Linear bulk diffusion into heterogeneous tissue

In this paper an expression is derived which describes the transient overall uptake of an inert solute by a section of tissue excised with parallel faces and placed upon an impermeable base. The approach diverges from the conventional analyses for perfused tissue (Morales and Smith,Bull. Math. Biophysics,6, 125–141, 1944;7, 47–99, 1945) because the extravascular zone is regarded as a heterogeneous diffusion medium. Account for this is taken by regarding tissue as effectively composed of two phases—a continuous (extracellular) phase similar to water, and a dispersed phase comprising cells of irregular profile. In both phases the relevant mode of uptake is taken as bulk diffusion rather than surface permeation, thus emphasizing the influence of the internal geometry of the tissue upon its overall exchange response.     

Radial bulk diffusion into heterogeneous tissue

An expression is derived which describes the transient distribution of solute diffusing into heterogeneous tissue from a fully-stirred cylindrical region in which there has been a step change in solute concentration. This is envisaged as a model for the uptake of drugs by vessel walls, although the same approach has been extended for estimating the mode of total uptake of substances by annular specimens of tissue. Tissue is regarded as effectively composed of two phases—an extracellular (continuous) phase, similar to water, and a dispersed phase comprising cells of irregular profile. In each phase the relevant mode of uptake is taken as bulk diffusion rather than the permeation of a surface membrane.     

Determination of diffusion and permeability coefficients in muscle

A theory is presented for the study of diffusion in heterogeneous tissue-like structures. It is applicable to a common type of measurement in which the change of the amount of substance remaining in the tissue is determined as the substance diffuses from the tissue into an adjacent medium, for instance, Ringer's solution. The main objective of this paper is to obtain a method for the calculation of the diffusion coefficient in the intercellular space and of the permeability coefficients between this space and the cells, based on the type of measurement mentioned above. Although the fundamental ideas upon which the theory is based are applicable to any type of tissue, the formulae derived are limited to the case in which the cells form a flat bundle of parallel fibers. The theory is applied to the experimental results of E. J. Harris and G. P. Burn on diffusion of sodium in the sartorius muscle of the frog. We find that if we know the ratio of the cellular and intercellular volumes of the muscle the ratio of the equilibrium concentrations of sodium outside and inside the cells can be determined. A very simple mathematical analysis of the experimental relation between the amount of substance diffusing out of the muscle and the time of diffusion gives us this ratio. The ratio of the equilibrium sodium concentrations in the case of the sartorius frog muscle is between about 10 and 30, depending on the muscle used. The same mathematical analysis makes it possible to obtain the permeability coefficients of muscle fibers through simple calculations, if their sizes are known. The permeability coefficients for the experimental work mentioned above using sodium are 1.25 to 11.5×10⁻⁸ cm/sec for the flow into the fibers and 3.2 to 16×10⁻⁷ cm/sec for the flow in the opposite direction. The determination of the diffusion coefficient in the intercellular space is more laborious and yields only an order of magnitude: 10⁻⁶ cm²/sec.     

The temperature dependence of erythrocyte water diffusion permeability

1. The activation energy of the diffusion water exchange in red blood cells increases with temperature. 2. Fetal blood has a higher activation energy for diffusion water exchange than adult blood. 3. Treatment of red cells with p-chloromercuribenzoate alters the activation energy and apparently allows a lipid and a protein pore pathway to be resolved. The permeability and activation energy of the treated cells is in the range found for lipid membranes; and the difference between treated and untreated cells, the "protein" pathway, has a diffusion activation energy comparable with that of free water. 4. A resolution of the discrepancies between the NMR methods of measuring diffusion water exchange is suggested.     

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.     

Determination of diffusion and permeability coefficients in nerve trunks

A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.     

Axial diffusion and wall permeability effects in perfused capillary-tissue structures

Attempts to experimentally examine oxygen supply and distribution in the isolated perfused heart and brain have renewed interest in mathematical models of artificially perfused capillary-tissue structures. The need to understand histograms of PO2 measurements from these isolated-perfused organ studies (modified Lagendorf preparations) has required that existing mathematical models and their boundary conditions be re-examined in the context of these experiments. A unifying system of equations and boundary conditions are examined here for the purpose of studying the effects of anisotropic diffusion, and capillary vessel wall permeability on both the capillary and tissue substrate supply. The mathematical models are explored for parameters of physiologic interest, and some comparisons are made with experimental determinations. The comparisons with data suggest an anisotropic transport of oxygen in the tissue that is unexplained by known physiologic mechanisms.     

Effect of non-well-mixed compartment and bulk flow on diffusion through a pore

The assumptions of well-mixed and zero bulk flow in compartmental analysis are reexamined. Using Poiseuille flow inside and radial flow outside a pore, the mass-transfer equations are solved by perturbations on simple diffusion. Formulas are obtained for solute distribution, total mass transfer, and apparent permeability. The effects of non-well mixing and bulk flow are discussed.     

Water permeability of plant cuticles: permeance,diffusion and partition coefficients

Summary Using isolated cuticular membranes from ten woody and herbaceous plant species, permeance and diffusion coefficients for water were measured, and partition coefficients were calculated. The cuticular membranes of fruit had much higher permeance and diffusion coefficients than leaf cuticular membranes from either trees or herbs. Both diffusion and partition coefficients increased with increasing membrane thickness. Thin cuticles, therefore, tend to be better and more efficient water barriers than thick cuticles. We compared the diffusion coefficients and the water content of cuticles as calculated from transport measurements with those obtained from water vapor sorption. There is good to fair agreement for cuticular membranes with a low water content, but large discrepancies appear for polymer matrix membranes with high permeance. This is probably due to the fact that diffusion coefficients obtained from transport measurements on membranes with high permeance and water content are underestimated. Water permeabilities of polyethylene and polypropylene membranes are similar to those of leaf cuticular membranes. However, leaf cuticles have much lower diffusion coefficients and a much greater water content than these synthetic polymers. This suggests that cuticles are primarily mobility barriers as far as water transport is concerned.     

Determination of the permeability of human lymphocytes with a microscope diffusion chamber

A diffusion chamber similar to that proposed by J.J. McGrath (J. Microsc., in press) was constructed which allows microscopic observation of osmotically induced volume changes of individual cells in small (microliter) sample volumes. The cells are kept fixed in position in the upper compartment of the chamber by means of a highly permeable membrane and exposed to a step-like change in concentration generated in the lower compartment. An electrical conductivity probe in the upper compartment was used to monitor the temporal change of salt concentration as experienced by the cells. The rise from isotonic to hypertonic can be approximated by an exponential function. Its time constant of tau = 2.08 sec seems to be mainly determined by the change in flushing solution as tau = 1.48 sec was measured with no membrane installed. With human lymphocytes, no loss of cell volume was detected before 5 sec, i.e., when 95% of the final concentration was reached extracellularly. A step change can hence be assumed when modeling exosmosis for determining the lymphocyte membrane permeability. The equations for coupled transport of water and salt were solved numerically and fitted to the experimental data. The results were also compared to various other transport models described in the literature. Human lymphocytes are almost ideally semipermeable with a hydraulic reference permeability of Lp = 4.23 X 10(-4) cm/sec (3.13 X 10(-3) micron X atm-1 X sec-1) at T = 23 degrees C. The temperature and concentration dependence are described by an activation energy Ea = 14.3 kJ/mol and a concentration coefficient alpha 2 = 0.261 osmol/kg. An osmotically inactive volume fraction of 36.9% was determined from the final cell volumes reached asymptotically after shrinkage.     

Determination of catecholamine permeability coefficients for passive diffusion across phospholipid vesicle membranes

Summary A convenient catecholamine transport assay has been developed which permits continuous, instantaneous monitoring of transmembrane flux. Epinephrine transport has been examined by spectrophotometrically monitoring adrenochrome formation resulting from the passive diffusion of catecholamine into unilamellar phospholipid vesicles containing entrapped potassium ferricyanide. Ferricyanide oxidation of epinephrine under the conditions employed is fast compared to membrane transport, which obviates the need for intravesicular concentration or volume determinations. Epinephrine transport data over a pH 6 to 7 range have been fitted to an integrated rate equation from which a permeability coefficient for neutral epinephrine of 2.7±1.5×10^–6 cm/sec has been obtained.     

Importance of intracellular water apparent diffusion to the measurement of membrane permeability

The exchange of water across biological membranes is of fundamental significance to both animal and plant physiology. Diffusional membrane permeability (P(d)) for the Xenopus oocyte, an important model system for water channel investigation, is typically calculated from intracellular water pre-exchange lifetime, cell volume, and cell surface area. There is debate, however, whether intracellular water motion affects water lifetime, and thereby P(d). Mathematical modeling of water transport is problematic because the intracellular water diffusion rate constant (D) for cells is usually unknown. The measured permeability may be referred to as the apparent diffusional permeability, P, to acknowledge this potential error. Herein, we show that magnetic resonance (MR) spectroscopy can be used to measure oocyte water exchange with greater temporal resolution and higher signal-to-noise ratio than other methods. MR imaging can be used to assess both oocyte geometry and intracellular water diffusion for the same single cells. MR imaging is used to confirm the dependence of intracellular water lifetime on intracellular diffusion. A model is presented to relate intracellular lifetime to true membrane diffusional permeability. True water diffusional permeability (2.7 +/- 0.4 microm/s) is shown to be 39 +/- 6% greater than apparent diffusional permeability for 8 oocytes. This discrepancy increases with cell size and permeability (such as after water channel expression) and decreases with increasing intracellular water D.     

Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability

A better understanding of how hemodynamic factors affect the integrity and function of the vascular endothelium is necessary to appreciate more fully how atherosclerosis is initiated and promoted. A novel technique is presented to assess the relation between fluid dynamic variables and the permeability of the endothelium to macromolecules. Fully anesthetized, domestic swine were intravenously injected with the albumin marker Evans blue dye, which was allowed to circulate for 90 min. After the animals were euthanized, silicone casts were made of the abdominal aorta and its iliac branches. Pulsatile flow calculations were subsequently made in computational regions derived from the casts. The distribution of the calculated time-dependent wall shear stress in the external iliac branches was directly compared on a point-by-point basis with the spatially varying in vivo uptake of Evans blue dye in the same arteries. The results indicate that in vivo endothelial permeability to albumin decreases with increasing time-average shear stress over the normal range. Additionally, endothelial permeability increases slightly with oscillatory shear index.