrodynamic acceleration of a plasma.

An investigation into the effect of mass-transfer processes and the forces of resistance on the electrodynamic acceleration of a plasma

We examine the mass-transferprocesses brought about by the physical phenomena of plasma recombination, ambipolar diffusion, and electrode erosion. We investigate the effect of resistance forces in their various relationships to the parameters of the accelerated plasma.