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At least 271 records · Page 15Linked to original sources
PubMed2006

A lattice-gas cellular automaton to model diffusion in restricted geometries.

Topological constraints play a fundamental role in problems involving the transfer of heat, matter, or information in a discrete network. Flows in microporous media are the most common cases in which the thermodynamic and transport properties of adsorbate are strongly influenced by its interactions with the confining medium. Combining two local Monte Carlo operations and a Lattice-Gas Cellular Automaton, we constructed an equilibrium synchronous network of cells highly sensitive to the state of their neighborhood and able to capture the effects of confinement by means of few flexible local parameters and a parallel, local evolution rule. Results of an application of the model to the specific problem of geometrical restricted long-range diffusion are used to interpret the behaviors of particles in tight confinement.

Journal Article↗
PubMed1998

Use of a diffusion model for assessing the performance of poly(vinyl alcohol) bioartificial pancreases.

Islets of Langerhans surrounded by a semipermeable membrane to prevent an immune response by the host immunosystem is a potential way of treating type I diabetes mellitus. In this study, poly(vinyl alcohol) (PVA) tubular membranes with added polyethylene glycol to create pores in the skin layer were prepared to improve their diffusion property. In a static incubation study, islets cultured in the PVA tubular membranes still demonstrated their function of secreting insulin after 30 days. When the tubular PVA bioartificial pancreas was perifused in a small chamber with RPMI-1640 medium containing glucose at concentrations of 5.6-16.6 mmol/L, insulin release began to increase without delay. Therefore, such a membrane is an alternative potential material for a bioartificial pancreas. In addition, a mathematical mass transfer model of insulin release was developed and compared with the perifusion data. It was shown that satisfactory kinetics could be achieved with a PVA membrane. However, the model showed that the insulin output of islets cultured in the PVA tubular membrane must be increased to improve the performance significantly. These findings suggest that a bioartificial pancreas using a PVA membrane is a promising material, but the technique for seeding islets in the chamber requires further modification.

Animals↗
PubMedDate not supplied

Modeling turbulent diffusion and advection of indoor air contaminants by Markov chains.

Turbulent eddy diffusion models are used to describe a continuous concentration gradient with distance from an in-room contaminant emission source. A refined diffusion model termed the Drivas model also accounts for contaminant reflection by wall surfaces and partially accounts for removal by exhaust air. This article develops two models based on Markov chains to describe indoor air contaminant dispersion by turbulent diffusion and advection, and removal by the exhaust airflow. Markov model I is equivalent to the Drivas model and is computationally simple. Markov model II can provide more realism by accounting for the locations of air inlets and outlets, advective flow patterns, in-room reflective surfaces, and contaminant removal mechanisms at specific room positions. The price paid for this greater realism is greater computational complexity. Both Markov models are explicitly probabilistic and estimate the expected concentration values at given room positions.

Air Pollution, Indoor↗
PubMedDate not supplied

[Diffusion modeling system of a neuron's molecular calculating machine].

Intracellular injection of cyclic nucleotides through 3-4 barrel microelectrodes usually results in depolarization in case of cyclic AMP and in hyperpolarization in case of cyclic GMP. But sometimes the neuron response is more complex and changes with time. Phosphodiesterase inhibitors, papaverine, 3-isobutyl-1-methylxantine, SQ-20009 increase and prolong the effects of cyclic nucleotides and the complex effect of cyclic GMP is transformed into simple hyperpolarization. Large neurons respond to cyclic AMP with a delay (1-3 sec) after the beginning of iontophoresis. The solution of diffusion equation presents the distance from the microelectrode tip to the point of cyclic AMP action as a function of the delay (100-160 microns). The maximum value of concentration that may be reached at this point after a prolonged injection (10(-5) M) is calculated as well. The system producing and destroying cyclic nucleotides is supposed to be a diffusion analog input of the cell molecular computer. This system can solve various equations of mathematical physics. For this reason guanylatecyclase is supposed to be connected with special biochemical system which realizes harmonic analysis.

Computers↗
PubMed2004

Speed of pattern appearance in reaction-diffusion models: implications in the pattern formation of limb bud mesenchyme cells.

It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern appearance. In the present study, we analyze how a small change in a specific parameter affects the speed of pattern appearance in a Turing reaction-diffusion system using linear stability analysis. It is shown that the sign of the change in appearance speed is qualitatively decided if the system is under the diffusion-driven instability condition, and this is confirmed by numerical simulations. Numerical simulations also show that a small change in parameter value induced easily detectable differences in the appearance speed of patterns. Analysis of the Gierer-Meinhardt model revealed that a change in a single parameter can explain two effects of FGF on limb mesenchyme cells-reinforcement of lateral inhibition and earlier appearance of pattern. These qualitative properties and easy detectability make this feature a promising tool to elucidate the underlying mechanisms of biological pattern formation where the quantitative parameters are difficult to obtain.

Animals↗
PubMed1994

Comparison of thymoxamine permeation between hairless rat and horse penile mucous membrane using an in vitro diffusion model.

Moxisylyte (or thymoxamine) administered intracavernously is known to improve erection in organically impotent patients. Prior to drug administration by percutaneous route, we have to define its in vitro permeation parameters after application of thymoxamine on both rat skin and horse penile mucous membrane. 24 h after drug application, the percentages of thymoxamine which diffused through the penile mucous and the rat skin were 88 and 75%, respectively. Thymoxamine flux varied according to the biological membrane tested. With regard to the penile mucous membrane, a maximal flux (1,774 nmol.h-1.cm-2) was observed 2.5 h after drug application, whereas for the rat skin a maximal flux (657 nmol.h-1.cm-2) was noted at 3.5 h. Thymoxamine flux decreased rapidly in the penile mucous membrane. This decrease was slower when thymoxamine penetrated the rat skin; the difference could be due to a different morphology of the tested biological membranes. In contrast to the rat skin, the external keratinized layer was absent in the penile mucous membrane. In conclusion, the ability of thymoxamine to penetrate easily and rapidly the biological membrane, and particularly the penile mucous membrane, suggests that thymoxamine could reach the pharmacological target represented by the corpus cavernosum of the penis.

Animals↗
PubMed1997

A diffusion model of cerebral microischemia.

We have recently published an experimental method useful for causing discrete cerebral microischemic foci in rabbits. In that study it was shown that on reaching the brain, plastic beads (with an average diameter of 80 or 110 microns) give rise to foci of increased [14C]2-deoxyglucose accumulation, indicating anaerobic glycolysis. Further, it was suggested that the relatively low accumulation of [14C]2-deoxyglucose, as observed in the center of some of the ischemic foci located in areas which are thought to have a poor collateral blood supply, was an indication of glucose depletion. This work is intended to be a useful approach for the study of diffusion-limited consumption of glucose and oxygen in microischemic regions, located in endarterial regions. It is shown that a mathematical model with reasonable parameters can be fitted to a measured [14C]2-deoxyglucose profile. The results of this study are compatible with the view that the glucose concentration in the ischemic center is very low and limits the rate of energy turnover. Together with animal experiments, this mathematical model may impart new information of importance for evaluating the treatment of subcortical infarctions in humans.

Animals↗
PubMed2001

Persistence in the one-dimensional A+B--> Ø reaction-diffusion model.

The persistence properties of a set of random walkers obeying the A+B--> Ø reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability P(t) that an annihilation process has not occurred at a given site has the asymptotic form P(t) approximately const+t(-straight theta), where straight theta is the persistence exponent (type I persistence). We argue that, for a density of particles rho>>1, this nontrivial exponent is identical to that governing the persistence properties of the one-dimensional diffusion equation, partial differential(t)straight phi= partial differential(xx)straight phi, where straight theta approximately 0.1207 [S. N. Majumdar, C. Sire, A. J. Bray, and S. J. Cornell, Phys. Rev. Lett. 77, 2867 (1996)]. In the case of an initial low density, rho(0)<<1, we find straight theta approximately 1/4 asymptotically. The probability that a site remains unvisited by any random walker (type II persistence) is also investigated and found to decay with a stretched exponential form, P(t) approximately exp(-constxrho(1/2)(0)t(1/4)), provided rho(0)<<1. A heuristic argument for this behavior, based on an exactly solvable toy model, is presented.

Journal Article↗
PubMed2004

Modeling diffusion in miscible polymer blend films.

Recent experiments designed to probe polymer transport in the bulk and in the vicinity of surfaces have examined the interdiffusion of multilayer sandwiches of isotopically labeled polymers. The measured time dependent concentration profiles normal to the surface are typically fit to Fick's law, with a single fitting parameter, the mutual binary diffusion coefficient (MBDC). The resulting MBDCs are found to vary over a broad range of film thicknesses and time, with the time dependence being viewed as a unique signature of the reptation mechanism of long chain motion, and the thickness dependence being attributed to the slowing down of chain dynamics near surfaces. Since the experiments are conducted at finite concentration, the MBDC, which is a product of the bare mobility and the concentration derivative of the chemical potential, could be dominated by the time and thickness dependence of this second term (which is ignored in Fick's law). To quantify this conjecture we consider the more rigorous Cahn formulation of the diffusion problem in terms of chemical potential gradients. We use square gradient theory to evaluate chemical potentials, and fit the resulting time dependent concentration profiles to the analytical solution of Fick's law. By thus mimicking the experimental analysis we find that the apparent MBDCs vary with time as t(-1/2) at short times, in good agreement with existing experiments. We show that this time dependence reflects the system's desire to minimize concentration gradients, a fact ignored in Fick's law. Since these arguments make no reference to the mechanism of chain motion, we argue that the time dependence of MBDC derived from interdiffusion experiments does not provide unequivocal support for the reptation mechanism of long chain transport. The MBDC values, which also vary with the degree of confinement, are predicted to increase with decreasing thickness for model parameters corresponding to experimental systems. In contrast, since the experimental fits yield an opposite trend, we suggest that the bare mobility of the chains decreases strongly with decreasing thickness. These findings strongly support the idea that the chains are "pinned" irreversibly to the surfaces, in good agreement with other, independent experiments.

Journal Article↗
PubMed1995

On the parameter estimation for diffusion models of single neuron's activities. I. Application to spontaneous activities of mesencephalic reticular formation cells in sleep and waking states.

For the Ornstein-Uhlenbeck neuronal model a quantitative method is proposed for the estimation of the two parameters characterizing the unknown input process, namely the neuron's mean input per unit time mu and the infinitesimal standard deviation per unit time sigma. This method is based on the experimentally observed first- and second-order moments of interspike intervals. The dependence of the estimates mu and ŝigma on the moments of the observed interspike intervals and on the neuronal parameters is clarified, and a comparison is made between the estimates based on the classical Wiener model and those yielded by the Ornstein-Uhlenbeck model. Comprehensive tables are included in which the displayed values of mu and ŝigma have been calculated in terms of physiologically realistic pairs of first- and second-order moments. Our method is finally applied to interspike interval data recorded from neurons in the mesencephalic reticular formation of the cat during hypothetical sleep, slow-wave sleep stage, and wake stage.

Animals↗