How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.     

On the Distribution of a Permeable Solute during Poiseuille Flow in Capillary Tubes

Equations are derived describing the dispersion of a permeable solute during Poiseuille flow in a capillary model. It is shown that for the normal range of physiological parameters such as capillary radius, capillary length, blood flow, permeability coefficients, and diffusion constants, the center of mass of a bolus of solute moves at a speed very close to the mean speed of flow and that the solute leaves the capillary with an exponential time course depending on the permeability but not on the diffusion constant. There is no appreciable difference in the dispersion of the solute or in its rate of permeation from the capillary whether one considers piston flow or Poiseuille flow. A bolus of arbitrary radial shape tends to become radially uniform very close to the arterial end of the capillary.     

TRANSIT TIMES THROUGH THE CYCLE PHASES OF JEJUNAL CRYPT CELLS OF THE MOUSE ANALYSIS IN TERMS OF THE MEAN VALUES AND THE VARIANCES

Mean transit times as well as variances of the transit times through the individual phases of the cell cycle have been determined for the crypt epithelial cells of the jejunum of the mouse. To achieve this the fraction of labelled mitoses (FLM) technique has been modified by double labelling with [³H] and [¹⁴C]thymidine. Mice were given a first injection of [³H]thymidine, and 2 hr later a second injection of [¹⁴C]thymidine. This produces a narrow subpopulation of purely ³H-labelled cells at the beginning of G₂-phase and a corresponding subpopulation of purely ¹⁴C-labelled cells at the beginning of the S-phase. When these two subpopulations progress through the cell cycle, one obtains FLM waves of purely ³H- and purely ¹⁴C-labelled mitoses. These waves have considerably better resolution than the conventional FLM-curves. From the temporal positions of the observed maxima the mean transit times of the cells through the individual phases of the cycle can be determined. Moreover one obtains from the width of the individual waves the variances of the transit times through the individual phases. It has been found, that the variances of the transit times through successive phases are additive. This indicates that the transit times of cells through successive phases are independently distributed. This statistical independence is an implicit assumption in most of the models applied to the analysis of FLM curves, however there had previously been no experimental support of this assumption. A further result is, that the variance of the transit time through any phase of the cycle is proportional to the mean transit time. This implies that the progress of the crypt epithelial cells is subject to an equal degree of randomness in the various phases of the cycle.     

Distribution of pulmonary capillary transit times in recruited networks

When pulmonary blood flow is elevated, hypoxemia can occur in the fastest-moving erythrocytes if their transit times through the capillaries fall below the minimum time for complete oxygenation. This desaturation is more likely to occur if the distribution of capillary transit times about the mean is large. Increasing cardiac output is known to decrease mean pulmonary capillary transit time, but the effect on the distribution of transit times has not been reported. We measured the mean and variance of transit times in single pulmonary capillary networks in the dependent lung of anesthetized dogs by in vivo videofluorescence microscopy of a fluorescein dye bolus passing from an arteriole to a venule. When cardiac output increased from 2.9 to 9.9 l/min, mean capillary transit time decreased from 2.0 to 0.8 s. Because transit time variance decreased proportionately (relative dispersion remained constant), increasing cardiac output did not alter the heterogeneity of local capillary transit times in the lower lung where the capillary bed was nearly fully recruited.     

Molecular dynamics simulation study for diffusion of Na+ ion in water-filled carbon nanotubes at 25°C

We present results of molecular dynamics simulations for diffusion of Na⁺ ion in water-filled carbon nanotubes (CNTs) at 25°C using the extended simple point charge water potential. Simulation results indicate the general trend that the diffusion coefficients of Na⁺ ion and water molecule in CNTs decrease with an increase in water density and are larger than those in the bulk solution. The average potential energies of ion–water and water–water, the radial distribution functions, the hydration numbers and the residence times of the hydrated water molecules are discussed. The classical solventberg picture describes Na⁺ ion in water adequately for systems with the small values of diffusion coefficients.     

Radial transport of salt and water in roots of the common reed (Phragmites australis Trin. ex Steudel)

To understand the root function in salt tolerance, radial salt and water transport were studied using reed plants growing in brackish habitat water with an osmotic pressure (π_M) of 0.63 MPa. Roots bathed in this medium exuded a xylem sap with NaCl as the major osmolyte and did so even at higher salt concentration (π_M up to 1.3 MPa). Exudation was stopped after a small increase of π_M (0.26 MPa) using polyethylene glycol 600 as osmolyte. The endodermis of fine lateral roots was found to be the main barrier to radial solute diffusion on an apoplastic path. Apoplastic salt transfer was proven by rapid replacement of stelar Na⁺ by Li⁺ in an isomolar LiCl medium. Water fluxes did not exert a true solvent drag on NaCl. Xylem sap concentrations of NaCl in basal internodes of transpiring culms were more than five times higher than in medial and upper ones. It was concluded that the radial NaCl flux was mainly diffusion through the apoplast, and radial water transport, because of the resistance of the cell wall matrix to convective mass flow, was confined to the symplast. Radial salt permeation in roots reduced the water stress exerted by the brackish medium.     

Permeability characteristics of the basement membrane (basal lamella) of the intestine of Ascaris suum

Permeability characteristics have been determined for isolated ribbons of the basement membrane of the intestine ofAscaris suum. The solute permeability coefficient (P_c) was measured for a series of hydrophobic, nonionic molecules of graded molecular size. The geometric pore area per unit path length (A_o/Δx) was estimated to be 24.0 cm from the diffusion rates for the various solute molecules. A filtration coefficient (L_p) of 18.1×10^?12 cm⁵/dyne-sec was determined by a method that employs osmotic pressure. The preceding values were used to calculate an average pore radius of 24.0 A for the membrane. The unstirred layer was estimated to be 30μm thick from measurements of the change in the rate of diffusion of water across the membrane with change in the rate of perfusion. The preceding values were used to calculate a reflection coefficien (σ), effective permeability coefficient (ω′), and a permeability coefficient (ω). The results support the view that this basement membrane functions as a filter and selective barrier to diffusion of constituents of the worm's body fluid.     

Diffusion in colloidal media

When the molecules of a solute diffuse through a medium containing large colloidal particles, which absorb the diffusing molecules, the latter are transported in the diffusion flow not as free molecules, but as absorbtion compounds: solute+colloid. When the colloidal particle is much larger than the molecule of the solute, and has therefore a much smaller mobility, this results in a reduction of the apparent diffusion coefficient for the solute. The biological implications of this are discussed.     

Mathematical Model of a Countercurrent Flow Multi-fibre Dialyser

Summary The closed form solution to a distributed parameter mathematical model of a countercurrent flow dialyser is presented. The model consisting of a bundle of hollow fibres in a shell accounts for axial convection and radial diffusion. The proposed model relates the fractional removal of a solute to mass transfer parameters such as Sherwood number, length Peclet number and system geometry. Excellent agreement with experimental beer dialysis data is demonstrated for the removal of alcohol using 8-lm thick 200-lm diameter cuprophane hollow-fibre membrane fibres. Potentially, this model could be very helpful in designing new processes involving dialysis. For example, removal efficiency better than 90% is achievable in systems operating with a Sherwood number of 2.0, length Peclet number of 5 · 105, unit tube-side/shell-side volumetric flow and length-to-diameter ratio of 5000. Results were obtained in this work from only the first eigenvalue and the case of no solute in the incoming dialysate stream.     

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.     

Colorimetric assay to quantify macromolecule diffusion across endothelial monolayers

Endothelial "capillary leak", the loss of vascular integrity in response to noxious stimuli, is characterized by extravasation of protein-richfluidfrom capillary lumen into surrounding tissue interstitium. This increase in vascular permeability, in response to inflammatory mediators, correlates with endothelial cell contraction and the formation of intercellular gaps within the monolayer. However, in vivo assessment of paracellular solute flow between endothelial cells may be complicated by multiple uncontrolled parameters. In vitro examinations of endothelial barrier leak have relied on electrical impedence or macromolecule diffusion techniques to determine the details pertinent to capillary barrier function. In this report, a simple, sensitive, nonradioactive, colorimetric assay to quantify the leak of a labeled protein marker across endothelial monolayers is described. This procedure avoids the hazards of radioisotope labels and the technical limitations of electrical resistance technology.     

A compartmental capillary, convolution integration model to investigate nutrient transport and metabolism in vivo from paired indicator/nutrient dilution curves.

Thirty-three paired indicator/nutrient dilution curves across the mammary glands of four cows were obtained after rapid injection of para-aminohippuric acid (PAH) plus glucose into the external iliac artery. For the measurement of extracellular volume and kinetics of nutrient uptake from indicator dilution curves, several models of solute dispersion and disappearance have been proposed. The Crone-Renkin models of exchange in a single capillary assume negligible washout of solutes from the extracellular space and do not describe entire dilution curves. The Goresky models include a distribution of capillary transit times to generate whole system outflow profiles but require two indicators to parametize extracellular behavior. A compartmental capillary, convolution integration model is proposed that uses one indicator to account for the extracellular behavior of the nutrient after a paired indicator/nutrient injection. With the use of an iterative approach to least squares, unique solutions for nonexchanging vessel transit time t(mu) and its variance sigma were obtained from all 33 PAH curves. The average of heterogeneous vascular transit times was approximated as 2sigma = 8.5 s. The remainder of indicator dispersion was considered to be due to washout from a well-mixed compartment representing extracellular space that had an estimated volume of 5.5 liters or 24% of mammary gland weight. More than 99% of the variation in the time course of venous PAH concentration after rapid injection into the arterial supply of the mammary glands was explained in an unbiased manner by partitioning the organ into a heterogeneous nonexchanging vessel subsystem and a well-mixed compartmental capillary subsystem.     

Molecular dynamics simulation on the decomposition of type SII hydrogen hydrate and the performance of tetrahydrofuran as a stabiliser

Molecular dynamics simulation is used to study the decomposition and stability of SII hydrogen and hydrogen/tetrahydrofuran (THF) hydrates at 150 K, 220 K and 100 bar. The modelling of the microscopic decomposition process of hydrogen hydrate indicates that the decomposition of hydrogen hydrate is led by the diffusive behaviour of H₂ molecules. The hydrogen/THF hydrate presents higher stability, by comparing the distributions of the tetrahedral angle of H₂O molecules, radial distribution functions of H₂O molecules and mean square displacements or diffusion coefficients of H₂O and H₂ molecules in hydrogen hydrate with those in hydrogen/THF hydrate. It is also found that the resistance of the diffusion behaviour of H₂O and H₂ molecules can be enhanced by encaging THF molecules in the (5¹²6⁴) cavities. Additionally, the motion of THF molecules is restricted due to its high interaction energy barrier. Accordingly, THF, as a stabiliser, is helpful in increasing the stability of hydrogen hydrate.     

Quantitative permeability imaging of plant tissues

A method for mapping tissue permeability based on time-dependent diffusion measurements is presented. A pulsed field gradient sequence to measure the diffusion encoding time dependence of the diffusion coefficients based on the detection of stimulated spin echoes to enable long diffusion times is combined with a turbo spin echo sequence for fast NMR imaging (MRI). A fitting function is suggested to describe the time dependence of the apparent diffusion constant in porous (bio-)materials, even if the time range of the apparent diffusion coefficient is limited due to relaxation of the magnetization. The method is demonstrated by characterizing anisotropic cell dimensions and permeability on a subpixel level of different tissues of a carrot (Daucus carota) taproot in the radial and axial directions.     

Optimisation of solute transport in dialysers using a three-dimensional finite volume model

Dialyser manufacturers only provide limited information about mass removal under well-defined flow and solute conditions in commercially available dialysers for hemodialysis. This computational study aimed at assessing the solute transport efficiency in a dialyser for different geometries (fiber lengths and diameters).

A three-dimensional finite volume model of a single fiber in a high flux polysulphone dialyser (Fresenius F60) was developed. Different equations describe blood and dialysate flow (Navier–Stokes), radial filtration flow (Darcy) and solute transport (convection–diffusion). Fluid and membrane properties were derived from in vitro and in vivo tests as well as from literature data. Urea (MW60) was used as marker to simulate small molecule removal, while middle molecule transport was modelled using vitamin B12 (MW1355) and inulin (MW5200). Keeping the fluid velocity in a single fiber constant, fiber diameter and length were changed in a wide range for evaluation of solute removal efficiency. Clearances were found enhanced by 13% (urea), 50% (vitamin B12) and 89% (inulin) for a fiber twice as long as a standard one and by 5.5% (vitamin B12) and 21% (inulin) for a fiber diameter of 150 μm instead of 200 μm. The impact of fiber dimensions was more pronounced for the middle molecules compared to urea.     

Stochastic analysis of the relationships between saturated hydraulic conductivity variance and solute dispersion in heterogeneous soils

The effect of three‐dimensional heterogeneity of saturated hydraulic conductivity on the vertical transport of solutes in soils is examined by means of controlled numerical experiments. Saturated hydraulic conductivity, an important transport parameter that controls the dispersion of pollutants in heterogeneous soils, is assumed to be composed of a homogeneous mean value and a perturbation caused by the vertical variability of soil properties, producing a stochastic process in the mean flow direction. The spatial heterogeneity of porous soils is characterized by the variance and correlation scale of the saturated hydraulic conductivity in the transport domain. Numerical experiments are carried out to evaluate the extent of contaminant dispersion in Hawaiian Oxic soils when uncertainty exists as a result of the spatial heterogeneity of saturated hydraulic conductivity. Statistical analysis of the saturated hydraulic conductivity measurements on undisturbed soil cores from two locations in Hawaiian Oxic soils indicated two different soils with the same mean and different variances. The partial differential equations describing three‐dimensional transient flow and solute transport in soils with a random conductivity field were solved to evaluate the effect of these two variance levels on the transport of a contaminant plume originating from the surface. The significance of the variance on the spatial and temporal distribution of tracer concentrations is demonstrated using solute breakthrough curves at various depths in the soil profile. The longitudinal macrodispersivity resulting from tracer spreading in the heterogeneous soils with a finite local dispersivity is also analyzed. The analysis shows a similar solute dispersion behavior for the two variances. However, there is an overall reduction in the dispersion of solutes resulting from a uniform velocity field with the same mean. Macrodispersivity values in heterogeneous soils are proportional to the variance at smaller travel distances but converge to the same value at larger travel distances.     

Hydraulic characteristics of aerobic granules using size exclusion chromatography

Elution of poly(ethylene glycol) of molecular weight 200-20,000 Da from a size exclusion chromatography column packed with phenol-fed aerobic granules of three different nominal sizes (types I-III) has been investigated. The pore sizes of the three types of granules were evaluated based on the mean hydraulic times of the elution curves that decreased directly proportional to the increased logarithm of the molecular mass of a standard tracer and increased as granule size decreased. The corresponding exclusion limits for types I-III granules were 139,000, 123,000, and 54,500 Da, respectively. A one-dimensional convection-dispersion model described the effective dispersion coefficients of the tracers through the granule column. The intra-granular permeabilities and convective and diffusional transit times through the granule interior were evaluated by a dual porosity model. For small molecules of molecular mass <5,000 Da, intra-granular convection dominated transport mechanisms at fast moving velocity. For comparatively larger molecules, diffusion barrier existed to limit nutrient supply to the granules. The size exclusion test provided intra granular transport characteristics using detailed analysis on the elution data.     

A Septin-Dependent Diffusion Barrier at Dendritic Spine Necks

Excitatory glutamatergic synapses at dendritic spines exchange and modulate their receptor content via lateral membrane diffusion. Several studies have shown that the thin spine neck impedes the access of membrane and solute molecules to the spine head. However, it is unclear whether the spine neck geometry alone restricts access to dendritic spines or if a physical barrier to the diffusion of molecules exists. Here, we investigated whether a complex of septin cytoskeletal GTPases localized at the base of the spine neck regulates diffusion across the spine neck. We found that, during development, a marker of the septin complex, Septin7 (Sept7), becomes localized to the spine neck where it forms a stable structure underneath the plasma membrane. We show that diffusion of receptors and bulk membrane, but not cytoplasmic proteins, is slower in spines bearing Sept7 at their neck. Finally, when Sept7 expression was suppressed by RNA interference, membrane molecules explored larger membrane areas. Our findings indicate that Sept7 regulates membrane protein access to spines.     

Fractionation of macromolecules in an alternating transverse electric field: simulation of the method

An electric field of alternating polarity applied in a direction transverse to the direction of solute transport is used as the basis of a method for the separation of biological macromolecules. The method derives directly from the ability of an electric field to induce movement of a charged macromolecule and from the physics of laminar fluid flow; no adsorptive immobile phase component is involved.

The method is simulated by computer for the case of solute molecules in a solvent flowing through a narrow chamber of recta generates an electric field orthogonal to the direction of solvent flow. Solute molecules repetitively traverse the solvent channel at rates determined by their electrophoretic mobility. During the transit across the channel, solute molecules are transported in the direction of solvent flow; at the channel wall, solvent velocity is negligible and solute transport is limited to that provided by transient diffusion into a mobile solvent zone. Molecules of different intrinsic electrophoretic mobility are separated.

The computer model was used to illustrate the process and to demonstrate the ‘tunability’ of the method as a function of the oscillation frequency and voltage wave form. Because of this tunability, a single instrument can function as the equivalent of several different chromatographic systems. Because fractionation is effected by direct physicochemical phenomena rather than via interaction with chromatographic sites, variations in fractionation results arising from formation of polymers for gel electrophoresis, packing of chromatography columns, or deterioration of columns with use are avoided. This method may be of particular use for the purification of nucleic acid fragments and for the analysis of protei: nucleic acid interactions.     

Variance and spatial scales in a tropical rain forest: changing the size of sampling units

The size of a sampling unit has a critical effect on our perception of ecological phenomena; it influences the variance and correlation structure estimates of the data. Classical statistical theory works well to predict the changes in variance when there is no autocorrelation structure, but it is not applicable when the data are spatially autocorrelated. Geostatistical theory, on the other hand, uses analytical relationships to predict the variance and autocorrelation structure that would be observed if a survey was conducted using sampling units of a different size. To test the geostatistical predictions, we used information about individual tree locations in the tropical rain forest of the Pasoh Reserve, Malaysia. This allowed us to simulate and compare various sampling designs. The original data were reorganised into three artificial data sets, computing tree densities (number of trees per square meter in each quadrat) corresponding to three quadrat sizes (5×5, 10×10 and 20×20 m⁽²⁾). Based upon the 5×5 m⁽²⁾ data set, the spatial structure was modelled using a random component (nugget effect) plus an exponential model for the spatially structured component. Using the within-quadrat variances inferred from the variogram model, the change of support relationships predicted the spatial autocorrelation structure and new variances corresponding to 10×10 m⁽²⁾ and 20×20 m⁽²⁾ quadrats. The theoretical and empirical results agreed closely, while the classical approach would have largely underestimated the variance. As quadrat size increases, the range of the autocorrelation model increases, while the variance and proportion of noise in the data decrease. Large quadrats filter out the spatial variation occurring at scales smaller than the size of their sampling units, thus increasing the proportion of spatially structured component with range larger than the size of the sampling units.