SEARCH · PubMed Health

Results for “directional 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 109 records · Page 6Linked to original sources

PubMed1994

Protein folding dynamics: the diffusion-collision model and experimental data.

The diffusion-collision model of protein folding is assessed. A description is given of the qualitative aspects and quantitative results of the diffusion-collision model and their relation to available experimental data. We consider alternative mechanisms for folding and point out their relationship to the diffusion-collision model. We show that the diffusion-collision model is supported by a growing body of experimental and theoretical evidence, and we outline future directions for developing the model and its applications.

Diffusion↗

PubMed2004

Modeling the anatomical distribution of sunlights.

One of the major technical challenges in calculating solar irradiance on the human form has been the complexity of the surface geometry (i.e. the surface-normal vis-a-vis the incident radiation). Over 80% of skin cancers occur on the face, head, neck and back of the hands. The quantification, as well as the mapping of the anatomical distribution of solar radiation on the human form, is essential if we are to study the etiology of skin cancers or cataracts or immune system suppression. Using advances in computer graphics, including high-resolution three-dimensional mathematical representations of the human form, the calculation of irradiance has been attained to subcentimeter precision. Lighting detail included partitioning of direct beam and diffuse skylight, shadowing effects and gradations of model surface illumination depending on model surface geometry and incident light angle. With the incorporation of ray-tracing and irradiance algorithms, the results are not only realistic renderings but also accurate representations of the distribution of light on the subject model. The calculation of light illumination at various receptor points across the anatomy provides information about differential radiant exposure as a function of subject posture, orientation relative to the sun and sun elevation. The integration of a geodesic sun-tracking model into the lighting module enabled simulation of specific sun exposure scenarios, with instantaneous irradiance, as well as the cumulative radiant exposure, calculated for a given latitude, date, time of day and duration. Illustration of instantaneous irradiance or cumulative radiant exposure is achieved using a false-color rendering--mapping light intensity to color--creating irradiance or exposure isopleths. This approach may find application in the determination of the reduction in exposure that one achieves by wearing a hat, shirt or sunglasses. More fundamentally, such an analysis tool could provide improved estimates of scenario-specific dose (i.e. absorbed radiant exposure) needed to develop dose-response functions for sunlight-induced disease.

Adult↗

PubMed2003

Directed motion of telomeres in the formation of the meiotic bouquet revealed by time course and simulation analysis.

Chromosome movement is critical for homologous chromosome pairing during meiosis. A prominent and nearly universal meiotic chromosome reorganization is the formation of the bouquet, characterized by the close clustering of chromosome ends at the nuclear envelope. We have used a novel method of in vitro culture of rye anthers combined with fluorescent in situ hybridization (FISH) detection of telomeres to quantitatively study bouquet formation. The three-dimensional distribution of telomeres over time was used to obtain a quantitative profile of bouquet formation intermediates. The bouquet formed through a gradual, continuous tightening of telomeres over approximately 6 h. To determine whether the motion of chromosomes was random or directed, we developed a computer simulation of bouquet formation to compare with our observations. We varied the diffusion rate of telomeres and the amount of directional bias in telomere movement. In our models, the bouquet was formed in a manner comparable to what we observed in cultured meiocytes only when the movement of telomeres was actively directed toward the bouquet site, whereas a wide range of diffusion rates were permitted. Directed motion, as opposed to random diffusion, was required to reproduce our observations, implying that an active process moves chromosomes to cause telomere clustering.

Chromosomes, Plant↗

PubMed1998

Direct injection of 90Y MoAbs into glioma tumor resection cavities leads to limited diffusion of the radioimmunoconjugates into normal brain parenchyma: a model to estimate absorbed radiation dose.

PURPOSE: Previously we have demonstrated that radioimmunoconjugates can be injected into glioma resection cavities to deliver a boost of radiation to the cavity edge with little toxicity to the normal brain. In the mathematical models we have previously published to assist in the development of this strategy we assumed that antibody remains associated with the cavity edge and no diffusion occurs. However, moderate diffusion might be beneficial while, if this were excessive, it would decrease the therapeutic index markedly. METHODS AND MATERIALS: Selected individuals with relapsed malignant glioma underwent further surgical debulking; 90Y MoAb radioimmunotherapy; and open biopsy to determine the extent to which the conjugate diffuses from the cavity edge. Samples from these patients were taken in radial tracts and the corrected activity in each sample was plotted against distance from the cavity wall to determine appropriate diffusion constants. RESULTS: Our data indicates that diffusion of radioimmunoconjugate from the edge of a glioma resection cavity appears to be an exponential process. The mean Ro for each patients data set ranged from 0.48-0.63 (overall mean 0.6) cm. A dosimetric model was developed that translates these measurements into estimates of radiation dose. Applying the clinical data to this model indicates that, in each patient, the peak dose is delivered 0.16-0.18 cm below the cavity margin, and the mean dose at 2 cm deep is 5.3% (4.4-5.8%) of the peak. CONCLUSION: The model described can be used to translate diffusion constants measured by any method into estimates of absorbed radiation dose. Assuming similar diffusion kinetics, it can also be used to predict the dose deposited if alternative radionuclides are linked to MoAb, although the effect of dose rate should also be considered. In the future, it may be possible to manipulate diffusion by using either different antibodies or antibody fragments for intracavity radioimmunotherapy. Before this can be done, however, further data are needed and a noninvasive approach to measuring diffusion would clearly be optimal.

Antibodies, Monoclonal↗

PubMed2001

Critical properties of the reaction-diffusion model 2A-->3A, 2A-->0.

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A-->3A, 2A-->0 is studied through the non-Hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of directed percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to 2 and the model no longer shows DP critical behavior. The exponents theta=nu(parallel)/nu(perpendicular) and beta/nu(perpendicular) are calculated numerically. The value of beta/nu(perpendicular) is close to the value of the parity conserving universality class, in spite of the absence of local conservation laws.

Journal Article↗

PubMed1997

A biased random walk model for the trajectories of swimming micro-organisms.

The motion of swimming micro-organisms that have a preferred direction of travel, such as single-celled algae moving upwards (gravitaxis) or towards a light source (phototaxis), is modelled as the continuous limit of a correlated and biased random walk as the time step tends to zero. This model leads to a Fokker-Planck equation for the probability distribution function of the orientation of the cells, from which macroscopic parameters such as the mean cell swimming direction and the diffusion coefficient due to cell swimming can be calculated. The model is tested on experimental data for gravitaxis and phototaxis and used to derive values for the macroscopic parameters for future use in theories of bioconvection, for example.

Algorithms↗

PubMed1977

Models for the active transport of cations...the steady-state analysis.

We summarise the progress that has been made in the analysis of active transport models, at the steady-state level. The two general classes of such model, counter-and co-transport, can be treated by a kinetic analysis which makes no assumptions as to the symmetry or asymmetry of the systems nor as to the presence of any particular rate-limiting steps. Precisely the same formalism is obeyed for primary active transport as for secondary active transport. Both are merely a generalisation of facilitated diffusion, in that they follow directly from accepted properties of carrier models. How affinities of such carriers for their substrates affect the efficiency of active transport is discussed and it is shown that in a number of cases, the affinity changes that the carrier demonstrates arise from inherent properties of the free carrier and not from any "high energy" properties of the chemical reactants. Methods of obtaining the kinetic parameters of the system from experimental data are reviewed, together with methods for testing and characterising the different transport models.

Binding Sites↗

PubMed2004

Diffusion and percolation in anisotropic random barrier models.

An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long-time diffusion coefficients, obtained using an effective medium approximation, follow an Arrhenius temperature dependence, with the same activation energy for each direction. Such activation energy is related to the anisotropic percolation properties of the lattice, and can be analyzed in terms of the critical percolation path approximation. The anisotropic effective medium approximation is shown to predict the correct percolation threshold for an anisotropic two-dimensional square lattice. In addition, results are compared with numerical simulations using a fast kinetic Monte Carlo algorithm.

Journal Article↗

PubMed2005

Validation of q-ball imaging with a diffusion fibre-crossing phantom on a clinical scanner.

Magnetic resonance (MR) diffusion imaging provides a valuable tool used for inferring structural anisotropy of brain white matter connectivity from diffusion tensor imaging. Recently, several high angular resolution diffusion models were introduced in order to overcome the inadequacy of the tensor model for describing fibre crossing within a single voxel. Among them, q-ball imaging (QBI), inherited from the q-space method, relies on a spherical Radon transform providing a direct relationship between the diffusion-weighted MR signal and the orientation distribution function (ODF). Experimental validation of these methods in a model system is necessary to determine the accuracy of the methods and to optimize them. A diffusion phantom made up of two textile rayon fibre (comparable in diameter to axons) bundles, crossing at 90 degrees , was designed and dedicated to ex vivo q-ball validation on a clinical scanner. Normalized ODFs were calculated inside regions of interest corresponding to monomodal and bimodal configurations of underlying structures. Three-dimensional renderings of ODFs revealed monomodal shapes for voxels containing single-fibre population and bimodal patterns for voxels located within the crossing area. Principal orientations were estimated from ODFs and were compared with a priori structural fibre directions, validating efficiency of QBI for depicting fibre crossing. In the homogeneous regions, QBI detected the fibre angle with an accuracy of 19 degrees and in the fibre-crossing region with an accuracy of 30 degrees .

Anisotropy↗

PubMed2005

Modeling of slow glutamate diffusion and AMPA receptor activation in the cerebellar glomerulus.

Synaptic conductances are influenced markedly by the geometry of the space surrounding the synapse since the transient glutamate concentration in the synaptic cleft is determined by this geometry. Our paper is an attempt to understand the reasons for slow glutamate diffusion in the cerebellar glomerulus, a structure situated around the enlarged mossy fiber terminal in the cerebellum and surrounded by a glial sheath. For this purpose, analytical expressions for glutamate diffusion in the glomerulus were considered in models with two-, three-, and fractional two-three-dimensional (2D-3D) geometry with an absorbing boundary. The time course of average glutamate concentration in the synaptic cleft of the mossy fiber-granule cell connection was calculated for both direct release of glutamate from the same synaptic unit, and for cumulative spillover of glutamate from neighboring release sites. Several kinetic schemes were examined, and the parameters of the diffusion models were estimated by identifying theoretical activation of AMPA receptors with direct release and spillover components of published experimental AMPA receptor-mediated EPSCs. For model selection, the correspondence of simulated paired-pulse ratio and EPSC increase after prevention of desensitization to experimental values were also taken into consideration. Our results suggest at least a 7- to 10-fold lower apparent diffusion coefficient of glutamate in the porous medium of the glomerulus than in water. The modeling of glutamate diffusion in the 2D-3D geometry gives the best fit of experimental EPSCs. We show that it could be only partly explained by normal diffusion of glutamate in the complex geometry of the glomerulus. We assume that anomalous diffusion of glutamate occurs in the glomerulus. A good match of experimental estimations and theoretical parameters, obtained in the simulations that use an approximation of anomalous diffusion by a solution for fractional Brownian motion, confirms our assumption.

Cerebellar Cortex↗

PubMed1999

Spatial instabilities in reaction random walks with direction-independent kinetics.

We study spatial instabilities in reacting and diffusing systems, where diffusion is modeled by a persistent random walk instead of the usual Brownian motion. Perturbations in these reaction walk systems propagate with finite speed, whereas in reaction-diffusion systems localized disturbances affect every part instantly, albeit with heavy damping. We present evolution equations for reaction random walks whose kinetics do not depend on the particles' direction of motion. The homogeneous steady state of such systems can undergo two types of transport-driven instabilities. One type of bifurcation gives rise to stationary spatial patterns and corresponds to the Turing instability in reaction-diffusion systems. The other type occurs in the ballistic regime and leads to oscillatory spatial patterns; it has no analog in reaction-diffusion systems. The conditions for these bifurcations are derived and applied to two model systems. We also analyze the stability properties of one-variable systems and find that small wavelength perturbations decay in an oscillatory manner.

Journal Article↗

PubMed1988

The role of diffusible molecules in regulating the cellular differentiation of Dictyostelium discoideum.

A central problem in developmental biology is to understand how morphogenetic fields are created and how they act to direct regionalized cellular differentiation. This goal is being pursued in organisms as diverse as moulds, worms, flies, frogs and mice. Each organism has evolved its own solution to the challenge of multicellularity but there appear to be common underlying principles and, once pattern formation is fully understood in any system, some general truths seem certain to be revealed. As a non-obligate metazoan, Dictyostelium discoideum has proven a particularly tractable system in which to identify and characterize cellular morphogens. Cyclic AMP and ammonia stimulate prespore cell differentiation and ammonia plays an additional role in repressing terminal cellular differentiation. Differentiation Inducing Factor (DIF) acts to direct prestalk cell differentiation and adenosine may play a synergistic role in repressing prespore cell differentiation. This review summarizes the evidence for these interactions and describes a number of models which show how this small repertoire of diffusible molecules, acting in concert, may direct the formation of a differentiated structure.

Cell Differentiation↗

PubMedDate not supplied

Chemoconvulsant seizures: advantages of focally-evoked seizure models.

Studies of short and long-term changes in regional metabolism, blood flow, gene expression (including immediate early genes and genes for neurotrophic factors), sprouting and cell death following seizures are pivotal to an understanding of the neural networks responsible for the generation of seizures. At the same time, this information forms a basis for understanding the pathophysiology associated with chronic, recurrent seizures. Systemic chemoconvulsant seizure models, produced by systemically administered chemoconvulsant agents, although convenient, are plagued with difficulties which confound the interpretation of their effects on the nervous system. These difficulties include widespread direct cellular and physiological effects of the chemoconvulsant drugs, most of which are independent of seizures. In addition, numerous physiological changes occur as a secondary consequence of, or ancillary to, seizures, and it can be especially difficult to separate these effects from the direct effects of the propagated seizure discharge itself. Some of these difficulties can be overcome by the use of focally-evoked seizure models. Such models avoid the diffuse presence of drug throughout the CNS and thereby eliminate most of the direct cellular and physiologic actions of the drug apart from seizure-induction. Large regions of the brain distant from the focal site of drug application then can be examined for molecular, structural and physiologic changes uncomplicated by the presence of drug. Moreover, different focal sites of drug application can be compared to evaluate the specificity of the molecular changes to the neural network engaged in the seizure discharge. For example, limbic seizures, evoked by chemoconvulsant application into area tempestas, can be compared with brainstem convulsions evoked by chemoconvulsant application into inferior colliculus.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMedDate not supplied

[Treatment of burn surfaces by proteinases: mathematical description of an enzyme distribution].

The process of penetration of a proteolytic enzyme applied to the surface of burn wound into the depth of necrotic tissue was considered. The model approximation describes three factors by a series of mathematical equations: inward-directed enzyme diffusion, counter-flow filtration of interstitial fluid (exudates), and irreversible inactivation of the enzyme by specific inhibitors present in exudates. According to the model, a quasi-stationary distribution of enzymatic activity through the thickness of the necrotic layer is achieved within 3 h and persists as long as the enzyme concentration on the wound surface is constant. The enzyme activity diminishes linearly from the wound surface to the mid-part of the necrotic layer. No enzyme activity is retained in the inner mid-part of the necrotic layer completely protected by the prevalent inhibitor. The ratio of enzyme concentration on the wound surface to inhibitor concentration in the interstitial fluid is the same as the ratio of the depth of active enzyme area to the depth of the inhibitor-protected area through the necrotic layer. The dynamics of accumulation of the active enzyme in the necrotic zone and the rate of enzyme inactivation in the wound by inhibitors were described by formulas applicable for practical purposes.

Burns↗

PubMed1990

A method for measuring the oxygen consumption of photoreceptor cells in the steady state and after a brief stimulation by light.

The rate of oxygen consumption (QO2) in living tissue cannot be directly measured but may be estimated by mathematically modelling the diffusion of oxygen in the tissue and measuring the local partial pressure of oxygen (PO2). The retina of arthropods contains only two types of cells, photoreceptor and glial cells, which are regularly distributed. Because of this simple structure, simple models of diffusion can be used to estimate the QO2 of the tissue, both in steady state and after a brief stimulation by light. We used a model of diffusion in a plane sheet to calculate the QO2 in a slice of honeybee drone retina, which contains a few thousand cells. We then modified the method slightly and used a model with spherical symmetry to calculate the QO2 in the cluster of three photoreceptor cells of the barnacle and in the single ventral photoreceptor cells of Limulus.

Animals↗

PubMed2002

Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness.

A dual wavelength time-resolved reflectance system was developed for monitoring haemoglobin saturation noninvasively. At each wavelength, the time-resolved reflectance data were fitted to a diffusion model of light propagation in a homogeneous, semi-infinite medium to yield the absolute scattering and absorption coefficients. The absorption coefficients were then used to calculate haemoglobin saturation. A two-layer phantom containing human erythrocytes in a scattering solution in the bottom layer was used to study system performance under more realistic conditions. The top layer was chosen to simulate either skin or fat and the oxygenation of the bottom layer, which corresponded to muscle, was controlled. The thickness of the fat layer was varied from 1.5 to 10 mm to investigate the effects of increasing the top layer thickness. These results, obtained with the simple diffusion model, were compared with simultaneous measurements of oxygenation made directly in the bottom layer. Errors in estimating haemoglobin saturation with this method ranged from 5-11% depending on the thickness of the top layer and its optical properties.

Hemoglobins↗

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↗