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.     

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     

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.     

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.

     

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)     

Intrinsic innervation in the tracheal smooth muscle of the large flying fox (Pteropus vampyrus): an immunohistochemical study

Structure and innervation of the trachea of the large flying fox (Pteropus vampyrus) were examined by mean hematoxylin-eosin staining and immunohistochemical methods. The tracheal rings were predominantly comprised of bone with a small amount of hyaline cartilage. Bone contained bone marrow and hyaline cartilage attached at the ends of the tracheal rings. The tracheal rings in the anterior third of the trachea were connected at each end with connective tissue to almost form a ring. A narrow membranous wall comprising a single layer of smooth muscle was present in the middle third, while inner and outer layers of smooth muscle were present in the posterior third. Protein gene product 9.5 (PGP 9.5)-, nitric oxide synthase (NOS)-, galanin- and vasoactive intestinal peptide (VIP)-immunoreactive nerve fibers were present in the epithelium, lamina propria, smooth muscle layer and tunica adventitia. In the tunica adventitia, many PGP 9.5- and NOS-immunoreactive neurons were found singly or in small ganglia, while some VIP- and galanin-immunoreactive neurons were observed. A few PGP 9.5- and NOS-immunoreactive neurons were found in the submucosal layer. These results suggest that the trachea of the large flying fox has a rigid structure of tracheal rings and that the posterior two-thirds of the trachea probably contract via the actions of smooth muscles innervated with peptidergic or nitrenergic neurons that are located in tracheal ganglia, whereas the anterior third is non-mobile.     

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.     

Quantitative measurement of smooth muscle shortening in isolated pig trachea

Matched porcine tracheal rings were exposed to theophylline and increasing doses of carbachol in Krebs solution. Histological sections of each ring were traced and each of the following dimensions measured: the external perimeter (Pe) and external area (Ae) defined by the outer border of smooth muscle and inner surface of cartilage, and the internal perimeter (Pi) and internal area (Ai) defined by the luminal surface of the epithelium and the muscle length (L) along its outer border. Absolute wall area (WA = Ae - Ai) and relative wall area (PW = WA/Ae) were calculated. Carbachol-treated tracheal ring dimensions were compared with those of their matched theophylline-treated rings. In tracheal rings with intact cartilage, maximal smooth muscle shortening of 44% was achieved with 10(-2) M carbachol. In tracheal rings in which anterior and posterior segments of cartilage were excised, the trachealis muscle passively shortened by 20% and maximal shortening (10(-3) M carbachol) was 57%. Although Ai decreased with maximal smooth muscle shortening, there were no changes in the length of Pi or in WA. These data show that the cartilage in the porcine trachea exerts both a preload that passively stretches the trachealis muscle and an afterload that limits maximal smooth muscle shortening.     

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.     

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.     

Strain distribution in the layered wall of the esophagus.

The function of the esophagus is to move food by peristaltic motion, which is the result of the interaction of the tissue forces in the esophageal wall and the hydrodynamic forces in the food bolus. To understand the tissue forces in the esophagus, it is necessary to know the zero-stress state of the esophagus, and the stress-strain relationships of the tissues. This article is addressed to the first topic: the representation of zero-stress state of the esophagus by the states of zero stress-resultant and zero bending moment of the mucosa-submucosa and the muscle layers. It is shown that at the states of zero stress-resultant and zero bending moment, these two layers are not tubes of smaller radii but are open sectors whose shapes are approximately cylindrical and more or less circular. When the sectors are approximated by circular sectors, we measured their radii, opening angles, and average thickness around the circumference. Data on the radii, thickness-to-radius ratios, and the opening angles of these sectors are presented. Knowing the zero-stress state of these two layers, we can compute the strain distribution in the wall at any in vivo state, as well as the residual strain in the esophageal wall at the no-load state. The results of the in vivo states are compared to those obtained by a conventional approach, which treats the esophageal wall as a homogeneous material, and to another popular simplification, which ignores the residual strains completely. It is shown that the errors caused by the homogeneous wall assumption are relatively minor, but those caused by ignoring the residual strains completely are severe.     

Congenital tracheal stenosis in lambs induced by maternal ingestion of Veratrum californicum

Seven of nine lambs born to six ewes gavaged with Veratum californicum root and rhizome material on days 31, 32 and 33 of gestation died from asphyxia within 5 minutes after birth. Five of the seven were autopsied and found to have severe stenosis of the trachea. None of the 12 lambs born to seven control ewes had tracheal stenosis. The defect was characterized by lateral flattening of the trachea throughout its entire length. Cartilaginous tracheal rings were reduced in number, nonuniform in size and shape, irregularly spaced, and with abnormal orientation. The rings were thinner than those of control tracheas, and had zones of chondrogenesis on outer and inner surfaces which were of equal width, rather than of unequal width as in controls. The smaller size and relatively noncurved shape of the cartilaginous rings of the stenotic trachea resulted in a nondistended lumen.     

Stress-modulated growth, residual stress, and vascular heterogeneity.

A simple phenomenological model is used to study interrelations between material properties, growth-induced residual stresses, and opening angles in arteries. The artery is assumed to be a thick-walled tube composed of an orthotropic pseudoelastic material. In addition, the normal mature vessel is assumed to have uniform circumferential wall stress, which is achieved here via a mechanical growth law. Residual stresses are computed for three configurations: the unloaded intact artery, the artery after a single transmural cut, and the inner and outer rings of the artery created by combined radial and circumferential cuts. The results show that the magnitudes of the opening angles depend strongly on the heterogeneity of the material properties of the vessel wall and that multiple radial and circumferential cuts may be needed to relieve all residual stress. In addition, comparing computed opening angles with published experimental data for the bovine carotid artery suggests that the material properties change continuously across the vessel wall and that stress, not strain, correlates well with growth in arteries.     

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.     

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.     

FGF10 controls the patterning of the tracheal cartilage rings via Shh

During embryonic development, appropriate dorsoventral patterning of the trachea leads to the formation of periodic cartilage rings from the ventral mesenchyme and continuous smooth muscle from the dorsal mesenchyme. In this work, we have investigated the role of two crucial morphogens, fibroblast growth factor 10 and sonic hedgehog, in the formation of periodically alternating cartilaginous and non-cartilaginous domains in the ventral mesenchyme. Using a combination of gain- and loss-of-function approaches for FGF10 and SHH, we demonstrate that precise spatio-temporal patterns and appropriate levels of expression of these two signaling molecules in the ventral area are crucial between embryonic day 11.5 and 13.5 for the proper patterning of the cartilage rings. We conclude that the expression level of FGF10 in the mesenchyme has to be within a critical range to allow for periodic expression of Shh in the ventral epithelium, and consequently for the correct patterning of the cartilage rings. We propose that disturbed balances of Fgf10 and Shh may explain a subset of human tracheomalacia without tracheo-esophageal fistula or tracheal atresia.     

黄缘闭壳龟消化系统、呼吸系统的解剖

黄缘闭壳龟消化管总长度为背甲长的3.5～4.2倍.食管和胃壁厚,扩展性强,内壁有数条纵行皱襞.小肠较长,约占消化管总长度的60.9%,无盲肠,肠内壁有大小不一的纵行皱襞.肝较大,为体重的4.8%左右.胰脏长条形,沿十二指肠分布.气管和支气管均由呈"O" 形完全闭合的软骨环和环间韧带所构成.气管较长,有45～55个软骨环;支气管较短,有30～40个软骨环.肺长囊形,蜂窝状,紧贴在背甲的内表面,从肩带一直延展到腰带.     

Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models

 Most soft biological tissues, including ventricular myocardium, are not stress free when all external loads are removed. Residual stress has implications for mechanical performance of the heart, and may be an indicator of patterns of regional growth and remodeling. Cross-sectional rings of arrested ventricles opened up when a radial cut was made (initial mean opening angles were 64 ± 17°), but further circumferential cuts revealed the presence of additional residual stresses in the tissue with further opening of the rings. In normal mouse hearts, the inner half of a short-axis ring opened more than the outer half, and this change was dependent on apex–base location. At the apex the inner section vs. outer section opening angles were 226 ± 47° vs. 89 ± 28°, while at the base the same two angles were 160 ± 30° vs. 123 ± 35°. A simple theoretical cylindrical shell model with incompressible hyperelastic material properties was used to model the experimental deformations based on the cutting experiments. The model predicts different residual stress fields depending on the nature of the opening after the circumferential cut (which is done after the conventional radial cut). The observed opening angles were consistent with steep stress gradients near the endocardium compared with those predicted if the first cut was assumed to relieve all residual stresses. These results imply a more complex distribution of residual stress and strain in ventricular myocardium than previously thought. Received: 23 May 2002 / Accepted: 30 September 2002 We would like to acknowledge the surgical skills and data analysis of Zuangjie Li. This work was supported in part by National Heart, Lung, and Blood Institute Grants HL-43026 and HL-64321.