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PubMed1999

Ultrastructural model for size selectivity in glomerular filtration.

A theoretical model was developed to relate the size selectivity of the glomerular barrier to the structural characteristics of the individual layers of the capillary wall. Thicknesses and other linear dimensions were evaluated, where possible, from previous electron microscopic studies. The glomerular basement membrane (GBM) was represented as a homogeneous material characterized by a Darcy permeability and by size-dependent hindrance coefficients for diffusion and convection, respectively; those coefficients were estimated from recent data obtained with isolated rat GBM. The filtration slit diaphragm was modeled as a single row of cylindrical fibers of equal radius but nonuniform spacing. The resistances of the remainder of the slit channel, and of the endothelial fenestrae, to macromolecule movement were calculated to be negligible. The slit diaphragm was found to be the most restrictive part of the barrier. Because of that, macromolecule concentrations in the GBM increased, rather than decreased, in the direction of flow. Thus the overall sieving coefficient (ratio of Bowman's space concentration to that in plasma) was predicted to be larger for the intact capillary wall than for a hypothetical structure with no GBM. In other words, because the slit diaphragm and GBM do not act independently, the overall sieving coefficient is not simply the product of those for GBM alone and the slit diaphragm alone. Whereas the calculated sieving coefficients were sensitive to the structural features of the slit diaphragm and to the GBM hindrance coefficients, variations in GBM thickness or filtration slit frequency were predicted to have little effect. The ability of the ultrastructural model to represent fractional clearance data in vivo was at least equal to that of conventional pore models with the same number of adjustable parameters. The main strength of the present approach, however, is that it provides a framework for relating structural findings to the size selectivity of the glomerular barrier.

Animals↗
PubMedDate not supplied

[Discrete probability of a model for information provision on early embryonic development].

A percolation model of the diffuse redistribution of morphogenetic information in early regulative development is analyzed. It is demonstrated that the statistical average values of cell connectedness remaining below the percolation threshold of the spatial redistribution of developmental determinants do not provide for the formation of cell structures of the necessary size. The average number of cell interactions should exceed the percolation threshold, and, therefore, the carriers of morphogenetic information in early development can move over distances comparable with the size of the entire embryo. The assumption concerning the percolation mechanism of cell death is used as a basis for estimating the statistical average value of cell connectedness at which the predicted number of cells theoretically isolated from the flow of signal molecules corresponds to the observed frequencies of dying embryonic cells. The estimated average number of cell interactions significantly exceeds the threshold of information resource percolation in the embryonic space and agrees with estimations of other authors, based on direct observations. The probable role of the diffusion front, or percolation cluster shell, in the regionalization of embryonic structures differing in their prospective values is discussed. It is shown that the duration of the communicative period, along with the statistical average number of channels providing for the intercellular transfer of signal molecules by diffusion, is a parameter controlling the processes of determination of embryonic structures.

Embryo, Mammalian↗
PubMed2001

Present state and future directions of modeling of geochemistry in hydrogeological systems.

A first step towards understanding and controlling the fate and dissemination of radioactive waste is to create a concise and comprehensive theoretical framework for the rather non-linear processes involved--hence, the need for geochemical models. Two classes of geochemical models are commonly used, i.e., static and hydrodynamic models. In contrast to static models, hydrodynamic models combine geochemical reactions with hydrogeological processes such as ground-water flow, diffusion and dispersion. In this review, we examine the present state of geochemical models in terms of included processes, thermodynamic databases, missing phenomena, numerical behavior and performance. It is shown that over the past decade, significant progress has been made with respect to modeling of geochemistry in hydrodynamic systems: this is illustrated by describing several applications. Finally, we focus on the perspectives of geochemical modeling in the assessment of the safety of nuclear waste disposal.

Colloids↗
PubMed1994

Research on health-related quality of life: dissemination into practical applications.

Strategies and processes for the effective dissemination and diffusion of research findings on health-related quality of life (HQL) into practical applications were explored at a workshop held in Montreal in April, 1994. A conceptual model for dissemination and diffusion of evidence about HQL was used to identify five different target groups: HQL assessors, policy makers, planners of clinical trials, developers of clinical practice guidelines, and those at the level of patient-practitioner clinical decision making. A framework designed to facilitate the translation of fundamental research knowledge into effective action was then used as a starting point for discussions about priorities for research on HQL. The most important problem identified at the workshop was how best to strike an appropriate balance between priorities deemed to be important to those directly involved in HQL research, and priorities deemed to be important to potential users of the results of HQL research?

Algorithms↗
PubMed2002

Human skin penetration of flufenamic acid: in vivo/in vitro correlation (deeper skin layers) for skin samples from the same subject.

Previously, the interest in in vivo/in vitro correlations in the dermal field of research has increased steadily. Unfortunately, in most cases the skin from different human donors was taken for in vivo and in vitro experiments, which led to problems concerning the interindividual variability of the skin. Therefore, we established a methodology to utilize the same skin for both sets of data. In time dependency, drug amounts in the stratum corneum and the deeper skin layers were determined from eight donors using the same skin area for in vivo and the corresponding in vitro tests. Penetration experiments were carried out with the lipophilic drug flufenamic acid dissolved in wool alcohols ointment as the model formulation, which was administered to the skin under "infinite dose" conditions. At different time points prior to starting the surgery, the drug preparation was applied topically on the edges of the skin area, which was planned for excision using Finn chambers. After anesthetizing the patient and disinfecting the operation area, the incubated skin pieces were cut off first and immediately frozen to limit further drug diffusion. In vitro experiments were performed on the remaining skin flap, using two different test systems, a penetration and a permeation model. At the end of all experiments (in vivo and in vitro) the skin specimens were segmented horizontally and the drug was extracted and quantified. The in vivo and in vitro drug amounts in the stratum corneum and the deeper skin layers, respectively, were compared. The inevitable use of unknown volumes of disinfectant in vivo (medical reasons) might be the reason why a correlation failed for the stratum corneum. Nevertheless, for both in vitro test systems a direct linear correlation was found for the deeper skin layers, which showed slopes of a = 3.2272 +/- 0.3933 (penetration model vs in vivo) and a = 1.7776 +/- 0. 1926 (permeation model vs in vivo). This difference demonstrates the varying influence of the test systems and represents a factor about which in vivo and in vitro data are shifted against each other. As far as the model drug flufenamic acid is concerned, this methodology represents a tool to predict drug penetration into the deeper skin layers in vivo after carrying out corresponding in vitro experiments. Therefore, the potential is given to reduce the number of in vivo experiments, the risk for the volunteers, and the costs for the development of new drug preparations.

Administration, Topical↗
PubMedDate not supplied

Simulated lipoprotein transport in the wall of branched arteries.

Study of arterial blood flow dynamics improves our understanding of the development of cardiovascular diseases such as atherosclerosis. The transport and accumulation of macromolecules in the arterial wall can be influenced by local fluid mechanics. We used numeric simulations to investigate such transport in a T-junction model. Presumably an in vitro experiment would consist of gel segments inserted in the walls of a mechanical flow T-junction model near branch points where separation and recirculation zones are expected. The transport of low density lipoprotein (LDL) was investigated theoretically at these sites in a two dimensional numeric T-branch model. In the numeric model, the hydraulic conductivity of the porous gel wall segments was varied for a fixed species diffusivity to provide simulations with wall transmural Peclet numbers ranging from 0.3 to 30. Steady state flow patterns in the lumen of the two dimensional T-branch were simulated at Reynolds numbers of 250 and 500, using the software package FIDAP 7.61 to implement the finite element method. The simulations demonstrated that wall Peclet numbers greater than 1.0 were needed to achieve species concentration gradients within the wall that varied in the axial direction, thereby reflecting the influence of disturbed flow and pressure patterns in the lumen. As expected, the transmural concentration gradients were steeper when convection predominated. Blood flow in the lumen can influence the distribution of macromolecules in the arterial wall and needs to be investigated for the relevance to atherosclerosis.

Arteries↗
PubMed2004

Probing microscopic diffusion by 2-photon flash photolysis: measurement of isotropic and anisotropic diffusion in lens fiber cells.

Two-photon excited flash photolysis (TPEFP) was used to photorelease caged fluorescein in test solutions and inside fiber cells of the eye lens. Accurate alignment between the focus of the IR beam and the probe beam from the confocal microscope was achieved with an accessory focussing lens and computer models of diffusion were fit to experimental data to extract apparent diffusion coefficients. Inside a fiber cell, the diffusion coefficient for fluorescein was 4 x 10(-7) cm(2)/s at 21 degrees C, a value an order of magnitude lower than observed in free solution. Fluorescence also diffused between fiber cells via gap junctions. In the periphery, diffusion between cells occurred mainly in a radial direction while deep in the lens the diffusion between cells appeared more isotropic. Diffusion between cells was slower than inside cells and corresponded to less than approximately 1% of the area between cells being available for diffusion. This value is in good agreement with that expected from measurements of gap junction structure and packing density if a 1-1.5-nm aqueous gap junction pore is nearly always open.

Animals↗
PubMed2004

A new interpretation of the Keller-Segel model based on multiphase modelling.

In this paper an alternative derivation and interpretation are presented of the classical Keller-Segel model of cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a population of cells moves through a fluid containing a diffusible chemical to which the cells are attracted. The cells and fluid are viewed as distinct components of a two-phase mixture. The principles of mass and momentum balance are applied to each phase, and appropriate constitutive laws imposed to close the resulting equations. A key assumption here is that the stress in the cell phase is influenced by the concentration of the diffusible chemical. By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. These equations may be written in the form of the Patlak-Keller-Segel model, naturally including density-dependent nonlinearities in the cell motility coefficients. There is a direct relationship between the random motility and chemotaxis coefficients, both depending in an inter-related manner on the chemical concentration. We suggest that this may explain why many chemicals appear to stimulate both chemotactic and chemokinetic responses in cell populations. After specialising our model to describe slime mold we then show how the functional form of the chemical potential that drives cell locomotion influences the ability of the system to generate spatial patterns. The paper concludes with a summary of the key results and a discussion of avenues for future research.

Body Patterning↗
PubMed1992

An adsorption isotherm for the interaction of membrane-permeable hydrophobic ions with lipid vesicles.

An adsorption isotherm is presented which describes the association of membrane-permeable hydrophobic ions with lipid vesicles. The theory is based upon the Langmuir adsorption isotherm, but is has been significantly extended to take into account diffusion of ions across the membrane and dissociation into the intravesicular space as well as electrical effects due to the build up of boundary potentials within the membrane. The boundary potentials are calculated according to the three-capacitor model of the lipid membrane. In contrast to the Gouy-Chapman theory, which is only applicable when the charged group is located directly at the membrane-solution interface, the theory presented here allows the charge to be located at any position within the membrane.

Journal Article↗
PubMed1994

An in vitro model of fibroblast activity and adhesion formation during flexor tendon healing.

We studied fibroblast activity during tendon healing with an in vitro tendon culture model. Tendons were embedded in a translucent collagen gel matrix whose porous nature permitted free nutrient diffusion, fibroblast migration out of the tendon, and microphotographic documentation of fibroblast activity. Experiments were performed using one or more tendons cultured in the same collagen gel. We identified three zones of fibroblast activity in the gel. Zone I was an area of randomly dispersed cells directly adjacent to the tendon where collagen synthesis and remodeling were probably taking place. In zone II, spindle-shaped fibroblasts were aligned pointing away from the cut tendon end forming a sunburst-like aggregate of cells. Zone II fibroblasts were responsible for formation of migration trails by exerting a mechanical force on the collagen matrix, which was evident as a local gel contraction. Zone III was the leading edge of the sunburst populated by the fastest moving fibroblasts, which responded to guidance by other cut tendon ends. We speculate that the collagen gel used in the culture system may help maintain a chemotactic concentration gradient that allows fibroblasts to locate other distal cut tendon surfaces also embedded in the collagen gel.

Animals↗
PubMed1995

Quantitative magnetic resonance flow and diffusion imaging in porous media.

Quantitative flow and diffusion measurements have been made for water in model porous media, using magnetic resonance micro-imaging methods. The samples consisted of compacted glass beads of various sizes down to 1 mm diameter. Typical flow and diffusion images exhibited a spatial resolution of 117 microns x 117 microns and velocities in the range 1-2 mm/s. Comparison of volume flow rates calculated from the flow velocity maps with values measured directly yielded good agreement in all cases. There was also good agreement between the mean diffusion coefficient of water calculated from the diffusion maps and the bulk diffusion coefficient for pure water at the same temperature. In addition, the mean diffusion coefficient did not depend on the pore sizes in the bead diameter range of 1-3 mm. Our results also show that partial volume effects can be compensated by appropriate thresholding of the images prior to the final Fourier transformation in the flow-encoding dimension.

Diffusion↗
PubMed2005

Separation of charged colloids by a combination of pulsating lateral electric fields and poiseuille flow in a 2D channel.

Separation of colloidal particles of different sizes is becoming increasingly important due to rapid developments in the area of proteomics, genetic engineering, drug discovery, etc. In particular, there is a need to accomplish these separations on a microscale in 'lab-on-a-chip' devices. In this paper, we propose a new method for accomplishing separation of charged colloids of different sizes in a microchannel. This method involves a combination of pulses of lateral electric fields and Poiseuille flow in the axial direction. We develop a model for this separation technique and obtain closed form solutions for the mean velocity and the dispersion coefficient for a pulse of molecules introduced into the channel. These expressions are then utilized to determine the channel length and the separation time. For reasonable value of design constants, the proposed technique can separate molecules of different sizes that have diffusivities of 10(-10) and 0.5 x 10(-10) m2/s in 15.7 s in a 3.7 mm long channel. The length and the time increase to 5.45 cm and 231 s if the ratio of the diffusivities is reduced from 2 to 1.2, i.e., the latter diffusivity is increased to 0.835 x 10(-10) m2/s, while keeping all the other parameters the same. If the diffusivities are about 10(-9) m(2)/s, the length and the time for separation are 1 cm and 17.5 s for D1/D2=2, and 16 cm and 269 s for D1/D2=1.2.

Journal Article↗
PubMed2007

Retention of inorganic arsenic by coryneform mutant strains.

The natural resistance mechanisms of corynebacteria to respond to the environments containing high levels of arsenic were successfully adopted to develop inexpensive and selective extractants for submicrogram amounts of arsenic. Kinetic and equilibrium characteristics were evaluated, and a preliminary exploration of the capability of these strains to be used for arsenic speciation was also made in this work. Three kinetics models were used to fit the experimental data. It was found that the pseudo-first-order kinetics model was not quite adequate to describe the retention process, while the intraparticle diffusion and the pseudo-second-order kinetics models provide the best fits. The equilibrium isotherm showed that the retention of arsenic was consistent with the Langmuir equation and that the Freundlich and Dubinin-Radushkevich models provided poorer fits to the experimental data. The maximum effective retention capacity for arsenic was about 15.4 ng As/mg biomass. The amount of arsenic retained was directly measured in the biomass by forward planning a slurry electrothermal atomic absorption spectrometric procedure.

Adsorption↗
PubMed1988

Effects of pH on contraction of rabbit fast and slow skeletal muscle fibers.

We have investigated (a) effects of varying proton concentration on force and shortening velocity of glycerinated muscle fibers, (b) differences between these effects on fibers from psoas (fast) and soleus (slow) muscles, possibly due to differences in the actomyosin ATPase kinetic cycles, and (c) whether changes in intracellular pH explain altered contractility typically associated with prolonged excitation of fast, glycolytic muscle. The pH range was chosen to cover the physiological pH range (6.0-7.5) as well as pH 8.0, which has often been used for in vitro measurements of myosin ATPase activity. Steady-state isometric force increased monotonically (by about threefold) as pH was increased from pH 6.0; force in soleus (slow) fibers was less affected by pH than in psoas (fast) fibers. For both fiber types, the velocity of unloaded shortening was maximum near resting intracellular pH in vivo and was decreased at acid pH (by about one-half). At pH 6.0, force increased when the pH buffer concentration was decreased from 100 mM, as predicted by inadequate pH buffering and pH heterogeneity in the fiber. This heterogeneity was modeled by net proton consumption within the fiber, due to production by the actomyosin ATPase coupled to consumption by the creatine kinase reaction, with replenishment by diffusion of protons in equilibrium with a mobile buffer. Lactate anion had little mechanical effect. Inorganic phosphate (15 mM total) had an additive effect of depressing force that was similar at pH 7.1 and 6.0. By directly affecting the actomyosin interaction, decreased pH is at least partly responsible for the observed decreases in force and velocity in stimulated muscle with sufficient glycolytic capacity to decrease pH.

Actomyosin↗
PubMed2001

Diffusion-based calibration for SPME analysis of aqueous samples.

When an SPME fiber is exposed for a short period of time to a flowing fluid sample, the amount of extracted analyte depends on its diffusion coefficient in the matrix medium, and it can be correlated to its concentration using a simple mathematical model. This work discusses the extension of this approach, already validated for gaseous samples and SPME fibers coated with strong adsorbent coatings, to the diffusion-based quantification of analytes present in aqueous samples. Dilute aqueous solutions of aromatic hydrocarbons were used as model samples and vials were modified to use conventional magnetic agitation with controlled tangential flow of the test solution around the fiber. It was demonstrated that, with proper selection of the stirring speed and sampling time, the same diffusion-based quantitative model used for gas samples could be employed. Under optimal conditions, the concentrations of the evaluated aromatic hydrocarbons were estimated with relative standard deviations between 0.8 and 3.6% and without deviation from the expected values within this precision range. Considering the extraction times involved, between 30 and 60 s, the approach here presented is the fastest possible technique for direct extraction of analytes from liquid samples.

Journal Article↗
PubMed2005

Diffuse-reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: evidence of temperature jump and slip velocity in microchannels.

We discuss the implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model for which the upwind finite difference scheme is used to solve the set of evolution equations recovered after discretization of the velocity space. Simulation of heat transport between two parallel walls at rest shows evidence of temperature jumps at the walls that increase with Knudsen number. When the walls move in opposite directions with speeds +/- u(W), fluid velocity slip is observed at the walls, together with temperature jumps.

Journal Article↗
PubMed2004

Effect of icodextrin on transperitoneal uric acid and albumin transport in vitro.

In the present study, we compared the influence of icodextrin (2 g/dL) on uric acid (20 mg/dL) and albumin (1 g/dL) transfer through isolated rabbit parietal peritoneum. In separate series of experiments, we used a mathematical model to calculate the transport rate of solutes from the interstitial to the mesothelial side of peritoneal membrane (I --> M) and in the opposite direction (M --> I) before and after introduction of glucose polymer. In control conditions, the rates of uric acid and albumin passage across the rabbit peritoneum remained constant. Mean values [x +/- standard error of the mean (SEM)] of the diffusive permeability coefficient P were 1.936 +/- 0.324 (I --> M) and 2.078 +/- 0.186 (M --> I) for uric acid and 0.341 +/- 0.066 (I --> M) and 0.389 +/- 0.084 (M --> I) for albumin (all x10(-4) cm/s), respectively. The introduction of glucose polymer into the experimental system did not alter the I --> M transport of either solute; but, in the opposite direction, it caused a 17% decline in the P for uric acid (p < 0.05), and an increase of 77% in the same parameter for albumin (p < 0.03). Hence, I --> M transfer dominated M --> I transfer of uric acid (p < 0.04). In contrast, in albumin transport, M --> I was higher than I --> M (p < 0.02). We conclude that, in vitro, icodextrin modifies the diffusive permeability of the peritoneum and induces transport asymmetry for some small and large solutes.

Albumins↗
PubMed2007

A PGSE diffusion and electrophoretic NMR study of Cs+ and Na+ dynamics in aqueous crown ether systems.

Multinuclear pulsed gradient spin-echo (PGSE) NMR diffusion and linewidth measurements were used to probe binding and transport in aqueous Na+-15-crown-5, Na+-18-crown-6, Cs+-15-crown-5 and Cs+-18-crown-6 systems. Since direct PGSE observation of many alkali cations is precluded by either low inherent sensitivity or rapid relaxation (or both), the feasibility of proton-detected electrophoretic NMR (ENMR) measurements to complement PGSE data was investigated. ENMR measurements were performed on aqueous Cs+-, Li+-, Na+-, K+-, and Rb+- 18-crown-6 systems. The data analysis is based on a two-site binding model and its corresponding association constants. Cs+ was found to bind considerably more tightly to 18-crown-6 (K=8 M-1) than to 15-crown-5 (K approximately 2 M-1), whereas Na+ had almost equal affinity (K approximately 4.5 M-1) for 15-crown-5 and 18-crown-6. The difficulties encountered in analysing the NMR parameters, methodological limitations and the implied need for more complicated binding models are discussed.

Cesium↗