四氧嘧啶糖尿病大鼠主动脉零应力状态的变化

目的和方法：将沿径向切开的糖尿病大鼠及对照大鼠主动脉坏分别转正圩Ｋｒｅｂｓ液中,向其中分别加入缩血管物质及舒血管物质达各种浓度;观察其角度变化。用Ｓ－Ｐ法对大鼠主动脉壁肌动蛋白进行染色。结果：四氧嘧啶糖尿病大鼠病程４周时主动脉环展开角显著大于对照（Ｐ〈０．００１）。使用药物后大鼠主动脉坏展开角与使用前相比无明显差异（Ｐ〉０．０５）。糖尿病大鼠主动脉壁肌动蛋白色较对照组明显加深、染色的光密度显著大于     

Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction

Examination of changes occurring in the zero-stress state of an organ provides a way to study cellular growth in the organ due to change of physical stresses. The zero-stress state of the aorta is not a tube. It is a sector with an opening angle that varies with the location on the aorta and changes with cellular remodeling. Blood vessel remodeling can be induced by imposing a constriction on the abdominal aorta by a metal clip (aortic banding), which causes an increase of blood pressure, hypertrophy of the aortic wall, and large change of opening angle. The correlation of the opening angle with the blood vessel wall thickness and blood pressure changes in rat's aorta due to aortic banding is presented in this report. The opening angle changes daily following the aortic banding. Blood pressure rises in vessels of the upper body, but that in the lower body decreases at first and then rises to an asymptotic value. Blood vessel wall thickness increases in rough proportion to blood pressure. Vessel diameter changes also. But the most dramatic is the course of change of the zero-stress state. Typically, the time to reach 50 percent of asymptotic hypertrophy of blood vessel wall thickness is about 3-5 days. The corresponding time for blood pressure is about 7 days. The opening angle of the zero-stress state, however, increases rapidly at first, reaches a peak in about 2 to 4 days, then decreases gradually to a reduced asymptote. The exact values of the time constants depend on the location along the aortic tree. In general, the course of change of residual strain is very different from those of the blood pressure and the blood vessel wall thickness.     

Zero-stress states of arteries

The no-load configuration of a living organ is, in general, not the zero-stress state. The difference can be revealed by cutting up an unloaded organ to such an extent that the stress becomes zero in the tissue everywhere. For the aorta, it is shown that the configuration of the zero-stress state differs considerably from being a cylindrical tube. It is, in fact, an open sector with opening angles varying along the arterial tree. This article presents data on the zero-stress state in the arteries of the rat in normal condition.     

Biomechanical and morphometric properties of the arterial wall referenced to the zero-stress state in experimental diabetes

Morphometric and passive biomechanical properties were studied in isolated segments of the thoracic and abdominal aorta, left common carotid artery, left femoral artery and the left pulmonary artery in 20 non-diabetic and 28 streptozotocin (STZ)-induced diabetic rats. The diabetic and non-diabetic rats were divided into groups living 1, 4, 8, and 12 weeks after the induction of diabetes (n = 7 for each diabetic group) or sham injection (n = 5 for each group). The mechanical test was performed as a distension experiment where the proximal end of the arterial segment was connected via a tube to the container used for applying pressures to the segment and the distal end was left free. The vessel diameter and length were obtained from digitized images of the arterial segments at pre-selected pressures and at no-load and zero-stress states. Circumferential and longitudinal stresses (force per area) and strains (deformation) were computed from the length, diameter and pressure data and from the zero-stress state data. The zero-stress state was obtained by cutting vessel rings radially causing the rings to open up into a sector. Diabetes was associated with pronounced morphometric changes, e.g., wall thickness. With respect to the biomechanical data, the opening angle increased and reached a plateau in 4 weeks after which it decreased again (p < 0.05). The opening angle was smallest in the thoracic aorta and largest in the pulmonary artery. Furthermore, it was found that the circumferential stiffness of the arteries studied increased with the duration of diabetes. In the longitudinal direction significant differences were found 8 weeks after injection of STZ in all arteries except the pulmonary artery. In the 12 weeks group, the femoral artery was stiffest in the circumferential direction whereas the thoracic aorta was stiffest in the longitudinal direction. The accumulated serum glucose level correlated with the arterial wall thickness and elastic modulus (correlation coefficient between 0.56 and 0.81).     

Use of tensorial description in tissue remodeling: examples of F-actin distributions in pulmonary arteries in hypoxic hypertension

A molecular configuration tensor Pij was introduced to analyze the distribution of fibrous proteins in vascular cells for studying cells and tissues biomechanics. We have used this technique to study the biomechanics of vascular remodeling in response to the changes of blood pressure and flow. In this paper, the remodeling of the geometrical arrangement of F-actin fibers in the smooth muscle cells in rat's pulmonary arteries in hypoxic hypertension was studied. The rats were exposed to a hypoxia condition of 10% for 0, 2, 12, and 24 hr at sea level. Remodeling of blood vessels were studied at the in vivo state under normal perfusion, no-load state when small rings from blood vessels were excised, and zero-stress state after the rings were cut open radially to release the residual stress. Tissue remodeling in response to changes in blood pressure is reflected in the zero-stress state. The tensor components were determined by analyzing the configuration of phalloidin stained F-actin fibers in the media layer of pulmonary arteries. The values of P31, P32, P33 in the in-vivo state, the no-load state, and the zero-stress state are obtained. This study demonstrated the distributions of fibrous molecules in tissue remodeling can be described quantitatively using the molecular configuration tensor.     

Opening angles and residual strains in normal rat trachea

The no-load state and zero-stress state of the normal rat trachea were analyzed. It was found that there exist compressive residual strains in the inner wall region of the rat trachea and tensile residual strains in the outer wall region. The fact that the opening angle of the rat trachea cut at the cartilaginous region is significantly larger than that cut at the muscular portion shows that residual strains exist mainly in the muscular region in the rat trachea. It was also indicated that the opening angles and residual strains expressed by cutting at the muscular portion are basically identical along longitudinal location and those expressed by cutting in the cartilaginous region tend to increase in the longitudinal direction in the normal rat, and that there exists quantitatively positive correlation between the opening angles and residual strains in rat trachea. The results will help to further understand the opening angles and residual strains in the trachea and study tracheal remodeling in response to mechanical environment.     

Opening angles and residual strains in normal rat trachea

The no-load state and zero-stress state o1 the normal rat trachea were analyzed. It was found that there exist compressive residual strains in the inner wall region of the rat trachea and tensile residual strains in the outer wall region. The fact that the opening angle of the rat trachea cut at the cartilaginous region is significantly larger than that cut at the muscular portion shows that residual strains exist mainly in the muscular region in the rat trachea. It was also indicated that the opening angles and residual strains expressed by cutting at the muscular portion are basically identical along longitudinal location and those expressed by cutting in the cartilaginous region tend to increase in the longitudinal direction in the normal rat, and that there exists quantitatively positive correlation between the opening angles and residual strains in rat trachea. The results will help to further understand the opening angles and residual strains in the trachea and study tracheal remodeling in response     

Zero-stress states of human pulmonary arteries and veins

The zero-stressstates of the pulmonary arteries and veins fromorder3 toorder9 were determined in six normal humanlungs within 15 h postmortem. The zero-stress state of each vessel was obtained by cutting the vessel transversely into a series of short rings, then cutting each ring radially, which caused the ring to springopen into a sector. Each sector was characterized by its opening angle.The mean opening angle varied between 92 and 163° in the arterialtree and between 89 and 128° in the venous tree. There was atendency for opening angles to increase as the sizes of the arteriesand veins increased. We computed the residual strains based on theexperimental measurements and estimated the residual stresses accordingto Hooke's law. We found that the inner wall of a vessel at the statein which the internal pressure, external pressure, and longitudinalstress are all zero was under compression and the outer wall was intension, and that the magnitude of compressive stress was greater thanthe magnitude of tensile stress.

     

Regional distribution of layer-specific circumferential residual deformations and opening angles in the porcine aorta

Information on the layer-specific residual deformations of aortic tissue and how these vary throughout the vessel is important for understanding the regionally-varying aortic functions and pathophysiology, but not so much can be found in the literature. Toward this end, porcine aortas were sectioned into eighteen rings, with one ring from each anatomical position radially cut to obtain the zero-stress state for the intact wall and the other ring dissected into intimal-medial and adventitial layers; these rings were then radially cut to reach the zero-stress state for the intima-media and adventitia. Peripheral variations in internal/external circumferences, thickness, and opening angle of the intact wall and its layers were measured through image analysis at the no-load and zero-stress states. Intact wall and layer circumferences at both states significantly declined along the aorta, as did intact wall and intimal-medial but not adventitial thickness. Adventitia exhibited the greatest opening angles, approaching 180 deg all over the aorta. The opening angles of the intima-media and intact wall were quite similar, with the highest values in the ascending aorta, the lowest at the diaphragm, and increasing subsequently. Bending-related residual stretches were released by radial cutting that were compressive internally and tensile externally, displaying distinct axial variation for the intima-media and intact wall, and non-significant variation for the adventitia. Evidence is provided for the release upon layer separation of compressive stretches in the intima-media and of tensile stretches in the adventitia, whose values were smallest in the descending thoracic aorta and highest near the iliac artery bifurcation.     

Biomechanical and morphological properties in rat large intestine

Intestinal stress-strain distributions are important determinants of intestinal function and are determined by the mechanical properties of the intestinal wall, the physiological loading conditions and the zero-stress state of the intestine. In this study the distribution of morphometric measures, residual circumferential strains and stress-strain relationships along the rat large intestine were determined in vitro. Segments from four parts of the large intestine were excised, closed at both ends, and inflated with pressures up to 2kPa. The outer diameter and length were measured. The zero-stress state was obtained by cutting rings of large intestine radially. The geometric configuration at the zero-stress state is of fundamental importance because it is the basic state with respect to which the physical stresses and strains are defined. The outer and inner circumferences, wall thickness and opening angle were measured from digitised images. Subsequently, residual strain and stress-strain distributions were calculated. The wall thickness and wall thickness-to-circumference ratio increased in the distal direction. The opening angle varied between approximately 40 and approximately 125 degrees with the highest values in the beginning of proximal colon (F=1.739, P<0.05). The residual strain at the inner surface was negative indicating that the mucosa-submucosal layers of the large intestine in no-load state are in compression. The four segments showed stress-strain distributions that were exponential. All segments were stiffer in longitudinal direction than in the circumferential direction (P<0.05). The transverse colon seemed stiffest both in the circumferential and longitudinal directions. In conclusion, significant variations were found in morphometric and biomechanical properties along the large intestine. The circumferential residual strains and passive elastic properties must be taken into account in studies of physiological problems in which the stress and strain are important, e.g. large intestinal bolus transport function.     

Effect of osmolarity on the zero-stress state and mechanical properties of aorta

Some pathological conditions may affect osmolarity, which can impact cell, tissue, and organ volume. The hypothesis of this study is that changes in osmolarity affect the zero-stress state and mechanical properties of the aorta. To test this hypothesis, a segment of mouse abdominal aorta was cannulated in vivo and mechanically distended by perfusion of physiological salt (NaCl) solutions with graded osmolarities from 145 to 562 mosM. The mechanical (circumferential stress, strain, and elastic modulus) and morphological (wall thickness and wall area) parameters in the loaded state were determined. To determine the osmolarity-induced changes of zero-stress state, the opening angle was observed by immersion of the sectors of mouse, rat, and pig thoracic aorta in NaCl solution with different osmolarities. Wall volume and tissue water content of the rings were also recorded at different osmolarities. Our results show that acute aortic swelling due to low osmolarity leads to an increase in wall thickness and area, a change in the stress-strain relationship, and an increase in the elastic modulus (stiffness) in mouse aorta. The opening angle, wall volume, and water content decreased significantly with increase in osmolarity. These findings suggest that acute aortic swelling and shrinking result in immediate mechanical changes in the aorta. Osmotic pressure-induced changes in the zero-stress state may serve to regulate mechanical homeostasis.     

The zero-stress state of rat veins and vena cava

The zero-stress state of a vein is, like that of an artery, not a closed cylindrical tube, but is a series of segments whose cross-sections are open sectors. An opening angle of each sector is defined as the angle subtended between two radii joining the midpoint of the inner wall to the tips of the inner wall. Data on the opening angles (mean +/- standard deviation) of the veins and vena cava of the rat are presented. For the superior vena cava and subclavian, jugular, facial, renal, common iliac, saphenous, and plantar veins, the opening angle varies in the range of 25 to 75 deg. The inferior vena cava (below the heart), however, has noncircular, nonaxisymmetric cross-sections, a curved axis, and a rapid longitudinal variation of its "diameter"; its zero-stress state is not circular sectors; but the opening angle is still a useful characterization. The mean opening angle of the interior vena cava varies in the range of 40 to 150 deg in the thoracic portion, and 75 to 130 deg in the abdominal portion, with the larger values occurring about the middle of each portion. There are considerable length, diameter reductions, and wall thickening of the vena cava from the homeostatic state to the no-load state in vitro. Physically, the zero-stress state is the basis of the stress analysis of blood vessels. The change of opening angle is a convenient parameter to characterize any nonuniform remodeling of the vessel wall due to changes in physical stress or chemical environment.(ABSTRACT TRUNCATED AT 250 WORDS)     

Study on cartilaginous and muscular strains of rat trachea

This paper introduces a new method, termed Twice Cutting, for obtaining the zero-stress states of cartilage and muscle of trachea. The method applied cuts at the two junctions of tracheal cartilage and muscle perpendicular to the tangent lines of cartilage at its tips. The cartilaginous and muscular opening angles are defined for the first time in Twice Cutting methods. Based on the analysis of cartilaginous and muscular geometric information in no-load and zero-stress states, it is found that there are compressive and tensile residual strains in the inner and outer walls of the cartilage respectively. Residual strains at the muscular inner wall of tracheal rings near bifurcation are negative, whereas those of other rings are positive, and residual strains at outer wall of all rings are positive. This phenomenon of tracheal muscle residual strains is different from those of vessel etc. The results also show that the absolute values of cartilaginous strains are considerably smaller than that of muscular ones, with the ratio being around 0.05. The values of all the tracheal parameters, including residual strains and opening angles, are reducing with the increasing value of tracheal rings’ position. So the consequences obtained in this paper not only indicate that the trachea is a non-uniform tissue along the circumferential and axial directions, but also reveal the differences between the trachea and other living tissues, such as vessel, esophagus. This is a basic research for further work, such as determining stress in trachea, to which the cartilaginous and muscular zero-stress states should be referred.     

Duration of no-load state affects opening angle of porcine coronary arteries

The zero-stress state of a blood vessel has been extensively studied because it is the reference state for which all calculations of intramural stress and strain must be based. It has also been found to reflect nonuniformity in growth and remodeling in response to chemical or physical changes. The zero-stress state can be characterized by an opening angle, defined as the angle subtended by two radii connecting the midpoint of the inner wall. All prior studies documented the zero-stress state or opening angle with no regard to duration of the no-load state. Our hypotheses were that, given the viscoelastic properties of blood vessels, the zero-stress state may have "memory" of prior circumferential and axial loading, i.e., duration of the no-load state influences opening angle. To test these hypotheses, we considered ring pairs of porcine coronary arteries to examine the effect of duration in the no-load state after circumferential distension. Our results show a significant reduction in opening angle as duration of the no-load state increases, i.e., vessels that are reduced to the zero-stress state directly from the loaded state attain much larger opening angles at 30 min after the radial cut than rings that are in the no-load state for various durations. To examine the effect of axial loading, we found similar reductions in opening angle with duration in the no-load from the in situ state, albeit the effect was significantly smaller than that of circumferential loading. Hence, we found that the zero-stress state has memory of both circumferential and axial loading. These results are important for understanding viscoelastic properties of coronary arteries, interpretation of the enormous data on the opening angle and strain in the literature, and standardization of future measurements on the zero-stress state.     

The villi contribute to the mechanics in the guinea pig small intestine

Previous studies have shown that intestinal mucosa is compressed in vivo. The present study investigated the contribution of the mucosal villi to the biomechanical properties in circumferential direction in the guinea pig jejunum. Eight 20-cm-long jejunal segments were excised and each separated into two 10-cm-long segments. The mucosal villi were scraped off from half the segments. The segments were pressurized in vitro with Krebs solution from 0-10cmH(2)O using a ramp distension protocol with simultaneous diameter recordings. Circumferential stresses and strains were computed from the diameter, pressure and the zero-stress state data. Removing the villi resulted in small opening angles (139+/-16 degrees vs 189+/-27 degrees with villi) and small absolute values of residual strain (inner: -0.05+/-0.03 vs -0.33+/-0.06 with villi; outer: 0.11+/-0.04 vs 0.33+/-0.08 with villi) (P<0.001). The outer diameter as a function of the pressure did not differ between jejunal segments with villi and without villi. The average mid-wall stress-strain curve without villi was shifted to the left compared to the segment with villi, indicating the wall was stiffer without villi. However, if the stress-strain computation for the segments with villi was referenced to the zero-stress state of the segments without villi, the curve was only partly shifted to the left. In conclusion, this paper provides the first direct experimental evidence that the villi are important for the biomechanical properties of guinea pig small intestine in circumferential direction, because the villi not only affect the zero-stress state configuration but also partially affect the stress-strain distribution in the intestinal wall. Therefore, the villi should be taken into account in the analysis of biomechanical properties of the intestinal wall.     

Changes of zero-stress state of rat pulmonary arteries in hypoxic hypertension

Zero-stress state of the main pulmonary arteries, from the main trunk to a vessel with a lumen diameter approximately 60 microns, was determined in 25 normal control and 38 hypoxic pulmonary hypertensive rats. Pulmonary hypertension was induced by placing the rats in a hypoxic chamber with 10% O2-90% N2 at atmospheric pressure. The zero-stress state of each vessel was obtained by first cutting the vessel transversely into a series of rings and then cutting each ring radially, whereupon the ring opened into a sector, which is characterized by an opening angle defined as the angle subtended between two lines originating from the midpoint of the inner wall (endothelium) to the tips of the inner wall. Whereas the pulmonary blood pressure increased monotonically during the development of pulmonary hypertension, the opening angle followed a different course; e.g., the values (means +/- SD) of the opening angle at the pulmonary trunk at times 0 (control) and 2, 12, 28, 96, 144, 240, 480, and 720 h after exposure to hypoxia are, respectively, 294 +/- 30 degrees, 378 +/- 24 degrees, 385 +/- 12 degrees, 374 +/- 11 degrees, 246 +/- 63 degrees, 267 +/- 49 degrees, 193 +/- 19 degrees, 195 +/- 83 degrees, and 239 +/- 38 degrees. Trends at other places on the artery are similar, but the magnitudes differ. In this period of time, intimal edema and thickening were found. The intima media thickened rapidly from 48 to 240 h and then more slowly from 240 to 720 h. Adventitia thickened later; its thickness exceeded that of the intima media at approximately 96 h. Thus the changes of zero-stress state of the pulmonary arteries are seen to be related to the nonuniform remodeling of the vessel wall as revealed by the edema, blebs, and thickening of different layers.     

Remodelling of the zero-stress state and residual strains in apoE-deficient mouse aorta

Atherosclerosis is the most frequent cause of death and severe chronic disability in North America and Europe. The atherosclerosis-prone apolipoprotein E (apoE)-deficient mice contain the entire spectrum of lesions observed during atherogenesis. Significant remodelling of the artery occurs in atherosclerosis. The aim was to study the remodelling of the zero-stress state of the aorta in apoE-deficient mice up to 56 weeks of age. Normal wild-type mice served as control groups. The mice were euthanised at ages 10, 28 and 56 weeks and tissue rings where excised from several locations along the aorta. The rings where photographed in the no-load state (without any external forces applied), then cut radially to obtain the zero-stress state and photographed again. The cross-sectional wall area and wall thickness increased over time in apoE-deficient mice compared to controls (P<0.001). The residual strains at the inner and outer surface varied as function of aortic location both in controls and apoE-deficient mice (P<0.001). From age 28 to age 56 weeks a gradual increase in positive strain at the outer surface and negative strain at the inner surface was found in the apoE-deficient mice when compared to age-matched control mice (P<0.001). Furthermore, the inner residual strain in the plaque location was significantly smaller than in the non-plaque location in the rings with atherosclerotic plaques (P<0.001). The change over time of the opening angle was especially pronounced in the aortic arch. The opening angle increased to app. 200 degrees in the aortic arch in apoE-deficient mice at 56 weeks of age whereas it in age-matched controls was app. 125 degrees. Correspondingly, atherosclerotic plaques were prominent in the apoE-deficient mice, especially at week 56 in the ascending aorta and the aortic arch. In conclusion, a pronounced remodelling of the biomechanical properties in aorta was found in apoE-deficient mice. The stress gradient across the vessel wall in the plaque region is likely larger in vivo due to the smaller residual strain in the plaque area.     

Species dependence of the zero-stress state of aorta: pig versus rat.

The zero-stress state of an aorta can be characterized by the angle with which each segment of the vessel opens up when it is cut radially. The opening angle varies with the region of the aorta: significantly with respect to the axial location, less significantly with respect to polar angle of the radial cut. Both pig and rat aortas have large opening angles in the neighborhood of 130 deg in the aortic arch region. In the thoracic region, the species difference is evident. The opening angle of the pig aorta in the middle thoracic region is rather constant in the neighborhood of 60 deg. The opening angle of the rat aorta in the thoracic region varies considerably, decreasing to 10 deg at the lower end of the thoracic region. In the abdominal region the opening angle of the pig increases from 60 to about 80 deg, that of the rat increases from about 10 to 90 deg. The potassium ion has effect on vascular smooth muscle, but has little effect on the opening angle. This suggests that the opening angle is not sensitive to smooth muscle contraction, similar to a previously known result that the opening angle is not affected by papaverine. The vessel wall thickness and vessel diameter were measured. It is shown that the ratio of the wall thickness to diameter of the pig is considerably larger than that of the rat throughout the aorta.(ABSTRACT TRUNCATED AT 250 WORDS)     

Study on cartilaginous and muscular strains of rat trachea

Han and Fung (1991)[1] studied the zero-stressstates of porcine and canine tracheas by cutting themidpoints of cartilage and muscle respectively. Themethod of Fung, termed Once Cutting method in thispaper, was also used by Liu, Wang and Teng (2002)[2]in studying residual strain of rat tracheas. They all re-ported that the no-load state of trachea is not itszero-stress state, but the residual stress (strain) existsin no-load tracheal ring. The tracheal ring would openup into a figure of “C…     

Changes in the rheological properties of blood vessel tissue remodeling in the course of development of diabetes.

Rheological properties of blood vessels are expected to change in disease process if the structure of the vessel wall changes. This is illustrated in diabetes, which can be induced in rat by a single injection of Streptozocin. One of the rheological properties of the blood vessel is the stress-strain relationship. The nonlinear stress-strain relationship of arteries is best expressed as derivations of a strain-energy function. In this paper, the stress-strain relations are measured and the coefficients in the strain energy function of arteries are determined for diabetic and control rats. The meaning of these coefficients are explained. The influence of diabetes on the elastic property of the arteries is expressed by the changes of these coefficients. A point of departure of the present paper from all other blood vessel papers published so far is that all strains used here are referred to the zero-stress state of the arteries, whereas all other papers refer strains to the no-load state. The existence of a large difference between the zero-stress state and no-load state of arteries is one of our recent findings. We have explained that the use of zero-stress state as a basis of strain measurements reveals that the in vivo circumferential stress distribution is quite uniform in the vessel wall at the homeostatic condition. It also makes the strain energy function much more accurate than those in which the residual stress is ignored. Using these new results, the stress and strain distribution in normal and diabetic arteries are presented.