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)     

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.     

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.     

Regional functional heterogeneity of aortic smooth muscle cells in rats

The aorta is a magistral artery, which has been traditionally looked upon as a vessel whose properties are invariable throughout its length. However, in the most recent decade, there have been accumulated data that provide evidence that different aorta sections arise from different embryonic origins and that the population of smooth muscle cells making up the vessel’s wall is, consequently, heterogenic. Tracing the fate of smooth muscle cells, the basic components of the vessel, with the aid of genetic marking methods revealed that the cells’ response to various factors is largely determined by the embryonic origin of a certain cell population. However, functional differences between the smooth muscle cells making up different aorta sections remain poorly understood. The aim of the current work was to compare the functional characteristics of the populations of aortic wall smooth muscle cells obtained from the aorta sections differing by their embryonic origin. Towards this end, we obtained smooth muscle cell cultures from the three aorta sections of linear rats, namely, the neural crest derived ascending thoracic aorta, the somites derived descending thoracic aorta, and splanchnic mesoderm derived abdominal aorta. Using immunocytochemistry and Western blotting, the cells from the different regions of aorta were compared on the basis of smooth muscle actin, vimentin, and SM22 content in them. Cell proliferation rate was estimated using the growth curves method. We have demonstrated that the three smooth muscle cell populations arising from different embryonic origins differ in their morphological characteristics as well as by smooth muscle actin and SM22 content. We have shown that smooth muscle cells from the ascending aorta proliferate more actively than the corresponding cells from the descending thoracic aorta. Thus, the functional properties of the populations of rat aortic smooth muscle cells are different and depend on the embryonic origin of the aorta section from which they were obtained.     

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.     

Interleukin-1beta causes different levels of nitric oxide-mediated depression of contractility in different positions of rat thoracic aorta.

Interleukin-1beta (IL-1beta) can be synthesized by macrophages, endothelial cells and vascular smooth muscle cells when stimulated by bacterial lipopolysaccharide (endotoxin) during septic shock. The IL-1beta levels in the blood vessel wall are also elevated in atherosclerosis. IL-1beta can cause induction of inducible nitric oxide synthase (iNOS) expression in vascular smooth muscle cells and produce vasorelaxation, hypotension and ultimately tissue damage. We studied the depressions of vascular smooth muscle contractions at 3 hours after exposure to IL-1beta in different positions of rat thoracic aorta. The data show that the aortic rings from the cranial end of rat thoracic aorta had little response to IL-1beta (0.5 and 1.0 ng/ml) while those from the caudal end of thoracic aorta had larger depressant response. S-methylisothiourea sulfate (SMT), an iNOS inhibitor, completely blocked the depression of contraction caused by IL-1beta in intact aortic rings. If the endothelium was removed from the aortic rings before exposure to IL-1beta, all rings from different parts of the thoracic aorta showed an equal amount of vasodepression. Thus, the difference in the depressant response of IL-1beta in different portions of thoracic aorta is endothelium-dependent and involves induction of NOS.     

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).     

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.     

Vascular smooth muscle cell stress as a determinant of cerebral artery myogenic tone

Although the level of myogenic tone (MT) varies considerably from vessel to vessel, the regulatory mechanisms through which the actual diameter set point is determined are not known. We hypothesized that a unifying principle may be the equalization of active force at the contractile filament level, which would be reflected in a normalization of wall stress or, more specifically, media stress. Branched segments of rat cerebral arteries ranging from <50 microm to >200 microm in diameter were cannulated and held at 60 mmHg with the objectives of: 1) evaluating the relationship between arterial diameter and the extent of myogenic tone, 2) determining whether differences in MT correlate with changes in cytosolic calcium ([Ca(2+)](i)), and 3) testing the hypothesis that a normalization of wall or media stress occurs during the process of tone development. The level of MT increased significantly as vessel size decreased. At 60 mmHg, vascular smooth muscle [Ca(2+)](i) concentrations were similar in all vessels studied (averaging 230 +/- 9.2 nM) and not correlated with vessel size or the extent of tone. Wall tension increased with increasing arterial size, but wall stress and media stress were similar in large versus small arteries. Media stress, in particular, was quite uniform in all vessels studied. Both morphological and calcium data support the concept of equalization of media stress (and, hence, vascular smooth muscle cell stress and force) as an underlying mechanism in determining the level of tone present in any particular vessel. The equalization of active (vascular smooth muscle cell) stress may thus explain differences in MT observed in the different-sized vessels constituting the arterial network and provide a link between arterial structure and function, in both short- and long-term (hypertension) pressure adaptation.     

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     

Alpha 1-adrenergic stimulation of platelet-derived growth factor A-chain gene expression in rat aorta.

Sympathetic nerves and catecholamines exert growth-promoting trophic influences on arterial smooth muscle in vivo, but the molecular signals mediating these trophic effects are unknown. We report here that the alpha-adrenergic agonist phenylephrine (PE) produced dose-dependent stimulation of platelet-derived growth factor A-chain (PDGF-A) gene expression in rat thoracic aorta via agonist occupancy of alpha 1-adrenergic receptors. Increases in aortic PDGF-A mRNA levels were rapid (maximal at 6 h, 10-fold) and transient. Among seven different tissues studied, PE evoked significant increases in PDGF-A mRNA levels only in the aorta. When periaortic fatty/connective tissues normally adherent to thoracic aorta were examined separately from the remaining aortic vessel wall (endothelium removed), stimulated PDGF-A gene expression was found only in vessel wall (presumably smooth muscle). The physiological alpha-adrenergic agonist norepinephrine also increased aortic PDGF-A mRNA levels. Angiotensin II or endothelin, despite producing blood pressure increases similar to PE, had little or no effect on PDGF-A mRNA abundance in rat aorta. PE-stimulated PDGF-A gene expression was accompanied by increased expression of other growth-related genes including c-fos, c-myc, and ornithine decarboxylase but not DNA synthesis. These results suggest a mechanism for previously described trophic effects of sympathetic nerves and catecholamines on arterial smooth muscle mass, i.e. regulation of growth-related gene expression via alpha 1-adrenergic receptors.     

Functional and structural pattern of arterial responses in hereditary hypertriglyceridemic and spontaneously hypertensive rats in early stage of experimental hypertension

It has been shown that endothelium-derived nitric oxide (NO) plays an important role in regulation of vascular tone in the prenatal and early postnatal period. The aim of this paper was to determine the reactivity and accompanying structural changes in thoracic aorta from 4-week-old spontaneously hypertensive rats (SHR) and rats with hereditary hypertriglyceridemia (hHTG) in comparison with age-matched normotensive controls. For functional studies thoracic aorta was excised, cut into rings and mounted in organ baths for measurement of isometric contractile force. For morphological studies cardiovascular system of rats was perfused with glutaraldehyde fixative (at 100 mm Hg) via cannula placed in the left ventricle. Morphological changes of thoracic aorta were measured using light microscopy. Systolic blood pressure (SBP) in SHR (98+/-1 mm Hg) did not significantly differ from that of age-matched control rats (95+/-4 mm Hg), but was slightly increased in hHTG rats (110+/-2 mm Hg, P<0.05). Heart weight/body weight ratio was higher in SHR and hHTG rats than in control group indicating the hypertrophy of the heart in both models of hypertension. Endothelium-dependent relaxation of aorta induced by acetylcholine was preserved in all groups and did not differ from that in control normotensive rats. The maximal isometric contraction of thoracic aorta to noradrenaline (NA) was reduced in hypertensive groups and the concentration-response curves to NA were shifted to the right indicating increased sensitivity of smooth muscle to NA. The values of wall thickness and cross sectional area as well as inner diameter of thoracic aorta in SHR and hHTG rats were significantly decreased in comparison to control groups. Endothelial dysfunction seems to be absent in all young rats before development of hypertension. In conclusion, our observations indicate that in early stage of experimental hypertension NO-dependent relaxation is preserved so that putative impairment of this function provides no significant pathogenic contribution to the onset of hypertension in these two experimental models.     

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.     

Passive elastic properties of the rat aorta

The passive anisotropic elastic properties of rat's aorta were studied in vitro by subjecting cylindrical segments of thoracic and abdominal aorta to a wide range of deformations. Using data on pressure, axial stretch, outer diameter, axial force and wall thickness, incremental moduli of elasticity in the circumferential, axial and radial directions were computed. Results indicate that while the elastic behavior of the aortic wall is globally anisotropic, there exists a state of deformation at which the vessel displays incremental isotropy. This state of deformation corresponds approximately to the loading conditions to which the aorta is exposed in situ. Values of the moduli, analyzed as a function of transmural pressure, show that the stiffness of the aortic wall is fairly constant at low pressures but raises steeply for pressures higher than physiological. For axial stretches as occurring in situ, the magnitudes of the circumferential and radial moduli do not differ significantly for the thoracic aorta; hence this vessel can be regarded as transversely isotropic over a wide range of pressures. The same observation is valid also for the abdominal aorta when pressures equal or smaller than physiological are considered. For both the thoracic and abdominal segments of the aorta, the circumferential and radial moduli are smaller than the axial modulus at low pressures, while the reverse is true for large pressures.     

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     

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.     

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.     

Influence of tensile strain on smooth muscle cell orientation in rat blood vessels.

Blood vessels are subject to tensile stress and associated strain which may influence the structure and organization of smooth muscle cells (SMCs) during physiological development and pathological remodeling. This study focused on the influence of the major tensile strain on the SMC orientation in the blood vessel wall. Several blood vessels, including the aorta, the mesenteric artery and vein, and the jugular vein of the rat were used to observe the normal distribution of tensile strains and SMC orientation; and a vein graft model was used to observe the influence of altered strain direction on the SMC orientation. The circumferential and longitudinal strains in these blood vessels were measured by using a biomechanical technique, and the SMC orientation was examined by fluorescent microscopy at times of 10, 20, and 30 days. Results showed that the SMCs were mainly oriented in the circumferential direction of straight blood vessels with an average angle of approximately 85 deg between the SMC axis and the vessel axis in all observed cases. The SMC orientation coincided with the principal direction of the circumferential strain, a major tensile strain, in the blood vessel wall. In vein grafts, the major tensile strain direction changed from the circumferential to the longitudinal direction at observation times of 10, 20, and 30 days after graft surgery. This change was associated with a decrease in the angle between the axis of newly proliferated SMCs and that of the vessel at all observation times (43 +/- 11 deg, 42 +/- 10 deg, and 41 +/- 10 deg for days 10, 20, and 30, respectively), indicating a shift of the SMC orientation from the circumferential toward the longitudinal direction. These results suggested that the major tensile strain might play a role in the regulation of SMC orientation during the development of normal blood vessels as well as during remodeling of vein grafts.     

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)