For modeling of a vascular tree for hemodynamic analysis, the well-known Weibel, Horsfield, and Strahler systems have three shortcomings: vessels of the same order are all treated as in parallel, despite the fact that some are connected in series; histograms of the diameters of vessels in the successive orders have wide overlaps; and the "small-twigs-on-large-trunks" phenomenon is not given a quantitative expression. To improve the accuracy of the hemodynamic circuit model, we made a distinction between vessel segments and vessel elements: a segment is a vessel between two successive nodes of bifurcation; an element is a union of a group of segments of the same order that are connected in series. In an equivalent circuit, all elements of the same order are considered as arranged in parallel. Then, we follow the ordering method of Horsfield and Strahler, with introduction of an additional rule for the assignment of order numbers. If Dn and SDn denote the mean and standard deviation of the diameters of vessels of order n, then our rule divides the gap between Dn--SDn and Dn--1 + SDn--1 evenly between orders n and n--1. Finally, we introduced a connectivity matrix with a component in the mth row and the nth column that is the average number of vessels of order m that grow out of the vessels of order n. This method was applied to the rat. We found that the rat pulmonary arterial tree has 11 orders of vessels and that the geometry is fractal within these orders. The ratios of diameters, lengths, and numbers of elements in successive orders are 1.58, 1.60, and 2.76, respectively. The connectivity matrix reveals interesting features beyond the fractal concept. New features are found in the variation of the total cross-sectional area of elements with order numbers.
Vascular endothelial cells (ECs) are constantly exposed to blood flow-induced shear stress; these forces strongly influence the behaviors of neighboring vascular smooth muscle cells (VSMCs). VSMC migration is a key event in vascular wall remodeling. In this study, the authors assessed the difference between VSMC migration in VSMC/EC coculture under static and shear stress conditions. Utilizing a parallel-plate coculture flow chamber system and Transwell migration assays, they demonstrated that human ECs cocultured with VSMCs under static conditions induced VSMC migration, whereas laminar shear stress (1.5 Pa, 15 dynes/cm2) applied to the EC side for 12 h significantly inhibited this process. The changes in VSMC migration is mainly dependent on the close interactions between ECs and VSMCs. Western blotting showed that there was a consistent correlation between the level of Akt phosphorylation and the efficacy of shear stress-mediated EC regulation of VSMC migration. Wortmannin and Akti significantly inhibited the EC-induced effect on VSMC Akt phosphorylation and migration. These results indicate that shear stress protects against endothelial regulation of VSMC migration, which may be an atheroprotective function on the vessel wall.
A dynamic model is proposed for shear stress induced adenosine triphosphate (ATP) release from endothelial cells (ECs). The dynamic behavior of the ATP/ADP concentration at the endothelial surface by viscous shear flow is investigated through simulation studies based on the dynamic ATP release model. The numerical results demonstrate that the ATP/ADP concentration against time at endothelium-fluid interface predicted by the dynamic ATP release model is more consistent with the experimental observations than that predicted by previous static ATP release model.
Background/Aims: Physiological mechanical stretch in vivo helps to maintain the quiescent contractile differentiation of vascular smooth muscle cells (VSMCs), but the underlying mechanisms are still unclear. Here, we investigated the effects of SIRT1 in VSMC differentiation in response to mechanical cyclic stretch. Methods and Results: Rat VSMCs were subjected to 10%-1.25Hz-cyclic stretch in vitro using a FX-4000T system. The data indicated that the expression of contractile markers, including 伪-actin, calponin and SM22伪, was significantly enhanced in VSMCs that were subjected to cyclic stretch compared to the static controls. The expression of SIRT1 and FOXO3a was increased by the stretch, but the expression of FOXO4 was decreased. Decreasing SIRT1 by siRNA transfection attenuated the stretch-induced expression of contractile VSMC markers and FOXO3a. Furthermore, increasing SIRT1 by either treatment with activator resveratrol or transfection with a plasmid to induce overexpression increased the expression of FOXO3a and contractile markers, and decreased the expression of FOXO4 in VSMCs. Similar trends were observed in VSMCs of SIRT1 (+/-) knockout mice. The overexpression of FOXO3a promoted the expression of contractile markers in VSMCs, while the overexpression of FOXO4 demonstrated the opposite effect. Conclusion: Our results indicated that physiological cyclic stretch promotes the contractile differentiation of VSMCs via the SIRT1/FOXO pathways and thus contributes to maintaining vascular homeostasis.
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