PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Diffusion models”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

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

At least 37 records · Page 2Linked to original sources
PubMed1991

Diffusion models for chemotaxis: a statistical analysis of noninteractive unicellular movement.

A program is developed for applying stochastic differential equations to models for chemotaxis. First a few of the experimental and theoretical models for chemotaxis both for swimming bacteria and for cells migrating along a substrate are reviewed. In physical and biological models of deterministic systems, finite difference equations are often replaced by a limiting differential equation in order to take advantage of the ease in the use of calculus. A similar but more intricate methodology is developed here for stochastic models for chemotaxis. This exposition is possible because recent work in probability theory gives ease in the use of the stochastic calculus for diffusions and broad applicability in the convergence of stochastic difference equations to a stochastic differential equation. Stochastic differential equations suggest useful data for the model and provide statistical tests. We begin with phenomenological considerations as we analyze a one-dimensional model proposed by Boyarsky, Noble, and Peterson in their study of human granulocytes. In this context, a theoretical model consists in identifying which diffusion best approximates a model for cell movement based upon theoretical considerations of cell physiology. Such a diffusion approximation theorem is presented along with discussion of the relationship between autocovariance and persistence. Both the stochastic calculus and the diffusion approximation theorem are described in one dimension. Finally, these tools are extended to multidimensional models and applied to a three-dimensional experimental setup of spherical symmetry.

Chemotaxis↗
PubMed1977

A diffusion model for mesoderm induction in amphibian embryos.

In this paper we try to answer the question whether diffusion is a possible mechanism to explain mesoderm induction in Amphibians. First the embryological data are discussed and a hypothesis for mesoderm formation is set forth. The blastula being essentially a hollow sphere, we assume that the induction mechanism in an embryo at the blastula stage can be simulated by diffusion-reaction processes on spherical surfaces. A model is constructed for the simple case when the source is held constant with respect to time, the decay proportional to the concentration and the diffusion coefficient a constant. From simulation we find a (best) value for the decay constant to be 6 x 10(-5)/sec and for the diffusion constant to be 0.24 x 10(-6) cm2/sec. The relation between the parameters is derived from an analytic solution for the diffusion process on a spherical surface with a continuously producing point source and the concentration proportional to the decay. The form and regulative properties of the steady concentration gradient are discussed.

Amphibians↗
PubMed1978

Estimation of dissolution rate of salicylamide in complexing media using a theoretical diffusion model.

Dissolution rates of salicylamide in water and caffeine solutions under perfect sink conditions were predicted by theoretical diffusion equations applicable to dissolution in complexing media. Experimental dissolution rates were measured using a compartmentalized rotating-basket apparatus under two sets of conditions. Agreement was found between experimental and predicted rates. Use of the theoretical equation for estimating dissolution rates involves simple calculations of diffusion coefficients and diffusion layer thickness under the operative dissolution conditions. The increase in dissolution rate caused by addition of the complexant can be calculated for diffusion-controlled dissolution directly if the stability constant and the drug solubility in water are known or measured.

Caffeine↗
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↗
PubMed1975

Diffusion model for fluidized-bed drying.

A sucrose-lactose-starch granulation was used to study particulate motion and attrition in a fluid bed dryer. There is some classification of material in the dryer as drying proceeds; fine particles are dried faster and become less dense, and the less dry but denser large particles show some (although not great) accumulation tendencies in the lower central area. Unlike countercurrent rotary drying, fluid bed drying cannot be accounted for by water diffusion inside the granule as the rate-limiting step. In its place, a model of external water vapor diffusion is proposed and is supported by vapor-concentration curves and by the linear dependence of the rate constants on the linear air velocities. The dried granulation exhibits the same trend as does countercurrent dried material in that larger particles have higher moisture contents than do smaller particles. Quantitative relationships between content of moisture and size were developed and are supported by experimental data. The granulation, upon storage, does not equilibrate, indicating that this type of water distribution is a problem in batch process granulations as well as in the earlier reported case of granulations for continuous production.

Diffusion↗
PubMed1988

Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording.

The lifetimes of the unitary currents from ion channels, as revealed from single-channel recording, are traditionally thought to follow exponential or multiexponential distributions. The interpretation of these event-time distributions is that the gating process follows Markov kinetics among a small number of states. There is recent evidence, however, that certain systems exhibit distributions that follow power laws or functions related to power laws. Likewise, it has been suggested that data sets that appear to be multiexponential may be fit to simple power laws as well. In this paper we propose a different view of ion-channel-gating kinetics that is consistent with these recent experimental observations. We retain the Markovian nature of the kinetics, but, in contrast to the traditional models, we suggest that ion-channel proteins have a very large number of states all of similar energy. Gating, therefore, resembles a diffusion process. We show that our simplest one-dimensional model exhibits single-channel distributions that follow power laws of the form t-a, where 1/2 less than or equal to a less than or equal to 3/2. Exponents determined from recent experiments approximately fall within this range. We believe that this model is consistent with modern views of protein dynamics and, thus, may provide a key to the molecular details of the gating process.

Computer Simulation↗
PubMed1985

Calcium diffusion models and transmitter release in neurons.

Calcium enters neurons or nerve terminals through the surface membrane, and then diffuses inwardly and is diluted. Calcium acts at membrane sites to release transmitter or modulate channels, or at organelles or the nucleus to regulate metabolism. Thus the average cytoplasmic calcium concentration is a poor predictor of calcium-dependent processes. Solutions of the diffusion equation with appropriate geometries and boundary conditions help considerably in our quantitative understanding of calcium-dependent processes in neurons.

Action Potentials↗
PubMed1989

Closed-time distribution of ionic channels. Analytical solution to a one-dimensional defect-diffusion model.

A one-dimensional version of the model recently proposed by Läuger (1988) to explain the closed-time distribution of ionic channels in cell membranes is solved analytically. While the probability density f(t) for closed-time lengths may show a well-defined exponential behavior at short times, a power-law decay is predicted at long times. The influence of an additional random distribution of defects in the current-conducting protein is investigated and found to be dominating at long times. Explicit expressions that may be used for fitting experimental data are given for the closed-time distribution. Some of the available data are discussed and shown to be in good agreement with the predictions of the model.

Animals↗