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Results for “directional diffusion models”

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PubMed2005

Solubilization of selected free fatty acids in palm oil by biodegradable ethoxylated surfactants.

The solubilization of three major components, viz., palmitic, oleic, and linoleic acids, in palm oil by ethoxylated surfactants was investigated. The results were analyzed in terms of the molecular properties of surfactants and free fatty acids (FFAs). It was found that the solubilities of these FFAs in various micellar solutions depend not only on their octanol-water partition coefficients (Kow), but also on their physicochemical properties. The study on the solubilization kinetics was conducted by choosing palmitic acid as a model solubilizate and Tergitol 15-S-7 as the model surfactant. A first-order film diffusion model, which accounts for the direct uptake of organic molecules at a solid surface into surfactant micelles, was adopted to analyze the effect of surfactant on dissolution of palmitic acid. It was observed that the presence of surfactant reduced the mass-transfer coefficient. Instead, the overall mass-transfer rate was enhanced because of the much higher driving force from the increased solubilization capacity.

Biodegradation, Environmental↗
PubMed2001

Characterization of patterned irregularity in locally interacting, spatially extended systems: Ventricular fibrillation.

The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation are produced by abnormal spatio-temporal patterns of propagation in the ventricular myocardium. These behaviors can be described by solutions of reaction-diffusion equation excitable medium models. The direct comparison of such solutions with existing experimental observations is virtually impossible as there are too many factors to be taken into account, including not only the complicated dynamics of the re-entrant waves of excitation in the tissue, but also the way the appearance of these waves on the surface is modified by the inhomogeneity, anisotropy and three-dimensional nature of heart tissue. One way of indirect comparison is to compare characteristics of the complexity of the model and the real data, that are invariant under these modifications of the signal. Karhunen-Loeve decomposition is a standard tool for evaluating the complexity of multidimensional signals. A comparison of the separate and conjoint complexities of the signals on the opposite sides of the preparation can be considered as an indicator how much three-dimensional effects are essential in the preparation behavior. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2005

Extracellular space diffusion in central nervous system: anisotropic diffusion measured by elliptical surface photobleaching.

Diffusion in the extracellular space (ECS) is crucial for normal central nervous system physiology. The determinants of ECS diffusion include viscous interactions with extracellular matrix/plasma membranes ("viscosity") and ECS geometry ("tortuosity"). To resolve viscosity versus tortuosity effects, we measured direction-dependent (anisotropic) diffusion in ECS in mouse spinal cord by photobleaching using an elliptical spot produced by a cylindrical lens in the excitation path. Anisotropic diffusion slowed fluorescence recovery when the long axis of the ellipse was parallel versus perpendicular to the direction of faster diffusion. A mathematical model was constructed to deduce diffusion coefficients (D(x), D(y)) from fluorescence recovery measured for parallel and perpendicular orientations of the long axis of the ellipse. Elliptical spot photobleaching was validated by photobleaching aqueous-phase fluorophores on a diffraction grating, where diffusion is one-dimensional. Measurement of the diffusion of 70 kDa FITC-dextran in spinal cord in living mice indicated that viscosity slows diffusion by approximately 1.8-fold compared with its diffusion in solution. ECS geometry hinders diffusion across (but not along) axonal fibers in spinal cord further by approximately fivefold. In cerebral cortex, however, approximately 50% of the hindrance to ECS diffusion comes from viscosity and approximately 50% from tortuosity. We suggest that the extracellular matrix might have evolved to facilitate rather than hinder diffusion even for large molecules.

Animals↗
PubMed1995

A biophysical model of passive and polarized active transport processes in Caco-2 cells: approaches to uncoupling apical and basolateral membrane events in the intact cell.

This report is aimed at the biophysical modeling of transmembrane events involving a passive diffusion and directional pumplike mechanism at the apical (AP) and basolateral (BL) membranes of cultured cell monolayers. The essence of the model is based on experimental evidences for the existence of a saturable, apically polarized transport system in Caco-2 cells for peptides which hindered apical to basolateral flux, enhanced basolateral to apical flux, and showed substrate specificity. This system was further inhibited by verapamil, suggesting some homology with P-glycoprotein, the principal mediator of drug resistance in multidrug resistant cancer cells. Preliminary evidence was also obtained suggesting an additional polarized uptake system for the same peptides in the basolateral membrane. Upon saturation and/or inhibition of the active transport mechanisms with verapamil, the peptide fluxes in apical-to-basolateral direction and the basolateral-to-apical direction converged and became controlled by the passive mechanism. Since the intent of the modeling was to provide useful templates for the design of probing experiments and to delineate and quantify mass transfer mechanisms at the AP and BL membranes and their interrelationships, theoretical equations were developed for a host of kinetic boundary conditions: (a) AP-->BL and BL-->AP transfluxes, (b) bidirectional effluxes from substrate-preloaded cells, (c) undirectional efflux across the AP or BL membrane from preloaded cells, and (d) uptake kinetics via the AP or BL membrane leading to equilibrium. Furthermore, flux expressions were reduced to membrane permeability coefficients to accommodate passive diffusion, saturation, inhibition, and directionality. The diffusional mass transport resistances of the aqueous boundary layers and microporous filter support of the cell monolayer were necessarily included.

Amino Acid Sequence↗
PubMed1996

Diffusion of six surgical endoscopic procedures in the Netherlands. Stimulating and restraining factors.

The diffusion of six surgical endoscopic procedures in the Netherlands was investigated. Questionnaires were sent to 138 laparoscopic surgeons. They were asked which of the following laparoscopic procedures they had adopted in their hospital: cholecystectomy, appendicectomy, Nissen fundoplication, inguinal hernia repair, large bowel resection and thoracoscopic procedures. Furthermore, they were asked to indicate the influence of 13 pre-defined factors: "budget', "competition', "conference', "extra benefit', "media', "nature of the technology', "patient demand', "planning/logistics', "reimbursement', "service industry', "support industry', "surgical technique' and "training/course' on the adoption of those procedures. The adoption rates for the procedures were: 100%, 69%, 19%, 43%, 19% and 52%, respectively. In general, factors were assessed more positively by adopters than by non-adopters. Significant differences were mainly found for "extra benefit', "nature of the technology', "surgical technique' and "conference'. The surgeon's perception of the additional benefits of an endoscopic technique and, to a lesser degree, of its technical aspects were the most important factors in deciding whether or not to adopt a procedure. In an ideal diffusion model, a description is given of when and how the 13 factors can influence the diffusion of an endoscopic procedure in the desired direction. In this model, the extra benefit of a new procedure must be proven before other factors are allowed to influence the diffusion.

Budgets↗
PubMed1999

Influence of enzyme distribution and diffusion on permeation profile of prodrug through viable skin: theoretical aspects for several steady-state fluxes in two transport directions.

A physical modeling and theoretical simulation aspect for the simultaneous transport and metabolism of prodrug in viable skin were described to understand the influence of enzyme distribution and diffusion. The physical model was formulated assuming that the viable epidermis and dermis have distinct diffusional and metabolic characteristics and that the metabolic reaction in each layer follows a first-order kinetics. The differential equations were analytically solved, and the steady-state flux of prodrug into receiver and that of metabolite into receiver and donor and the total flux in forward (epidermis to dermis) and backward (dermis to epidermis) directions were derived. The flux of prodrug in the forward direction always equals that in the backward direction. The metabolite flux into receiver became transport direction-dependent when the diffusional characteristic of epidermis was different from that of dermis regardless of enzyme distribution. The metabolite flux into donor in the backward direction relative to that in the forward direction increased with increase of dermis/epidermis ratio of any parameters among metabolic rate constant, partition coefficient and diffusion coefficient of prodrug and metabolite. The difference of total flux between the 2 transport directions was caused by the difference in metabolic rate constant, partition coefficient and diffusion coefficient of prodrug between epidermis and dermis. The higher any parameters were for dermis, the higher was total flux in the backward direction.

Biological Transport↗
PubMed2026

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

Models, Biological↗
PubMed2003

Modelling of silica diffusion experiments with 32Si in Boom Clay.

A mathematical model describing the dissolution of nuclear glass directly disposed in clay combines a first-order dissolution rate law with the diffusion of dissolved silica in clay. According to this model, the main parameters describing the long-term dissolution of the glass are etaR, the product of the diffusion accessible porosity eta and the retardation factor R, and the apparent diffusion coefficient D(app) of dissolved silica in clay. For determining the migration parameters needed for long-term predictions, four Through-Diffusion (T-D) experiments and one percolation test have been performed on undisturbed clay cores. In the Through-Diffusion experiments, the concentration decrease after injection of 32Si (radioactive labelled silica) was measured in the inlet compartment. At the end of the T-D experiments, the clay cores were cut in thin slices and the activity of labelled silica in each slice was determined. The measured activity profiles for these four clay cores are well reproducible. Since no labelled silica could be detected in the outlet compartments, the Through-Diffusion experiments are fitted by two In-Diffusion models: one model assuming linear and reversible sorption equilibrium and a second model taking into account sorption kinetics. Although the kinetic model provides better fits, due to the sufficiently long duration of the experiments, both models give approximately similar values for the fit parameters. The single percolation test leads to an apparent diffusion coefficient value about two to three times lower than those of the Through-Diffusion tests. Therefore, dissolved silica appears to be strongly retarded in Boom Clay. A retardation factor R between 100 and 300 was determined. The corresponding in situ distribution coefficient K(d) is in the range 25-75 cm(3) g(-1). The apparent diffusion coefficient of dissolved silica in Boom Clay is estimated between 2 x 10(-13) and 7 x 10(-13) m(2) s(-1). The pore diffusion coefficient is in the range from 6 x 10(-11) to 1 x 10(-10) m(2) s(-1).

Aluminum Silicates↗
PubMed2005

Inferences about information flow and dispersal for spatially extended population systems using time-series data.

This work explores an information-theoretic approach to drawing inferences about coupling of spatially extended ecological populations based solely on time-series of abundances. The efficacy of the approach, time-delayed mutual information, was explored using a spatially extended predator-prey model system in which populations at different patches were coupled via diffusive movement. The approach identified the relative magnitude and direction of information flow resulting from animal movement between populations, the change in information flow as a function of distance separating populations, and the diffusive nature of the information flow. In addition, when the diffusive movement was eliminated from the model, mutual information correctly provided no evidence of information flow, even when population synchrony was generated by a common environmental driving function. Thus, for this model system, time-delayed mutual information was useful in discriminating between the Moran effect and animal movement as causes of population synchrony, as well as in characterizing dispersal in terms of direction, relative speed and diffusive nature.

Computer Simulation↗
PubMed2001

Importance of needle age and shoot structure on canopy net photosynthesis of balsam fir (Abies balsamea): a spatially inexplicit modeling analysis.

We have developed a spatially inexplicit model of canopy photosynthesis for balsam fir (Abies balsamea (L.) Mill.) that accounts for key processes of light-shoot interaction including irradiance interception by the shoot, spatial aggregation of shoots into branches and crowns, the differential propagation of diffuse and direct light within the canopy, and an ideal representation of penumbra. Also accounted for in the model are the effects of the average radiative climate and shoot age on needle retention, light interception, and photosynthetic capacity. We used reduced versions of this model to quantify the effects of simplifying canopy representation on modeled canopy net photosynthesis. Simplifications explored were the omission of direct beam transformation into penumbral light and the use of different constant shoot properties throughout the canopy. The model was parameterized for a relatively dense balsam fir stand (leaf area index of 5.8) north of Québec City, Canada, and run using hourly meteorological data obtained at the site. The overall performance of the complete model was satisfactory, with maximum values of canopy net photosynthesis of 23 micromol (m(2) ground)(-1) s(-1) (83 mmol m(-2) h(-1)), and a near-saturation of the canopy at a photosynthetically active radiation photon flux density of about 750 micromol m(-2) s(-1) (2.7 mol m(-2) h(-1)). The omission of penumbral effects through the use of unattenuated direct (beam) radiation at all layers of the canopy, as used for broad-leaved species, reduced canopy net photosynthesis by 3.7%. Analysis of the results show that the small impact of penumbra on canopy net photosynthesis stems from the high proportion of diffuse radiation (73%) estimated from our meteorological data set; single-hour results under clear sky conditions approach theoretical bias values of about 30%. Use of mean shoot photosynthetic, light capture and light transmission properties throughout the canopy biased canopy net photosynthesis by less than 3%. However, simulations carried out based on properties of 1-year-old shoots throughout the canopy overestimated canopy net photosynthesis by 9%. Use of the shoot as our smallest functional unit was a potential source of bias because the differential absorption of direct and diffuse radiation within the shoot could not be factored into the model. Other sources of potential bias are discussed.

Abies↗
PubMed1995

Assessment of a model for measuring drug diffusion through implant-generated fibrous capsule membranes.

Fibrous tissue, which encapsulates subcutaneously implanted silastic, vinyl, polyurethane and Teflon discs in rats, has been isolated, characterized and tested for drug permeability in order to develop an in vitro model for determining the effect of this tissue on drug disposition from implant sites. With all materials, capsule tissue thickness and collagen content (approximately 59%) was consistent from 2 to 4 months after implantation. Silastic implants afforded the most consistent and usable tissue in terms of thickness and lack of vascularity, and these capsule membranes were used for determining the transport of three model compounds in an in vitro diffusion cell model. The rank ordering of permeability through these membranes was estrone (60.2 x 10(-6) cm s-1) > 3-O-methylglucose (18.7 x 10(-6) cm s-1) > dextran of molecular weight 70 000 (5.6 x 10(-6) cm s-1), which is consistent with expectations based on the molecular weights and partitioning behaviour of the model compounds. The results of these studies indicate that implant-generated encapsulating membranes can be successfully isolated and employed to study drug diffusion in an in vitro model, providing a direct assessment of the barrier properties of encapsulating membranes.

3-O-Methylglucose↗
PubMed2005

Calculating spatial statistics for velocity jump processes with experimentally observed reorientation parameters.

Mathematical modelling of the directed movement of animals, microorganisms and cells is of great relevance in the fields of biology and medicine. Simple diffusive models of movement assume a random walk in the position, while more realistic models include the direction of movement by assuming a random walk in the velocity. These velocity jump processes, although more realistic, are much harder to analyse and an equation that describes the underlying spatial distribution only exists in one dimension. In this communication we set up a realistic reorientation model in two dimensions, where the mean turning angle is dependent on the previous direction of movement and bias is implicitly introduced in the probability distribution for the direction of movement. This model, and the associated reorientation parameters, is based on data from experiments on swimming microorganisms. Assuming a transport equation to describe the motion of a population of random walkers using a velocity jump process, together with this realistic reorientation model, we use a moment closure method to derive and solve a system of equations for the spatial statistics. These asymptotic equations are a very good match to simulated random walks for realistic parameter values.

Animals↗
PubMed1996

Metabolite channeling in the origin of life.

A central question in the origin of life concerns whether primitive metabolites and catalysts interacted randomly in solution, as often envisaged, or whether they were arranged from the start in ordered metabolic complexes. The latter possibility would be consistent with the hypothesis of metabolite channeling in extant cells, which holds that intermediates in many pathways are transferred directly, without diffusion, between pathway enzymes. A model on this basis is proposed in which life originated autotrophically de novo in metabolic complexes organized on FeS2 (pyrite) mineral surfaces. Because metabolites and catalysts arose at specific sites in these complexes, they could interact specifically with neighbouring species in evolving pathways prior to the existence of protein enzymes with precise substrate binding sites. In successive stages, RNA catalysts and protein enzymes could be incorporated in these arrays. The overall process may be viewed as a molecular analogue of embryonic development, with the formation and positioning of each new component continuously transforming the whole. A corollary of the hypothesis relates to the evolution of translation and the genetic code. By virtue of channeling, biosynthetically related amino acids (e.g., aspartic acid and threonine) would have arisen close together in the complex. A second premise is that tRNAs with similar base sequences, and thus similar anticodons, were also clustered together in the complex and channeled to adjacent sites. As a result of these combined effects, tRNAs with similar anticodons would necessarily have been positioned close to, and thus more likely to have been charged with, metabolically related amino acids. This mechanism affords a new rationale for the observed codon structure of the genetic code, in which biosynthetically related amino acids possess similar codons.

Animals↗
PubMed2001

Leaf area distribution and radiative transfer in open-canopy forests: implications for mass and energy exchange.

Leaf area and its spatial distribution are key canopy parameters needed to model the radiation regime within a forest and to compute the mass and energy exchange between a forest and the atmosphere. A much larger proportion of available net radiation is received at the forest floor in open-canopy forests than in closed-canopy forests. The proportion of ecosystem water vapor exchange (lambda E) and sensible heat exchange from the forest floor is therefore expected to be larger in open-canopy forests than in closed-canopy forests. We used a combination of optical and canopy geometry measurements, and robust one- and three-dimensional models to evaluate the influence of canopy architecture and radiative transfer on estimates of carbon, water and energy exchange of a ponderosa pine (Pinus ponderosa Dougl. ex Laws.) forest. Three-dimensional model simulations showed that the average probability of diffuse and direct radiation transmittance to the forest floor was greater than if a random distribution of foliage had been assumed. Direct and diffuse radiation transmittance to the forest floor was 28 and 39%, respectively, in the three-dimensional model simulations versus 23 and 31%, respectively, in the one-dimensional model simulations. The assumption of randomly distributed foliage versus inclusion of clumping factors in a one-dimensional, multi-layer biosphere-atmosphere gas exchange model (CANVEG) had the greatest effect on simulated annual net ecosystem exchange (NEE) and soil evaporation. Assuming random distribution, NEE was 41% lower, net photosynthesis 3% lower, total lambda E 10% lower, and soil evaporation 40% lower. The same comparisons at LAI 5 showed a similar effect on annual NEE estimates (37%) and lambda E (12%), but a much larger effect on net photosynthesis (20%), suggesting that, at low LAI, canopies are mostly sunlit, so that redistribution of light has little effect on net photosynthesis, whereas the effect on net photosynthesis is much greater at high LAIs.

Biomass↗
PubMed2004

Modeling of submicrometer aerosol penetration through sintered granular membrane filters.

We present a deep-bed aerosol filtration model that can be used to estimate the efficiency of sintered granular membrane filters in the region of the most penetrating particle size. In this region the capture of submicrometer aerosols, much smaller than the filter pore size, takes place mainly via Brownian diffusion and direct interception acting in synergy. By modeling the disordered sintered grain packing of such filters as a simple cubic lattice, and mapping the corresponding 3D connected pore volume onto a discrete cylindrical pore network, the efficiency of a granular filter can be estimated, using new analytical results for the efficiency of cylindrical pores. This model for aerosol penetration in sintered granular filters includes flow slip and the kinetics of particle capture by the pore surface. With a unique choice for two parameters, namely the structural tortuosity and effective kinetic coefficient of particle adsorption, this semiempirical model can account for the experimental efficiency of a new class of "high-efficiency particulate air" ceramic membrane filters as a function of particle size over a wide range of filter thickness and texture (pore size and porosity) and operating conditions (face velocity).

Journal Article↗
PubMed2006

Wave-front dynamics in systems with directional anomalous diffusion.

In this paper we study the solutions of a generalized reaction-diffusion system with a bistable reaction term, and considering directional anomalous diffusion. We use the well-known properties of fractional derivatives to model asymmetric anomalous diffusion, and obtain traveling wave solutions that propagate in a direction that depends on the metastability of the front, the fractional exponent and the asymmetry of the diffusion.

Journal Article↗
PubMed2004

Chirality of electrodeposits grown in a magnetic field.

Electrodeposits grown around a point cathode in a flat, horizontal electrochemical cell have fractal form. When grown in the presence of a perpendicular applied magnetic field, the deposits develop a spiral structure with chirality which reverses on switching the field direction. These structures are modeled numerically using biased variants of the diffusion limited aggregation (DLA) model. The effects of electric and magnetic fields are modeled successfully by varying the probabilities that a random walker will move in a given direction as a result of a Coulomb force and the Lorentz force-induced flow of electrolyte past the deposit surface. By contrast, a numerical model which considers only the effect of the Lorentz force on individual ions, without reference to the surface of the growing deposit, produces spiral structures with incorrect chirality. The modified DLA model is related to the differential equations for diffusion, migration, and convection. Length scales in the problem are understood by associating the step length of the random walker with the diffusion layer thickness, the lookup radius with the hydrodynamic boundary layer thickness and a point on the numerical deposit with a nucleation center for growth of a crystallite.

Journal Article↗
PubMed2005

The diffusive vesicle supply center model for tip growth in fungal hyphae.

We propose the diffusive vesicle supply center model for tip growth in fungal hyphae. The model is based on the three-dimensional vesicle supply center (VSC) model [Gierz, G., Bartnicki-García, S., 2001. A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept: J. Theor. Biol. 208, 151-164], but incorporates two aspects of a more realistic vesicle delivery mechanism: vesicle diffusion from the VSC and a finite rate constant for vesicle fusion with the cell membrane. We develop a framework to describe tip growth for a general class of models based on the vesicle supply center concept. Combining this with a method for calculating the steady state distribution of diffusive vesicles we iteratively solve for stationary cell shapes. These show a blunter tip than predicted by the original VSC model, which we attribute to increased forward-directed vesicle delivery via diffusion. The predicted distance between the VSC and the utmost tip of the cell is set by the ratio between the diffusion constant and the rate constant for vesicle exocytosis. Combined with the cell radius, these define the only dimensionless parameter for our model.

Cytoplasmic Vesicles↗