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Results for “directional diffusion models”

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PubMed2006

Directed percolation with incubation times.

We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Lévy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Lévy parameter.

Journal Article↗

PubMed2006

Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves.

An acoustic transmissivity method is proposed for measuring flow resistivity of porous materials having rigid frame. Flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The transmission scattering operator for a slab of porous material is derived from the response of the medium to an incident acoustic pulse. The flow resistivity is determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed.

Journal Article↗

PubMed2006

Diffusion delays and unstirred layer effects at monolayer cultures of Chinese hamster ovary cells: radioligand binding, confocal microscopy, and mathematical simulations.

Cells grown in monolayer culture offer a convenient system for binding and other experiments under conditions that preserve the complexity of the living state. Kinetics experiments, however, may be distorted by the time course of drug penetration into even so simple a "tissue" as the monolayer. The impediments include unstirred layers both above and between the cells, the congregation of receptors within the confined space between cells, and nonspecific binding to membrane components. The contributions of these factors were investigated in cultures of Chinese hamster ovary (CHO) cells either nontransfected or stably transfected with mu opioid receptors. The dissociation of [3H]naloxone was four times faster under displacement than under infinite dilution conditions, clearly demonstrating the "retention effect" of receptors confined in space. Even the penetration of this ligand between nontransfected cells showed salient delays with respect to diffusion into a slab, indicating that nonspecific, low-affinity binding to membrane components was arresting its progress. The optical sectioning capabilities of confocal microscopy demonstrated that the kinetics of two fluorescent antagonists depended on the vertical plane, providing direct evidence for slowed diffusion down a single cell depth. Modeling shows that kinetic errors increase with receptor density, forward rate constant, and the thickness of the unstirred layer.

Animals↗

PubMed1987

On diffusion in organized assemblies and in biological membranes.

The following paper is a brief presentation of problems related to the concepts of diffusion coefficient D and so-called viscosity eta used to characterize the cohesion of biological membranes. The first approach to this problem is a recall of the definition of D and eta in liquids. It appears that the models developed with exogenous probes to account for the diffusion-viscosity relationship are not verified in membranes. The existence of complex diffusional mechanisms, the influence of the size of the probe are presented. The results of a model calculation suggest that there is no direct correlation other than great simplifications, between the diffusion coefficient and viscosity. The calculations are then extended to actual biological assemblies and the influence of proteins on the motion of the probe considered. The limitations of the methods involving exogenous probes for determining the cohesion of biological membranes are discussed.

Cell Membrane↗

PubMed1970

Possible role of pyrophosphate linkage in the active transport of sodium ions.

Based upon the observation that the pyrophosphate group has a greater affinity for sodium ion than for potassium ion, and that both of these ions catalyze transphosphorylation, a simple molecular mechanism is formulated for the active transport of sodium ions across biological membranes. It is assumed that the active transport takes place along a chain of phosphomonoester groups in the membrane. Pyrophosphate linkages are synthesized at the inner boundary of the membrane by a sodium-activated kinase and hydrolyzed at the outer boundary of the membrane by a potassium-activated pyrophosphatase. It is shown that in such a model the pyrophosphate linkages can diffuse across the membrane and carry sodium ions in the direction of increasing sodium ion concentration.

Biological Transport, Active↗

PubMedDate not supplied

Region specific modeling of cardiac muscle: comparison of simulated and experimental potentials.

This article investigates the quantitative predictive capabilities of region-specific models by comparing experimental electrograms obtained from in vivo mapping of the ventricular free wall with those obtained through simulation of a region specific three-dimensional bidomain model that incorporates measured fiber orientations. Epicardial electrograms were recorded from canine left ventricles during and after unipolar pacing using a 528-channel electrode plaque. Fiber directions throughout the tissue were estimated from diffusion-weighted MRI and from pace mapping. Electrograms were computed in the bidomain model with experimentally derived properties during paced activations at the same spatiotemporal resolution as those recorded experimentally. Epicardial potentials from model and experiment were directly compared, and sensitivities of these comparisons to reference electrode location and to the choice of material properties were analyzed. The comparisons performed here demonstrate, that (1) the stimulus artifact can be used to estimate the in vivo myocardial fiber architecture, (2) the correlation between simulated and experimental electrograms decreases with increasing pacing depth, and (3) the quantitative comparisons between bidomain model and experimental data are sensitive to both the description of the fiber architecture, and the location of the unipolar reference electrode, but relatively insensitive to moderate changes in the bidomain conductivities.

Animals↗

PubMed1992

Mechanisms for intracellular distribution of mRNA: in situ hybridization studies in muscle.

The intracellular distribution of mRNA in striated muscle fibers is highly ordered, as is the structural organization of the fibers' contractile apparatus. Results from in situ hybridization of muscle mRNA are reviewed in an attempt to discern the mechanisms involved in mRNA distribution and to determine its relationship to developmental, growth, and repair processes in muscle. Nonradioactively labeled complementary RNA probes allow anatomic localization of mRNA at the light and electron microscopic level. Myosin mRNA in striated muscle is concentrated around transcriptionally active nuclei, myosin mRNA is excluded by the myofibrillar mass, myosin mRNA distribution correlates with that of cytoskeletal elements, and myosin mRNA is concentrated in regions of rapid growth and repair. The even distribution of myosin mRNA along the length of myofibrils gives no indication of specific association with either the thick or thin filaments. Of the possible mechanisms directing mRNA distribution, results from in situ hybridization and other analyses support a restricted diffusion model. Diffusion of mRNA (and polysomes) is severely limited by the myofibrillar lattice. It is possible that myosin mRNA is also associated with a cytoskeletal element, which may direct the mRNA to specific intracellular locations and affect translational activity.

Animals↗

PubMed1995

A mechanistic study of ultrasonically-enhanced transdermal drug delivery.

Although ultrasound has been shown to enhance the transdermal transport of a variety of drugs, the mechanisms underlying this phenomenon are not clearly understood. In this paper, we evaluate the roles played by various ultrasound-related phenomena, including cavitation, thermal effects, generation of convective velocities, and mechanical effects, in the ultrasonic enhancement of transdermal drug delivery (sonophoresis). Our experimental findings suggest that among all the ultrasound-related phenomena evaluated, cavitation plays the dominant role in sonophoresis using therapeutic ultrasound (frequency range, 1-3 MHz; intensity range, 0-2 W/cm2). Furthermore, confocal microscopy results indicate that cavitation occurs in the keratinocytes of the stratum corneum upon ultrasound exposure. It is hypothesized that oscillations of the cavitation bubbles induce disorder in the stratum corneum lipid bilayers, thereby enhancing transdermal transport. Evidence supporting this hypothesis is presented using skin electrical resistance measurements. Finally, a theoretical model is developed to predict the effect of ultrasound on the transdermal transport of drugs. The model predicts that sonophoretic enhancement depends most directly on the passive permeant diffusion coefficient, rather than on the permeability coefficient through the skin. Specifically, permeants passively diffusing through the skin at a relatively slow rate are expected to be preferentially enhanced by ultrasound. The experimentally measured sonophoretic transdermal transport enhancement for seven permeants, including estradiol, testosterone, progesterone, corticosterone, benzene, butanol, and caffeine, agree quantitatively with the model predictions. These experimental and theoretical findings provide quantitative guidelines for estimating the efficacy of sonophoresis in enhancing transdermal drug delivery.

Administration, Cutaneous↗

PubMed2005

Simulating biochemical networks at the particle level and in time and space: Green's function reaction dynamics.

We present a technique, called Green's function reaction dynamics (GFRD), for particle-based simulations of reaction-diffusion systems. GFRD uses a maximum time step such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equations are solved analytically using Green's functions, which are used to set up an event-driven algorithm. We apply the technique to a model of gene expression. Under biologically relevant conditions, GFRD is up to 5 orders of magnitude faster than conventional particle-based schemes.

Algorithms↗

PubMed2002

Studies on rifampicin release from ethylcellulose coated nonpareil beads.

The rifampicin release studies from ethylcellulose coated nonpareil beads were studied. Propylene glycol and Castor oil were used as plasticizers. The in vitro dissolution studies revealed that the release rate is inversely proportional to percent of coating thickness. The release rate also depends on the type of plasticizer used in the coating polymer. The mechanism of drug release follows Higuchi diffusion model. Water vapour permeation studies indicated that the water vapour transport rate through free films is directly related to the drug release rate. DSC thermograms and IR spectras revealed that there is no interaction between rifampicin and other additives. SEM photographs of coated beads, before dissolution and after dissolution, also indicates that the drug release mechanism follows diffusion model.

Cellulose↗

PubMed2003

The role of prey taxis in biological control: a spatial theoretical model.

We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient. The prey population reproduces logistically, and the local population interactions follow the Holling Type II trophic function. On the scale of the population, our spatially explicit approach subdivides the predation process into random movement represented by diffusion, directed movement described by prey taxis, local prey encounters, and consumption modeled by the trophic function. Thus, our model allows studying the effects of large-scale predator spatial activity on population dynamics. We show under which conditions spatial patterns are generated by prey taxis and how this affects the predator ability to maintain the pest population below some economic threshold. In particular, intermediate taxis activity can stabilize predator-pest populations at a very low level of pest density, ensuring successful biological control. However, very intensive prey taxis destroys the stability, leading to chaotic dynamics with pronounced outbreaks of pest density.

Animals↗

PubMed2006

Geometrically constrained two-tensor model for crossing tracts in DWI.

MR diffusion tensor imaging (DTI) of the brain and spine provides a unique tool for both visualizing directionality and assessing intactness of white matter fiber tracts in vivo. At the spatial resolution of clinical MRI, much of primate white matter is composed of interdigitating fibers. Analyses based on an assumed single diffusion tensor per voxel yield important information about the average diffusion in the voxel but fail to reveal structure in the presence of crossing tracts. Until today, all clinical scans assume only one tensor, causing potential serious errors in tractography. Since high angular resolution imaging remains, so far, untenable for routine clinical use, a method is proposed whereby the single-tensor field is augmented with additional information gleaned from standard clinical DTI. The method effectively resolves two distinct tract directions within voxels, in which only two tracts are assumed to exist. The underlying constrained two-tensor model is fitted in two stages, utilizing the information present in the single-tensor fit. As a result, the necessary MRI time can be drastically reduced when compared with other approaches, enabling widespread clinical use. Upon evaluation in simulations and application to in vivo human brain DTI data, the method appears to be robust and practical and, if correctly applied, could elucidate tract directions at critical points of uncertainty.

Animals↗

PubMed2005

Generating controlled molecular gradients in 3D gels.

A new method for producing molecular gradients of arbitrary shape in thin three dimensional gels is described. Patterns are produced on the surface of the gel by printing with a micropump that dispenses small droplets of solution at controlled rates. The molecules in the solution rapidly diffuse into the gel and create a smooth concentration profile that is independent of depth. The pattern is relatively stable for long times, and its evolution can be accurately described by finite element modeling of the diffusion equation. As a demonstration of the method, direct measurements of protein gradients are performed by quantitative fluorescence microscopy. A complementary technique for measuring diffusion coefficients is also presented. This rapid, flexible, contactless approach to gradient generation is ideally suited for cell culture experiments to investigate the role of gradients of diffusible substances in processes such as chemotaxis, morphogenesis, and pattern formation, as well as for high-throughput screening of system responses to a wide range of chemical concentrations.

Collagen↗

PubMed1998

Force generation in RNA polymerase.

RNA polymerase (RNAP) is a processive molecular motor capable of generating forces of 25-30 pN, far in excess of any other known ATPase. This force derives from the hydrolysis free energy of nucleotides as they are incorporated into the growing RNA chain. The velocity of procession is limited by the rate of pyrophosphate release. Here we demonstrate how nucleotide triphosphate binding free energy can rectify the diffusion of RNAP, and show that this is sufficient to account for the quantitative features of the measured load-velocity curve. Predictions are made for the effect of changing pyrophosphate and nucleotide concentrations and for the statistical behavior of the system.

Adenosine Triphosphatases↗

PubMed1986

On the relationship among three theories of relaxation in disordered systems.

Empirical evidence has accumulated showing the wide occurrence of a stretched-exponential relaxation decay law for many diverse condensed-matter systems. Several theories based on different physical mechanisms have been successful in deriving the stretched-exponential decay law in a natural way. Three of these theories, the direct-transfer model, the hierarchically constrained dynamics model, and the defect-diffusion model are shown here to have an underlying common mathematical structure.

Journal Article↗

PubMed1998

Homologous chromosome pairing in Drosophila melanogaster proceeds through multiple independent initiations.

The dynamics by which homologous chromosomes pair is currently unknown. Here, we use fluorescence in situ hybridization in combination with three-dimensional optical microscopy to show that homologous pairing of the somatic chromosome arm 2L in Drosophila occurs by independent initiation of pairing at discrete loci rather than by a processive zippering of sites along the length of chromosome. By evaluating the pairing frequencies of 11 loci on chromosome arm 2L over several timepoints during Drosophila embryonic development, we show that all 11 loci are paired very early in Drosophila development, within 13 h after egg deposition. To elucidate whether such pairing occurs by directed or undirected motion, we analyzed the pairing kinetics of histone loci during nuclear cycle 14. By measuring changes of nuclear length and correlating these changes with progression of time during cycle 14, we were able to express the pairing frequency and distance between homologous loci as a function of time. Comparing the experimentally determined dynamics of pairing to simulations based on previously proposed models of pairing motion, we show that the observed pairing kinetics are most consistent with a constrained random walk model and not consistent with a directed motion model. Thus, we conclude that simple random contacts through diffusion could suffice to allow pairing of homologous sites.

Animals↗

PubMed2005

Phenanthrene and pyrene sorption and intraparticle diffusion in polyoxymethylene, coke, and activated carbon.

We report sorption isotherms and uptake kinetics for phenanthrene and pyrene with three organic model sorbents: polyoxymethylene (POM), coke, and activated carbon. We combine batch equilibration and kinetic experiments with the direct observation of the long-term diffusion of phenanthrene and pyrene as measured within cross-sectioned particles using microprobe laser-desorption laser-ionization mass spectroscopy (muL2MS). For POM pellets, the intraparticle concentration profiles predicted from kinetic batch experiments and a polymer diffusion model with spherical geometry are in agreement with the independent muL2MS measurements. For coke particles, the apparent diffusivities decreased with smaller particle size. These trends in diffusivities were described by a sorption-retarded pore diffusion model with a particle-size-dependent solid-water partitioning coefficient obtained from apparent equilibrium observed in the kinetic batch studies. For activated carbon, the muL2MS measurements showed faster radial diffusion of phenanthrene and pyrene into the particle interior than predicted from diffusion models based on a single sorption domain and diffusivity. A branched pore kinetic model, comprising polycyclic aromatic hydrocarbon (PAH) macropore diffusion with kinetic exchange of PAH between macroporous and microporous domains, fits the experimental observations better. Because of parallel macro- and microdiffusion processes, nonlinear sorption isotherms, and a concentration-dependent diffusivity, it is not possible to make independent parameter estimations for intraparticle diffusion in activated carbon using our present procedures.

Adsorption↗

PubMed1982

Comparing two head injury treatments by linear logistic model.

A linear logistic model is used to compare the performance of a series of head injured patients treated in Auckland with a series obtained from the International Data Bank (IDB), on head injured patients. The IDB patients were treated along conventional lines of neurosurgical management. The Auckland patients were submitted to a regime of elective artificial ventilation of the lungs and heavy sedation, directed against diffuse brain swelling. Two types of comparison were used. First, a model was constructed from the Auckland data of the relationship of outcome to factors relating to the severity of the head injury. This input-output relationship was used to predict the distributions of outcome in the IDB series. Secondly, a descriptive model on the combined Auckland and IDB data was given the option of selecting a dummy variable to indicate whether the source of the patient, Auckland or IDB, had significantly influenced outcome for a given set of other determinants. Differences between Auckland and IDB were only significant if the severity of the head injury in the IDB cases was represented by the set of scores indicating their best condition over the first 24 hours of coma. The scores indicating the condition of the Auckland patients might be comparable to either the 24 hour best or the 24 hour worst IDB scores. One cannot say whether any differences in input-output relationships between the two series arise from differences in coding the input data or from real differences in outcome for given sets of determinants of outcome.

Adolescent↗