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At least 199 records · Page 11Linked to original sources
PubMed2000

Nonlocal-response diffusion model of holographic recording in photopolymer

The standard one-dimensional diffusion equation is extended to include nonlocal temporal and spatial medium responses. How such nonlocal effects arise in a photopolymer is discussed. It is argued that assuming rapid polymer chain growth, any nonlocal temporal response can be dealt with so that the response can be completely understood in terms of a steady-state nonlocal spatial response. The resulting nonlocal diffusion equation is then solved numerically, in low-harmonic approximation, to describe grating formation. The effects of the diffusion rate, the rate of polymerization, and a new parameter, the nonlocal response length, are examined by using the predictions of the model. By applying the two-wave coupled-wave model, assuming a linear relationship between polymerized concentration and index modulation, the resulting variation of the grating diffraction efficiency is examined.

Journal Article↗
PubMed2005

Numerical investigation of the spreading-receding cycle in a concentration-dependent lattice gas automaton diffusion model.

This work forms the second part of a numerical study about the dynamics of diffusive fronts in concentration-dependent diffusion processes. We previously demonstrated that one-dimensional spreading of a density front in a concentration-dependent microscopically heterogeneous, macroscopically homogeneous isotropic lattice gas automaton (LGA) substantially deviates from the t(1/2) relation expected from Fick's law over large periods of time. The time exponent was found to be larger than 1/2 , i.e., spreading of the density front is enhanced with respect to standard Fickian diffusion. In this note, we specifically investigate the dynamics of receding by using the same LGA model. We show here that the receding process essentially scales as t(1/2). The LGA simulations of diffusive fronts thus lead to the paradoxical result of Fick's-compatible receding and anomalous superdiffusive spreading for the same microscopic random structure and the same boundary conditions. The results also suggest that hysteresis of the spreading-receding cycle could arise from the contrasted dynamics between spreading and receding. A conceptual model of "offer and demand" which includes both the diffusivity gradient dD(rho)/d(rho) and the conditions applied at boundaries as main parameters is proposed to tentatively account for the dynamics of diffusive fronts in concentration-dependent diffusion processes.

Journal Article↗
PubMed2004

Isometric graphing and multidimensional scaling for reaction-diffusion modeling on regular and fractal surfaces with spatiotemporal pattern recognition.

Heterogeneous surface reactions exhibiting complex spatiotemporal dynamics and patterns can be studied as processes involving reaction-diffusion mechanisms. In many realistic situations, the surface has fractal characteristics. This situation is studied by isometric graphing and multidimensional scaling (IGMDS) of fractal surfaces for extracting geodesic distances (i.e., shortest scaled distances that obtain edges of neighboring surface nodes and their interconnections) and the results obtained used to model effects of surface diffusion with nonlinear reactions. Further analysis of evolved spatiotemporal patterns may be carried out by IGMDS because high-dimensional snapshot data can be efficiently projected to a transformed subspace with reduced dimensions. Validation of the IGMDS methodology is carried out by comparing results with reduction capabilities of conventional principal component analysis for simple situations of reaction and diffusion on surfaces. The usefulness of the IGMDS methodology is shown for analysis of complex patterns formed on both regular and fractal surfaces, and using generic nonlinear reaction-diffusion systems following FitzHugh Nagumo and cubic reaction kinetics. The studies of these systems with nonlinear kinetics and noise show that effects of surface disorder due to fractality can become very relevant. The relevance is shown by studying properties of dynamical invariants in IGMDS component space, viz., the Lyapunov exponents and the KS entropy for interesting situations of spiral formation and turbulent patterns.

Diffusion↗
PubMed1977

Diffusion model for drug release from suspensions I: theoretical considerations.

A new mathematical model based on physicochemical principles is presented; it does not require a "diffusion layer" for the release of a suspended drug from a semisolid vehicle. This general model has wide range application to systems where release is controlled by the diffusion rate or dissolution rate of a drug. The appropriate mathematical relationships are derived and evaluated. Theoretical drug concentration distributions in the vehicle and a membrane and the predicted cumulative drug mass uptake by blood under specified conditions are presented. The dissolution rate of solid drug in the vehicle markedly influences predicted drug release using the model presented. It is anticipated that the model will stimulate further research to confirm or reject the assumption that the dissolution rate may be slow enough to be important in the systems studied.

Biological Transport↗
PubMed1991

Diffusion model in ion channel gating. Extension to agonist-activated ion channels.

Previously, we described a model which treats ion channel gating as a discrete diffusion problem. In the case of agonist-activated channels at high agonist concentration, the model predicts that the closed lifetime probability density function from single channel recording approximates a power law with an exponent of -3/2 (Millhauser, G. L., E. E. Salpeter, and R. E. Oswald. 1988a. Proc. Natl. Acad. Sci. USA. 85: 1503-1507). This prediction is consistent with distributions derived from a number of ligand-gated channels at high agonist concentration (Millhauser, G. L., E. E. Salpeter, and R. E. Oswald. 1988b. Biophys. J. 54: 1165-1168.) but does not describe the behavior of ion channels at low activator concentrations. We examine here an extension of this model to include an agonist binding step. This extended model is consistent with the closed time distributions generated from the BC3H-1 nicotinic acetylcholine receptor for agonist concentrations varying over three orders of magnitude.

Animals↗
PubMed2003

Differential uptake of volatile agents into brain tissue in vitro. Measurement and application of a diffusion model to determine concentration profiles in brain slices.

BACKGROUND: The rate of onset of drug actions in experiments with brain slices in vitro can vary widely. One factor that influences the rate is access to tissue sites of action. To study the effects of the nonimmobilizer 1,2-dichlorohexafluorocyclobutane (F6, also termed 2N in the literature) on physiologic processes under defined tissue concentrations, the authors performed electrophysiologic measurements of the effects of F6 and halothane, measured the uptake of these agents into brain tissue, and performed computational modeling to determine concentration-depth profiles during drug application. METHODS: Hippocampal brain slices 500 microm thick were prepared from adult rats. Evoked population responses in the CA1 region were obtained using extracellular recordings and electrical stimulation of the Schaffer collateral pathway. F6 (24 microm) and halothane (270 microm) were applied via superfusion for 40 min. Uptake of drug into tissue slices was measured using gas chromatography. Computational modeling was used to obtain estimates of drug diffusion coefficients in brain tissue and to calculate tissue concentration as a function of time and depth during drug application. RESULTS: Halothane reduced the amplitude of the evoked population spike and reduced the population excitatory postsynaptic potential slope. F6 had no effect on either measure. Uptake experiments yielded a diffusion coefficient of 0.1 x 10-6 cm2/s for F6 and 0.8 x 10-6 cm2/s for halothane. After 40 min of drug application, the concentration reached at tissue depths from which physiologic signals were obtained, approximately the top 200 microm of the slice, was estimated to be 58% of the final equilibrium value for F6 and 93% for halothane. CONCLUSIONS: Diffusion into tissue is substantially slower for F6 than for halothane, and its impact is great enough that this must be considered when designing or interpreting in vitro experiments. However, impaired access does not account for the lack of effect of F6 on electrophysiologic responses in rat hippocampal slices.

Algorithms↗
PubMed2002

Directionality of stripes formed by anisotropic reaction-diffusion models.

Turing mechanism explains the formation of striped patterns in a uniform field in which two substances interact locally and diffuse randomly. In a twin paper, to explain the directionality of stripes on fish skin in closely related species, we studied the effect of anisotropic diffusion of the two substances on the direction of stripes, in the cases in which both substances have high diffusivity in the same direction. In this paper, we study the direction of stripes in more general situations in which the diffusive direction may differ between the two substances. We derive a formula for the direction of stripes, based on a heuristic argument of unstable modes of deviation from the uniform steady state. We confirm the accuracy of the formula by computer simulations. When the diffusive direction is different between two substances, the directions of stripes in the spatial pattern change smoothly with the magnitude of anisotropy of two substances. When the diffusive direction of the two substances is the same, the stripes are formed either parallel or perpendicular to the common diffusive direction, depending on the relative magnitude of the anisotropy. The transition between these two phases occurs sharply.

Animals↗
PubMed2006

Side diffusion modeling by the explicit consideration of a space-charge buildup under the mask during strip waveguide formation in the Ag+ -Na+ field-assisted ion-exchange process.

A space-charge buildup under the blocking mask in a field-assisted Ag+ -Na+ ion-exchange modeling is assumed. It results in the distortion of electric field lines in the direction under the mask edges. As a result, side diffusion occurs and the numerical model shows the same range of side diffusion as the experimental data. Explicit consideration of the space-charge buildup under the mask and solving the Poisson equation for the electric field determination make it possible to use more realistic boundary conditions in the numerical model, compared to the boundary conditions generally used.

Journal Article↗
PubMed2006

Diffusive model of protein folding dynamics with Kramers turnover in rate.

We study the folding kinetics of a three-helix bundle protein using a coarse polymer model. The folding dynamics can be accurately represented by one-dimensional diffusion along a reaction coordinate selected to capture the transition state. By varying the solvent friction, we show that position-dependent diffusion coefficients are determined by microscopic transitions on a rough energy landscape. A maximum in the folding rate at intermediate friction is explained by "Kramers turnover" in these microscopic dynamics that modulates the rate via the diffusion coefficient; overall folding remains diffusive even close to zero friction. For water friction, we find that the "attempt frequency" (or "speed limit") in a Kramers model of folding is about 2 micros-1, with an activation barrier of about 2kBT, and a folding transition path duration of approximately equal to 100 ns, 2 orders of magnitude less than the folding time of approximately equal to 10 micros.

Diffusion↗
PubMed2006

Effect of input diffusivity in an axisymmetric mass diffusivity model for liquid metals with an applied magnetic field.

Depending on the magnitude of the diffusivity, convective contamination may result in erroneous measurement of mass diffusivity even in microgravity. The effect of natural or buoyant convection is numerically investigated for liquid germanium with an axisymmetric model using two different magnetic field strengths and four heat transfer conditions. Since the reported input diffusivity value may vary due to inaccuracies in measurements, an order of magnitude lower and higher input diffusivity from the base value of D0 = 2 x 10(-4) cm2/sec was used to evaluate the behavior of liquid germanium in the presence of a magnetic field. From the numerical results, the temperature nonuniformity and the flow velocities in the liquid vary according to the input diffusivity (i.e., an order of magnitude lower and higher than the base cases). The heat transfer pattern is important in achieving a larger temperature nonuniformity in the liquid during the experiments. A stronger magnetic field can tolerate a higher temperature nonuniformity as expected.

Journal Article↗
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↗
PubMed1997

A Reaction-Diffusion Model can Account for the Anatomical Pattern of the Cardiac Conal Valves in Fish

The conus arteriosus of fish bears a variable number of swallownest-like valves arranged in transverse rows. We propose that a reaction-diffusion mechanism coupled with the specific growth dynamics of the conus arteriosus, and probably, with a system of positional information, can account for the pattern formation of the conal valves in these primitive vertebrates. The reaction-diffusion mechanism, according to our hypothesis, would determine the regular arrangement of the places where the endocardial cells are activated and they transform into mesenchymal cells. These cells populate the subendocardial space, giving rise to the primordia of the conal valves. We have carried out simple computer simulations, based on reaction-diffusion/lateral inhibition models, which were able to generate all the anatomical diversity of the fish conal valves allowing changes only in the growth rate of the structure. Furthermore, we have found similarities between the sequential morphologies generated by our simulations and those actually occurring in embryos of Scyliorhinus canicula. We have derived three testable predictions from our hypothesis: (1) the number of discrete areas of epithelial-mesenchymal transition should correlate with the definitive number of valves in the conus arteriosus; (2) the small valves intercalated between the large ones should develop later than these latter; and (3) the longitudinal growth rate of the conus arteriosus in fish should be proportional to the number of transverse rows of valves. Copyright 1997 Academic Press Limited

Journal Article↗