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S Weinbaum

Publications and source records attributed to S Weinbaum.

At least 55 records · Page 3Linked to original sources
PubMed1988

On the time dependent diffusion of macromolecules through transient open junctions and their subendothelial spread. 2. Long time model for interaction between leakage sites.

In Part 1 of this study (Weinbaum et al., 1988) a short time model has been proposed to describe the initial time dependent leakage of macromolecules at short distances (5 microns or less) from the exit of a transient open junction which the authors have hypothesized as a characteristic feature of endothelial cells in the process of turnover (Weinbaum et al., 1985). This open junction pathway has also been proposed (Weinbaum et al., 1988) to be the primary ultrastructural correlate of the 20 nm diameter large pore suggested by Renkin et al. (1977) using the predictions of cylindrical pore theory. The short time model in (Weinbaum et al., 1988), however, has major limitations in that it neglects the interaction between leakage sites, macromolecular entry through other pathways, the finite thickness of the vessel wall and the curvature of the cell perimeter. The longer time model developed herein will attempt to describe each of these features and also present an improved model and analytic solution for the steady state flux and uptake. In the previous steady state model developed by Weinbaum et al. (1985) the effect of the resistance of the transient open junctions and the non-isotropic diffusion in the underlying tissue due to the internal elastic lamina (IEL) were both neglected. New solutions are first presented which describe the effect of these important model refinements on the steady state macromolecular permeability of the major arteries. Time dependent solutions are then presented to predict the transient longer time labeling following the introduction of tracer macromolecules of varying size. These solutions and the corresponding short time solutions in Weinbaum et al. (1988) are the first solutions to our knowledge to describe the difficult time-dependent boundary value problem to determine how the channel exit concentration and flux at a leaky junction vary with time. This is accomplished by casting the boundary value problem in the form of an integral equation for the unknown flux at the cleft exit and then solving this problem using a specially designed numerical technique. The theoretical predictions are used to interpret the behavior of the localized leaks to HRP and albumin that have been reported in Stemerman et al. (1986) and our own recent experiments (Lin et al., 1988).

Animals↗
PubMed1988

On the time-dependent diffusion of macromolecules through transient open junctions and their subendothelial spread. I. Short-time model for cleft exit region.

In this two-part study we shall quantitatively study, using time-dependent models, the hypothesis that transient open junctions associated with widely scattered endothelial cells undergoing mitosis are the structural equivalent for the large pore pathway via which macromolecules the size of albumin or larger cross the vascular endothelium. In an earlier steady-state model [Am. J. Physiol. 248, H945-960 (1985)], the authors demonstrated that such an open-junction pathway could quantitatively account for the regional differences in macromolecular permeability observed in various mammalian arteries in regions of enhanced cell turnover as indicated by 3H-thymidine although these cells were less than 1% of the population and the open junctions occupied less than 10(-5) of the endothelial surface. The time-dependent models described herein have been used to identify a time window and size of probe molecule wherein this hypothesis could be tested experimentally in the larger blood vessels. The first stages of these experiments have now been completed and provide convincing evidence that the junctions of virtually all endothelial cells in the M phase of the cell cycle are leaky to macromolecules (Lin et al., 1988). The statistical frequency of such leakage sites has also been determined. The time-dependent models developed herein contain two important refinements that were not contained in the earlier steady state model. First the finite resistance of the open cleft as a function of molecular size is accounted for by introducing a diffusion coefficient ratio Dj/Dz describing the relative resistance of the open cleft compared to the subendothelial tissue in the direction normal to the endothelial surface. Second the non-isotropy of the vessel wall due to the elastic lamina is considered by introducing a second diffusion coefficient ratio Dx/Dz describing the relative resistance in the lateral as compared to the normal direction. This second ratio can be as large as 100 for the arterial intima, but is of order unity for capillaries. In Part I a short time model is presented to describe the initial labeling of the open cleft and the subendothelial space in the vicinity of the cleft exit following the introduction of a tracer macromolecule. This model is valid for both larger vessels and capillaries since wall thickness and curvature and the interaction between leakage sites does not enter into the model description. In Part II (Wen et al., 1988) a long-time model is developed for larger vessels only which is valid for greater times including steady-state labeling.

Albumins↗
PubMed1988

The role of arterial endothelial cell mitosis in macromolecular permeability.

The present experiments were performed on twelve male Wistar rats to study the quantitative, topographic correlation between transendothelial permeability of Evans Blue-albumin (EBA) conjugate and endothelial cell replication at the single-cell level. En face preparations of the thoracic aorta were examined by fluorescence microscopy. We found a high degree of correlation between endothelial cell mitosis and EBA leaky spots. Although endothelial cell mitosis is very rare in occurrence, nearly all junctions around the dividing cells were leaky (99%), in contrast to only 0.03% of the non-mitotic cells. In addition, electron microscopic observations showed that the junction around a dividing endothelial cell is leaky, whereas that around a dying cell is not. With the aid of our theoretical model, we were able to analyze the dynamics of macromolecular passage through leaky endothelial junctions. The duration of endothelial cell mitosis was estimated to be 67 min, which constituted 0.01% of the duration of the total cell cycle. The time-dependent change in junctional geometry during endothelial cell turnover leads to an inverse relationship between macromolecular size and duration of junctional leakage. For albumin the duration of leakiness across aortic endothelial cell is approximately 3.7 hr. The present findings lend support to our hypothesis that transiently open junctions surrounding the dividing endothelial cells provide the major pathway through which macromolecules enter the subendothelial space to result in lipid accumulation.

Animals↗
PubMed1988

Enhanced macromolecular permeability of aortic endothelial cells in association with mitosis.

Experiments were performed on thoracic aortae of 12 male Sprague-Dawley [corrected] rats to determine the statistical frequency of isolated leaks to Evans blue-albumin (EBA) conjugate at the level of individual cells and to assess the relationship of such leaks to the cell turnover process. Fluorescence microscopy was used to detect leakage of EBA around individual cells, and hematoxylin staining was used to identify cells in mitosis on the same specimens. Although endothelial cell mitosis is very rare in occurrence, 99% of the cells in the M phase were associated with EBA leakage. Since these dividing cells accounted for only one third of all cellular leakage sites, we concluded that significant leakage also occurred in other phases of the cell cycle, probably prior to and after the M phase, or during non-denuding desquamation.

Albumins↗
PubMed1988

On the generalization of the Weinbaum-Jiji bioheat equation to microvessels of unequal size; the relation between the near field and local average tissue temperatures.

The extensive series of experiments reported in Lemons et al. [1] show that measureable local tissue temperature fluctuations are observed primarily in the vicinity of the 100-500 micron countercurrent vessels of the microcirculation and thus strongly support the basic hypothesis in the new bioheat equation of Weinbaum and Jiji [2] that these countercurrent microvessels are the principal determinants of local blood-tissue heat transfer. However, the detailed temperature profiles in the vicinity of these vessels indicate that large asymmetries in the local temperature field can result from the significant differences in size between the countercurrent artery and vein. Using the superposition techniques of Baish et al. [9], the paper first presents a solution to the classic problem of an unequal countercurrent heat exchanger with heat loss to the far field. This solution is then used to generalize the Weinbaum-Jiji bioheat equation and the conductivity tensor that appears in this equation to vessels of unequal size. An asymptotic analysis has also been developed to elucidate the relationship between the near field temperature of the artery-vein pair and the local average tissue temperature. This analysis is used to rigorously prove the closure approximation relating the local arterial-venous temperature difference and the mean tissue temperature gradient which had been derived in [2] using a more heuristic approach.

Arterioles↗
PubMed1988

A combined macro and microvascular model for whole limb heat transfer.

A new prototype model for whole limb heat transfer is proposed wherein the countercurrent heat exchange from the large central arteries and veins in the core of the limb is coupled to microvascular models for the surrounding muscle and the cutaneous tissue layers. The local microvascular temperature field in the muscle tissue is described by the bioheat equation of Weinbaum and Jiji. The new model allows for an arbitrary axial variation of cross-sectional area and blood distribution between the muscle and cutaneous tissue, accounts for the blood flow to and heat loss from the hand and treats the venous return temperature and surface temperature distribution as unknowns that are determined as part of the solution to the overall boundary value problem. Representative solutions are presented for a wide range of environmental conditions for a limb in both the resting state and during exercise.

Arm↗
PubMed1987

A theoretical model for peripheral tissue heat transfer using the bioheat equation of Weinbaum and Jiji.

In this paper the new bioheat equation derived in Weinbaum and Jiji is applied to the three layer conceptual model of microvascular surface tissue organization proposed in. A simplified one-dimensional quantitative model of peripheral tissue energy exchange is then developed for application in limb and whole body heat transfer studies. A representative vasculature is constructed for each layer and the enhancement in the local tensor conductivity of the tissue as a function of vascular geometry and blood flow is examined. Numerical solutions for the boundary value problem coupling the three layers are presented and these results used to study the thermal behavior of peripheral tissue for a wide variety of physiological conditions from supine resting state to maximum exercise.

Animals↗
PubMed1987

Significance of vessel size and type in vascular heat transfer.

This study was undertaken to gain a better understanding of the fundamental mechanisms of micro- and macrovascular heat transfer by experimentally identifying those vessels most important in the process. Tissue temperature fields around thermally nonequilibrated vessels were determined using a small temperature sensor that was guided through the rabbit thigh to generate a detailed temperature map. The measurements revealed that the lower limit of vessel size for thermal nonequilibration was 100 microns for arteries and 400 microns for veins. Local temperature fields were found around four of the five (80%) arteries that were greater than 300 microns in diameter but in only 3 of the 12 (25%) veins greater than 400 microns. These experimental results are in good agreement with previously published theoretical studies (5) in which it was concluded that thermal equilibration in the branching countercurrent vascular network of the rabbit limb occurs in vessels an order of magnitude larger than the capillaries. In those studies the smallest vessels capable of carrying heat were predicted to be 50 microns ID with the major blood tissue heat exchange occurring in vessels greater than 100 micron ID. These findings contrast with the view that most heat transfer occurs in the capillaries and suggest that vascular heat transfer analysis must take into account the vascular architecture of the 50- to 1,000-micron vessels where most heat transfer occurs.

Animals↗
PubMed1986

A theoretical model to study the effect of convection and leaky junctions on macromolecule transport in artery walls.

A mathematical model is presented herein to determine the effect of convection on macromolecular transport across an artery wall due to transmural or osmotic pressure differences. The model is based on an extension of the leaky junction-cell turnover model of Weinbaum et al. (1985) to take into account a combined transport mechanism of convection and diffusion and also to provide the leaky junctions in the model with a finite resistance, thus allowing the results to be extended to intercellular clefts with a retarding extracellular matrix or to macromolecules whose dimensions are nearly the same as the junctional width. The results from this improved model show that the effect of pressure on transarterial macromolecular transport is important especially for cell turnover rates greater than 1% and that significant changes in the equilibrium balance of the cholesterol carrying LDL molecules in the arterial wall can occur due to a very small fraction of leaky junctions. At very high turnover rates (large fraction of leaky junctions) the effect of convection on macromolecular transport becomes dramatic and explains the very large increases in uptake observed experimentally after artificially inducing extensive endothelial damage.

Animals↗
PubMed1986

Parametric studies on the three-layer microcirculatory model for surface tissue energy exchange.

The new three-layer microvascular mathematical model for surface tissue heat transfer developed in, which is based on detailed vascular casts and tissue temperature measurements in the rabbit thigh, is used to investigate the thermal characteristics of surface tissue under a wide variety of physiological conditions. Studies are carried out to examine the effects of vascular configuration, arterial blood supply rate, distribution of capillary perfusion, cutaneous blood circulation and metabolic heat production on the average tissue temperature profile, the local arterial-venous blood temperature difference in the thermally significant countercurrent vessels, and surface heat flux.

Body Temperature Regulation↗
PubMed1985

A steady-state filtration model for transluminal water movement in small and large blood vessels.

It is now generally accepted that the intercellular cleft between adjacent endothelial cells is the primary pathway for the transluminal movement of water and small ions in the vasculature. A steady-state theoretical model has been developed to show quantitatively how the geometry of the intercellular cleft between adjacent endothelial cells is related to both the water movement and pressure distribution in the subendothelial space and to examine how the existence of a subendothelial interaction layer affects the hydraulic resistance of the media of vessels of varying wall thickness. The velocity and pressure fields in the media are described using porous matrix theory based on Darcy's law and a lubrication-type analysis is used to describe the flow in a variable geometry intercellular cleft. These two equations are solved simultaneously to determine the unknown pressure distribution beneath the endothelium and the flow in the arterial media. Application of this model shows that, when the tight junction in the cleft is 26 A or less, more than half of the total hydraulic resistance of the wall occurs across the endothelial cell monolayer, for a vessel whose wall thickness is less than 0.02 cm. This finding is in good agreement with the experimental findings of Vargas, et al. (1978) for rabbit aorta. Contrary to previous belief, the model shows that the filtration resistance of an arterial wall with intact endothelium does not scale linearly with wall thickness due to the highly nonlinear resistance of the endothelial interaction layer.

Animals↗
PubMed1985

A new simplified bioheat equation for the effect of blood flow on local average tissue temperature.

A new simplified three-dimensional bioheat equation is derived to describe the effect of blood flow on blood-tissue heat transfer. In two recent theoretical and experimental studies [1, 2] the authors have demonstrated that the so-called isotropic blood perfusion term in the existing bioheat equation is negligible because of the microvascular organization, and that the primary mechanism for blood-tissue energy exchange is incomplete countercurrent exchange in the thermally significant microvessels. The new theory to describe this basic mechanism shows that the vascularization of tissue causes it to behave as an anisotropic heat transfer medium. A remarkably simple expression is derived for the tensor conductivity of the tissue as a function of the local vascular geometry and flow velocity in the thermally significant countercurrent vessels. It is also shown that directed as opposed to isotropic blood perfusion between the countercurrent vessels can have a significant influence on heat transfer in regions where the countercurrent vessels are under 70-micron diameter. The new bioheat equation also describes this mechanism.

Animals↗
PubMed1985

Effect of cell turnover and leaky junctions on arterial macromolecular transport.

A new quantitative model is presented to explore the changes in vascular permeability that would result if the intercellular clefts around widely scattered endothelial cells were to become leaky to macromolecules in the range of roughly 4-10 nm during normal cell turnover. Although these open junctions occupy less than 10(-5) of the en face area of the endothelial surface, it is shown that the endothelial permeability can increase by 50-100% due to the experimentally observed regional variations in turnover in the larger arteries, whereas in the thinner walled veins and smaller arteries the subendothelial concentration is not significantly elevated. These results provide a very plausible explanation for the observed focal differences in the uptake of 125I-albumin and 131I-fibrinogen in blue and white areas and the nonselectivity of the local enhancement in uptake for these two molecules as a function of molecular size. The model has important implications for the localization of atherogenesis and the importance of endothelial cell turnover on the transport of proteins in vessels of all sizes.

Arteries↗
PubMed1984

Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer--Part I: Anatomical foundation and model conceptualization.

A new theoretical model supported by ultrastructural studies and high-spatial resolution temperature measurements is presented for surface tissue heat transfer in a two-part study. In this first paper, vascular casts of the rabbit thigh prepared by the tissue clearance method were serially sectioned parallel to the skin surface to determine the detailed variation of the vascular geometry as a function of tissue depth. Simple quantitative models of the basic vascular structures observed were then analyzed in terms of their characteristic thermal relaxation lengths and a new three-layer conceptual model proposed for surface tissue heat transfer. Fine wire temperature measurements with an 80-micron average diameter thermocouple junction and spatial increments of 20 micrometers between measurement sites have shown for the first time the detailed temperature fluctuations in the microvasculature and have confirmed the fundamental assumptions of the proposed three-layer model for the deep tissue, skeletal muscle and cutaneous layers.

Animals↗
PubMed1984

Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer--Part II: Model formulation and solution.

In this paper the conceptual three-layer representation of surface tissue heat transfer proposed in Weinbaum, Jiji and Lemons [1], is developed into a detailed quantitative model. This model takes into consideration the variation of the number density, size and flow velocity of the countercurrent arterio-venous vessels as a function of depth from the skin surface, the directionality of blood perfusion in the transverse vessel layer and the superficial shunting of blood to the cutaneous layer. A closed form analytic solution for the boundary value problem coupling the three layers is obtained. This solution is in terms of numerically evaluated integrals describing the detailed vascular geometry, a capillary bleed-off distribution function and parameters describing the shunting of blood to the cutaneous layer. Representative heat transfer results for typical physiological conditions are presented.

Animals↗