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     

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…     

Residual strains in porcine and canine trachea

Residual strains exist in canine and porcine tracheas. They are revealed by cutting the trachea first perpendicular to its axis into rings, then radially into sectors. Each sector is characterized by an opening angle which is defined as the angle subtended between two radii joining the middle point of the inner wall to the tips of the inner wall. The trachea being non-axisymmetric, the opening angle depends on the position of the radial cut. The trachea being also nonuniform in the axial direction, the opening angle varies along the length of the trachea. In the dog, the opening angle of the trachea cut at the anterior position (cartilaginous) is about 100 degrees at the larynx; it increases fairly linearly to 180 degrees midway down the trachea; then increases slowly to about 200 degrees at the lower end where the trachea bifurcates into the main bronchi. Dog trachea cut in the posterior (muscular) position have an opening angle of about 50 degrees at the larynx, which increases to about 70 degrees three-quarters of the way down the trachea, then drops to 60 degrees at the lower end. In the pig, the opening angle of the trachea is much smaller, the values at anterior and posterior cuts are similar (without significant difference), and their mean value decreases from about 15 degrees at the laryngeal end to about 5 degrees at the lower end. These species and regional differences are discussed in relation to tracheal geometry and structure.(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.     

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.     

Alternate method for the analysis of residual strain in the arterial wall

If an artery is cut transversely into rings, and the rings are then cut radially, they spring open into sectors. This phenomenon implies the existence of residual stresses and strains in the arterial wall in the non-loaded state. In the present paper, we propose a new method to calculate the residual strain from the measured wall dimensions and a polar angle of a specimen in the stress-free state, assuming that the wall is homogeneous and incompressible, and that a radially cut, stress-free specimen forms a circular sector. For this analysis, edge angles were measured at the edges of the opened-up specimen. Residual strains were obtained for the descending thoracic aorta, the common carotid artery, and the femoral artery in the rabbit. The results obtained indicated that the magnitude of residual strain was largest in the femoral artery and smallest in the aorta among the three arteries. The opening angle did not depend upon the length of a ring specimen if the ratio of the length to the diameter was ≤ 3.     

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)     

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.     

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.

     

Postsurgical changes of the opening angle of canine autogenous vein graft.

The opening angles of 30 canine autogenous vein grafts were measured to determine the postsurgical change of residual strain in the vein graft. Canine femoral veins were grafted to femoral arteries in the end-to-end anastomosis fashion. When harvested, the vein grafts were cut into short segments and the segments were cut open radially. The opened-up configurations were taken as the zero-stress states of the vessels. Opening angle, defined as the angle between the two lines from the middle point to the tips of the inner wall, was used to describe the zero-stress states. Results show that the opening angles (mean +/- SD) are 63.0 +/- 30.6 deg for normal femoral veins, and -0.4 +/- 4.6, 6.1 +/- 19.4, 25.4 +/- 20.1, and 47.8 +/- 11.4 deg for vein grafts at 1 day, 1 week, 4 and 12 weeks postsurgery, respectively. The postsurgical changes in opening angle reveal nonuniform transmural tissue remodeling in the vascular wall. The relations between the changes in opening angle and the changes in the morphology of the vein grafts are discussed. Intimal hyperplasia is correlated to the opening angle and is suggested to be the main factor for the postsurgical increase in opening angle. The longitudinal strain in the vein graft is found to decrease postsurgically.     

Effect of Danshen on the Zero-Stress State of Rat's Abdominal Aorta

The objective of our study was to study the effect of danshen, a Chinese herbal medicine known to prevent hypertension, on the zero-stress state of rat's abdominal aorta. The zero-stress state of a blood vessel represents the release of residual stress on the vessel wall, and is the basic configuration of blood vessel affected solely by intrinsic parameters. At the in vivo state, the rat's abdominal aorta was subjected to blood pressure and flow and longitudinal stress. After dissecting from the abdominal aorta, the aortic specimens were cut into small rings at no-load state, in which the internal pressure, external pressure, and longitudinal stress in a short ring-shaped segment were all zero; by cutting radially to release the residual stress in the wall, the vessel ring opened up into a sector quickly, and the sector's configuration would not change at 20 min after cutting and was defined as the zero-stress state of a blood vessel, which was characterized by its residual strain and opening angle. Then aqueous extract of danshen prepared with methanol was added in the Krebs solution, and the changes of the aorta's zero-stress state were monitored by taking photos routinely for analysis to determine the opening angle and residual strain. Additionally, other sets of samples were tested in a Norepinephrine-Krebs solution as positive control or a Krebs solution as negative control, respectively. It was demonstrated that the zero-stress state of rat's abdominal aorta was affected by danshen extract and norepinephrine in two different patterns, while the Krebs solution did not have similar effects. The present work provides a new approach to study the anti-hypertension effect and mechanism of danshen.     

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)     

Opening angle and residual strain in a three-layered model of pig oesophagus

Studies of various biological tissues have shown that residual strains are important for tissue function. Since a force balance exists in whole wall thickness specimens cut radially, it is evident that layer separation is an important procedure in the understanding of the meaning of residual stresses and strains. The present study investigated the zero-stress state and residual strain distribution in a three-layer model of the pig oesophagus. The middle part of the oesophagus was obtained from six slaughterhouse pigs. Four 3-mm-wide rings were serially cut from each oesophagus. Two of them were used for separating the wall into mucosa-submucosa, inner and outer muscle layers. The remaining two rings were kept as intact rings. The inner and outer circumferences and wall thickness of different layers in intact and separated rings were measured from the digital images in the no-load state and zero-stress state. The opening angle was measured and the residual strain at the inner and outer surface of different layers and the intact wall were computed. Compared with intact sectors (62.8+/-9.8 degrees ), the opening angles were smaller in the inner muscle sectors (37.2+/-11.4 degrees , P<0.01), whereas the opening angles of mucosa-submucosa (63.9+/-6.8 degrees ) and outer muscle sectors (63.9+/-6.8 degrees ) did not differ (P>0.1). Referenced to the zero-stress state of the intact sectors, the inner and outer residual strains of the intact rings was -0.128+/-0.043 and outer residual strain was 0.308+/-0.032. Referenced to the "true" zero-stress state of separated three-layered sectors, the inner residual strain of intact rings were -0.223+/-0.021 (P<0.01) and 0.071+/-0.022 (P<0.01). Referenced to the "true" zero-stress state, the residual strain distribution of different layers in intact rings was shown that the inner surface residual strain was negative at mucosa-submucosa and inner muscle layers and was positive at outer muscle layer, whereas the outer surface residual strain was negative at the mucosa-submucosa layer and positive at the inner and outer muscle layers. For the separated different layered rings, the inner residual strain was negative and outer residual strain was positive; however, the absolute values did not differ (P>0.1). In conclusion, it is possible to microsurgically separate the oesophagus into three layers, i.e., mucosa-submucosa, inner muscle and outer muscle layers, the residual strain differ between the layers, and the residual strain distribution was more uniform after the layers were separated.     

Residual strains in conduit arteries

Residual strains and stresses are those that exist in a body when all external loads are removed. Residual strains in arteries can be characterized by the opening angle of the sector-like cross-section which arises when an unloaded ring segment is radially cut. A review of experimental methods for measuring residual strains and the main results about the variation of the opening angle with arterial localization, age, smooth muscle activity, mechanical environment and certain vascular pathologies are presented and discussed. It is shown that, in addition to their well-established ability to homogenize the stress field in the arterial wall, residual strains make arteries more compliant and thereby improve their performance as elastic reservoirs and ensure more effective local control of the arterial lumen by smooth muscle cells. Finally, evidence that, in some cases, residual strains remain in arteries even after they have been cut radially is discussed.     

Effect of smooth muscle tone on morphometry and residual strain in rat duodenum, jejunum and ileum

It is difficult to measure gastrointestinal smooth muscle (SM) tone except in sphincter regions. Since tone affects the biomechanical properties, the aim of the present study was to evaluate intestinal SM tone by studying the morphometry and biomechanical properties with and without muscle tone. Circumferential rings of 0.8-1mm in width were cut from the rat duodenum, jejunum and ileum. Sectors were obtained by cutting the rings opposite to the mesentery. The rings and the sectors were immersed in physiological Krebs solution in order to maintain the tone and into Krebs solution without Ca(++) and with EGTA to abolish the tone. The circumferences, area, the circularity and residual strain of the mucosal and serosal surfaces, opening angle, and opening angle tone/non-tone ratio were measured or computed. The tone affects the opening angle and residual strain in the intestinal sectors. The opening angle in the tissue sectors with tone was smaller (P<0.05) than those without tone in all three segments. The opening angle tone/non-tone ratio was 0.40+/-0.05, 0.43+/-0.06 and 0.36+/-0.11 for duodenum, jejunum and ileum, respectively, and did not differ among the three intestinal segments. The residual strain between sectors with and without SM tone differed in duodenal and jejunal mucosa and in the serosa of all three segments (P<0.05). The intestinal rings with tone showed axial variation for luminal area (P<0.001), for wall area (P<0.05), and for the mucosal and serosal residual strains (P<0.05). In conclusion, the intestinal mechanical properties are affected by intestinal SM tone. The tone can be evaluated by measuring the opening angle and residual strains of sectors in intestinal segments with and without SM tone.     

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     

Evaluating residual strain throughout the murine female reproductive system

Mounting evidence suggests that cells within soft tissues seek to maintain a preferred biomechanical state. Residual stress is defined as the stress that remains in a tissue when all external loads are removed and contributes to tissue mechanohomeostasis by decreasing the transmural gradient of wall stress. Current computational models of pelvic floor mechanics, however, often do not consider residual stress. Residual strain, a result of residual stress can be quantitatively measured through opening angle experiments. Therefore, the objective of this study is to quantify the regional variations in opening angles along the murine female reproductive system at estrus and diestrus, to quantify residual strain in the maintenance state of sexually mature females. Further, evidence suggests that hydrophilic glycosaminoglycan/proteoglycans are integral to cervical remodeling. Thus, variations in opening angles following hypo-osmotic loading are evaluated. Opening angle experiments were performed along the murine reproductive system in estrus (n = 8) and diestrus (n = 8) and placed in hypo-osmotic solution. Measurements of thickness and volume were also obtained for each group. Differences (p < 0.05) in opening angle were observed with respect to region and loading, however, differences with respect to estrous stage were not significant. Thickness values were significant (p < 0.05) with respect to region only. The effects of both estrous cycle and region resulted in significant differences (p < 0.05) in observed volume. The observed regional differences indicate variation in the stress-free state among the reproductive system which may have implications for future computational models to advance women’s reproductive health.     

Small intestinal morphometric and biomechanical changes during physiological growth in rats

Changes in small intestinal geometry, residual strain and stress-strain properties during physiological growth were studied in rats ranging from 1 to 32 weeks of age. Small intestinal mass and dimensions increased many-fold with age, e.g. the weight per unit length increased five-fold with age and the wall cross-sectional area increased four-fold. The opening angle of duodenum obtained at zero-stress state was approximately 220 degrees and 290 degrees during the first and second week after birth and decreased to 170 degrees at other ages (p < 0.005). The opening angle of ileum ranged between 120 degrees and 150 degrees . The residual strain of duodenum at the mucosal surface did not vary with age (p > 0.05) whereas the residual strain of ileum at the mucosal surface decreased with age (p < 0.001). The circumferential and longitudinal stress-strain curves fitted well to a mono-exponential function. At a given circumferential stress, the corresponding strain values increased during the first 8 weeks of age (p < 0.05) where after no further change was observed. Hence, the small intestine became more compliant during early life. At a given longitudinal stress, the corresponding strains of ileum and duodenum became larger during the first 2-4 weeks of age (p < 0.05) where after no further change was observed. The small intestine was stiffer in longitudinal direction compared to the circumferential direction. In conclusion, pronounced morphometric and biomechanical changes were observed in the rat small intestine during physiological growth. Such data may prove useful in the understanding of the functional changes of the digestive tract during early life.     

Residual strain in ischemic ventricular myocardium.

Structural remodeling during acute myocardial infarction affects ventricular wall stress and strain. To see whether acute myocardial infarction alters residual stress and strain in the left ventricle (LV), we measured opening angles in rat hearts after 30 minutes of left coronary artery occlusion. The mean opening angle in 18 ischemic hearts (51 +/- 20 deg) was significantly greater than in five sham-operated controls (29 +/- 11 deg, P < 0.05). To determine whether these alterations in residual strain may be associated with strain softening caused by systolic overstretch of the noncontracting ischemic tissue, we also measured opening angles in isolated hearts that had been passively inflated to high LV pressures (120 mmHg). The mean opening angle of the strain-softened hearts was not significantly different from the sham-operated hearts (34 +/- 27 deg, P = 0.74). Mean collagen area fractions in the myocardium were not significantly different between ischemic hearts (0.027 +/- 0.014) and the nonischemic group (0.022 +/- 0.011). Although there were significant differences in opening angles measured with ischemia, they do not appear to be a result of altered extracellular collagen content or softening associated with overstretch. Thus, there is a significant change in residual strain associated with acute ischemia that may be related to changes in collagen fiber structure, myocyte structure, or metabolic state.     

鼠颈总动脉超低温处理后的血管零应力状态研究

采用超低温冷冻方法除去鼠颈总动脉血管的内皮细胞,用Fung的残余应力方法研究血管零应力状态,用以了解超低温冷冻方法对血管力学性能如血管零应力状态是否有影响。结果发现超低温处理后血管的零应力状态时展开角有所增大。