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PubMedDate not supplied

Effect of periodic stimulus on a neuronal diffusion model with signal-dependent noise.

To relate the noise intensity with a periodically modulated input signal in a single neuron stochastic model we introduce a diffusion model with both time modulated drift and diffusion coefficient. Such a model is the continuous version of a Stein model with time oscillating frequencies for the Poisson processes describing the inputs impinging on the neuron. We focus here on some aspects of the resonance phenomenon for such a model. We compare the corresponding interspike interval distribution with the analogous distribution for a model sharing the same parameter values, but with constant noise intensity. Examples with two different levels for this noise intensity are discussed. The enhancement of the height of the peaks in the interspike interval distribution appearing at the modulation period, the improvement of the phase locking behavior and an enlargement of the noise ranges where a resonance like behavior arises are the main features observed in the considered cases.

Models, Neurological↗
PubMed1999

Connectionist and diffusion models of reaction time.

Two connectionist frameworks, GRAIN (J. L. McClelland, 1993) and brain-state-in-a-box (J. A. Anderson, 1991), and R. Ratcliff's (1978) diffusion model were evaluated using data from a signal detection task. Dependent variables included response probabilities, reaction times for correct and error responses, and shapes of reaction-time distributions. The diffusion model accounted for all aspects of the data, including error reaction times that had previously been a problem for all response-time models. The connectionist models accounted for many aspects of the data adequately, but each failed to a greater or lesser degree in important ways except for one model that was similar to the diffusion model. The findings advance the development of the diffusion model and show that the long tradition of reaction-time research and theory is a fertile domain for development and testing of connectionist assumptions about how decisions are generated over time.

Adult↗
PubMed2004

A diffusion model account of the lexical decision task.

The diffusion model for 2-choice decisions (R. Ratcliff, 1978) was applied to data from lexical decision experiments in which word frequency, proportion of high- versus low-frequency words, and type of nonword were manipulated. The model gave a good account of all of the dependent variables--accuracy, correct and error response times, and their distributions--and provided a description of how the component processes involved in the lexical decision task were affected by experimental variables. All of the variables investigated affected the rate at which information was accumulated from the stimuli--called drift rate in the model. The different drift rates observed for the various classes of stimuli can all be explained by a 2-dimensional signal-detection representation of stimulus information. The authors discuss how this representation and the diffusion model's decision process might be integrated with current models of lexical access.

Adult↗
PubMed2006

Accessing the dynamics of end-grafted flexible polymer chains by atomic force-electrochemical microscopy. Theoretical modeling of the approach curves by the elastic bounded diffusion model and Monte Carlo simulations. Evidence for compression-induced lateral chain escape.

The dynamics of a molecular layer of linear poly(ethylene glycol) (PEG) chains of molecular weight 3400, bearing at one end a ferrocene (Fc) label and thiol end-grafted at a low surface coverage onto a gold substrate, is probed using combined atomic force-electrochemical microscopy (AFM-SECM), at the scale of approximately 100 molecules. Force and current approach curves are simultaneously recorded as a force-sensing microelectrode (tip) is inserted within the approximately 10 nm thick, redox labeled, PEG chain layer. Whereas the force approach curve gives access to the structure of the compressed PEG layer, the tip-current, resulting from tip-to-substrate redox cycling of the Fc head of the chain, is controlled by chain dynamics. The elastic bounded diffusion model, which considers the motion of the Fc head as diffusion in a conformational field, complemented by Monte Carlo (MC) simulations, from which the chain conformation can be derived for any degree of confinement, allows the theoretical tip-current approach curve to be calculated. The experimental current approach curve can then be very satisfyingly reproduced by theory, down to a tip-substrate separation of approximately 2 nm, using only one adjustable parameter characterizing the chain dynamics: the effective diffusion coefficient of the chain head. At closer tip-substrate separations, an unpredicted peak is observed in the experimental current approach curve, which is shown to find its origin in a compression-induced escape of the chain from within the narrowing tip-substrate gap. MC simulations provide quantitative support for lateral chain elongation as the escape mechanism.

Aluminum Oxide↗
PubMedDate not supplied

Development of a bioartificial nerve graft. I. Design based on a reaction-diffusion model.

A simple reaction-diffusion model has been developed to describe the mass transport of nutrients and nerve growth factor within a bioartificial nerve graft (BNG). The BNG consists of a porous polymer conduit that is preseeded with Schwann cells in its lumen. The Schwann cells produce growth factors to stimulate nerve regeneration within the lumen of the conduit. The model can predict the wall thickness, porosity, and Schwann cell seeding density needed to maximize the axon extension rate while ensuring that sufficient nutrients, especially oxygen, are made available to the neurons until the formation of the neovasculature. The model predicts a sixteen-fold increase in the levels of nerve growth factor by dropping the porosity from 95 to 55% but only at the expense of reducing the oxygen concentration. At higher porosities, increasing the wall thickness and increasing the Schwann cell seeding density both have the same effect of increasing the concentration of nerve growth factor within the lumen of the conduit. This model provides a simple tool for evaluating various conduit designs before continuing with experimental studies in vivo.

Animals↗
PubMed2005

Hybrid radiative-transfer-diffusion model for optical tomography.

A hybrid radiative-transfer-diffusion model for optical tomography is proposed. The light propagation is modeled with the radiative-transfer equation in the vicinity of the laser sources, and the diffusion approximation is used elsewhere in the domain. The solution of the radiative-transfer equation is used to construct a Dirichlet boundary condition for the diffusion approximation on a fictitious interface within the object. This boundary condition constitutes an approximative distributed source model for the diffusion approximation in the remaining area. The results from the proposed approach are compared with finite-element solutions of the radiative-transfer equation and the diffusion approximation and Monte Carlo simulation. The results show that the method improves the accuracy of the forward model compared with the conventional diffusion model.

Computer Simulation↗
PubMed1999

Characterization of ocular pharmacokinetics of beta-blockers using a diffusion model after instillation.

PURPOSE: To characterize the ocular pharmacokinetics of beta-blockers (timolol and tilisolol) after instillation in the albino rabbit using a mathematical model that includes a diffusion process. METHODS: The disposition of fluorescein isothiocyanate-dextran (FITC-dextran, molecular weight 4400), timolol, and tilisolol was determined in tear fluid and aqueous humor after instillation or ocular injection in rabbits. The in vivo penetration parameters were estimated by fitting the concentration-time profiles to the Laplace equations based on a diffusion model using MULTI(FILT) program. The in vitro permeability of drugs was measured across cornea using a two-chamber diffusion cell. RESULTS: Concentration-time profiles of drugs in the tear fluid after instillation showed a monoexponential curve. Although a monoexponential curve was observed in the aqueous humor concentration of FITC-dextran after injection into the aqueous chamber, timolol and tilisolol showed a biexponential curve. On the basis of these results, an in vivo pharmacokinetic model was developed for estimation of penetration parameters. The in vitro partition parameters were higher than those of the in vivo parameters. CONCLUSIONS: The ocular absorption of timolol and tilisolol was characterized using an in vivo pharmacokinetic model and in vivo penetration parameters.

Absorption↗
PubMed1993

A diffusion model of a neuron and neural nets.

In the paper a diffusion model of a neuron is treated. A new, less restrictive than usually, condition of applicability of a diffusion model is presented. As a result the point-process-to-point-process model of a neuron is obtained, which produces an output signal of the same kind as the accepted input signals.

Action Potentials↗
PubMed2000

Introduction of a sink-diffusion model to describe the interaction between volatile organic compounds (VOCs) and material surfaces.

A sink-diffusion model to describe the interaction between material surfaces and volatile organic compounds (VOCs) in indoor air has been introduced. The model is based on adsorption/desorption on the material surfaces and diffusion into the materials. Test chamber experiments with exposure of nylon carpet and polyvinyl chloride (PVC) covering against alpha-pinene and toluene were used to validate the model and to make comparisons with a sink model based on the Langmuir adsorption isotherm. The results showed that the sink-diffusion model gave a better description of the desorption curve than the Langmuir model. The model predictions improved with increasing sorption effect. The Langmuir model gave good predictions of relative weak sorption effects, whereas the sink-diffusion model improved the predictions for stronger sorption effects. In this case, nylon carpet showed substantial stronger sorption than PVC covering and alpha-pinene showed stronger sorption than toluene. Controlled field experiments with combinations of building materials and a mixture of VOCs, encountered in real indoor environments, are needed to further validate the sink-diffusion model.

Adsorption↗
PubMed2005

Mixed-mode pattern in Doublefoot mutant mouse limb--Turing reaction-diffusion model on a growing domain during limb development.

It has been suggested that the Turing reaction-diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the present study, we found that in Doublefoot mutant mice, which have supernumerary digits due to overexpansion of the limb bud, thin digits exist in the proximal part of the hand or foot, which sometimes become normal abruptly at the distal part. We found that exactly the same behaviour can be reproduced by numerical simulation of the simplest possible Turing reaction-diffusion model on a growing domain. We analytically showed that this pattern is related to the saturation of activator kinetics in the model. Furthermore, we showed that a number of experimentally observed phenomena in this system can be explained within the context of a Turing reaction-diffusion model. Finally, we make some experimentally testable predictions.

Animals↗
PubMed2004

Diffusion model of photoaligning in azo-dye layers.

The model of the rotational diffusion of the azo-dye molecules under the action of polarized uv light was used to explain the formation of the photoinduced order in azo-dye layers. We consider both the approximations of negligible and strong molecular interaction during the process of the reorientation under the field of a polarized light. We constructed an experimental setup, based on a photoelastic modulator, that allows accurate in situ measurements of the phase retardation delta of thin film as a function of the exposure time t(exp) and exposure power W (W/ cm(2) ). A good agreement with experiment was observed. Fitting the experimental curves delta ( t(exp) ) for different power values W, we can estimate the coefficient of rotational diffusion D, azo-dye order parameter S ( t(exp) ), and other parameters of the rotational diffusion model.

Journal Article↗
PubMed2000

Prediction of pesticide concentrations in the atmosphere using an atmospheric diffusion model (linear source plume model).

The foundational model to predict concentration of pesticides in the atmosphere outside of the sprayed area was developed using the results of measured concentration in the atmosphere, in reference to the atmospheric diffusion model utilized for the air pollution prediction model. The atmospheric diffusion model assumes that the applied area was a topographically flat farmland, that wind direction and wind speeds were constant, and the pesticide was constantly discharged from the emission line sources. Therefore the linear source plume model (LSPLM) was developed. The concentration in the atmosphere was predicted by assigning the property of the pesticides and various conditions of measurements of the model, and compared with the measured them, then the adaptability of the model was examined. As a result, the correlation between the measured value and the predicted value in paddy and forested areas was significant (P < 0.01) although deviations in the order of tens were observed, the measured value and the predicted value were generally in agreement.

Agriculture↗
PubMed2000

A diffusion model and optimal cell loading for immobilized cell biocatalysts.

A diffusion model based on the random pore model is derived for immobilized cell biocatalysts and verified with 19 sets of experimental diffusion data. The predicted effective diffusivity relative to that for the support matrix reflects a quadratic dependence on the cell loading and contains a single parameter that depends on the intracellular diffusivity and the chemical partitioning coefficient. The model is used to predict optimal cell loadings that maximize the total reaction rate in an immobilized cell biocatalyst. A rule of thumb based on the diffusion model is obtained to the effect that the cell loading should be at least (1/3) for single reactions regardless of the kinetics and diffusional resistances. A means of calculating improved lower bounds is provided for cases where the cellular diffusional resistance is known but the kinetics are not. The optimal cell loadings for reversible first-order and for Michaelis-Menten kinetics are presented and demonstrated to be within the range of conditions of practical interest.

Biotechnology↗
PubMed2000

A diffusion model account of masking in two-choice letter identification.

The diffusion model developed by R. Ratcliff (1978, 1981, 1985, 1988) for 2-choice decisions was applied to data from 2 letter identification experiments. In the experiments, stimulus letters were displayed and then masked, and the stimulus onset asynchrony between letter and mask was manipulated to vary accuracy from near chance to near ceiling. A standard reaction time procedure was used in one experiment and a deadline procedure in the other. Two hypotheses about the effect of masking on the information provided to the decision process were contrasted: (a) The output of perception to the decision process varies with time, so that the information used by the decision process rises and falls, reflecting the stimulus onset and mask onset. (b) The output of perception to the decision is constant over time, reflecting information integrated over the time between the stimulus and mask onsets. The data were well fit by the diffusion model only with the assumption of constant information over time.

Adult↗
PubMed2002

Reaction and concentration dependent diffusion model.

We study the formation of patterns in the genuinely nonlinear reaction diffusion model equation u(t)+2a(u(2))(x) = (u(2))(xx)+F(x,u), where u may be viewed as an amplitude of a thermal wave in plasma or density of a biological species and F = u(1-u) or F = q(x)u(l), l = 0,2. We provide a transformation which maps the model into a purely diffusive process free of its interacting part and its intrinsic temporal and spatial scales. The well known attractors of the diffusive process enable us to completely characterize the emerging patterns which, depending on F and initialization, may be a semicompact, or a compact, traveling wave or a nontrivial equilibrium.

Diffusion↗
PubMed2004

Running pulses of complex shape in a reaction-diffusion model.

In a one-dimensional reaction-diffusion model of an active medium, stable steady-state wave pulses of a new type are described. They are called multihumped because their waveforms contain several maxima of similar size. Presumably, the multihumped pulses arise via a bifurcation at which an unstable trigger wave disappears. The parameter governing this bifurcation is the diffusion coefficient for the model inhibitor. The model is analyzed by varying this parameter to determine the conditions for the emergence of multihumped pulses. The results of this analysis show how their waveform and dynamics of excitation depend on the inhibitor diffusion coefficient.

Biophysics↗
PubMed2002

Estimating parameters of the diffusion model: approaches to dealing with contaminant reaction times and parameter variability.

Three methods for fitting the diffusion model (Ratcliff, 1978) to experimental data are examined. Sets of simulated data were generated with known parameter values, and from fits of the model, we found that the maximum likelihood method was better than the chi-square and weighted least squares methods by criteria of bias in the parameters relative to the parameter values used to generate the data and standard deviations in the parameter estimates. The standard deviations in the parameter values can be used as measures of the variability in parameter estimates from fits to experimental data. We introduced contaminant reaction times and variability into the other components of processing besides the decision process and found that the maximum likelihood and chi-square methods failed, sometimes dramatically. But the weighted least squares method was robust to these two factors. We then present results from modifications of the maximum likelihood and chi-square methods, in which these factors are explicitly modeled, and show that the parameter values of the diffusion model are recovered well. We argue that explicit modeling is an important method for addressing contaminants and variability in nondecision processes and that it can be applied in any theoretical approach to modeling reaction time.

Humans↗
PubMed2001

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids.

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations.

Diffusion↗