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At least 19 recordsLinked to original sources
PubMed2000

Restricted diffusion model for surface diffusion in reversed-phase liquid chromatography

The analysis of experimental results in reversed-phase liquid chromatography (RPLC) allows further discussion of the restricted diffusion model of surface diffusion formulated on the basis of the absolute rate theory. Chromatographic data were acquired on different RPLC systems with two series of homologous compounds, several stationary phases having different alkyl ligand densities and ligands of various lengths, and methanol/water mobile phases of different compositions. The enthalpy-entropy compensation observed and the linear free energy relationships found for surface diffusion suggest that the surface diffusion mechanism remains probably the same in all RPLC conditions studied. Whereas the isosteric heat of adsorption approaches zero with decreasing retention, the activation energy of surface diffusion tends toward a finite limit and the surface diffusion coefficient tends toward a value near the corresponding molecular diffusivity. These results support the validity of the restricted diffusion model. The influence of different factors on the validity of this model (i.e., the activation energy and the frequency factor of surface diffusion, and the surface tortuosity) was also considered.

Journal Article↗
PubMed2003

Modeling diffusion and adsorption in compacted bentonite: a critical review.

The current way of describing diffusive transport through compacted clays is a simple diffusion model coupled to a linear adsorption coefficient (K(d)). To fit the observed results of cation diffusion, this model is usually extended with an adjustable "surface diffusion" coefficient. Description of the negative adsorption of anions calls for a further adjustment through the use of an "effective porosity". The final model thus includes many fitting parameters. This is inconvenient where predictive modeling is called for (e.g., for waste confinement using compacted clay liners). The diffusion/adsorption models in current use have been derived from the common hydrogeological equation of advection/dispersion/adsorption. However, certain simplifications were also borrowed without questioning their applicability to the case of compacted clays. Among these simplifications, the assumption that the volume of the adsorbed phase is negligible should be discussed. We propose a modified diffusion/adsorption model that accounts for the volume of the adsorbed phase. It suggests that diffusion through highly compacted clay takes place through the interlayers (i.e., in the adsorbed phase). Quantitative prediction of the diffusive flux will necessitate more detailed descriptions of surface reactivity and of the mobility of interlayer species.

Adsorption↗
PubMed2001

Analysis of the surface diffusion of alkylbenzenes and p-alkylphenols in reversed-phase liquid chromatography using the surface-restricted molecular diffusion model.

Surface diffusion of alkylbenzene and p-alkylphenol derivatives was measured in reversed-phase liquid chromatography on a C18-silica column with a methanol/water mixture (70/30, v/v) as the mobile phase. They were analyzed on the basis of the restricted molecular diffusion model for surface diffusion. The temperature dependence of the surface diffusion coefficient (Ds) arises probably from that of molecular diffusivity, suggesting a correlation between surface and molecular diffusion. Other correlations were also observed: (1) an enthalpy-entropy compensation of the retention equilibrium constant, (2) a linear free energy relationship between the retention and surface diffusion, and (3) a linear correlation between the restriction energy of surface diffusion and the isosteric heat of adsorption. The physical meaning of parameters involved in the surface-restricted molecular diffusion model is discussed on the basis of these results. A practical and convenient procedure for the estimation of Ds is also suggested. This study demonstrates how surface diffusion phenomena can be accounted for on the basis of the correlation between surface and molecular diffusion.

Journal Article↗
PubMed1988

Delayed-exponential approximation of a linear homogeneous diffusion model of neuron.

The diffusion models of neuronal activity are general yet conceptually simple and flexible enough to be useful in a variety of modeling problems. Unfortunately, even simple diffusion models lead to tedious numerical calculations. Consequently, the existing neural net models use characteristics of a single neuron taken from the "pre-diffusion" era of neural modeling. Simplistic elements of neural nets forbid to incorporate a single learning neuron structure into the net model. The above drawback cannot be overcome without the use of the adequate structure of the single neuron as an element of a net. A linear (not necessarily homogeneous) diffusion model of a single neuron is a good candidate for such a structure, it must, however, be simplified. In the paper the structure of the diffusion model of neuron is discussed and a linear homogeneous model with reflection is analyzed. For this model an approximation is presented, which is based on the approximation of the first passage time distribution of the Ornstein-Uhlenbeck process by the delayed (shifted) exponential distribution. The resulting model has a simple structure and has a prospective application in neural modeling and in analysis of neural nets.

Mathematics↗
PubMed1985

Multicompartment kinetic models for lead. I. Bone diffusion models for long-term retention.

The long-term retention of lead in bone poses a number of difficulties for the usual multicompartment models. The use of diffusion models based on exchange of lead between blood in canaliculi and the crystalline bone of the osteon allows a linear compartmental approximation suitable for statistical estimation of kinetic parameters in peripheral compartments. The model is applied to lead retention by beagle dogs.

Animals↗
PubMed2004

A diffusion model account of normal and impaired readers.

Acquired aphasics and dyslexics with even very profound word reading impairments have been shown to perform relatively well on the lexical decision task, but direct contrasts with unimpaired participant's data is often complicated by extremely long reaction times for patient data. The dissociation between lexical decision and word naming performance shown by these patients is of theoretical importance, and here we present an analysis of processing underlying the lexical decision task. We are able to determine what aspects of performance are affected by acquired aphasics in the lexical decision task. We fit lexical decision data from aphasic patients and from normal readers with a sequential sampling model (the diffusion model) that simultaneously considers reaction time and accuracy. This model provides a powerful means of assessing processes involved in impaired and unimpaired lexical decision. Our results suggest that lexical decision may tap impairments at both a linguistic and a nonlinguistic level. These impairments combine to make patients produce the exaggerated lexical decision reaction times typical of neurolinguistic patients: we demonstrate that patients have compromised decision and nondecision processes but that the quality of the information upon which they base their decisions is not much different from that of unimpaired participants.

Aphasia↗
PubMed2006

Dissociations between reaction times and temporal order judgments: a diffusion model approach.

A diffusion model for simple reaction time (RT) and temporal order judgment (TOJ) tasks was developed to account for a commonly observed dissociation between these 2 tasks: Most stimulus manipulations (e.g., intensity) have larger effects in RT tasks than in TOJ tasks. The model assumes that a detection criterion determines the level of sensory evidence needed to conclude that a stimulus has been presented. Analysis of the performance that would be achieved with different possible criterion settings revealed that performance was optimal with a lower criterion setting for the TOJ task than for the RT task. In addition, the model predicts that effects of stimulus manipulations should increase with the size of the detection criterion. Thus, the model suggests that commonly observed dissociations between RT and TOJ tasks may simply be due to performance optimization in the face of conflicting task demands.

Algorithms↗
PubMed2004

Reaction-diffusion models of development with state-dependent chemical diffusion coefficients.

Reaction-diffusion models are widely used to model developmental processes. The great majority of current models invoke constant diffusion coefficients. However, the diffusion of metabolites or signals through tissues is frequently such that this assumption may reasonably be questioned. We consider several different physical mechanisms leading to effective diffusion coefficients in biological tissues which vary with the local conditions, including models in which juxtacrine signaling results in the diffusion of a signal in the absence of material transport. We develop a mathematical formalism for transforming local transport laws into diffusive terms. This procedure is appropriate when the typical length scale over which the concentrations change significantly is much greater than the dimensions of a cell. We review previous developmental models which considered the possibility of state-dependent diffusion coefficients. We also provide a few new motivating examples.

Animals↗
PubMed2004

Interpreting the parameters of the diffusion model: an empirical validation.

The diffusion model (Ratcliff, 1978) allows for the statistical separation of different components of a speeded binary decision process (decision threshold, bias, information uptake, and motor response). These components are represented by different parameters of the model. Two experiments were conducted to test the interpretational validity of the parameters. Using a color discrimination task, we investigated whether experimental manipulations of specific aspects of the decision process had specific effects on the corresponding parameters in a diffusion model data analysis (see Ratcliff, 2002; Ratcliff & Rouder, 1998; Ratcliff, Thapar, & McKoon, 2001, 2003). In support of the model, we found that (1) decision thresholds were higher when we induced accuracy motivation, (2) drift rates (i.e., information uptake) were lower when stimuli were harder to discriminate, (3) the motor components were increased when a more difficult form of response was required, and (4) the process was biased toward rewarded responses.

Adult↗
PubMed2004

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics.

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC.

Algorithms↗
PubMed1984

Analysis of lung multiple indicator data with an effective diffusivity model of capillary exchange.

In this study, we have compared an effective diffusivity model with several models previously used to describe lung microvascular exchange of small molecules (multiple indicator curves): the Crone integral extraction model, the Sangren-Sheppard model, and the Rowlett-Harris model. The parameters of each model were adjusted to achieve a best fit of multiple-tracer data from six isolated dog lung preparations perfused under zone III conditions at three flows and from five awake sheep before and after histamine infusion. The effective diffusivity model was the best at matching the data and the unique falling extraction pattern observed in the lung. When the isolated lung data was analyzed, the permeability-surface area products (PS) of three models were all significantly lower at lower flows. However, the effective diffusivity model parameter (D 1/2 S, an effective diffusivity-surface area product) was not significantly affected by flow reduction. Lung lymph flow and lymph-to-plasma protein ratios from the awake sheep indicated that PS and D 1/2 S should have increased, and except for the Sangren-Sheppard model, all models predicted significantly increased values. By use of sensitivity analysis, the parameters of the effective diffusivity model were found to be more independently determined than those of the Sangren-Sheppard model, but data collected at longer times were necessary to reliably identify the extravascular volume parameter (LS, diffusing distance-surface area product) of the effective diffusivity model. We conclude that the effective diffusivity model is a better descriptor of multiple tracer data from the lung, that its parameters are more reliably and independently determined, and that it more reliably describes the effects of flow and histamine infusion on capillary-tissue exchange.

Albumins↗
PubMed2004

Fractional diffusion modeling of ion channel gating.

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe nonexponential, power-law-like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter, and Oswald [Proc. Natl. Acad. Sci. U.S.A. 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous-time random walk composed of nearest-neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. U.S.A. 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial power law features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels.

Animals↗
PubMed2002

Analysis of diffusion models for protein adsorption to porous anion-exchange adsorbent.

The ion-exchange adsorption kinetics of bovine serum albumin (BSA) and gamma-globulin to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments. Various diffusion models, that is, pore diffusion, surface diffusion, homogeneous diffusion and parallel diffusion models, are analyzed for their suitabilities to depict the adsorption kinetics. Protein diffusivities are estimated by matching the models with the experimental data. The dependence of the diffusivities on initial protein concentration is observed and discussed. The adsorption isotherm of BSA is nearly rectangular, so there is little surface diffusion. As a result, the surface and homogeneous diffusion models do not fit to the kinetic data of BSA adsorption. The adsorption isotherm of gamma-globulin is less favorable, and the surface diffusion contributes greatly to the mass transport. Consequently, both the surface and homogeneous diffusion models fit to the kinetic data of gamma-globulin well. The adsorption kinetics of BSA and gamma-globulin can be very well fitted by parallel diffusion model, because the model reflects correctly the intraparticle mass transfer mechanism. In addition, for both the favorably bound proteins, the pore diffusion model fits the adsorption kinetics reasonably well. The results here indicate that the pore diffusion model can be used as a good approximate to depict protein adsorption kinetics for protein adsorption systems from rectangular to linear isotherms.

Adsorption↗
PubMed2003

Nonlinear parameter estimation for solution-diffusion models of membrane pervaporation.

An optimization-based procedure for estimating unknown parameters in solution-diffusion models of membrane pervaporation is presented. Permeation of two components through a polymer membrane is described by distinct solution and diffusion models. The solution model is based on a modified form of Flory-Huggins theory that accounts for interactions between the two penetrants. The diffusion model is derived from Fick's law, where the diffusion coefficients are allowed to depend on the local concentration of each component in the membrane. A phenomenologic relation is used to account for the effect of temperature on the component fluxes. The solution and diffusion models, as well as the temperature-flux relation, contain parameters that are not directly measurable. It is shown that these parameters can be estimated effectively from sorption and flux data by the solution of suitably formulated nonlinear optimization problems. The separation of styrene and ethylbenzene with a polyurethane membrane is used to illustrate the parameter estimation procedure.

Chemistry↗
PubMed2001

An integrated sorption-diffusion model for the calculation of consistent distribution and diffusion coefficients in compacted bentonite.

A thermodynamic sorption model and a diffusion model based on electric double layer (EDL) theory are integrated to yield a surface chemical model that treats porewater chemistry, surface reactions, and the influence of charged pore walls on diffusing ions in a consistent fashion. The relative contribution of Stern and diffuse layer to the compensation of the permanent surface charge represents a key parameter; it is optimized for the diffusion of Cs in Kunipia-F bentonite, at a dry density of 400 kg/m3. The model is then directly used to predict apparent diffusivities (Da) of Cs, Sr, Cl-, I- and TcO4- and corresponding distribution coefficients (Kd) of Cs and Sr in different bentonites as a function of dry density, without any further adjustment of surface chemical and EDL parameters. Effective diffusivities (De) for Cs, HTO, and TcO4- are also calculated. All calculated values (Da, De, Kd) are fully consistent with each other. A comparison with published, measured data shows that the present model allows a good prediction and consistent explanation of (i) apparent and effective diffusivities for cations, anions, and neutral species in compacted bentonite, and of (ii) Kd values in batch and compacted systems.

Adsorption↗
PubMed1992

A compartment model for percutaneous absorption: compatibility of lag time and steady-state flux with diffusion model.

The lag times and steady-state flux predicted by a specific case of the compartment model, which was recently proposed to generate finite-dose percutaneous permeation pharmacokinetics, are compared with those predicted by the diffusion model. When the intercompartmental transfer rate constants are defined so that the three statistical moments of the compartmental model (the mean residence times of a drug in the vehicle and that in the skin and the variance of residence time in the vehicle) are identical to those in the diffusion model, the lag times and steady-state flux values predicted by the two models are the same.

Animals↗