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Results for “directional diffusion models”

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At least 145 records · Page 8Linked to original sources
PubMed2003

Computation of log BB values for compounds transported through carrier-mediated mechanisms using in vitro permeability data from brain microvessel endothelial cell (BMEC) monolayers.

PURPOSE: To explore the possibility of determining in vivo log BB values (the logarithm value of brain to plasma concentration ratio) from in vitro permeability data measured in brain microvessel endothelial cell (BMEC) monolayers. METHODS: An equilibrium mathematical model was developed: log BB = log(Ca/Cb) + log Kbr:pl, where Cb and Ca are the drug concentrations at equilibrium in the basolateral (B) and apical (A) sides of BMECs in an A-to-B directional diffusion system and Kbr:pl is the brain-plasma partition coefficient. With this model, murine log BB values were calculated for 24 pharmaceutical compounds, mostly Pgp substrates. RESULTS: Calculated log BB values correlated well to experimental values (r2 = 0.854, slope = 0.907 +/- 0.080), demonstrating that the model could reasonably predict brain penetration for compounds that are involved in carrier-mediated transport mechanisms. For a second data set that included volatile organic compounds (log BB = log Kbr:pl), log Kbr:pl values were also shown to correlate well with their respective experimental log BB values (r2 = 0.876, slope = 0.973 +/- 0.082), demonstrating that log Kbr:pl is an excellent descriptor for log BB when a compound penetrates the blood-brain barrier by passive diffusion only. CONCLUSION: The equilibrium model demonstrated a reasonable ability to compute in vivo log BB values, regardless of the involvement or mechanisms of carrier-mediated transport.

Animals↗
PubMed2002

Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data.

This work details the observation of non-Gaussian apparent diffusion coefficient (ADC) profiles in multi-direction, diffusion-weighted MR data acquired with easily achievable imaging parameters (b approximately 1000 s/mm(2)). A technique is described for modeling the profile of the ADC over the sphere, which can capture non-Gaussian effects that can occur at, for example, intersections of different tissue types or white matter fiber tracts. When these effects are significant, the common diffusion tensor model is inappropriate, since it is based on the assumption of a simple underlying diffusion process, which can be described by a Gaussian probability density function. A sequence of models of increasing complexity is obtained by truncating the spherical harmonic (SH) expansion of the ADC measurements at several orders. Further, a method is described for selection of the most appropriate of these models, in order to describe the data adequately but without overfitting. The combined procedure is used to classify the profile at each voxel as isotropic, anisotropic Gaussian, or non-Gaussian, each with reference to the underlying probability density function of displacement of water molecules. We use it to show that non-Gaussian profiles arise consistently in various regions of the human brain where complex tissue structure is known to exist, and can be observed in data typical of clinical scanners. The performance of the procedure developed is characterized using synthetic data in order to demonstrate that the observed effects are genuine. This characterization validates the use of our method as an indicator of pathology that affects tissue structure, which will tend to reduce the complexity of the selected model.

Brain↗
PubMed2004

Exactly soluble noisy traveling-wave equation appearing in the problem of directed polymers in a random medium.

We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of N evolving particles which can be described by a noisy traveling-wave equation with a noise of order N(-1/2). Our model can be viewed as the infinite range limit of a directed polymer in random medium with N sites in the transverse direction. Despite some peculiarities of the traveling-wave equations in the absence of noise, our exact solution allows us to test the validity of a simple cutoff approximation and to show that, in the weak noise limit, the position of the front can be completely described by the effect of the noise on the first particle.

Journal Article↗
PubMed2003

Deviations from the diffusion tensor model as revealed by contour plot visualization using high angular resolution diffusion-weighted imaging (HARDI).

The standard diffusion tensor model is limited in its ability to provide detailed information about multidirectional fiber architecture in human white matter. Additional directional acquisition of diffusivity properties with high angular resolution diffusion-weighted imaging (HARDI) acquisition schemes may deliver more information on areas with fiber crossings than standard DTI. However, representation of the additional information and the rating and visualization of fiber complexity is challenging. We used projection 2D-plots in combination with a HARDI acquisition scheme of 129 diffusion directions and compared the spherical diffusion variance index (SDI) with the relative anisotropy index (RAI). In normal controls, white matter areas with unidirectional fiber arrangement and areas with more complex fiber composition were identified with this approach. HARDI confirms and can visualize deviations from the tensor-like representation, thereby providing information on fiber structure complexity, which may be of considerable interest for clinical studies.

Anisotropy↗
PubMed1982

Transfer of 1,3-diphosphoglycerate between glyceraldehyde-3-phosphate dehydrogenase and 3-phosphoglycerate kinase via an enzyme-substrate-enzyme complex.

On the basis of the alternatives of direct inter-enzyme transfer vs. dissociation followed by random diffusion, two kinetic models for metabolite transfer between consecutive enzymes are developed. These two models are readily distinguishable experimentally for the transfer of 1,3-diphosphoglycerate (1,3-P2G) between glyceraldehyde-3-phosphate dehydrogenase (GPDH) and 3-phosphoglycerate kinase (PGK). Since 1,3-P2G is exceedingly tightly bound to PGK, the kinetics of its transfer to GPDH are predictably different for each of these two models. Our experiments unambiguously demonstrate that 1,3-P2G is directly transferred between these two enzymes via an enzyme-substrate-enzyme complex. This direct transfer is described by a Michaelis-Menten scheme in which PGK . 1,3-P2G is the "substrate" for GPDH. At high concentrations of PGK . 1,3-P2G, the transfer reaction becomes nearly PGK . 1,3-P2G concentration independent. The rate of the transfer reaction is activated 3.5-fold by saturating quantities of ATP and 20-fold by saturating quantities of 3-PG. Evidence is presented that the PGK . 1,3-P2G complex is structurally distinct from either PGK itself or other PGK . ligand complexes.

Animals↗
PubMed1995

The biophysics of DNA hybridization with immobilized oligonucleotide probes.

A mathematical model based on receptor-ligand interactions at a cell surface has been modified and further developed to represent heterogeneous DNA-DNA hybridization on a solid surface. The immobilized DNA molecules with known sequences are called probes, and the DNA molecules in solution with unknown sequences are called targets in this model. Capture of the perfectly complementary target is modeled as a combined reaction-diffusion limited irreversible reaction. In the model, there are two different mechanisms by which targets can hybridize with the complementary probes: direct hybridization from the solution and hybridization by molecules that adsorb nonspecifically and then surface diffuse to the probe. The results indicate that nonspecific adsorption of single-stranded DNA on the surface and subsequent two-dimensional diffusion can significantly enhance the overall reaction rate. Heterogeneous hybridization depends strongly on the rate constants for DNA adsorption/desorption in the non-probe-covered regions of the surface, the two-dimensional (2D) diffusion coefficient, and the size of probes and targets. The model shows that the overall kinetics of DNA hybridization to DNA on a solid support may be an extremely efficient process for physically realistic 2D diffusion coefficients, target concentrations, and surface probe densities. The implication for design and operation of a DNA hybridization surface is that there is an optimal surface probe density when 2D diffusion occurs; values above that optimum do not increase the capture rate. Our model predicts capture rates in agreement with those from recent experimental literature. The results of our analysis predict that several things can be done to improve heterogeneous hybridization: 1) the solution phase target molecules should be about 100 bases or less in size to speed solution-phase and surface diffusion; 2) conditions should be created such that reversible adsorption and two-dimensional diffusion occur in the surface regions between DNA probe molecules; 3) provided that 2) is satisfied, one can achieve results with a sparse probe coverage that are equal to or better than those obtained with a surface totally covered with DNA probes.

Base Composition↗
PubMed2002

Modelling the effect of diffuse light on canopy photosynthesis in controlled environments.

A layered canopy model was used to analyze the effects of diffuse light on canopy gross photosynthesis in controlled environment plant growth chambers, where, in contrast to the field, highly diffuse light can occur at high irradiance. The model suggests that high diffuse light fractions (approximately 0.7) and irradiance (1400 micromoles m-2 s-1) may enhance crop life-cycle canopy gross photosynthesis for hydroponic wheat by about 20% compared to direct light at the same irradiance. Our simulations suggest that high accuracy is not needed in specifying diffuse light fractions in chambers between approximately 0.7 and 1, because simulated photosynthesis for closed canopies plateau in this range. We also examined the effect of leaf angle distribution on canopy photosynthesis under growth chamber conditions, as these distributions determine canopy extinction coefficients for direct and diffuse light. We show that the spherical leaf angle distribution is not suitable for modeling photosynthesis of planophile canopies (e.g., soybean and peanut) in growth chambers. Also, the absorption of the light reflected from the surface below the canopy should generally be included in model simulations, as the corresponding albedo values in the photosynthetically active range may be quite high in growth chambers (e.g., approximately 0.5). In addition to the modeling implications, our results suggest that diffuse light conditions should be considered when drawing conclusions from experiments in controlled environments.

Computer Simulation↗
PubMed1997

Effects of anastomoses on solute transcapillary exchange in countercurrent systems.

OBJECTIVE: To investigate effects of anastomoses between the descending vasa recta (DVR) and the ascending vasa recta (AVR) on the distribution of small solutes in the interstitial fluid of the renal medulla. METHODS: Countercurrent capillary loops, surrounded by a secretory epithelium, were used to model microvessels in the renal medulla. Anastomoses between the DVR and AVR were modeled as a decrease in cross-sectional area of the vessels and a decrease in flow velocity from the base to the tip of the capillary loop. When experimental data were used to evaluate parameters of the model, it was seen that diffusive transport of solute in the axial direction of the capillary was negligible, and the equations could be greatly simplified. RESULTS: General formulae of the solute concentration distribution were derived for different degrees of shunting between the two limbs of the capillary loop. Analytical solutions for the steady-state solute distribution were obtained when the sizes of capillaries and flows in them were assumed to decrease linearly with the distance from the base to the tip of the capillary loop. When the effects of reduction in the size of the limbs were compared with the effects of reduction of flow velocities on solute distribution, it was found that, in the presence of anastomoses, change in flow velocity increases the axial gradient of the solute concentration more than change in the cross-sectional area. The combined effects of a decrease in flow velocity and cross-sectional area can easily double the axial gradient of the solute concentration for a modest degree of anastomotic shunting. CONCLUSIONS: In this study, we separated effects of anastomotic flow between the DVR and AVR from other factors affecting the complicated countercurrent solute exchanges in the renal medulla. Results from the model show that anastomoses increase the solute concentration in the medullary interstitium and also the axial gradient of the solute concentration there.

Animals↗
PubMed1999

Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold.

The cultivation of cartilage cells (chondrocytes) in polymer scaffolds leads to implants that may potentially be used to repair damaged joint cartilage or for reconstructive surgery. For this technique to be medically applicable, the physical parameters that govern cell growth in a polymer scaffold must be understood. This understanding of cell behavior under in vitro conditions, where diffusion is the primary mode of transport of nutrients, may aid in the scale-up of the cartilage generation process. A mathematical model of chondrocyte generation and nutrient consumption is developed here to analyze the behavior of cell growth in a biodegradable polymer matrix for a series of different thickness polymers. Recent literature has implied that the diffusion of nutrients is a major factor that limits cell growth (Freed et al., 1994). In the present paper, a mathematical model is developed to directly relate the effects of increasing cell mass in the polymer matrix on the transport of nutrients. Reaction and diffusion of nutrients in the cell-polymer system are described using the fundamental species continuity equations and the volume averaging method. The volume averaging method is utilized to derive a single averaged nutrient continuity equation that includes the effective transport properties. This approach allows for the derivation of effective diffusion and rate coefficients as functions of the cell volume fraction. The cell volume fraction as a function of time is determined by solution of a material balance on cell mass. Growth functions including the Moser, a modified Contois, and an nth-order heterogeneous growth kinetic model are evaluated through a parameter analysis, and the results are compared to experimental data found in the literature. The results indicate that cellular functions in conjunction with mass transfer processes can account partially for the general trends in the cell growth behavior for various thickness polymers. The Contois growth function appeared to describe the data more accurately in terms of the lag period at early times and the long time limits. However, all kinetic growth functions required variations in the kinetic parameters to fully describe the effects of polymer thickness. This result implies that restricted diffusion of nutrients is not the sole factor limiting cell growth when the thickness of the polymer is changed. Therefore, further experimental data and model improvements are needed to accurately describe the cell growth process.

Animals↗
PubMed1996

Weighted-ensemble Brownian dynamics simulations for protein association reactions.

A new method, weighted-ensemble Brownian dynamics, is proposed for the simulation of protein-association reactions and other events whose frequencies of outcomes are constricted by free energy barriers. The method features a weighted ensemble of trajectories in configuration space with energy levels dictating the proper correspondence between "particles" and probability. Instead of waiting a very long time for an unlikely event to occur, the probability packets are split, and small packets of probability are allowed to diffuse almost immediately into regions of configuration space that are less likely to be sampled. The method has been applied to the Northrup and Erickson (1992) model of docking-type diffusion-limited reactions and yields reaction rate constants in agreement with those obtained by direct Brownian simulation, but at a fraction of the CPU time (10(-4) to 10(-3), depending on the model). Because the method is essentially a variant of standard Brownian dynamics algorithms, it is anticipated that weighted-ensemble Brownian dynamics, in conjunction with biophysical force models, can be applied to a large class of association reactions of interest to the biophysics community.

Algorithms↗
PubMed2003

Nonlinear parameter estimation for solution-diffusion models of membrane pervaporation.

An optimization-based procedure for estimating unknown parameters in solution-diffusion models of membrane pervaporation is presented. Permeation of two components through a polymer membrane is described by distinct solution and diffusion models. The solution model is based on a modified form of Flory-Huggins theory that accounts for interactions between the two penetrants. The diffusion model is derived from Fick's law, where the diffusion coefficients are allowed to depend on the local concentration of each component in the membrane. A phenomenologic relation is used to account for the effect of temperature on the component fluxes. The solution and diffusion models, as well as the temperature-flux relation, contain parameters that are not directly measurable. It is shown that these parameters can be estimated effectively from sorption and flux data by the solution of suitably formulated nonlinear optimization problems. The separation of styrene and ethylbenzene with a polyurethane membrane is used to illustrate the parameter estimation procedure.

Chemistry↗
PubMed2006

Computational model of interstitial transport in the spinal cord using diffusion tensor imaging.

Local drug delivery methods, including convection-enhanced delivery (CED), are being used to increase distribution in selected regions of nervous tissue. There is a need for 3D models that predict spatial drug distribution within these tissues. A methodology was developed to process magnetic resonance microscopy (MRM) and diffusion tensor imaging (DTI) scans, segment gray and white matter regions, assign tissue transport properties, and model the interstitial transport of macromolecules. Fiber tract orientation was derived from DTI data and used to assign directional dependence of hydraulic conductivity, K, and tracer diffusivity, Dt, transport tensors. Porous media solutions for interstitial fluid pressure, velocity, and albumin distribution were solved using a finite volume method. To test this DTI-based methodology, a rat spinal cord transport model was developed to simulate CED into the dorsal white matter column. Predicted distribution results correspond well with small volume (approximately 1 microl) trends found experimentally, although albumin loss was greater at larger infusion volumes (>2 microl). Simulations were similar to those using fixed transport properties due to the bulk alignment of white matter fibers along the cord axis. These findings help to validate the DTI-based methodology which can be applied to modeling regions where fiber tract organization is more complex, e.g., the brain.

Animals↗
PubMed2006

Detection of correlated dynamics on multiple timescales by measurement of the differential relaxation of zero- and double-quantum coherences involving sidechain methyl groups in proteins.

Multiple effects may lead to significant differences between the relaxation rates of zero-quantum coherences (ZQC) and double-quantum coherences (DQC) generated between a pair of nuclei in solution. These include the interference between the anisotropic chemical shifts of the two nuclei participating in formation of the ZQC or DQC, the individual dipolar interactions of each of the two nuclei with the same proton, and the slow modulation of the isotropic chemical shifts of the two nuclei due to conformational exchange. Motional events that occur on a timescale much faster than the rotational correlation time (ps-ns) influence the first two effects, while the third results from processes that occur on a far slower timescale (mus-ms). An analysis of the differential relaxation of ZQC and DQC is thus informative about dynamics on the fast as well as the slow timescales. We present here an experiment that probes the differential relaxation of ZQC and DQC involving methyl groups in protein sidechains as an extension to our recently proposed experiments for the protein backbone. We have applied the methodology to (15)N, (13)C-labeled ubiquitin and used a detailed analysis of the measured relaxation rates using a simple single-axis diffusion model to probe the motional restriction of the C(next)H(next) bond vector where C(next) is the carbon that is directly bonded to a sidechain methyl carbon (C(methyl)). Comparison of the present results with the motional restriction of the C(next)C(methyl) bond (S(axis)(2)) reveals that the single-axis diffusion model, while valid in the fringes of the protein and for shorter chain amino acids, proves inadequate in the central protein core for long chain, asymmetrically branched amino acids where more complex motional models are necessary, as is the inclusion of the possibility of correlation between multiple motional modes. In addition, the present measurements report on the modulation of isotropic chemical shifts due to motion on the mus-ms timescale. Three Leu residues (8, 50, and 56) are found to display these effects. These residues lie in regions where chemical shift modulation had been detected previously both in the backbone and sidechain regions of ubiquitin.

Anisotropy↗
PubMed1986

Radial and longitudinal compartmental analysis of gas transport during high-frequency ventilation.

A model of gas exchange by low-tidal-volume (VT), high-frequency ventilation (HFV) is presented, based on the physical principles of dispersion. These are the nonuniformity of the velocity profile and the nonreversible mixing of fluid components in a diffusive manner. A numerical method was used to incorporate these principles into a quantitative model. The airways of a symmetrically bifurcating bronchial-tree model were partitioned in the radial direction into two concentric layers representing the kinematic dispersion by nonuniformity of the velocity profile. Mixing between the layers was invoked in proportion to the diffusivity and local dimensions. The effects of frequency (f), VT, shape of the velocity profile, and bronchial-model configuration were tested in the model, with favorable comparison to available experimental data. The model predicts that for a frequency-dependent velocity profile, the rate of tracer exchange is proportional to the square root of f and to the square of VT-V0, where V0 is a constant small volume under which gas exchange was nil. Intracycle asymmetric mixing is predicted to have a stronger effect on gas exchange than asymmetric velocity profile. Gas exchange when turbulent-flow regime is assumed is predicted to be less for the higher VT values than with laminar flow and with mixing by molecular diffusivity. This model was found to be didactic, flexible, and capable of modeling combinations of factors affecting either one of the two fundamental processes of dispersion.

Animals↗
PubMedDate not supplied

A theoretical model for intraperitoneal delivery of cisplatin and the effect of hyperthermia on drug penetration distance.

A theoretical model for the intraperitoneal (i.p.) delivery of cisplatin and heat to tumor metastases in tissues adjacent to the peritoneal cavity is presented. The penetration distance (the depth to which drug diffuses directly from the cavity into tissues) is predicted to be on the order of 0.5 mm. The model shows that exchange with the microvasculature has more effect than cellular uptake in limiting the penetration distance. Possible effects of hyperthermia are simulated, including increased cell uptake of drug, increased cell kill at a given level of intracellular drug, and decreased microvascular density. The model suggests that the experimental finding of elevated intracellular platinum levels up to a depth of 3 to 5 mm when drug is delivered i.p. by a heated infusion solution is due to penetration of heat to this distance, causing increased cell uptake of drug. Beyond a depth of about 0.5 mm, the drug is delivered mainly through the circulation. Use of sodium thiosulfate to deactivate systemic cisplatin may therefore be counterproductive when heat is delivered locally. The model suggests that i.p. delivery of heat, combined with systemic delivery of drug, may be as effective as i.p. delivery of heat and drug.

Animals↗
PubMed1979

Preaggregative cell motion in Dictyostelium.

The motions of a large number (495) of preaggregative D. discoideum NC-4 cells in sparse fields are recorded on time-lapse film and analysed using a specially constructed computer graphics system. All films are produced under a standard set of conditions, so that the range of cell behaviours under given conditions can be characterized. The mean velocity of pre-aggregative D. discoideum NC-4 is 7.19 micrometers/min. The mean velocity time course has a significant early peak at about 3 h. The distribution of mean velocities is fairly broad with a long high velocity tail. A modified random walk model using the parameters diffusion constant and persistence time describes well the changes in cell direction with time. Persistence can be described as an exponentially distributed 'memory' of movement direction, with a mean of 4.89 min. High velocity cells never have long persistence times, and persistence time shows no relationship with age. A nearest neighbour model of cell spacing shows that cells are randomly (Poisson) distributed at low densities. Measurements of cell contacts are compared to a simple model of contact frequency based on the kinetic theory of gases to show that cells at low densities have an affinity for making collisions. The length of contact durations is indicative of some mechanical adhesion between cells, and cells in contact move significantly though not dramatically slower. A cross-correlation analysis shows that the various parameters of motion are significantly interrelated in numerous ways. Finally mutants and strains related to D. discoideum NC-4 exhibit a number of new behaviours, suggesting that motion is a distinctive characteristic of cell type.

Agglutination↗
PubMed1997

A mechanistic study of griseofulvin dissolution into surfactant solutions under laminar flow conditions.

The in vivo dissolution of many poorly soluble drugs is enhanced by the action of surfactants secreted into the upper gastrointestinal (GI) tract. These substances may act by solubilizing individual drug molecules into two separate liquid phases: the free aqueous phase and a micellar phase in which the drug is incorporated into a complex of two or more surfactant molecules. This complex process, micellar solubilization, was the subject of this in vitro study, wherein griseofulvin (gris) dissolution was observed in flowing surfactant solutions. Aqueous solutions of sodium dodecyl sulfate (SDS), an anionic surfactant, were pumped over a gris tablet embedded in a laminar flow device to simulate flow in the human upper GI tract. SDS solutions were well above the critical micellar concentration (cmc approximately 6-7 mM), and flow rates ranged from 4 to 7 mL/min. Gris solubility in premicellar (4 mM), near-micellar (6 mM), and micellar (>6 mM) SDS solutions was also determined. The measured solubility of gris increased linearly with SDS concentrations above the cmc. Drug solubility in SDS concentrations below the cmc was also higher than that in water. Gris diffusion coefficients were measured using pulsed-field gradient NMR spectroscopy. To determine the controlling mechanism for surfactant-enhanced dissolution, a mathematical model was developed. The model solution, an equation for drug dissolution rate, was compared with experimental data to demonstrate that drug transport away from the solid surface is the slow step in the process. Measured gris diffusion coefficients and solubility values were used as constants in the mathematical model solution and were combined to calculate an effective gris diffusion coefficient. Using these experimentally determined properties, model-calculated dissolution rates were within 7% of the measured values. As hypothesized, dissolution rates were found to be directly proportional to the transport properties of the system (effective drug diffusion coefficient and fluid flow rate) as well as to the drug solubility. To further verify transport-limited dissolution, the measured dissolution rates were found to be proportional to the surrounding medium flow rate to the 1/3 power, as predicted by the model dissolution rate equation.

Antifungal Agents↗
PubMed2002

Orientational diffusion reflects fiber structure within a voxel.

Several new MR techniques have been introduced to infer direction through diffusion in multiple nerve fiber bundles within a voxel. To date, however, there has been no physical model reported to evaluate these methodologies and their ability to determine fiber orientation. In this article a model of diffusion analogous to nerve fibers is presented. Diffusion measurements at multiple closely spaced angles of 15 degrees in samples with different fiber orientations are compared with theoretical calculations for restricted diffusion in cylindrical geometry. Orientational diffusion measurements are shown to reflect fiber geometry and theoretical predictions to within 10%. Simulations of fiber crossings within a voxel suggest fiber orientation does not correspond to the direction of the largest measured diffusion coefficient, but theoretical knowledge of signal decay curves can predict the shape of these diffusion coefficient contours for given fiber orientation probabilities.

Anisotropy↗