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PubMed1997

A mechanistic study of griseofulvin dissolution into surfactant solutions under laminar flow conditions.

The in vivo dissolution of many poorly soluble drugs is enhanced by the action of surfactants secreted into the upper gastrointestinal (GI) tract. These substances may act by solubilizing individual drug molecules into two separate liquid phases: the free aqueous phase and a micellar phase in which the drug is incorporated into a complex of two or more surfactant molecules. This complex process, micellar solubilization, was the subject of this in vitro study, wherein griseofulvin (gris) dissolution was observed in flowing surfactant solutions. Aqueous solutions of sodium dodecyl sulfate (SDS), an anionic surfactant, were pumped over a gris tablet embedded in a laminar flow device to simulate flow in the human upper GI tract. SDS solutions were well above the critical micellar concentration (cmc approximately 6-7 mM), and flow rates ranged from 4 to 7 mL/min. Gris solubility in premicellar (4 mM), near-micellar (6 mM), and micellar (>6 mM) SDS solutions was also determined. The measured solubility of gris increased linearly with SDS concentrations above the cmc. Drug solubility in SDS concentrations below the cmc was also higher than that in water. Gris diffusion coefficients were measured using pulsed-field gradient NMR spectroscopy. To determine the controlling mechanism for surfactant-enhanced dissolution, a mathematical model was developed. The model solution, an equation for drug dissolution rate, was compared with experimental data to demonstrate that drug transport away from the solid surface is the slow step in the process. Measured gris diffusion coefficients and solubility values were used as constants in the mathematical model solution and were combined to calculate an effective gris diffusion coefficient. Using these experimentally determined properties, model-calculated dissolution rates were within 7% of the measured values. As hypothesized, dissolution rates were found to be directly proportional to the transport properties of the system (effective drug diffusion coefficient and fluid flow rate) as well as to the drug solubility. To further verify transport-limited dissolution, the measured dissolution rates were found to be proportional to the surrounding medium flow rate to the 1/3 power, as predicted by the model dissolution rate equation.

Antifungal Agents↗
PubMed2002

Orientational diffusion reflects fiber structure within a voxel.

Several new MR techniques have been introduced to infer direction through diffusion in multiple nerve fiber bundles within a voxel. To date, however, there has been no physical model reported to evaluate these methodologies and their ability to determine fiber orientation. In this article a model of diffusion analogous to nerve fibers is presented. Diffusion measurements at multiple closely spaced angles of 15 degrees in samples with different fiber orientations are compared with theoretical calculations for restricted diffusion in cylindrical geometry. Orientational diffusion measurements are shown to reflect fiber geometry and theoretical predictions to within 10%. Simulations of fiber crossings within a voxel suggest fiber orientation does not correspond to the direction of the largest measured diffusion coefficient, but theoretical knowledge of signal decay curves can predict the shape of these diffusion coefficient contours for given fiber orientation probabilities.

Anisotropy↗
PubMed2003

Mathematical modeling of drug release from bioerodible microparticles: effect of gamma-irradiation.

Bioerodible polymers used in controlled drug delivery systems, such as poly(lactic-co-glycolic acid) (PLGA) undergo radiolytic degradation during gamma-irradiation. In spite of the considerable practical importance, yet only little knowledge is available on the consequences of this sterilization method on the resulting drug release patterns in a quantitative way. The major objectives of the present study were: (i) to monitor the effects of different gamma-irradiation doses on the physicochemical properties of drug-free and drug-loaded, PLGA-based microparticles; (ii) to analyze the obtained experimental results using adequate mathematical models; (iii) to get further insight into the occurring physical and chemical phenomena; and (iv) to relate the applied gamma-irradiation dose in a quantitative way to the resulting drug release rate. 5-Fluorouracil-loaded, PLGA-based microparticles were prepared with an oil-in-water solvent extraction method and exposed to gamma-irradiation doses ranging from 0 to 33 kGy. Size exclusion chromatography, differential scanning calorimetry, scanning electron microscopy, particle size analysis, determination of the actual drug loading and in vitro drug release kinetics were used to study the effects of the gamma-irradiation dose on the physicochemical properties of the microparticles. Two mathematical models-a simplified and a more comprehensive one-were used to analyze the experimental results. The simplified model considers drug diffusion based on Fick's second law for spherical geometry and a Higuchi-like pseudo-steady-state approach. The complex model combines Monte Carlo simulations (describing polymer erosion) with partial differential equations quantifying drug diffusion with time-, position- and direction-dependent diffusivities. Interestingly, exponential relationships between the gamma-irradiation dose and the initial drug diffusivity within the microparticles could be established. Based on this knowledge both models were used to predict the resulting drug release kinetics as a function of the gamma-irradiation dose. Importantly, the theoretical predictions were confirmed by experimental results.

Dose-Response Relationship, Radiation↗
PubMed2004

Modeling of TCE diffusion to the atmosphere and distribution in plant stems.

Fate of chlorinated solvents in phytoremediation has been delineated by many discoveries made in recent years. Plant uptake, metabolism, rhizosphere degradation, accumulation, and volatilization were shown to occur to differing degrees for many organic contaminants including chlorinated solvents. Among these mechanistic findings, recent research confirmed that volatile organic compounds (VOCs) volatilize from stems and that the resulting diffusive flux to the atmosphere is related to exposure concentration and to height up the stem. A comprehensive model was developed based upon all identified fate and transport mechanisms for VOCs, including translocation in the xylem flow and diffusion. The dispersion and diffusion in the radial direction were considered as one process (effective diffusion) as the two could not be investigated individually. The mechanism-based model mathematically indicates an exponential decrease of concentrations with height. While an analytic solution for the comprehensive model was not attained, it can serve as a starting point for other modeling efforts. The comprehensive model was simplified in this work for practical application to experimentally obtained data on trichloroethylene (TCE) fate. Model output correlated well with experimental results, and effective diffusivities for TCE in plant tissues were obtained through the model calibrations. The simplified model approximated TCE concentrations in the transpiration stream as well as TCE volatilization to the atmosphere. Xylem transport, including advection, dispersion, and diffusion through cell walls with subsequent volatilization to the atmosphere, is a major fate for VOCs in phytoremediation.

Atmosphere↗
PubMed1990

Air quality in the vicinity of urban roads.

Motor vehicle emissions are a major source of CO, NOx and lead particulate concentrations to urban air quality. London urban Boroughs with high traffic densities are therefore a particular cause for concern. The air quality was monitored at an urban background site in the London Borough of Haringey for 2-years. The results of this study are assessed and their effect on human health is considered in the light of EC Directives and WHO guidelines. A desk top modelling technique based on Gaussian diffusion theory was used to predict the CO levels found at the background site. All predicted levels had a accuracy of better than 30%.

Air Pollution↗
PubMed2000

Light intensity distribution in the externally illuminated cylindrical photo-bioreactor and its application to hydrogen production by Rhodobacter capsulatus.

The light distribution in the externally illuminated cylindrical photo-bioreactor for production of hydrogen by a photosynthetic bacterium Rhodobacter capsulatus ST-410 was estimated. The estimation was performed on the basis of the Matsuura and Smith's diffuse model [1]. In the diffuse model, the incident light rays are assumed to proceed in every direction and the local intensity is calculated as the sum of the intensities of light. Since Lambert-Beer's law, extensively used in photometry, was not useful for explaining the decrease in the intensity of light by the biomass, an empirical expression was used. The measurement of the intensities from every direction was conducted in an externally illuminated cylindrical photo-bioreactor having an inner diameter of 60mm and a working volume of 550ml. The obtained results confirmed our estimation. The light distribution was applied to estimate the hydrogen production by R. capsulatus ST-410 using the same photo-bioreactor. The overall hydrogen-production rate was successfully estimated.

Journal Article↗
PubMed1992

In vitro magnesium absorption and the role of intestinal motility.

Magnesium (Mg) is known as an inhibitor of spontaneously contracting muscular tissues. To increase extracellular Mg in vivo, high doses of Mg must be given orally. Therefore, we investigated the effect of different doses of Mg given from the mucosal side of the small intestine of rats. According to the model of Trendelenburg, a system for the perfusion of isolated small intestine was developed, which allows the simultaneous recording of absorption and muscle contractions. Increasing doses of Mg were applied serosally or intraluminally. Intramulinal Mg did not affect intestinal motility. In contrast, increasing concentrations of serosal Mg resulted in a 50% inhibition of motility at 2.9 mmol/l Mg. This indicates no influence on intestinal motility of high doses of Mg acting from the mucosal side. In further studies, the addition of citric acid or taurocholic acid did not alter Mg absorption. Serosally applied amiloride (1 mmol/l) inhibited absorption, but also resulted in complete loss of motility. Since in this model passive diffusion is the most important mechanism of Mg transport, a direct influence of amiloride on Mg absorption can be excluded. From these data, we conclude that intestinal motility influences absorption--also of ions in aqueous solution--and should therefore be taken into account in absorption studies.

Amiloride↗
PubMed2001

Animal models for primary sclerosing cholangitis.

Since the aetiopathogenesis of primary sclerosing cholangitis (PSC) in humans remains undefined, investigators have studied a variety of animal models to gain insights into immunopathogenetic mechanisms associated with obliterative fibrous cholangitis of intra- and extra-hepatic bile ducts. To date, no animal model has been developed that exhibits all of the attributes of PSC. Rodent models instigated by bacterial cell components or colitis are promising because they may help to explain the strong association between PSC and inflammatory bowel disease (IBD). Other models of direct injury to biliary epithelia, peribiliary vascular endothelia or portal venous endothelia indicate that inflammation, chemokines and cytokines can produce diffuse sclerosis of bile ducts. Models of toxic, infectious or intra-luminal injury of the biliary tract also exhibit focal biliary sclerosis mediated by inflammation and cytokines. The histopathology of several models suggests a sequence of events beginning with secretion of proinflammatory cytokines by activated hepatic macrophages followed by peribiliary infiltration with CD4 and CD8 T cells with a T helper 1 phenotype. These results strongly suggest co-ordinated, pathogenetic roles for both the innate and adaptive immune responses. However, the stimuli that initiate and perpetuate peribiliary fibrosis remain unknown. Interestingly, several models are also associated with the development of anti-neutrophil cytoplasmic antibodies that react in a perinuclear and cytoplasmic pattern similar to that observed in patients with ulcerative colitis and/or PSC. Finally, models of extra-hepatic biliary obstruction continue to provide important information about the pathogenesis of portal fibrosis and secondary biliary cirrhosis that occurs in PSC and other diseases with obstruction of bile flow. Future studies in either existing or new animal models should advance our understanding of the pathogenesis of PSC, the major prerequisite for the development of effective therapies.

Animals↗
PubMed1990

Computer simulation of oral fluoride clearance.

The presence of fluoride in saliva and dental plaque is important for prevention of dental caries. The elimination of fluoride from the oral cavity after introduction of a fluoride containing agent is a complicated physiological process. This process was simulated with a Pascal program running under MS-DOS on IBM-compatible microcomputers. The program calculated the fluoride concentration in saliva as a function of time from several input parameters, the most important being the amount of fluoride, salivary stimulation due to the fluoride vehicle, resting salivary flow rate and volume factors. Furthermore, factors such as excretion of fluoride in the saliva following fluoride absorption in the intestinal tract were modeled. The fluoride concentration in dental plaque due to diffusion was also calculated. Output was directed to files which could be processed by a graphics interface. The results of the computations were very similar to findings in vivo.

Algorithms↗
PubMed2004

Dpp gradient formation by dynamin-dependent endocytosis: receptor trafficking and the diffusion model.

Developing cells acquire positional information by reading the graded distribution of morphogens. In Drosophila, the Dpp morphogen forms a long-range concentration gradient by spreading from a restricted source in the developing wing. It has been assumed that Dpp spreads by extracellular diffusion. Under this assumption, the main role of endocytosis in gradient formation is to downregulate receptors at the cell surface. These surface receptors bind to the ligand and thereby interfere with its long-range movement. Recent experiments indicate that Dpp spreading is mediated by Dynamin-dependent endocytosis in the target tissue, suggesting that extracellular diffusion alone cannot account for Dpp dispersal. Here, we perform a theoretical study of a model for morphogen spreading based on extracellular diffusion, which takes into account receptor binding and trafficking. We compare profiles of ligand and surface receptors obtained in this model with experimental data. To this end, we monitored directly the pool of surface receptors and extracellular Dpp with specific antibodies. We conclude that current models considering pure extracellular diffusion cannot explain the observed role of endocytosis during Dpp long-range movement.

Amino Acid Sequence↗
PubMed2003

Experimental evidence against diffusion control of Hg evasion from soils.

Elemental Hg (Hg(0)) evolution from soils can be an important process and needs to be measured in more ecosystems. The diffusion model for soil gaseous efflux has been applied to modeling the fluxes of several gases in soils and deserves testing with regard to Hg(0). As an initial test of this model, we examined soil gaseous Hg(0) and CO(2) concentrations at two depths (20 and 40 cm) over the course of a controlled environment study conducted in the EcoCELLs at the Desert Research Institute in Reno, Nevada. We also compared small, spatially distributed gas wells against the more commonly used large gas wells. In this study, two EcoCELLs were first watered (June 2000) and then planted (July 2000) with trembling aspen (Populus tremuloides). Following that, trees were harvested (October 2000) and one EcoCELL (EcoCELL 2) was replanted with aspen (25 April 2001). During most of the experiment, there was a strong vertical gradient of CO(2) (increasing with depth, as is typical of a diffusion-driven process), but no vertical gradient of soil gaseous Hg(0). Strong diel variations in soil gas Hg(0) concentration were noted, whereas diel variations in CO(2) were small and not statistically significant. Initial watering and planting caused increases in both soil gas CO(2) and Hg(0). Replanting in EcoCELL 2 caused a statistically significant increase in soil gas CO(2) but not Hg(0). Calculated Hg(0) effluxes using the diffusion model produced values two orders of magnitude lower than those measured using field chambers placed directly on the soil or whole-cell fluxes. Neither soil gas Hg(0) concentrations nor calculated fluxes were correlated with measured Hg(0) efflux from soil or from whole EcoCELLs. We conclude that (1) soil gas Hg(0) flux is not diffusion-driven and thus soil gas Hg(0) concentrations cannot be used to calculated soil Hg(0) efflux; (2) soil gas Hg(0) concentrations are increased by watering dry soil, probably because of displacement/desorption processes; (3) soil gas Hg(0) concentrations were unaffected by plants, suggesting that roots and rhizosphere processes are unimportant in controlling Hg(0) evasion from the soil surface. We recommend the use of the small wells in all future studies because they are much easier to install and provide more resolution of spatial and temporal patterns in soil gaseous Hg(0).

Carbon Dioxide↗
PubMed1998

Modelling DNA damage induced by different energy photons and tritium beta-particles.

PURPOSE: To model the production of single- and double-strand breaks (ssb and dsb) in DNA by ionizing radiations. To compare the predicted effectiveness of different energy photon radiations and tritium beta-particles. MATERIALS AND METHODS: Modelling is carried out by Monte Carlo and includes consideration of direct energy depositions in DNA molecules, the production of species, their diffusion and interactions with each other and DNA. Computer-generated electron tracks in liquid water are used to model energy deposition and to derive the initial positions of chemical species. Atomistic representation of the DNA in B form with a first hydration shell is used. Photon radiations in the energy range 70keV-1MeV and tritium beta-particles are considered. RESULTS: A tentative increase for dsb yield has been predicted for 70 keV photons and tritium compared with 137Cs. This increase is more pronounced for complex dsb. Double-strand breaks are much more prone compared with ssb to combine with additional strand breaks and base damage, which contributes to break complexity. At least half of DNA breaks are hydroxyl radical mediated. CONCLUSIONS: The developed model makes predictions compatible with features of available experimental data. Break complexity has to be addressed in biophysical modelling when the relative effectiveness of radiations in DNA damage is studied. Obtained data strongly argue against the dominance of direct radiation action in DNA damage in the cellular environment predicted by some theoretical studies.

Computer Simulation↗
PubMed1976

Pharmacokinetics of halothane in the dog. Comparison of theory and measurement in individuals.

After surgical preparation under pentobarbitone anaesthesia seven dogs of mean body weight 31 kg were ventilated with 1% halothane for 80 min. At 1, 2, 5, 10, 20, 40 and 80 min after the start of the halothane administration blood samples were taken from the femoral artery and pulmonary artery and from a cerebral, a renal and a femoral vein. At 80 min a biopsy sample of skeletal muscle (psoas) was taken. The halothane tension in all samples was determined by extraction into carbon tetrachloride followed by gas chromatographic analysis using chloroform as an internal standard. The measured tensions were compared with tensions computed from a multi-compartment model of the uptake and distribution of halothane in the body. The model was quantified by measurements, in each individual, of total body mass, the masses of the major organs and the solubility of halothane in the major organs and tissues; by measurements of blood volume and solubility in blood at the start and finish of the halothane administration; and by repeated measurements of alveolar ventilation, cardiac output and body temperature. For the original version of the model, the computed tensions deviated from the measured tensions to an extent greater than could be attributed to experimental error and in a manner which could be attributed to metabolism of halothane and probably to direct diffusion of halothane from well-perfused organs and lean tissues into fat. Direct experimental evidence of diffusion into perirenal fat was obtained in supplementary experiments. With the quantitation of the model distorted to mimic the processes of metabolism and diffusion, measured arterial tensions could be predicted with a mean error of -0.2 mm Hg (SD 0.6 mm Hg). The mean measured arterial tension was 3.5 mm Hg.

Animals↗
PubMed2004

A two-dimensional mathematical model of percutaneous drug absorption.

BACKGROUND: When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearance. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. METHODS: Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. RESULTS: Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. CONCLUSION: Based on the values of r, conclusions are drawn about (1) the flow rate of the drug, (2) the flux and the cumulative amount of drug eliminated into the receptor cell, (3) the steady-state value of the flux, (4) the time to reach the steady-state value of the flux and (5) the optimal value of r, which gives the maximum absorption of the drug. The paper gives valuable information which can be obtained by this two-dimensional model, that cannot be obtained with one-dimensional models. Thus this model improves upon the much simpler one-dimensional models. Some future directions of the work based on this model and the one-dimensional non-linear models that exist in the literature, are also discussed.

Humans↗
PubMed1998

A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads.

The theoretical basis and quantitative evaluation of a new approach for modeling biofilm growth are presented here. Soluble components (e.g., substrates) are represented in a continuous field, whereas discrete mapping is used for solid components (e.g., biomass). The spatial distribution of substrate is calculated by applying relaxation methods to the reaction-diffusion mass balance. A biomass density map is determined from direct integration in each grid cell of a substrate-limited growth equation. Spreading and distribution of biomass is modeled by a discrete cellular automaton algorithm. The ability of this model to represent diffusion-reaction-microbial growth systems was tested for a well-characterized system: immobilized cells growing in spherical gel beads. Good quantitative agreement with data for global oxygen consumption rate was found. The calculated concentration profiles of substrate and biomass in gel beads corresponded to those measured. Moreover, it was possible, using the discrete spreading algorithm, to predict the spatial two- and three-dimensional distribution of microorganisms in relation to, for example, substrate flux and inoculation density. The new technique looks promising for modeling diffusion-reaction-microbial growth processes in heterogeneous systems as they occur in biofilms.

Algorithms↗
PubMed1998

Studies on the Diffusion of Molecules through Pores in Monolayer and Multilayer Films.

A one-parameter model for species flux through pores in a crystalline monolayer or multilayer film is developed. The model is based on surface diffusion of the species on the upstream surface of the monolayer and one-directional diffusion of the species into the pores of the monolayer. It is found that the Fickian diffusivity depends on the concentration of adsorbed species on surface sites and on the pore coverage. The model contains an important parameter, the rate constant of activation, which is function of the diffusing species and film surface properties. The model is compared with experimental data on ion and gas flux through single and multilayer films. Good agreement between theory and experiment is found with all sets of the data with the rate constant as a sole adjustable parameter. Copyright 1998 Academic Press.

Journal Article↗
PubMed2007

Line FRAP with the confocal laser scanning microscope for diffusion measurements in small regions of 3-D samples.

We present a truly quantitative fluorescence recovery after photobleaching (FRAP) model for use with the confocal laser scanning microscope based on the photobleaching of a long line segment. The line FRAP method is developed to complement the disk FRAP method reported before. Although being more subject to the influence of noise, the line FRAP model has the advantage of a smaller bleach region, thus allowing for faster and more localized measurements of the diffusion coefficient and mobile fraction. The line FRAP model is also very well suited to examine directly the influence of the bleaching power on the effective bleaching resolution. We present the outline of the mathematical derivation, leading to a final analytical expression to calculate the fluorescence recovery. We examine the influence of the confocal aperture and the bleaching power on the measured diffusion coefficient to find the optimal experimental conditions for the line FRAP method. This will be done for R-phycoerythrin and FITC-dextrans of various molecular weights. The ability of the line FRAP method to measure correctly absolute diffusion coefficients in three-dimensional samples will be evaluated as well. Finally we show the application of the method to the simultaneous measurement of free green fluorescent protein diffusion in the cytoplasm and nucleus of living A549 cells.

Algorithms↗
PubMed2004

Physiological characterization of human ovarian cancer cells in a rat model of intraperitoneal antineoplastic therapy.

Destruction of cancer cells by therapies directed against new molecular targets requires their effective delivery to the tumor. To study diffusion and convection of intraperitoneal (ip) therapy to ip tumors, we established a new athymic rat (RNU) model with ovarian tumor cells (SKOV3 and OVCAR3) implanted in the abdominal wall. The model simulates metastatic tumor and facilitates the measurement of physiological parameters that govern transport forces. CD31 immunohistochemistry revealed unique patterns of angiogenesis, with a tissue-averaged vascular volume of approximately 0.01 ml/g for each tumor. The extracellular volume (SKOV3: 0.54 +/- 0.11 ml/g, n=5; OVCAR3: 0.61 +/- 0.03, n=5) was over twice that of the adjacent normal muscle (0.22 +/- 0.06 ml/g, n=5). Intravenous-injected antibody tumor clearance was two to three times that of muscle. Interstitial pressures were higher than normal tissue with a median of 10-15 mmHg. Quantitative autoradiography of frozen tissue slices from rats exposed to ip solutions containing [14C]mannitol or 125I-immunoglobulin G (trastuzumab) was performed to determine transport of small and large molecules. With ip pressure of 0-6 mmHg, both mannitol and immunoglobulin G displayed steep concentration profiles close to the tumor surface with limited penetration deeper within the tumor tissue; antibody penetration was significantly affected by ip pressure. These results demonstrated effects of molecular size, ip pressure, the limited but highly permeable tumor vasculature, and the expanded interstitium on drug penetration from the peritoneal cavity. In conclusion, we have characterized physical and chemical parameters that determine transport of therapeutic agents in our unique tumor-bearing rat model.

Animals↗