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 α-actin, calponin and SM22α, 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.

Arteries often endure axial twist due to body movement and surgical procedures, but how arteries remodel under axial twist remains unclear. The objective of this study was to investigate early stage arterial wall remodeling under axial twist. Porcine carotid arteries were twisted axially and maintained for three days in ex vivo organ culture systems while the pressure and flow remained the same as untwisted controls. Cell proliferation, internal elastic lamina (IEL) fenestrae shape and size, endothelial cell (EC) morphology and orientation, as well as the expression of matrix metalloproteinases (MMPs), MMP-2 and MMP-9, and tissue inhibitor of metalloproteinase-2 (TIMP-2) were quantified using immunohistochemistry staining and immunoblotting. Our results demonstrated that cell proliferation in both the intima and media were significantly higher in the twisted arteries compared to the controls. The cell proliferation in the intima increased from 1.33±0.21% to 7.63±1.89%, and in the media from 1.93±0.84% to 8.27±2.92% (p < 0.05). IEL fenestrae total area decreased from 26.07±2.13% to 14.74±0.61% and average size decreased from 169.03±18.85μm2 to 80.14±1.96μm2 (p < 0.01), but aspect ratio increased in the twisted group from 2.39±0.15 to 2.83±0.29 (p < 0.05). MMP-2 expression significantly increased (p < 0.05) while MMP-9 and TIMP-2 showed no significant difference in the twist group. The ECs in the twisted arteries were significantly elongated compared to the controls after three days. The angle between the major axis of the ECs and blood flow direction under twist was 7.46±2.44 degrees after 3 days organ culture, a decrease from the initial 15.58±1.29 degrees. These results demonstrate that axial twist can stimulate artery remodeling. These findings complement our understanding of arterial wall remodeling under mechanical stress resulting from pressure and flow variations.

The reversibility of tissue remodeling is of general interest to medicine. Pulmonary arterial tissue remodeling during hypertension induced by hypoxic breathing is well known, but little has been said about the recovery of the arterial wall when the blood pressure is lowered again. We hypothesize that tissue recovery is a function of the oxygen concentration, blood pressure, location on the vascular tree, and time. We measured the changes of blood pressure, vessel lumen, vessel wall thicknesses, and opening angle of each segment of the blood vessel at its zero-stress state after step changes of the oxygen concentration in the breathing gas. The zero-stress state of each vessel is emphasized because it is important to the analysis of stress and strain and in morphometry. Experimental results are presented as histories of tissue parameters after step changes of the oxygen level. Tissue characteristics are examined under the hypothesis that they are linearly related to changes in the local blood pressure. Under this linearity hypothesis, each aspect of the tissue change can be expressed as a convolution integral of the blood pressure history with a kernel called the indicial response function. It is shown the indicial response function for rising blood pressure is different from that for falling blood pressure. This difference represents a major nonlinearity of the tissue remodeling process of the blood vessels.indicial response function ͉ blood vessel opening angle at zero-stress state ͉ nonlinearity of tissue remodeling I t is well known that blood flow in pulmonary arteries becomes hypertensive when an animal breathes a gas the oxygen concentration of which is lower than that of normal sea level air. It is also known that hypertension leads to hypertrophy in blood vessels, and returning to normal blood pressure mitigates the symptom. The question is whether the processes of hypertrophy and recovery are symmetric. Considerable data on the building up of the lung tissue due to pulmonary hypertension have been obtained (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). Some data on recovery from hypertension are also given in refs. 1, 4, and 5. These studies considered neither the zero-stress state, which is characterized by an opening angle of the blood vessels, nor the elastic moduli of the blood vessel walls. The significance of the zero-stress state and the change of Young's modulus were recognized later (8,10,11,(15)(16)(17)(18)(19).So far as we are aware, there has been no study on the recovery of the zero-stress state of a vascular tissue that was subjected to hypertension for some time but was returned to the normal condition later. Recovery can be expected to be a complex function of space, time, stress, and strain. The objective of this article is to clarify these points. Materials and MethodsAnimals. Ninety-two male Sprague-Dawley rats (Harlan, San Diego), Ϸ3 months old, body weight 300-350 g, raised in normal air at sea level, were used. These rats were cared for 1 week or more after arrival at the vivari...

Blood vessels often experience torsion along their axes and it is essential to understand their biological responses and wall remodeling under torsion. To this end, a rat model was developed to investigate the arterial wall remodeling under sustained axial twisting in vivo. Rat carotid arteries were twisted at 180 degrees along the longitudinal axis through a surgical procedure and maintained for different durations up to 4 weeks. The wall remodeling in these twisted arteries was examined using histology, immunohistochemistry and fluorescent microscopy. Our data showed that arteries remodeled under twisting in a time-dependent manner during the 4 weeks post-surgery. Cell proliferation, MMP-2 and MMP-9 expressions, medial wall thickness and lumen diameter increased while collagen to elastin ratio decreased. While the size and number of internal elastic lamina fenestrae increased with elongated shapes, the endothelial cells elongated and aligned towards the blood flow direction gradually. These results demonstrated that sustained axial twisting results in artery remodeling in vivo. The rat carotid artery twisting model is an effective in vivo model for studying arterial wall remodeling under long-term torsion. These results enrich our understanding of vascular biology and arterial wall remodeling under mechanical stresses.