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At least 109 records · Page 6Linked to original sources
PubMed1976

Pore diffusion model for a two-substrate enzymatic reaction: application to galactose oxidase immobilized on porous glass particles.

An analysis of the pore diffusion model involving a two-substrate enzymatic reaction is presented. The resulting equations have been applied to the case of galactose oxidase catalyzed oxidation of galactose when the enzyme is immobilized on porous glass particles. The physical constants of the system were obtained by theoretical predictions and the enzyme concentration in the porous medium was derived from the experimental results. The calculations were performed with the assumption that the kinetic parameters of the enzyme remain unchanged upon immobilization. The theoretically calculated effectiveness factors were compared with the experimental effectiveness factors determined from the batch kinetic experiments and were found to be in agreement. The results are presented as effectiveness factor plots graphed as functions of bulk galactose and oxygen concentrations. The model was extended in order to study the effect of external mass transfer coefficients and pore enzyme concentrations on the effectiveness factors.

Adsorption↗
PubMed1988

Diffusion model of the optical absorbance of whole blood.

Photon-diffusion theory has had limited success in modeling the optical transmittance of whole blood. Therefore we have developed a new photon-diffusion model of the optical absorbance of blood. The model has benefited from experiments designed to test its fundamental assumptions, and it has been compared extensively with transmittance data from whole blood. The model is consistent with both experimental and theoretical notions. Furthermore, when all parameters associated with a given optical geometry are known, the model needs no variational parameters to predict the absolute transmittance of whole blood. However, even if the exact value of the incident light intensity is unknown (which is the case in many situations), only a single additive constant is required to scale experiment to theory. Finally, the model is shown to be useful for simulating scattering effects and for delineating the relative contributions of the diffuse transmittance and the collimated transmittance to the total optical density of whole blood. Applications of the model include oximetry and measurements of the arteriovenous oxygen difference in whole, undiluted blood.

Absorption↗
PubMed1999

Diffusion modeling of percutaneous absorption kinetics. 1. Effects of flow rate, receptor sampling rate, and viable epidermal resistance for a constant donor concentration.

A diffusion model for the percutaneous absorption of a solute through the skin is developed for the specific case of a constant donor concentration with a finite removal rate from the receptor due to either perfusion rate or sampling. The model has been developed to include a viable epidermal resistance and a donor-stratum corneum interfacial resistance. Numerical inversion of the Laplace domain solutions were used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption. Limits of the Laplace domain solutions were used to define the steady-state flux, lag time, and receptor concentration. Steady-state approximations obtained from the solutions were used to relate the steady-state flux and the effective permeability coefficient to the viable epidermis resistance, a donor-stratum corneum interfacial resistance, receptor removal rate, and partitioning between the receptor and donor phases. The lag time was shown to be dependent on these parameters and on the volume of the receptor phase. It is concluded that curvilinear cumulative amount and flux-time profiles are dependent on the processes affecting percutaneous absorption, the shapes of the profiles reflecting the processes most determining transport.

Computer Simulation↗
PubMed2003

Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence.

Steady-state diffusion theory models of fluorescence in tissue have been investigated for recovering fluorophore concentrations and fluorescence quantum yield. Spatially resolved fluorescence, excitation and emission reflectance Carlo simulations, and measured using a multi-fibre probe on tissue-simulating phantoms containing either aluminium phthalocyanine tetrasulfonate (AlPcS4), Photofrin meso-tetra-(4-sulfonatophenyl)-porphine dihydrochloride The accuracy of the fluorophore concentration and fluorescence quantum yield recovered by three different models of spatially resolved fluorescence were compared. The models were based on: (a) weighted difference of the excitation and emission reflectance, (b) fluorescence due to a point excitation source or (c) fluorescence due to a pencil beam excitation source. When literature values for the fluorescence quantum yield were used for each of the fluorophores, the fluorophore absorption coefficient (and hence concentration) at the excitation wavelength (mu(a,x,f)) was recovered with a root-mean-square accuracy of 11.4% using the point source model of fluorescence and 8.0% using the more complicated pencil beam excitation model. The accuracy was calculated over a broad range of optical properties and fluorophore concentrations. The weighted difference of reflectance model performed poorly, with a root-mean-square error in concentration of about 50%. Monte Carlo simulations suggest that there are some situations where the weighted difference of reflectance is as accurate as the other two models, although this was not confirmed experimentally. Estimates of the fluorescence quantum yield in multiple scattering media were also made by determining mu(a,x,f) independently from the fitted absorption spectrum and applying the various diffusion theory models. The fluorescence quantum yields for AlPcS4 and TPPS4 were calculated to be 0.59 +/- 0.03 and 0.121 +/- 0.001 respectively using the point source model, and 0.63 +/- 0.03 and 0.129 +/- 0.002 using the pencil beam excitation model. These results are consistent with published values.

Algorithms↗
PubMed2006

Pesticide sorption and desorption by lignin described by an intraparticle diffusion model.

Lignin was used as a model compound for soil organic matter to gain insight into the mechanisms that control the kinetics of pesticide sorption and desorption. Hydrolytic lignin was immobilized in a matrix of alginate gel, and sorption-desorption experiments were undertaken with isoproturon. Sorption increased with time and was close to equilibrium after 14 days. Desorption was measured after sorption for different time intervals and for a number of successive desorption steps of different lengths. The results showed strong differences between the sorption and desorption isotherms. The ratio of sorbed to dissolved pesticide approached and even exceeded the equilibrium ratio, depending on the number of desorption steps and the length of each equilibration period. A numerical diffusion model was developed to describe radial diffusion into the lignin particles in combination with Freundlich sorption inside the particles. Key model parameters were adjusted to fit the sorption data, and the same parameters were then used to predict stepwise desorption. Desorption was well described by the model, which suggests that sorption and desorption were driven by the same mechanism and occurred at the same rate. The observed difference between the sorption and desorption isotherms could be fully explained by the nonattainment of equilibrium due to slow diffusion into and out of the lignin particles.

Adsorption↗
PubMed1975

Transition densities for neutral multi-allele diffusion models.

Kimura [1955, 1956] partially solved the problem of finding the transition density function which describes the behavior of a diffusion model for evolution at one genetic locus with many neutral alleles. We complete the solution using a system of polynomials biorthogonal to polynomials suggested by Appell [1881] as generalizations of Jacobi polynomials.

Alleles↗
PubMed2006

Development of a convective diffusion model for lead pipe rigs operating in laminar flow.

As part of achieving lower lead standards water undertakers are utilising lead pipe rigs to quantify the benefit of treatment measures. A convective diffusion model is developed for lead pipe rigs operating in laminar flow, and applied to the three operating steps of flushing, sampling and stagnation. The model is used to determine the appropriate time-scales for each stage, and the sensitivity of the measure to variations in flow-rate. In contrast to rigs operating in turbulent flow the average lead observed leaving the pipe and that in the pipe, after a period of stagnation, are substantially different. Equations are derived for both, and take into account the residual distribution of lead left in the pipe after flushing. It is shown that the lead concentration observed leaving the pipe is well approximated by a single exponential term in contrast to the concentration within the pipe. Predictions are made on the residual lead concentration that can be achieved through flushing, and its dependence on flow-rate. The relevance of the laminar flow model to that in domestic lead pipes is discussed.

Algorithms↗
PubMed2005

A diffusion model for the fluids confined in micropores.

The self-diffusion coefficients were calculated by molecular dynamics simulations and the effects of pore width, temperature, and fluid density on diffusion behavior of simple fluid argon and polar fluid water confined in micropores were analyzed and studied. A mathematical model describing diffusion behavior of fluids confined in micropores was proposed from the theories of molecular dynamics and molecular kinematics, and validated on the basis of the simulation results at various conditions. The model indicates that the diffusion coefficient is proportional to the square root of the pore width and to the temperature divided by the density squared. It is applicable to either liquid or gas states and only two parameters are required.

Journal Article↗
PubMedDate not supplied

[Diffusion model for the dynamics of fibroblast initial attachment].

The simplest model for the formation of initial cell--substrate contact from the discrete multitude of the contacts of small cell surface projections named spheropodia (SP) is presented. The main points of the model are: 1) the multitude of SP is homogenous; 2) there are at least two states of SP, S0--free SP, S1--attached SP; 3) transitions between the states are stochastic and independent. There were two criteria for the selection of concrete models. Firstly it must assume the great number of microcontacts. Secondly the parameters of the model function v(t, x) must coincide with the parameters of experimental function v(t, x). The model function is the probability that at the moment t the cell has the attachment force not smaller than the threshold value x. It is shown that the diffusion model satisfied these criteria. In this model the stochastic process of cell attachment is described as a diffusion process with positive drift in the one-dimensional space of the summing cell attachment force.

Animals↗
PubMed2005

Reaction-diffusion model for pattern formation in E. coli swarming colonies with slime.

A new experimental colonial pattern and pattern transition observed in E. coli MG1655 swarming cells grown on semisolid agar are described. We present a reaction-diffusion model that, taking into account the slime generated by these cells and its influence on the bacterial differentiation and motion, reproduces the pattern and successfully predicts the observed changes when the colonial collective motility is limited. In spite of having small nonhyperflagellated swarming cells, under these experimental conditions E. coli MG1655 can very rapidly colonize a surface, with a low branching rate, thanks to a strong fluid production and a locally incremented density of motile, lubricating cells.

Bacterial Adhesion↗
PubMed2004

A reaction-diffusion model of basic fibroblast growth factor interactions with cell surface receptors.

Basic fibroblast growth factor (FGF-2) is a potent angiogenic growth factor involved in the development of diseases such as cancer, atherosclerosis, and heart and limb ischemia, as well as normal wound healing and tissue development. Despite being one of the most heavily studied angiogenic growth factors, the binding kinetics and signaling pathways of FGF-2 are still incompletely understood. In this study, we address the role of the low-affinity heparan sulfate proteoglycans (HSPGs), the identity of the minimal signaling complex leading to FGF-2 activity, and the importance of FGF-2 dimerization using a mathematical model of FGF-2 diffusion and ligand-receptor binding. Unique model features include the degradation of internalized cell surface species, the binding of a second FGF-2 ligand to a high-affinity FGF receptor (FGFR), and the dimerization of FGF-2 ligands. All experimentally determined reaction rates and diffusivity values are scaled to 37 degrees C. Our model results suggest that FGF-2-induced cellular response is the result of a temporal combination of triads (FGF-2/HSPG/FGFR complexes), double triads (2 FGF-2/HSPG/FGFR complexes), and FGF-2-bound HSPGs (FGF-2/HSPG complexes). Moreover, ligand dimerization is shown to potentially regulate FGF-2 activity by shifting the distribution of signaling complexes from the less stable triads to the more stable double triads.

Animals↗
PubMed2005

Characterization of polyvinyl alcohol/acrylamide holographic memories with a first-harmonic diffusion model.

Several theoretical models have been proposed to predict the behavior of photopolymers as holographic recording materials. Basically these models have been applied to study thin layers (around 100 microm thick). The increasing importance of holographic memories recorded in photopolymers (thickness of > 500 microm) makes it necessary to extend the ideas proposed by these models to study thick photopolymer layers. We calculate the temporal evolution of the diffraction efficiencies for thick layers using a first-harmonic diffusion model, and the results obtained are compared with the corresponding values for thin layers. Furthermore, the values of the average diffusivity of the polymer chains after the grating is formed are also obtained. In general, we find that the monomer and polymer diffusivity increases when higher values of thickness are used.

Journal Article↗
PubMed2000

A qualitative comparison of some diffusion models for neural activity via stochastic ordering.

A number of diffusion processes have been proposed as a continuous analog of Stein's model for the subthreshold membrane potential of a neuron. Interspike intervals are then described as the first-passage-time of the corresponding diffusion model through a suitable threshold. Various biological considerations suggest the use of more sophisticated models in lieu of the Ornstein-Uhlenbeck model. However, the advantages of the additional complexity are not always clear. Comparisons among different models generally use numerical methods in specific examples without a general sensitivity analysis on the role of the model parameters. Here, we compare the distribution of interspike intervals from different models using the method of stochastic ordering. The qualitative comparison of the role of each parameter extends the results obtained from numerical simulations. One result on neurons with high positive net excitation is that the reversal potential models considered do not greatly differ from the Ornstein-Uhlenbeck model. For neurons with increased inhibition, the models give greater differences among the interspike interval distributions. In particular, when the mean trajectories are matched, the Feller model gives shorter times than the Ornstein-Uhlenbeck model but longer times than our double reversal potential model.

Action Potentials↗
PubMed2002

Study on protein adsorption kinetics to a dye-ligand adsorbent by the pore diffusion model.

Adsorption kinetics of bovine serum albumin (BSA) and bovine hemoglobin (bHb) to Cibacron Blue 3GA (CB) modified Sepharose CL-6B has been studied. The effects of liquid-phase ionic strength and CB coupling density on the uptake rates of these two proteins in Tris-HCl buffer (pH 7.5) were evaluated by effective pore diffusivity derived from a pore diffusion model. The results showed that despite their similar molecular masses and sizes, the effects of aqueous-phase ionic strength and CB density on the effective pore diffusivities of BSA and bHb were distinctly different. The effective pore diffusivity of BSA to CB-Sepharose increased significantly with decreasing CB density and increasing liquid-phase ionic strength. This was considered due to the decrease in electrostatic repulsion between the BSA and CB molecules of like charge. That is, the increase in ionic strength and the decrease in CB coupling density reduced the electrostatic hindrance effect on BSA diffusion to CB-Sepharose, facilitating the hindered pore diffusion. In contrast, because of the higher isoelectric point of bHb (7.0) compared to BSA (4.7), bHb suffered little electrostatic hindrance effect during its diffusion to CB-Sepharose. Therefore, the effective pore diffusivity of bHb was unchanged with the change in liquid-phase ionic strength and CB coupling density.

Adsorption↗
PubMed1986

Assessment of microleakage of restorative materials by a diffusion model.

The time-dependent microleakage behaviour of two types of restorative materials, a microfilled composite resin and a glass ionomer, was studied. A dentine bonding agent was also included. This study was based on a diffusion model of microleakage. It was found that the initial gap sizes of the restorations increased progressively for restorations microfilled with bonding agent, microfilled alone, and glass ionomers, in that order. Analysis of microleakage over some periods suggests that the gap size of the restorations by microfilled with bonding agent may increase with time, and that while restorations by glass ionomer and microfilled composite resin decrease in gap sizes with time, glass ionomer restorations show a faster rate of decrease.

Adhesives↗
PubMed2003

Deriving reaction-diffusion models in ecology from interacting particle systems.

We use a scaling procedure based on averaging Poisson distributed random variables to derive population level models from local models of interactions between individuals. The procedure is suggested by using the idea of hydrodynamic limits to derive reaction-diffusion models for population interactions from interacting particle systems. The scaling procedure is formal in the sense that we do not address the issue of proving that it converges; instead we focus on methods for computing the results of the scaling or deriving properties of rescaled systems. To that end we treat the scaling procedure as a transform, in analogy with the Laplace or Fourier transform, and derive operational formulas to aid in the computation of rescaled systems or the derivation of their properties. Since the limiting procedure is adapted from work by Durrett and Levin, we refer to the transform as the Durrett-Levin transform. We examine the effects of rescaling in various standard models, including Lotka-Volterra models, Holling type predator-prey models, and ratio-dependent models. The effects of scaling are mostly quantitative in models with smooth interaction terms, but ratio-dependent models are profoundly affected by the scaling. The scaling transforms ratio-dependent terms that are singular at the origin into smooth terms. Removing the singularity at the origin eliminates some of the unique dynamics that can arise in ratio-dependent models.

Animals↗
PubMed2006

Aging, practice, and perceptual tasks: a diffusion model analysis.

Practice effects were examined in a masked letter discrimination task and a masked brightness discrimination task for college-age and 60- to 75-year-old subjects. The diffusion model (Ratcliff, 1978) was fit to the response time and accuracy data and used to extract estimates of components of processing from the data. Relative to young subjects, the older subjects began the experiments with slower and less accurate performance; however, across sessions their accuracy improved because the quality of the information on which their decisions were based improved, and this, along with reduced decision criteria, led to shorter response times. For the brightness, but not the letter, discrimination task, the older subjects' performance matched that of the younger group by the end of 4 sessions, except that their nondecision components of processing were slightly slower. These analyses illustrate how a well-specified model can provide a unified view of multiple aspects of data that are often interpreted separately.

Adult↗
PubMed2006

Reaction diffusion modeling of calcium dynamics with realistic ER geometry.

We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations.

Animals↗