The effects of resolution and segmentation on the accuracy and precision of the WSS algorithm were quantified. We were able to calculate volumetric WSS in the carotid bifurcation and the aorta.
The aim of this study is to quantify the porcine coronary arterial branching pattern and to use this quantification for the interpretation of flow heterogeneity. Two casts of the coronary arterial tree were made at diastolic arrest and maximal dilation. The relation between length and diameter of arterial segments was quantified, as well as the area expansion ratio and diameter symmetry of vascular nodes. These relations were used to construct computer models of the coronary arterial tree, covering diameters between 10 and 500 microns. Topology of these simulated trees was analyzed using Strahler ordering: Bifurcation ratio, diameter ratio, and length ratio were constant along orders 2-8 and equal to 3.30, 1.51, and 1.63, respectively. In each order, the number of segments per Strahler vessel was almost geometrically distributed. For the lowest orders, these predictions were confirmed by direct observations. From the network model, local pressure and flow were also predicted: Pressure fell from 90 to 32 mm Hg at the 10-microns level. The coefficient of variation (CV) of flow in individual segments was dependent on the number of perfused terminal segments (Nt) according to the fractal relation CV(Nt) approximately Nt(1-D), where D is the fractal dimension (1.20). CV of flow in 1-g tissue units was predicted to be 18%. This study shows that the structure of the coronary arterial bed is an important determinant of the fractal nature of local flow heterogeneity.
Local vessel wall shear stress is considered to be important for vessel growth. This study is a theoretical investigation of how this mechanism contributes to the structure of a vascular network. The analyses and simulations were performed on vascular networks of increasing complexity, ranging from single-vessel resistance to large hexagonal networks. These networks were perfused by constant-flow sources, constant-pressure sources, or pressure sources with internal resistances. The mathematical foundation of the local endothelial shear stress and vessel wall adaptation was as follows: delta d/delta t = K*(tau-tau desired)*d, where d is vessel diameter, tau desired is desired shear stress, and K is a growth factor. Single vessels and networks with vessels in series developed stable optimal diameters when perfused at constant flow or with a constant-pressure source with internal resistance. However, when constant-pressure perfusion was applied, these vessels developed ever-increasing diameters or completely regressed. In networks with two vessels in parallel, only one; vessel attained an optimal diameter and the other regressed, irrespective of the nature of the perfusion source. Finally, large hexagonal networks regressed to a single vessel when perfused with a pressure source with internal resistance. The behavior was independent of variation in parameters, although the adaptation rate and the diameter of the final vessel were altered. Similar conclusions hold for models of vascular trees. We conclude that the effect of shear stress on vascular diameter alone does not lead to stable network structures, and additional factor(s) must be present.
. Localization of the permeability barrier to solutes in isolated arteries by confocal microscopy. Am J Physiol Heart Circ Physiol 285: H2848-H2856, 2003. First published August 7, 2003 10.1152/ajpheart.00117.2003.-Endothelial cells are covered by a surface layer of membraneassociated proteoglycans, glycosaminoglycans, glycoproteins, glycolipids, and associated plasma proteins. This layer may limit transendothelial solute transport. We determined dimension and transport properties of this endothelial surface layer (ESL) in isolated arteries. Rat mesenteric small arteries (diameter ϳ150 m) were isolated and cannulated with a double-barreled -pipette on the inlet side and a regular pipette on the outlet side. Dynamics and localization of intraarterial fluorescence by FITC-labeled dextrans (FITC-⌬s) and the endothelial membrane dye DiI were determined with confocal microscopy. Large FITC-⌬ (148 kDa) filled a core volume inside the arteries within 1 min but was excluded from a 2.6 Ϯ 0.5-m-wide region on the luminal side of the endothelium during 30 min of dye perfusion. Medium FITC-⌬ (50.7 kDa) slowly penetrated this ESL within 30 min but did not permeate into the arterial wall. Small FITC-⌬ (4.4 kDa) quickly passed the ESL and accumulated in the arterial wall. Prolonged luminal fluorochrome illumination with a bright mercury lamp destroyed the ϳ3-m exclusion zone for FITC-⌬148 within a few minutes. This study demonstrates the presence of a thick ESL that contributes to the permeability barrier to solutes. The layer is sensitive to phototoxic stress, and its damage could form an early event in atherosclerosis. vascular permeability; isolated artery; endothelial surface layer; confocal microscopy; glycocalyx ENDOTHELIAL CELLS (ECs) are covered by a surface layer of membrane-associated proteoglycans, glycosaminoglycans, glycoproteins, glycolipids, and associated plasma proteins, known as the endothelial surface layer (ESL) (30). The functional properties of the ESL have been extensively described only recently. Biochemical research elucidates receptor functions of glycosaminoglycans within the ESL and the binding patterns of proteins to heparan sulfates (8,31,34). Biodegradation of sialic acid, an important constituent of the ESL, by neuraminidase inhibits shear-induced nitric oxide production (12, 29). The role of the ESL in the control of vascular wall permeability has been addressed in experimental studies (1, 21, 38) on microvessels and in new theoretical transport models (18). Vascular permeability forms an important parameter in the regulation of water and solute exchange between the circulation and tissues (10, 26). It is important that the intrusion of certain macromolecules into the arterial wall is limited. Inclusion of albumin and lowdensity lipoproteins into the subendothelial space forms part of the process of atherogenesis. Thus ESL dysfunction may contribute to the microvascular disease phenotype of atherosclerosis (4, 23, 24). An altered vascular permeability is one of the earliest detectable symptoms...
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