Point source atmospheric diffusion model with variable wind and diffusivity profiles.
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Air Movements↗
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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.
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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↗
Time course of transmitter release calculated from simulations of a calcium diffusion model.
A three-dimensional presynaptic calcium diffusion model developed to account for characteristics of transmitter release was modified to provide for binding of calcium to a receptor and subsequent triggering of exocytosis. When low affinity (20 microM) and rapid kinetics were assumed for the calcium receptor triggering exocytosis, and stimulus parameters were selected to match those of experiments, the simulations predicted a virtual invariance of the time course of transmitter release to paired stimulation, stimulation with pulses of different amplitude, and stimulation in different calcium solutions. The large temperature sensitivity of experimental release time course was explained by a temperature sensitivity of the model's final rate limiting exocytotic process. Inclusion of calcium tail currents and a saturable buffer with finite binding kinetics resulted in high peak calcium transients near release sites, exceeding 100 microM. Models with a single class of calcium binding site to the secretory trigger molecule failed to produce sufficient synaptic facilitation under this condition. When at least one calcium ion binds to a different site having higher affinity and slow kinetics, facilitation again reaches levels similar to those seen experimentally. It is possible that the neurosecretory trigger molecule reacts with calcium at more than one class of binding site.
Animals↗
Generating synthetic genotypes using diffusion models.
SUMMARY: In this paper, we introduce the first diffusion model designed to generate complete synthetic human genotypes, which, by standard protocols, one can straightforwardly expand into full-length, DNA-level genomes. The synthetic genotypes mimic real human genotypes without just reproducing known genotypes, in terms of approved metrics. When training biomedically relevant classifiers with synthetic genotypes, accuracy is near-identical to the accuracy achieved when training classifiers with real data. We further demonstrate that augmenting small amounts of real with synthetically generated genotypes drastically improves performance rates. This addresses a significant challenge in translational human genetics: real human genotypes, although emerging in large volumes from genome wide association studies, are sensitive private data, which limits their public availability. Therefore, the integration of additional, insensitive data when striving for rapid sharing of biomedical knowledge of public interest appears imperative. AVAILABILITY AND IMPLEMENTATION: All non proprietary data and the code to replicate the experiments is available on Github.
Humans↗
Diffusion model for drug release from suspensions II: release to a perfect sink.
Numerical mathematical methods are applied to a diffusion model based on physicochemical principles to predict drug release from suspensions of drug in semisolid vehicles. The predicted mass of drug released versus time curves using this model are in agreement with some reported experimental data but differ from predictions using the classical model for semisolid suspensions. The differences are discussed in relation to the drug dissolution rate and diffusion rate in the vehicle.
Biological Transport↗
Pharmacokinetic analysis of drug absorption from muscle based on a physiological diffusion model: effect of molecular size on absorption.
In a rabbit hind leg perfusion experiment, the absorption of radiolabeled water and carbohydrates of various molecular sizes from muscle was analyzed using a physiological diffusion model and, also, by statistical moment analysis. The model takes into account diffusion in the interstitial space, transcapillary movement, and removal by the blood circulation and pharmacokinetic parameters representing these processes were computed by curve-fitting. The apparent diffusion coefficients of water and small sugars in the interstitial space (Dm) were proportional to their free diffusion coefficients in water (Df), whereas the diffusion of 14C-inulin was hampered by interstitial structures. The first moments of each absorption process were also determined to assess the quantitative contribution of each absorption process to overall absorption. For carbohydrate molecules, residence time in the depot (td) accounted for most of the absorption time after injection, whereas for 3H-water, residence times in muscle (tm) and in the depot (td) were similar.
Absorption↗
Random genetic drift and selection in a triallelic locus: a continuous diffusion model.
The Kolmogorov forward diffusion equation is used to examine the evolution of three alleles at one locus under viability selection and random genetic drift. Separation of variables and Chebyschev approximations are employed to solve this equation for long times. As an example, one artificial viability set is examined in detail; its general implications for the evolution at a triallelic locus are discussed.
Alleles↗
Replication of viruses in a growing plaque: a reaction-diffusion model.
An understanding of the viral replication process commonly referred to as "plaque growth" is developed in the context of a reaction-diffusion model. The interactions among three components: the virus, the healthy host, and the infected host are represented using rates of viral adsorption and desorption to the cell surface, replication and release by host lysis, and diffusion. The solution to the full model reveals a maximum in the dependence of the velocity of viral propagation on its equilibrium adsorption constant, suggesting that conditions can be chosen where viruses which adsorb poorly to their hosts will replicate faster in plaques than those which adsorb well. Analytic expressions for the propagation velocity as a function of the kinetic and diffusion parameters are presented for the limiting cases of equilibrated adsorption, slow adsorption, fast adsorption, and large virus yields. Hindered diffusion at high host concentrations must be included for quantitative agreement with experimental data.
Bacterial Physiological Phenomena↗
A general diffusion model for analyzing the efficacy of synaptic input to threshold neurons.
We describe a general diffusion model for analyzing the efficacy of individual synaptic inputs to threshold neurons. A formal expression is obtained for the system propagator which, when given an arbitrary initial state for the cell, yields the conditional probability distribution for the state at all later times. The propagator for a cell with a finite threshold is written as a series expansion, such that each term in the series depends only on the infinite threshold propagator, which in the diffusion limit reduces to a Gaussian form. This procedure admits a graphical representation in terms of an infinite sequence of diagrams. To connect the theory to experiment, we construct an analytical expression for the primary correlation kernel (PCK) which profiles the change in the instantaneous firing rate produced by a single postsynaptic potential (PSP). Explicit solutions are obtained in the diffusion limit to first order in perturbation theory. Our approximate expression resembles the PCK obtained by computer simulation, with the accuracy depending strongly on the mode of firing. The theory is most accurate when the synaptic input drives the membrane potential to a mean level more than one standard deviation below the firing threshold, making such cells highly sensitive to synchronous synaptic input.
Computer Simulation↗
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↗
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↗
Ca2+ movement in smooth muscle cells studied with one- and two-dimensional diffusion models.
Although many of the processes involved in the regulation of Ca2+ in smooth muscle have been studied separately, it is still not well known how they are integrated into an overall regulatory system. To examine this question and to study the time course and spatial distribution of Ca2+ in cells after activation, one- and two-dimensional diffusion models of the cell that included the major processes thought to be involved in Ca regulation were developed. The models included terms describing Ca influx, buffering, plasma membrane extrusion, and release and reuptake by the sarcoplasmic reticulum. When possible these processes were described with known parameters. Simulations with the models indicated that the sarcoplasmic reticulum Ca pump is probably primarily responsible for the removal of cytoplasmic Ca2+ after cell activation. The plasma membrane Ca-ATPase and Na/Ca exchange appeared more likely to be involved in the long term regulation of Ca2+. Pumping processes in general had little influence on the rate of rise of Ca transients. The models also showed that spatial inhomogeneities in Ca2+ probably occur in cells during the spread of the Ca signal following activation and during the subsequent return of Ca2+ to its resting level.
Animals↗
Convective diffusion model for a transport-controlled dissolution rate process.
A mathematical model based on convective diffusion was developed to describe the rate of dissolution form the surface of a compressed compact. Experimental studies were carried out to test the model. The basic experimental apparatus consisted of a modified rotating-filter-stationary basket dissolution test apparatus. Dissolution rates from rectangular and circular surfaces of an homologous series of p-aminobenzoate esters permitted testing the theory with respect to solubility, geometry, and agitation conditions. The correlation between experimental results and theory was reasonalby good considering that the test conditions were somewhat less than ideal.
Aminobenzoates↗
The effect of auxiliary conditions on intestinal unstirred layer diffusion modelled by numerical simulation.
Estimation of intestinal unstirred layer thickness usually involves inducing transmural potential difference changes by altering the content of the solution used to perfuse the small intestine. Osmotically active solutes, such as mannitol, when added to the luminal solution diffuse across the unstirred water layer (UWL) and induce osmotically dependent changes in potential difference. As an alternative procedure, the sodium ion in the luminal fluid can be replaced by another ion. As the sodium ion diffuses out of the UWL, the change in concentration next to the intestinal membrane alters the transmural potential difference. In both cases, UWL thickness is calculated from the time course of the potential difference changes, using a solution to the diffusion equation. The diffusion equation solution which allows the calculation of intestinal unstirred layer thickness was examined by simulation, using the method of numerical solutions. This process readily allows examination of the time course of diffusion under various imposed circumstances. The existing model for diffusion across the unstirred layer is based on auxiliary conditions which are unlikely to be fulfilled in the same intestine. The present simulation additionally incorporated the effects of membrane permeability, fluid absorption and less than instantaneous bulk phase concentration change. Simulation indicated that changes within the physiologically relevant range in the chosen auxiliary conditions (with the real unstirred layer length kept constant) can alter estimates of the apparent half-time. Consequently, changes in parameters unassociated with the unstirred layer would be misconstrued as alterations in unstirred layer thickness.
Gastrointestinal Contents↗
Application of a convective diffusion model to membrane transport.
Studies were carried out on the permeation rate of butambed through a dimethicone membrane. Under conditions of "aqueous diffusion layer control", the permeation rate was accurately described by a mathematical model based on convective diffusion theory. In accordance with model, the rate of permeation from a saturated donor phase was shown to be equal to the rate of dissolution from a pure solid.
Aminobenzoates↗
Systems approach to study of solute transport across membranes using suspension cultures of mammalian cells III: steady-state diffusion models.
General physical models are derived for the diffusional transport of drugs across membranes of mammalian cells in culture suspension. These models represent different sets of possible physical processes taking place during the transport of a drug molecule. Once the diffusing species reaches the cell barrier, it may gain entrance to the cell kinetically by one of the principal quasisteady-state mechanisms, all of which assume the cell membrane to be an integral part of the total barrier.
Biological Transport↗
Multiregion, multilayer, nonuniform diffusion model of an oxygen electrode.
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Diffusion↗
Metastable crystals of beta-cyclodextrin complexes and the membrane diffusion model.
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Crystallography↗