To establish a mathematical model of the tree like arteries for the purpose of hemodynamic analysis, a complete set of morphometric data of pig coronary arteries is presented. For the purpose of mathematical modeling, three innovations in morphometry are introduced: 1) a rule for assigning the order numbers of the vessels on the basis of diameter ranges, 2) a connectivity matrix to describe asymmetric branching, and 3) a measurement of the fraction of vessel segments connected in series. The morphometric measurements were made with the silicone elastomer-casting method. Data on smaller vessels were obtained from histological specimens by optical sectioning. Data on larger vessels were obtained from vascular casts. The order number, diameter, length, connectivity matrix, and fractions of the vessels of a given order connected in series were measured for all orders of vessels of the right coronary artery and the left anterior descending and left circumflex branches. The data can be used to analyze the longitudinal distribution of blood pressure and volume and spatial distribution of perfusion in myocardium.

The microstructural basis for the mechanical properties of blood vessels has not been directly determined because of the lack of a nondestructive method that yields a three-dimensional view of these vascular wall constituents. Here, we demonstrate that multiphoton microscopy can be used to visualize the microstructural basis of blood vessel mechanical properties, by combining mechanical testing (distension) of excised porcine coronary arteries with simultaneous two-photon excited fluorescence and second-harmonic generation microscopy. Our results show that second-harmonic generation signals derived from collagen can be spectrally isolated from elastin and smooth muscle cell two-photon fluorescence. Two-photon fluorescence signals can be further characterized by emission maxima at 495 nm and 520 nm, corresponding to elastin and cellular contributions, respectively. Two-dimensional reconstructions of spectrally fused images permit high-resolution visualization of collagen and elastin fibrils and smooth muscle cells from intima to adventitia. These structural features are confirmed by coregistration of multiphoton microscopy images with conventional histology. Significant changes in mean fibril thickness and overall wall dimension were observed when comparing no load (zero transmural pressure) and zero-stress conditions to 30 and 180 mmHg distension pressures. Overall, these data suggest that multiphoton microscopy is a highly sensitive and promising technique for studying the morphometric properties of the microstructure of the blood vessel wall.

As the function of the gastrointestinal tract is to a large degree mechanical, it has become increasingly popular to acquire distensibility data in motility research based on various parameters. Hence it is important to know on which geometrical and mechanical assumptions the various parameters are based. Currently, compliance and tone derived from pressure-volume curves are by far the most often used parameters. However, pressure-volume relations obtained in tubular organs must be carefully interpreted as they provide no direct measure of luminal cross-sectional area and other variables useful in plane stress and strain analysis. Thus, erroneous conclusions concerning tissue distensibility may be deduced. Other parameters, such as wall tension, stress and strain, give more useful information about mechanical behaviour. Distensibility data procure significance in fluid mechanics and in the study of tone, peristaltic reflexes, and mechanoreceptor kinematics. Such data are needed for the determination of the interaction between stimulus, electrical responses in neurons and the mechanical behaviour of the gut. Furthermore, from a clinical perspective, investigation of visco-elastic properties is important because GI diseases are associated with growth and remodelling. For example, prestenotic dilatation, increased collagen synthesis, dysmotility and altered distensibility are common features of obstructive diseases. The purpose of this review is to discuss the physiological and clinical importance of acquiring biomechanical data, distensibility parameters and interpretation of these results and their associated errors. We will also discuss some aspects of the relationship between morphology, growth and biomechanics. Finally, we will outline a number of techniques to study the mechanical properties of the GI tract.

Blood vessels are under constant mechanical loading from blood pressure and flow which cause internal stresses (endothelial shear stress and circumferential wall stress, respectively). The mechanical forces not only cause morphological changes of endothelium and blood vessel wall, but also trigger biochemical and biological events. There is considerable evidence that physiologic stresses and strains (stretch) exert vasoprotective roles via nitric oxide and provide a homeostatic oxidative balance. A perturbation of tissue stresses and strains can disturb biochemical homeostasis and lead to vascular remodelling and possible dysfunction (e.g. altered vasorelaxation, tone, stiffness, etc.). These distinct biological endpoints are caused by some common biochemical pathways. The focus of this brief review is to point out some possible commonalities in the molecular pathways in response to endothelial shear stress and circumferential wall stretch.

Objective-The regulation of AMP-activated protein kinase (AMPK) is implicated in vascular biology because AMPK can phosphorylate endothelial NO synthase (eNOS). In this study, we investigate the regulation of the AMPK-eNOS pathway in vascular endothelial cells (ECs) by shear stress and the activation of aortic AMPK in a mouse model with a high level of voluntary running (High-Runner). Methods and Results-By using flow channels with cultured ECs, AMPK Thr172 phosphorylation was increased with changes of flow rate or pulsatility. The activity of LKB1, the upstream kinase of AMPK, and the phosphorylation of eNOS at Ser1179 were concomitant with AMPK activation responding to changes in flow rate or pulsatility. The blockage of AMPK by a dominant-negative mutant of AMPK inhibited shear stress-induced eNOS Ser1179 phosphorylation and NO production. Furthermore, aortic AMPK activity and level of eNOS phosphorylation were significantly elevated in the aortas of High-Runner mice. Conclusions-Our results suggest that shear stress activates AMPK in ECs, which contributes to elevated eNOS activity and subsequent NO production. Hence, AMPK, in addition to serving as an energy sensor, also plays an important role in regulating vascular tone. Key Words: endothelium Ⅲ AMPK Ⅲ nitric oxide synthase Ⅲ shear stress Ⅲ exercise E ndothelium-derived NO can enhance vascular functions, including vessel relaxation, survival of vascular endothelial cells (ECs), inhibition of platelet aggregation, and attenuation of leukocyte infiltration. 1,2 Impaired NO bioavailability has been suggested as one of the earliest pathophysiological events preceding endothelial dysfunction and contributing to atherosclerosis. 3,4 Shear stress is an important physiological stimulus that enhances the production of NO by ECs. 2,5 An increase in shear stress such as in exercise augments the EC-mediated bioavailability of NO. 6 Endothelial NO synthase (eNOS), the key enzyme for NO production in ECs, is tightly regulated not only at the transcriptional level but also by several post-translational mechanisms. The enhanced phosphorylation of Ser1179 of bovine eNOS (Ser1177 in humans) leads to increased eNOS activity. Mounting evidence has shown that shear stress enhances the phosphorylation of Ser1177/1179. 7-9 Use of the phosphatidylinositol 3-kinase (PI3K) inhibitor wortmannin and LY 294002 has demonstrated that Akt phosphorylates eNOS Ser1177/1179 in response to shear stress. 7,8 However, dominant-negative mutants of Akt were unable to block the shear stress-stimulated Ser1179 phosphorylation. 9 Further, H89, a protein kinase A (PKA) inhibitor, and an adenovirusexpressing PKA inhibitor (PKI) blocked the eNOS Ser1179 phosphorylation, which indicates the involvement of PKA. 9 -12 Functioning as a metabolic master switch, AMP-activated protein kinase (AMPK) senses and regulates the cellular energy status in various cell types. AMPK is activated by several physiological and pathological stresses such as exercise, hypoxia, and nutrient depletion that result in incre...

To provide a morphometric basis for any mathematical modeling of the coronary vasculature, data on the network of coronary capillary blood vessels and the topology of the arteriolar supply and venular drainage relative to the capillaries are presented. The diameters, lengths, and branching patterns of the coronary capillary blood vessels in the right and left ventricles of four pigs were measured. The locations of the coronary arterioles and venules were identified, topological maps were constructed, and the mean functional length of capillaries connecting an arteriole to an adjacent venule was measured. The vasculature was fixed by perfusing the coronary vessels with a catalyzed polymer. After the polymer hardened, plugs of the myocardium were removed, sectioned, dehydrated, and cleared to render the capillary network visible in a light microscope. The capillaries then were traced by optical sectioning. We designated the capillaries as blood vessels of order number zero; we further designated the capillaries as those fed directly by arterioles (C0a), those drained directly into venules (C0v), and those capillary vessels connected to C0a and C0v. The capillaries are connected in patterns identified as Y, T, H, or hairpin and anastomosed through capillary cross-connections (Ccc). The Ccc vessels may connect adjacent capillaries or capillaries originating from different arterioles. The connection among the capillaries, arteries, and veins is presented in terms of a connectivity matrix. Combining the present data with those for the arterial and venous trees, we have obtained a complete set of statistical data of all the blood vessels of the heart of the pig. Such a data set will serve as the basis of coronary hemodynamics.

This is a third part of tripartite morphometric data of the pig coronary blood vessels, giving a complete quantitative description of the arterial tree [Kassab et al., Am. J. Physiol. 265 (Heart Circ. Physiol. 34): H350-H365, 1993], capillary network [Kassab and Fung, Am. J. Physiol. 267 (Heart Circ. Physiol. 36): H319-H325, 1994], and venous tree (this article). Together they provide the quantitative anatomic foundation for coronary hemodynamics. The coronary venules have a unique morphology. Unlike coronary arterioles, which have cylindrical cross sections and a fairly constant diameter in each segment, the venules have approximately elliptical cross sections, are usually wavy in the longitudinal direction, and often converge like fingers to a hand. Measurements were made with the silicone elastomer casting method on five pig hearts. Data on smaller vessels were obtained from histological specimens by optical sectioning. Data on larger vessels were obtained from vascular casts. Arcading veins and anastomoses on the epicardial surface have a unique topology. Data on the number of vessels in each order, the major and minor axes, length, connectivity matrix, and the fractions of the vessels of a given order connected in series in all orders of vessels of the sinusal and thebesian veins are presented. It is shown that of the blood in the coronary blood vessels of a pig heart 27.4% is in the arteries (> 200 microns), 37.1% is in veins (> 200 microns), and 35.5% is in microcirculation (< 200 microns), of which 89.4% is in the capillaries.

The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e.g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaling laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steady-state conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles.