Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Diffusion models”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19Linked to original sources
PubMed2004

Human whole-blood relaxometry at 1.5 T: Assessment of diffusion and exchange models.

Human whole-blood relaxometry experiments were performed to allow the prediction of blood signal changes with blood oxygen saturation (Y) and refocusing interval (tau180). Such predictions are particularly relevant for spin-echo (SE) blood oxygenation level-dependent (BOLD) experiments and a recently proposed noninvasive fMRI method for measuring cerebral blood volume (CBV). Ensemble fitting of the entire set of T2 estimates, obtained over an extensive range of Y and tau180 values, was performed with the use of both a fast chemical exchange model and a model of diffusion in weak magnetic field inhomogeneities. The diffusion modeling resulted in a large reduction in the residual sum-of-squares compared to the fast exchange modeling. The longitudinal relaxation rate decreased linearly with Y, and increased with hematocrit. The results support the application of the recently reported diffusion model to describe deoxyhemoglobin (dHb)-induced blood transverse relaxation rate enhancement at 1.5 T.

Analysis of Variance↗
PubMed1989

Diffusion approximations of the two-locus Wright-Fisher model.

Diffusion approximations are established for the multiallelic, two-locus Wright-Fisher model for mutation, selection, and random genetic drift in a finite, panmictic, monoecious, diploid population. All four combinations of weak or strong selection and tight or loose linkage are treated, though the proof in the case of strong selection and loose linkage is incomplete. Under certain conditions, explicit formulas are obtained for the stationary distributions of the two diffusions with loose linkage.

Genetic Linkage↗
PubMedDate not supplied

A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo.

A model based upon steady-state diffusion theory which describes the radial dependence of diffuse reflectance of light from tissues is developed. This model incorporates a photon dipole source in order to satisfy the tissue boundary conditions and is suitable for either refractive index matched or mismatched surfaces. The predictions of the model were compared with Monte Carlo simulations as well as experimental measurements made with tissue simulating phantoms. The model describes the reflectance data accurately to radial distances as small as 0.5 mm when compared to Monte Carlo simulations and agrees with experimental measurements to distances as small as 1 mm. A nonlinear least-squares fitting procedure has been used to determine the tissue optical properties from the radial reflectance data in both phantoms and tissues in vivo. The optical properties derived for the phantoms are within 5%-10% of those determined by other established techniques. The in vivo values are also consistent with those reported by other investigators.

Diffusion↗
PubMed2002

Self-similar Gaussian processes for modeling anomalous diffusion.

We study some Gaussian models for anomalous diffusion, which include the time-rescaled Brownian motion, two types of fractional Brownian motion, and models associated with fractional Brownian motion based on the generalized Langevin equation. Gaussian processes associated with these models satisfy the anomalous diffusion relation which requires the mean-square displacement to vary with t(alpha), 0<alpha<2. However, these processes have different properties, thus indicating that the anomalous diffusion relation with a single parameter is insufficient to characterize the underlying mechanism. Although the two versions of fractional Brownian motion and time-rescaled Brownian motion all have the same probability distribution function, the Slepian theorem can be used to compare their first passage time distributions, which are different. Finally, in order to model anomalous diffusion with a variable exponent alpha(t) it is necessary to consider the multifractional extensions of these Gaussian processes.

Journal Article↗
PubMedDate not supplied

Immobilized particles in gel matrix-type porous media. Homogeneous porous media model.

Diffusion in pure gels and gels with immobilized cells was analyzed. A model of diffusion assuming a homogeneous cell distribution in gel was improved by introducing a tortuosity value. By theoretical analysis and numerical modeling it was shown that the tortuosity of a gel with immobilized cells is the product of two factors: (1) tortuosity generated by the cells, Tc, and (2) tortuosity of the gel matrix, Tg, both variables being a function of cell volume fraction, phi(c). Total tortuosity is thus T(Sigma) = TcTg. On the basis of this approach, it was possible to analyze diffusivity data for gels with immobilized cells. It was shown that, in these systems, the diffusivity eta = D(e)/D(0) is a complex function of (1) diffusivity in the gel, eta(g), and (2) diffusivity in immobilized cells, eta(c). The developed model allowed for the description of the dependence of D(e)/D(0) on phi(c). Comparison with numerous published experimental data showed a good fit. Observed deviations might be explained by nonhomogeneous cell distributions inside the gel matrix.

Cells, Immobilized↗
PubMed1998

Restricted diffusion and exchange of intracellular water: theoretical modelling and diffusion time dependence of 1H NMR measurements on perfused glial cells.

Intracellular diffusion properties of water in F98 glioma cells immobilized in basement membrane gel threads, are investigated with a pulsed-field-gradient spin-echo NMR technique at diffusion times from 6 to 2000 ms and at different temperatures. In extended model calculations the concept of 'restricted intracellular diffusion at permeable boundaries' is described by a combined Tanner-Kärger formula. Signal components in a series of ct experiments (constant diffusion time) are separated due to different diffusion properties (Gaussian and restricted diffusion), and physiological as well as morphological cell parameters are extracted from the experimental data. The intracellular apparent diffusion coefficients strongly depend on the diffusion time and are up to two orders of magnitude smaller than the self diffusion constant of water. Propagation lengths are found to be in the range of 4-7 microns. Hereby intracellular signals of compartments with a characteristic diameter could be selected by an appropriate gradient strength. With cg experiments (constant gradient) a mean intracellular residence time for water is determined to be about 50 ms, and the intrinsic intracellular diffusion constant is estimated to 1 x 10(-3)mm2/s. Studying the water diffusion in glial cells provides basic understanding of the intracellular situation in brain tissue and may elucidate possible influences on the changes in the diffusion contrast during ischemic conditions.

Animals↗
PubMed2005

Adsorption of Acid Blue 193 from aqueous solutions onto DEDMA-sepiolite.

The adsorption of Acid Blue 193 (AB193) onto dodecylethyldimethylammonium (DEDMA)-sepiolite was investigated in aqueous solution in a batch system with respect to contact time, pH and temperature. The surface modification of DEDMA-sepiolite was examined by the FT-IR technique. The pseudo-first-order, pseudo-second-order kinetic models and the intraparticle diffusion model were used to describe the kinetic data and the rate constants were evaluated. The experimental data fitted very well with the pseudo-second-order kinetic model and also followed the simple external diffusion model up to initial 10 min and then by intraparticle diffusion model up to 75 min, whereas diffusion is not only the rate-controlling step. The adsorption capacities of natural sepiolite and DEDMA-sepiolite at pH 1.5 and 20 degrees C were (1.19 and 2.57) x 10(-4) mol g(-1), respectively. The above results indicate that DEDMA-sepiolite has around two times higher adsorption capacity than natural sepiolite. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms and the isotherm constants were also determined. The Freundlich model agrees with experimental data well. The activation energy, change of Gibbs free energy, enthalpy and entropy of adsorption were also evaluated for the adsorption of AB193 onto DEDMA-sepiolite.

Adsorption↗
PubMed1986

Free volume model for lipid lateral diffusion coefficients. Assessment of the temperature dependence in phosphatidylcholine and phosphatidylethanolamine bilayers.

The lipid lateral diffusion coefficients, DT, in fluid-phase phosphatidylcholine and phosphatidylethanolamine bilayers have been analysed in terms of the free-volume diffusion model by fitting the expression: DT = AT exp[- B/(T - T0)] to the observed temperature dependence, where A, B and T0 are the parameters to be optimized. Application of an unconstrained optimization procedure to data obtained from excimer formation (Galla et al. (1979) J. Membrane Biol. 48, 215-236) and from fluorescence photobleaching (Vaz et al. (1985) Biochemistry 24, 781-786) provides statistical evidence for a free-volume model as opposed to a simple Stokes-Einstein model (T0 = 0), only in certain cases. In the instances for which the parameter T0 can be determined with a reasonable degree of accuracy, it is found that this characteristic temperature at which the free volume extrapolates to zero lies below the bilayer gel-to-fluid phase transition temperature and does not coincide with the pre-transition temperature for phosphatidylcholines.

Diffusion↗
PubMed2001

Modeling effective diffusivity of volatile organic compounds in activated carbon fiber.

Volatile organic compounds (VOCs) comprise 67% of total hazardous air pollutants (HAPs) that are emitted by major industrial point sources into the U.S. atmosphere (1). Adsorption by activated carbon fiber (ACF) has been recognized as one of the feasible regenerative control processes to separate and recover VOCs for reuse. Characteristics of VOCs transport in ACFs are required to efficiently design ACF sorption systems. However, extensive resources are spent experimentally obtaining transient sorption data to design adsorption systems. As an alternative, this work develops a new model that predicts effective diffusivities of VOCs into ACFs. The diffusion process is modeled as Knudsen transport into the ACF open pore spaces coupled with activated surface diffusion on the ACF's internal surface area. Temperature and Darken's factors are included in the surface diffusion model to provide corrections for thermodynamic state and deviation from Fick's Law, respectively. Depth of the adsorption potential well is considered as the product of the heat of adsorption of a reference VOC, an adsorption similarity factor, and a surface diffusion energy factor. Introduction of the adsorption similarity factor in the effective diffusivity model is a new concept providing a means to predict effective diffusivity of similar adsorption systems from a reference system. Experimental data from a short length column are used to determine effective diffusivity of acetone in ACF. Results from this diffusivity model are compared to experimental values for the acetone/ACF system to describe the degree of closure between modeled and experimental results.

Adsorption↗
PubMed2002

Stretched exponential relaxation in a diffusive lattice model.

We studied the single dimer dynamics in a lattice diffusive model as a function of particle density in the high densification regime. The mean square displacement is found to be subdiffusive both in one and two dimensions. The spatial dependence of the self-part of the van Hove correlation function displays as a function of r a single peak and signals a dramatic slow down of the system for high density. The self-intermediate scattering function is fitted to the Kohlrausch-Williams-Watts law. The exponent beta extracted from the fits is density independent while the relaxation time tau follows a scaling law with an exponent 2.5.

Journal Article↗
PubMed1990

Role of geometry and anisotropic diffusion for modelling PO2 profiles in working red muscle.

A 3-dimensional analytical model of O2 diffusion in heavily working muscle is proposed which considers anisotropic, myoglobin (Mb)-facilitated O2 diffusion inside the muscle fiber and a carrier-free layer separating erythrocytes and fiber. The model is used to study the effects of some commonly applied simplifying assumptions (reduced dimensionality, neglected anisotropy) on the resulting PO2 distributions: (1) In order not to underestimate PO2 drops near erythrocytes, modelling O2 transport in 3 dimensions is important. (2) For a capillary-to-fiber ratio of 1, the results from the 2-dimensional version of the present model and from a Krogh-type model which incorporates a carrier-free layer agree well. (3) This is not true if the capillary-to-fiber ratio is 2. (4) In neither case, a Hill-type model furnishes a good description of the PO2 distributions. (5) Anisotropic diffusion may become important under critical O2 supply conditions. For a capillary-to-fiber ratio of 1, a Krogh-type model in which the O2 fluxes within the carrier-free layer are adapted according to Hellums (Microvasc. Res. 13: 131, 1977) yields almost identical PO2 distributions as the present 3-dimensional model.

Animals↗
PubMed2001

A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations.

A photon diffusion model has been developed to calculate the steady-state spatially resolved fluorescence from pencil beam excitation in layered tissue. The model allows the calculation of both the excitation reflectance and the fluorescence escape for an arbitrary continuous depth distribution of tissue optical properties and fluorophore concentration. The validity of this model was verified by comparison with Monte Carlo simulations and experimental measurements using phantoms with tissue-like optical properties. The potential usefulness of the spatially resolved fluorescence was explored using the model and simulations of realistic drug distributions. It was shown that using this technique it may be possible to quantify the diffusion of a topically administered drug into the skin, or the photobleaching of a sensitizer during photodynamic therapy.

Algorithms↗
PubMed1985

A new model of diffuse interstitial pulmonary fibrosis in the rat.

We have produced experimental diffuse interstitial pulmonary fibrosis in rats with a combination of low and repeated doses of paraquat plus continuous exposure to normobaric 74% O2 in the breathing air for several weeks. Pulmonary fibrosis was evaluated histologically and biochemically, through the determination of total collagen content in the lung. Our procedure is characterized by low initial mortality, the development of extensive distortion of the pulmonary architecture, and the presence of severe and diffuse interstitial fibrosis. The model was compared with bleomycin-induced pulmonary fibrosis in the same rat strain, in which the process is focal and leaves most of the lung unaffected. We conclude that lung damage produced by the combination of low doses of paraquat plus normobaric 74% O2 concentration in the breathing air is an adequate experimental model of diffuse interstitial pulmonary fibrosis as it occurs in many of the human cases of this condition.

Animals↗
PubMed1996

Modeling solute sorption into plastic tubing during organ perfusion and intravenous infusions.

The uptake of solutes into plastic infusion and perfusion tubing has been well documented, but the kinetics of the uptake process is not well-defined. Three mathematical models have been developed to describe the outflow fraction concentration--time profiles for solutes sorbed into the plastic tubing during infusion and perfusions. The models are referred to as model 1, convection--diffusion; model 2, convention-- interfacial resistance--diffusion; ad model 3, convection--interfacial resistance--infinite sink models. In each model, plug flow is assumed and, in order to minimize the number of variables required, solutions are limited to early times when the plastic behaves as an infinite sink. Initial conditions of (i) no solution in the tubing and (ii) a preloading of tubing with drug solution are considered for each of the three models. Two parameters, one being the transit time of solution through tubing (tmin) and the other a measure of the affinity and diffusivity of the solute in the plastic (SN), are sufficient to describe the outflow concentration--time profiles for solutes with sorption into tubing being limited by diffusion in the plastic (model 1). A single parameter, which is the effective interfacial permeability coefficient (H), is sufficient to describe the outflow concentration--time profiles for solutes with sorption into tubing being limited by an aqueous--plastic interfacial barrier (model 3). The three parameters (tmin, SN, and H) are required when uptake into tubing is limited by a combination of diffusion into plastic and an interfacial resistance (model 3). Each model has a characteristic outflow concentration--time profile determined by the relative magnitude of diffusivity of the solute in the plastic to that across the interfacial barrier. The sorption of nitroglycerin and isosorbide dinitrate are adequately described by the convection--diffusion model (model 1 (ii)) whereas the convection--interfacial resistance--diffusion model (model 2 (ii)) is required to describe the sorption of diazepam and chlorpromazine.

Adsorption↗
PubMed1997

A cellular automata model of diffusion in aqueous systems.

A cellular automata model of a solute diffusing in water has been created and studied for the influential attributes. The results with this model are in agreement with experimental results; that is, that lipophilic solutes diffuse faster than do polar solutes. The model reveals that a solution composed of a relatively lipophilic solute permits a greater extent of diffusion of another solute. This observation is in agreement with the model showing a diffusion preference of a solute between two solutions made up of differing polarities. The solute diffuses farther into the lipophilic solution. A temperature-lipophilicity phase diagram shows the influence of these two attributes on the rate of diffusion. A model of diffusion through solutions containing stationary ingredients reveals a faster rate when the ingredient is lipophilic. We are led to a conclusion that the relative lipophilicity of solutes or stationary ingredients in a solution has a direct influence on the rates of diffusion of other solutes in their midst.

Diffusion↗
PubMed2001

Coexistence of large amplitude stationary structures in a model of reaction-diffusion system.

The two-variable reaction-diffusion model of a chemical system describing the spatiotemporal evolution to large amplitude stationary periodical structures in a one-dimensional open, continuous-flow, unstirred reactor is investigated. Numerical solutions show that the structures are generated by divisions of the traveling impulse and its stopping at the boundary of the system. Analyses of projections of numerical solutions on the phase plane of two variables elaborated in the present paper allow qualitative explanation of the results. The coexistence of the large amplitude stationary periodical structures is shown. A number of coexisting structures grows strongly with increasing length of the reactor and may be as large as one wishes. The relationship of these results to biological systems is stressed.

Journal Article↗
PubMed2006

A comparative study of ion exchange kinetics in zinc/lead-modified zeolite-clinoptilolite systems.

The kinetics of zinc and lead ions removal by modified zeolite-clinoptilolite has been investigated. The rate of the ion exchange process for lead ions is faster than for zinc ions, as well as the time needed to reach the equilibrium. The ion exchange capacity of zeolite of lead ions is doubly higher than that of zinc ions. Diffusion models according to the Vermeulen's approximation, the parabolic diffusion model and the homogeneous diffusion model have been tested with the experimental data of ion exchange for zinc and lead. For both systems examined, the best fit of the models proposed with the experimental data was shown by the Vermeulen's approximation and the homogeneous diffusion model with t-->t(infinity). The diffusion coefficients are calculated from kinetic models of lead ions they are of the order of 10(-6)cm(2)/min, constant for all examined initial concentrations and not dependent on time. The diffusion coefficients in the system of zinc ions is of the order of 10(-8)cm(2)/min, also independent of initial concentrations, but decreasing with time from the beginning of ion exchange to the equilibrium.

Algorithms↗
PubMed2003

Modeling controlled nutrient release from a population of polymer coated fertilizers: statistically based model for diffusion release.

A statistically based model for describing the release from a population of polymer coated controlled release fertilizer (CRF) granules by the diffusion mechanism was constructed. The model is based on a mathematical-mechanistic description of the release from a single granule of a coated CRF accounting for its complex and nonlinear nature. The large variation within populations of coated CRFs poses the need for a statistically based approach to integrate over the release from the individual granules within a given population for which the distribution and range of granule radii and coating thickness are known. The model was constructed and verified using experimentally determined parameters and release curves of polymer-coated CRFs. A sensitivity analysis indicated the importance of water permeability in controlling the lag period and that of solute permeability in governing the rate of linear release and the total duration of the release. Increasing the mean values of normally distributed granule radii or coating thickness, increases the lag period and the period of linear release. The variation of radii and coating thickness, within realistic ranges, affects the release only when the standard deviation is very large or when water permeability is reduced without affecting solute permeability. The model provides an effective tool for designing and improving agronomic and environmental effectiveness of polymer-coated CRFs.

Diffusion↗