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PubMed2001

Coupling particles and fields in a diffusive hybrid model.

A general scheme to patch together discrete and continuous descriptions of diffusion within the same physical space is studied. In the discrete description, diffusion is described by microscopic random walkers on a lattice; in the continuous description, diffusion is described through the macroscopic diffusion equation. The coupling scheme is based on the mutual exchange of mass flux across the discrete-continuous interface. Detailed tests of the scheme, coupling particle, and field descriptions are particularly illustrative for the diffusion problem. Both the nonequilibrium transport behavior and the equilibrium fluctuations of the combined discrete-continuous system are in agreement with theoretical predictions.

Journal Article↗
PubMed1999

HPMC-matrices for controlled drug delivery: a new model combining diffusion, swelling, and dissolution mechanisms and predicting the release kinetics.

PURPOSE: The purpose of this study was to investigate the drug release mechanisms from hydroxypropyl methylcellulose (HPMC)-matrices, and to develop a new model for quantitative predictions of controlled drug delivery. METHODS: The dissolved mass of pure HPMC-matrices and the drug release rate from propranolol HCl-loaded HPMC-matrices were determined experimentally. Based on Fick's second law of diffusion for cylinders, the transport of water and drug were modeled considering (i) both radial and axial diffusion, (ii) concentration-dependent drug diffusivities, (iii) matrix swelling and (iv) HPMC dissolution. RESULTS: Good agreement between theory and experiment (dissolved mass and drug release studies) was obtained, proving the validity of the presented model. The water and drug diffusivities are strongly dependent on the matrix swelling ratio. Diffusion, swelling and dissolution are the governing mechanisms involved in the overall drug release process. CONCLUSIONS: The practical benefit of the presented model is to identify the required shape and dimensions of drug-loaded HPMC-matrices in order to achieve desired release profiles, thus facilitating the development of new controlled drug delivery products. This will be demonstrated in a future study.

Delayed-Action Preparations↗
PubMed1989

The binding of G-protein to rod outer segment phospholipids at the nitrogen-water interface.

In the visual process, one photoexcited rhodopsin (R*) catalyzes the activation of hundreds of G-proteins. It remains to be determined whether G-protein and R* find one another by membrane surface diffusion of these components (diffusion model) or by diffusion of G-protein through the aqueous phase (hopping model). A monolayer of each main rod outer segment (ROS) phospholipid interacting with a subphase containing G-protein, has been used to simulate the interaction of G-protein with the cytoplasmic surface of discal membranes. The possible diffusion of G-protein through the aqueous phase was then measured by observing its adsorption-desorption in the monolayer of each main ROS phospholipid. From examination of surface pressure and ellipsometric isotherms at the nitrogen-water interface, we have determined that once incorporated into the monolayer, the G-protein remains associated, independent of surface pressure, thus providing evidence against the hopping model.

Animals↗
PubMed2005

A model for diffusion in white matter in the brain.

Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging is a powerful noninvasive method to characterize neuronal tissue in the human brain in vivo. As a first step toward understanding the relationship between the measured macroscopic apparent diffusion tensor and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the apparent diffusion tensor and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for diffusion tensor imaging and for the possible in situ estimation of microstructural parameters from diffusion-weighted MR data are discussed in the context of this modeling framework.

Algorithms↗
PubMed1997

Engineering the tissue which encapsulates subcutaneous implants. I. Diffusion properties.

This report uses normal rat subcutis as a reference point to provide a quantitative analysis of small analyte transport through the tissue which encapsulates implants. Polyvinyl alcohol (PVA) with 60- and 350-micron mean pore size (PVA-60, PVA-350), nonporous PVA (PVA-skin), and stainless-steel cage (SS) specimens were implanted in the subcutis of Sprague-Dawley rats for 4 weeks to elicit a range of capsular wound-healing tissues. Histologic examination showed that the capsular tissue which formed around PVA-skin and SS specimens was densely fibrous and avascular. That forming around PVA-60 and PVA-350 was less densely fibrous and more vascular. The fibrous content of capsular tissue and subcutis was determined from eosin-stained histologic sections. Dual-chamber diffusion measurements of sodium fluorescein (Mw 376 g/mol) through capsular tissue and normal rat subcutis were used to quantitatively compare the effective diffusion coefficients of small analytes on the order of glucose. The two most fibrous capsular tissues exhibited diffusion coefficients that were statistically (p < 0.05) less than that determined for rat subcutis by 50 and 25% for PVA-skin and SS, respectively. The diffusion coefficients of the less dense capsular tissue which formed around the porous implants were not statistically different from subcutis. The experimentally measured diffusion coefficients of the two most fibrous capsular tissues were closely predicted by a simple two-component diffusion model consisting of an aqueous interstitium with an array of impenetrable bodies equal in volume fraction to the fibrous content of the tissue. This model overestimates the diffusion coefficients measured for the least fibrous tissues. Using the diffusion coefficient measured for the PVA-skin capsular tissue, a finite difference model predicts that a 200-microns-thick capsular layer would increase from 5 to 20 min the time required for subcutaneously implanted sensor to detect 95% of the blood analyte concentration. This study suggests that the fibrous capsule forming around a subcutaneously implanted smooth-surface sensor imposes a significant diffusion barrier to small analytes such as glucose, thus increasing the lag time of the sensor by as much as threefold. A corollary observation is that a sensor with a porous surface which allows tissue ingrowth may be more responsive to blood analyte fluctuations as a result of its a more vascular and less fibrous encapsulation tissue.

Animals↗
PubMed2005

An investigation into the inputs controlling predictions from a diffuse phosphorus loss model for the UK; the Phosphorus Indicators Tool (PIT).

A simple catchment scale model simulating diffuse phosphorus (P) loss from agricultural land to water, the Phosphorus Indicators Tool (PIT), has been developed. Previous research has shown that this model worked well in simulating the average annual P lost from two catchments: Windermere and Windrush, but it was not known which drivers in the model had the greatest control on predicted P delivery to water from agricultural land. In order to simulate the P export from each catchment source via each hydrological pathway specified individually, 108 coefficients are used in the model code. A univariate sensitivity analysis was conducted to evaluate which coefficient exerted the greatest control on the model output. Results from the univariate analysis suggest that the model is sensitive to a number of coefficients, but importantly, not all of the coefficients that were varied in the sensitivity analysis, altered the model output. The PIT model has been calibrated by optimizing results from the univariate analysis against observed data in the Windermere catchment. The simulated results from model calibration fit the observed data well, at the 95% level. This paper describes the methodology developed for the univariate analysis and evaluates the model calibration procedure against observed data from the Windermere catchment.

Agriculture↗
PubMed2002

Linear single-step image reconstruction in the presence of nonscattering regions.

There is growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in using this technique for obtaining tomographic images of the neonatal head, with the view of determining the level of oxygenated and deoxygenated blood within the brain. Because of computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases where a nonscattering region exists. We present reconstructed images, using linear algorithms, of models that contain a nonscattering region within a diffusing material. The forward data are calculated by using the radiosity-diffusion model, and the inverse problem is solved by using either the radiosity-diffusion model or the diffusion-only model. When using data from a model containing a clear layer and reconstructing with the correct model, one can reconstruct the anomaly, but the qualitative accuracy and the position of the reconstructed anomaly depend on the size and the position of the clear regions. If the inverse model has no information about the clear regions (i.e., it is a purely diffusing model), an anomaly can be reconstructed, but the resulting image has very poor qualitative accuracy and poor localization of the anomaly. The errors in quantitative and localization accuracies depend on the size and location of the clear regions.

Algorithms↗
PubMed1997

In vivo evaluation of acyclovir prodrug penetration and metabolism through rat skin using a diffusion/bioconversion model.

PURPOSE: In order to evaluate the in vivo penetration of prodrugs which undergo metabolism in skin, we analyzed the in vivo penetration profiles of acyclovir prodrugs based on a two-layer skin diffusion model in consideration of metabolic process. METHODS: Acyclovir prodrugs (e.g., valerate, isovalerate and pivarate) were used as model prodrugs and the amounts excreted in urine were measured after percutaneous application. In vivo penetration profiles were then estimated by employing a deconvolution method and the penetration of acyclovir prodrugs was analyzed using a diffusion model. Subsequently, diffusion, partitioning and metabolic parameters were compared under in vitro and in vivo conditions. RESULTS: Although total penetration amounts at the end of the experiment were similar for the three prodrugs, the ratio of intact prodrug to total penetration amount differed significantly. Moreover, the excretion and absorption profiles were also very different for each prodrug. Enzymatic hydrolysis rate constants calculated under in vivo conditions were considerably larger than those obtained in the skin homogenate and in vitro penetration experiments. CONCLUSIONS: The present skin diffusion/bioconversion model combined with computer analysis enables us to comprehensively account for diffusion, partitioning and metabolism during in vivo percutaneous absorption. Nevertheless, different enzymatic hydrolysis rate constants obtained under both in vivo and in vitro conditions demonstrate the difficulty of obtaining accurate values for in vivo enzymatic activity from related in vitro experiments.

Acyclovir↗
PubMed1991

Convergence of one-dimensional diffusion processes to a jump process related to population genetics.

A conjecture on the convergence of diffusion models in population genetics to a simple Markov chain model is proved. The notion of bi-generalized diffusion processes and their limit theorems are used systematically to prove the conjecture. Three limits; strong selection-weak mutation limit, moderate selection-weak mutation limit, weak selection-weak mutation limit are considered for typical diffusion models in population genetics.

Genetics, Population↗
PubMed2006

Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging.

An efficient computation of the time-dependent forward solution for photon transport in a head model is a key capability for performing accurate inversion for functional diffuse optical imaging of the brain. The diffusion approximation to photon transport is much faster to simulate than the physically correct radiative transport equation (RTE); however, it is commonly assumed that scattering lengths must be much smaller than all system dimensions and all absorption lengths for the approximation to be accurate. Neither of these conditions is satisfied in the cerebrospinal fluid (CSF). Since line-of-sight distances in the CSF are small, of the order of a few millimeters, we explore the idea that the CSF scattering coefficient may be modeled by any value from zero up to the order of the typical inverse line-of-sight distance, or approximately 0.3 mm(-1), without significantly altering the calculated detector signals or the partial path lengths relevant for functional measurements. We demonstrate this in detail by using a Monte Carlo simulation of the RTE in a three-dimensional head model based on clinical magnetic resonance imaging data, with realistic optode geometries. Our findings lead us to expect that the diffusion approximation will be valid even in the presence of the CSF, with consequences for faster solution of the inverse problem.

Adult↗
PubMed2003

Adsorption behavior of reactive dye in aqueous solution on chemical cross-linked chitosan beads.

A batch system was applied to study the adsorption of reactive dye (reactive red 189) from aqueous solutions by cross-linked chitosan beads. The ionic cross-linking reagent sodium tripolyphosphate was used to obtain more rigid chitosan beads. To stabilize chitosan in acid solutions, chemical cross-linking reagent epichlorohydrin (ECH), glutaraldehyde and ethylene glycol diglycidyl ether was used and ECH shows a higher adsorption capacity. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms at different particle sizes and isotherm constants were determined. The Langmuir model agrees very well with experimental data and its calculated maximum monolayer adsorption capacity has very large value of 1802-1840 (g/kg) at pH 3.0, 30 degrees C. The kinetics of the adsorption with respect to the initial dye concentration, temperature, pH, ionic strength, and wet/dry beads were investigated. The pseudo-first-order, second-order kinetic models and intraparticle diffusion model were used to describe the kinetic data and the rate constants were evaluated. The dynamical data fit well with the second-order kinetic model, except for the dry beads fitting better with the first-order model. The adsorption capacity increases largely with decreasing solution pH or with increasing initial dye concentration. Thermodynamic parameters such as change in free energy (deltaG(0)), enthalpy (deltaH(0)), entropy (deltaS(0)) and activation energy were also determined. The adsorption mechanism is shown to be the electrostatic interactions between the dye and chitosan beads. The desorption data shows that the removal percent of dye RR 189 from the cross-linked chitosan beads is 63% in NaOH solutions at pH 10.0, 30 degrees C. The desorbed chitosan beads can be reused to adsorb the dye and to reach the same capacity as that before desorption.

Adsorption↗
PubMed2001

The cultured branchial epithelium of the rainbow trout as a model for diffusive fluxes of ammonia across the fish gill.

A novel branchial epithelial preparation grown in L-15 medium in culture was used as a model system for understanding the diffusion of ammonia across the gills of the rainbow trout Oncorhynchus mykiss. The epithelium is known to contain both respiratory and mitochondria-rich cells in the approximate proportion in which they occur in vivo and to exhibit diffusive fluxes of Na+ and Cl- similar to in vivo values, but does not exhibit active apical-to-basolateral transport of Na+. Transepithelial resistance and paracellular permeability are also known to increase when the apical medium is changed from L-15 medium (symmetrical conditions) to fresh water (asymmetrical conditions). In the present study, net basolateral-to-apical ammonia fluxes increased as basolateral total ammonia concentration, basolateral-to-apical pH gradients and basolateral-to-apical P(NH(3)) gradients were experimentally increased and were greater under asymmetrical than under symmetrical conditions. The slope of the relationship between ammonia flux and P(NH(3)) gradient (i.e. NH(3) permeability) was the same under both conditions and similar to values for other epithelia. The higher fluxes under asymmetrical conditions were explained by an apparent diffusive flux of NH(4)+ that was linearly correlated with transepithelial conductance and was probably explained by the higher electrochemical gradient and higher paracellular permeability when fresh water was present on the apical surface. In this situation, NH(4)(+) diffusion was greater than NH(3) diffusion under conditions representative of in vivo values, but overall fluxes amounted to only approximately 20% of those in vivo. These results suggest that branchial ammonia excretion in the intact animal is unlikely to be explained by diffusion alone and, therefore, that carrier-mediated transport may play an important role.

Ammonia↗
PubMed1981

Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases.

A reaction-diffusion system which describes the spatial spread of bacterial diseases is studied. It consists of two nonlinear parabolic equations which concern the evolution of the bacteria population and of the human infective population in an urban community, respectively. Different boundary conditions of the third type are considered, for the two variables. This model is suitable to study oro-faecal transmitted diseases in the European Mediterranean regions. A threshold parameter is introduced such that for suitable values of it the epidemic eventually tends to extinction, otherwise a globally asymptotically stable spatially inhomogeneous stationary endemic state appears. The case in which the bacteria diffuse but the human population does not, has also been considered.

Bacterial Infections↗
PubMed2002

Glandular regulation of interstitial diffusion: a model and simulation of a novel physiological mechanism.

In endocrine glands, vigorous and coordinated responses are often elicited by modest changes in the concentration of the agonist molecule. The mammalian parathyroid gland is a representative case. Small (5%) changes in serum calcium result in 10-fold (1,000%) changes in glandular parathyroid hormone (PTH) release. In vitro, single isolated cells are observed to secrete fewer hormones than cells residing within a connected group, suggesting that a network has emergent regulatory properties. In PTH-secreting tumors, however, the ability to respond quickly to changes in calcium is strongly damped. A unifying hypothesis that accounts for these phenomena is realized by extracellular modulation of calcium diffusivity. A theoretical model and computational experiments demonstrate qualitative agreement with published experimental results. Our results suggest that, in addition to the cellular mechanisms, endocrine glandular networks may have regulatory prowess at the level of interstitial transport.

Animals↗
PubMed2003

Modeling the stability of electroless plating bath--diffusion of nickel colloidal particles from the plating frontier.

Electroless nickel (EN) plating is a process in which Ni2+ ions are reduced by hydrogen atoms adsorbed at a fresh Ni surface. However, detaching of a handful of tiny Ni metal particles from a substrate causes the entrance of these particles into the plating solution. The metal particles offer very reactive surfaces for the reduction of Ni2+ ions, which in turn aggravates the detachment, causing a self-accelerated cycle. Eventually the plating solution will be subject to an overwhelming precipitation of Ni black. This paper proposes a one-dimensional diffusion model to explain the dependence of the bath stability on the plating time under different bath loadings. This mathematical model contains Vd, defined as the decomposition volume, a measure to judge chemical stability of a plating solution. To obtain Vd experimentally, a PdCl2 solution was purposely introduced into a model solution (the addition leads to immediate generation of metal particles) until the very moment of onset of massive deposition of colloidal Ni. The Vd data from the experiment were then used to perform simulation in order to complete the model proposed. Other than the effects of bath loadings and plating time, an adsorption model was also created to describe the temperature effect. To coordinate the adsorption model, l-cysteine was used as an adsorbate that plays a deactivation role. The under bump metallization process on patterned silicon wafers has been used to support the main theme of this study.

Journal Article↗
PubMed2006

Kinetics of integrated electron transfer in the mitochondrial respiratory chain: random collisions vs. solid state electron channeling.

Recent evidence, mainly based on native electrophoresis, has suggested that the mitochondrial respiratory chain is organized in the form of supercomplexes, due to the aggregation of the main respiratory chain enzymatic complexes. This evidence strongly contrasts the previously accepted model, the Random Diffusion Model, largely based on kinetic studies, stating that the complexes are randomly distributed in the lipid bilayer of the inner membrane and functionally connected by lateral diffusion of small redox molecules, i.e., coenzyme Q and cytochrome c. This review critically examines the experimental evidence, both structural and functional, pertaining to the two models and attempts to provide an updated view of the organization of the respiratory chain and of its kinetic consequences. The conclusion that structural respiratory assemblies exist is overwhelming, whereas the expected functional consequence of substrate channeling between the assembled enzymes is controversial. Examination of the available evidence suggests that, although the supercomplexes are structurally stable, their kinetic competence in substrate channeling is more labile and may depend on the system under investigation and the assay conditions.

Animals↗