Effect of villosity and distension on the absorptive and secretory flux in the small intestine

The effects of villosity and distension on the absorptive and secretory flux in the small intestine were investigated theoretically in a simplified model. In the case of low epithelial permeability, villosity increases both fluxes by surface enlargement, but in the case of high epithelial permeability, this occurred only if the intervillous spaces are very narrow. Otherwise, the flux is reduced due to the intervillous diffusion resistance, which is more effective than the enlargement of the surface area in that case. Distension increases the fluxes due to the additional surface exposed, by opening the intervillous spaces. In the case of low epithelial permeability this increase exceeds that expected from the enlargement of the smooth inner cylindrical surface area. In the case of high epithelial permeability, however, the increase of the fluxes exceeds surface enlargement only in the first phase, just after opening the intervillous spaces. Otherwise, the increase of the flux is less, since the hindrance by the intervillous diffusion resistance is more effective than the increase of the smooth inner cylindrical surface area. In the intervillous spaces the concentration gradient is non-linear with the steepest slope at the entrance due to the permeation through the lateral surfaces of the villi. The gradient approaches linearity in the center of broad intervillous spaces and becomes steeper when the width decreases and the epithelial permeability increases. In rat small intestine broad intervillous spaces are formed at the front sides of the trapezoidal villi by the predominant circular distension. The diffusion resistance in these spaces and the increase of the supravillous diffusion resistance weaken the increase of the absorptive and secretory flux by distension, especially in the case of high epithelial permeability.     

Analysis of ultrafiltration and mass transfer in a bioartificial pancreas

A bioartificial pancreas is an implantable device which contains insulin secreting cells (Langerhans islets), separated from the circulating blood by a semi-permeable membrane to avoid rejection. This paper describes the operation of such a device and evaluates the respective contributions of diffusion and ultrafiltration to the glucose and insulin mass transfer. It is shown that the pressure drop along the blood channel produces across the first half of the channel an ultrafiltration flux toward the islet compartment followed in the second half by an equal flux in reverse direction from islets to blood. The mass transfer analysis is carried out for an optimal geometry in which a U-shaped blood channel surrounds closely a very thin islet compartment formed by a folded flat membrane. A complete model of insulin release by this device is developed and is compared with in vitro data obtained with rats islets. Satisfactory kinetics is achieved with a polyacrylonitrile membrane used in hemodialysis. But the model shows that the membrane hydraulic permeability should be increased by a factor of 10 to significantly improve the performance.     

Determination of intrinsic membrane transport parameters from perfused intestine experiments: a boundary layer approach to estimating the aqueous and unbiased membrane permeabilities

A boundary layer approach is developed for estimating the aqueous resistance in a perfused rat intestine experiment. Knowing the aqueous resistance allows the membrane surface concentration to be calculated as a function of the perfusate inlet concentration and perfusional flow rate. Determination of membrane uptake as a function of the membrane surface concentration rather than the perfusate concentration gives the intrinsic, unbiased membrane parameters for the uptake mechanism of Michaelis-Menten-type kinetics in parallel with passive diffusion. The aqueous resistance derived in the analysis is verified by comparison with flux data for 1-leucine and progesterone measured at various flow rates and intestinal lengths. The approach allows for a direct estimate to be made of the unbiased membrane permeability parameters.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

A model relating root permeability to flux and potentials: application to existing data from soybean and other plants

A model that relates hydraulic permeability to water flux and to gradients in pressure potential and solute potential was tested using soybean (Glycine max) plants. Water flux was varied by additions of polyethylene glycol 6,000 around one portion of a divided root system and by changing the light intensity and CO₂ concentration around the plants. The data are compatible with the model only if the hydraulic permeability varies with flux; however, the data were insufficient for rigorous testing. Three sets of published data fit the model only if hydraulic permeability varies. Evidence originally presented as involving constant hydraulic permeability is shown, rather, to require variable hydraulic permeability.     

Hydraulic resistance and fouling of microfilters by Candida utilis in fermentation broth

The hydraulic resistance and membrane fouling effects of Candida utilis in fermentation broth were investigated using Millipore PVDF 0.22-mum membranes (GVWP and GVHP) in a stirred-cell system at 50 kPa and 700 rpm. With the various components of broth, spent medium, which contains colloidal particles and macromolecules having sizes (0.32 to 2.67 mum) comparable with the membrane pores (actual range 0.26 to 0.63 mum), was found to be the major contributing factor to the membrane fouling by broth through pore plugging. This led the spent medium to exhibit the highest hydraulic resistance (R(sm) of 5.8E + 12 m(-1)) and percentage flux loss (81.0%) when compared with either intact cells alone in buffer or to whole broth. Intact cells appeared to physically block and protect the pores without significant adhesion, because of the relatively hydrophilic nature of their cell walls (hydrophobicity of 5.9% at hour 36), resulting in the lowest hydraulic resistance (Rsbc of 7.5E + 11m(-1)) and percentage flux loss (19.3%).However, the hydraulic resistance and percentage flux loss of broth increased as cells aged. This was attributed to the increase in particle loading (intact cells by 15.37%, released cell contents and cell fragments) and in the hydrophobicity of cell walls. Autoclaved broth, lysed broth and aged broth, which contained a larger portion of colloidal particles and released cell contents caused a more pronounced fouling effect. This was revealed by the absence of flux recovery after depressurization with continuous stirring, even when a hydrophilic membrane was used. Furthermore, the hydrophobicity of C. utilis was found to increase with yeast extract present in medium, and use of hydrophobic membranes helped enhance the fouling effect. Overall, the degree of irreversible membrane fouling could be revealed by the value of R(sm)/R(t') and the hydraulic resistance, which resulted from concentration polarrzation, could be revealed by the value of R(c)/R(t') where R(t) = R(m) + R(sm) + R(c') and R(m) is the clean membrane resistance. (c) 1995 John Wiley & Sons, Inc.     

The specific hydraulic conductivity of bovine serum albumin.

Previous studies of extracellular matrix hydraulic conductivity have characterized the flow resistance of glycosaminoglycans, proteoglycans and collagen. This work focuses on serum albumin, present in significant quantities in many connective tissues, but not previously considered for its role in determining connective tissue flow resistance. The specific hydraulic conductivity of bovine serum albumin solutions, as a function of concentration, was calculated from sedimentation and ultrafiltration data available in the literature. A rigid particle hydrodynamic model compared favorably with these results. Experimental measurements on an albumin ultrafiltration cell were in agreement with this model (within experimental error); furthermore, the experimental data confirmed the theoretical prediction that there is no (or negligible) pressure drop through the concentration polarization layer. Use of the hydrodynamic model for albumin specific hydraulic conductivity with literature values for the hindrance of albumin when passing through a glycosaminoglycan (GAG) matrix allows an estimate of the relative importance of the albumin on tissue hydraulic conductivity: in non-cartilaginous tissues with moderate GAG concentrations, tissue levels of albumin can generate flow resistance effects comparable to those of the GAGs, although well less than the flow resistance of these tissues.     

Cholinergic and adrenergic effects on diffusional water flux in the toadfish, Opsanus beta

Intraperitoneal injections of adrenaline resulted in increased tritiated water efflux rate in the toadfish, Opsanus beta. Adrenaline-stimulated water flux was inhibited by the beta-adrenergic blocker, propranolol, but not by the alpha-adrenergic blocker, phentolamine. Propranolol on its own had no effect but phentolamine significantly stimulated water flux; this action was attributed to a beta-mimetic effect of the drug. The cholinergic neurotransmitter acetylcholine, had no effect while the parasympathico-mimetic carbachol, significantly stimulated water flux. Arguments were advanced to explain the similarity in the effects of the adrenergic and cholinergic drugs although they are both known to produce opposing vascular haemodynamic effects in fish gills. Adrenaline substantially stimulated tritiated water flux in the toadfish, Opsanus beta. The adrenaline-stimulated water flux exhibited a linear dose-response curve up to an adrenaline dosage of 750 micrograms kg-1; wt. At higher doses there was apparently a desensitization of the beta-adrenergic receptor sites. The adrenaline effect was inhibited by the beta-blocker propranolol, but not by the alpha-blocker, phentolamine. This suggests that the adrenaline-stimulated water flux was due predominantly to beta-receptor site stimulation. Stimulation of water flux by phentolamine on its own could be due to the stimulation of endogenous catecholamine release by the drug. We have proposed that the beta-stimulated water efflux could be due to an increase in surface area of the branchial epithelium, a decrease in water to blood diffusion distance, a direct metabolic effect or any combination of these effects by adrenaline. Carbachol caused an increase in tritiated water efflux. The carbachol-stimulated water flux was inhibited by atropine thus suggesting that the drug acts via muscarinic receptor sites. We have suggested that the action of the drug on hydraulic water conductivity, water to blood diffusion distance, hydrostatic pressure or a direct effect on membrane diffusion coefficient.     

A two-dimensional mathematical model of non-linear dual-sorption of percutaneous drug absorption

Background  

Certain drugs, for example scopolamine and timolol, show non-linear kinetic behavior during permeation process. This non-linear kinetic behavior is due to two mechanisms; the first mechanism being a simple dissolution producing mobile and freely diffusible molecules and the second being an adsorption process producing non-mobile molecules that do not participate in the diffusion process. When such a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, C, the donor concentration. The present paper studies the effect of the parameter value, C, when the region of the contact of the skin with drug, is a line segment on the skin surface. To confirm that dual-sorption process gives an explanation to non-linear kinetic behavior, the characteristic features that are used in one-dimensional models are (1) prolongation of half-life if the plot of flux versus time are straight lines soon after the vehicle removal, (2) the decrease in half-life with increase in donor concentration. This paper introduces another feature as a characteristic to confirm that dual-sorption model gives an explanation to the non-linear kinetic behavior of the drug. This new feature is "the prolongation of half-life is not a necessary feature if the plots of drug flux versus time is a non-linear curve, soon after the vehicle removal".     

Erythrocytes possess an intrinsic barrier to nitric oxide consumption

It has been reported that free hemoglobin (Hb) reacts with NO at an extremely high rate (K(Hb) approximately 10(7) M(-1) s(-1)) and that the red blood cell (RBC) membrane is highly permeable to NO. RBCs, however, react with NO 500-1000 times slower. This reduction of NO reaction rate by RBCs has been attributed to the extracellular diffusion limitation. To test whether additional limitations are also important, we designed a competition test, which allows the extracellular diffusion limitation to be distinguished from transmembrane or intracellular resistance. This test exploited the competition between free Hb and RBCs for NO generated in a homogenous phase by an NO donor. If the extracellular diffusion resistance is negligible, then the results would follow a kinetic model that assumes homogenous reaction without extracellular diffusion limitation. In this case, the measured effective reaction rate constant, K(RBC), would remain invariant of the hematocrit, extracellular-free Hb concentration, and NO donor concentration. Results show that the K(RBC) approaches a constant only when the hematocrit is greater than 10%, suggesting that at higher hematocrit, the extracellular diffusion resistance is negligible. Under such a condition, the NO consumption by RBCs is still 500-1000 times slower than that by free Hb. This result suggests that intrinsic RBC factors, such as transmembrane diffusion limitation or intracellular mechanisms, exist to reduce the NO consumption by RBCs.     

Modeling water flow through arterial tissue

A simple model of, water flow through deformable porous media has been developed with emphasis on application to arterial walls. The model incorporates a strain-dependent permeability function into Darcy's Law which is coupled, to the force balance for the bulk material. A simple analytical expression relating water flux (volume flux) to pressure differential is developed which shows how strain-dependent permeability can lead to a reduction in hydraulic conductivity with increasing differential pressure as observed in experiments with arteries. The variation of permeability with position in the wall, which may influence the convective diffusion of macromolecules, is determined for both cylindrical and planar segments and a marked influence of geometry is noted.     

The Diffusion of Oxygen, Carbon Dioxide, and Inert Gas in Flowing Blood

Measurements were made of exchange rates of oxygen, carbon dioxide, and krypton-85 with blood at 37.5°C. Gas transfer took place across a 1 mil silicone rubber membrane. The blood was in a rotating disk boundary layer flow, and the controlling resistance to transfer was the concentration boundary layer. Measured rates were compared with rates predicted from the equation of convective diffusion using velocities derived from the Navier-Stokes equations and diffusivities calculated from the theory for conduction in a heterogeneous medium. The measured absorption rate of krypton-85 was closely predicted by this model. Significant deposition of material onto the membrane surface, resulting in an increased transfer resistance, occurred in one experiment with blood previously used in a nonmembrane type artificial lung. The desorption rate of oxygen from blood at low P_o2¹ was up to four times the corresponding transfer rate of inert gas. This effect is described somewhat conservatively by a local equilibrium form of the convective diffusion equation. The carbon dioxide transfer rate in blood near venous conditions was about twice that of inert gas, a rate significantly greater than predicted by the local equilibrium theory. It should be possible to apply these theoretical methods to predict exchange rates with blood flowing in systems of other geometries.     

Role of t-tubules in the control of trans-sarcolemmal ion flux and intracellular Ca2+ in a model of the rat cardiac ventricular myocyte

The t-tubules of mammalian ventricular myocytes are invaginations of the surface membrane that form a complex network within the cell, with restricted diffusion to the bulk extracellular space. The trans-sarcolemmal flux of many ions, including Ca(2+), occurs predominantly across the t-tubule membrane and thus into and out of this restricted diffusion space. It seems possible, therefore, that ion concentration changes may occur in the t-tubule lumen, which would alter ion flux across the t-tubule membrane. We have used a computer model of the ventricular myocyte, incorporating a t-tubule compartment and experimentally determined values for diffusion between the t-tubule lumen and bulk extracellular space, and ion fluxes across the t-tubule membrane, to investigate this possibility. The results show that influx and efflux of different ion species across the t-tubule membrane are similar, but not equal. Changes of ion concentration can therefore occur close to the t-tubular membrane, thereby altering trans-sarcolemmal ion flux and thus cell function, although such changes are reduced by diffusion to the bulk extracellular space. Slowing diffusion results in larger changes in luminal ion concentrations. These results provide a deeper understanding of the role of the t-tubules in normal cell function, and are a basis for understanding the changes that occur in heart failure as a result of changes in t-tubule structure and ion fluxes.     

Radial Oxygen Loss from Roots: The Theoretical Basis for the Manipulation of Flux Data Obtained by the Cylindrical Platinum Electrode Technique

A résumé is given of the cylindrical platinum electrode technique for measuring the rate of oxygen release from the submerged roots of intact plants. Methods are then described for manipulating the oxygen flux data to quantify the following root characteristics: total effective internal diffusional resistance, non-metabolic (pore-space) resistance, internal apical oxygen concentration, effective diffusion coefficient of internal transport and fractional porosity, and the respiratory contribution to internal transport. The diffusional resistance of the root wall is discussed and the method formerly suggested for converting low temperature flux data to the appropriate room temperature values (Armstrong 1971) is revised. Finally, suggestions are made for overcoming the difficulties encountered in using flux data for comparative work if the roots differ in their apical radii.     

New mathematical model to estimate tissue blood perfusion, thermal contact resistance and core temperature

Analytical solutions were developed based on the Green's function method to describe heat transfer in tissue including the effects of blood perfusion. These one-dimensional transient solutions were used with a simple parameter estimation technique and experimental measurements of temperature and heat flux at the surface of simulated tissue. It was demonstrated how such surface measurements can be used during step changes in the surface thermal conditions to estimate the value of three important parameters: blood perfusion (w(b)), thermal contact resistance (R"), and core temperature of the tissue (T(core)). The new models were tested against finite-difference solutions of thermal events on the surface to show the validity of the analytical solution. Simulated data was used to demonstrate the response of the model in predicting optimal parameters from noisy temperature and heat flux measurements. Finally, the analytical model and simple parameter estimation routine were used with actual experimental data from perfusion in phantom tissue. The model was shown to provide a very good match with the data curves. This demonstrated the first time that all three of these important parameters (w(b), R", and T(core)) have simultaneously been estimated from a single set of thermal measurements at the surface of tissue.     

Computer simulation of single-file transport

A stochastic model of single-file transport was developed as the Markov process in continuous time technique. The model was constructed using an EC-1060 computer. Unidirectional fluxes were investigated and populations of channels were correlated with flux fluctuations. The profiles of channel populations were shown to have nonlinear shapes even with the transport of nonelectrolyte (the classical diffusion approach gives linear profiles). The relationship between the paired correlation function F(AB) and the concentration of transported particles was examined. The F(AB) profile was shown to become flattened (or exponential for asymmetrical cases) at high concentrations. The concentration dependence jA/jA0 ratio were analyzed, where jA is a single-file unidirectional flux, jA0 is unidirectional flux for the case of free diffusion. An interesting "stack" phenomenon was observed for abnormal time correlations of single-file fluxes.     

The volume dependence of the erythrocyte water diffusion permeability

The product of the water diffusion permeability and the membrane area of a human erythrocyte has been found to be nearly independent of the cell volume. The product was measured by an NMR technique. This result conflicts with previous flow tube determinations but is in accord with recent measurements of the hydraulic permeability and various solute permeabilities. The results are consistent with the major part of the water fllux traversing the membrane through a fixed number of pores. There may also be a minor non-pore flux. It appears to be practicable to follow volume changes in the red blood cell by an NMR technique.