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.     

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.     

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.     

Linked mechanical and biological aspects of remodeling in mouse pulmonary arteries with hypoxia-induced hypertension

Supravalvular aortic stenosis (SVAS) is associated with decreased elastin and altered arterial mechanics. Mice with a single deletion in the elastin gene (ELN(+/-)) are models for SVAS. Previous studies have shown that elastin haploinsufficiency in these mice causes hypertension, decreased arterial compliance, and changes in arterial wall structure. Despite these differences, ELN(+/-) mice have a normal life span, suggesting that the arteries remodel and adapt to the decreased amount of elastin. To test this hypothesis, we performed in vitro mechanical tests on abdominal aorta, ascending aorta, and left common carotid artery from ELN(+/-) and wild-type (C57BL/6J) mice. We compared the circumferential and longitudinal stress-stretch relationships and residual strains. The circumferential stress-stretch relationship is similar between genotypes and changes <3% with longitudinal stretch at lengths within 10% of the in vivo value. At mean arterial pressure, the circumferential stress in the ascending aorta is higher in ELN(+/-) than in wild type. Although arterial pressures are higher, the increased number of elastic lamellae in ELN(+/-) arteries results in similar tension/lamellae compared with wild type. The longitudinal stress-stretch relationship is similar between genotypes for most arteries. Compared with wild type, the in vivo longitudinal stretch is lower in ELN(+/-) abdominal and carotid arteries and the circumferential residual strain is higher in ELN(+/-) ascending aorta. The increased circumferential residual strain brings the transmural strain distribution in ELN(+/-) ascending aorta close to wild-type values. The mechanical behavior of ELN(+/-) arteries is likely due to the reduced elastin content combined with adaptive remodeling during vascular development.     

Rheological properties and wall structures of large veins

The static and dynamic viscoelastic properties were studied of longitudinal and circumferential strips excised from various large veins of dogs. The mechanical behavior in longitudinal direction could be regarded as elastic, while that in circumferential direction was highly viscoelastic. No distinct regionality was observed in either of the longitudinal and the circumferential groups. Noradrenaline and papaverine did not alter the elastic behavior of the longitudinal strips. In circumferential strips, however, noradrenaline caused a considerable decrease in stress relaxation and some steepening in the slope of the upper limb of hysteresis loop. Papaverine did not affect the circumferential characteristics. These findings suggest the dominant contribution of smooth muscle tone to the circumferential characteristics of venous walls. Pretreatment with formic acid abolished the occurrence of stress relaxation in circumferential direction but produced no change in the longitudinal behavior. This indicates that elastin fibers may be a principal determinant of the elastic behavior in longitudinal direction and that a residual tension observed in stress-relaxation tests of circumferential strips may be due to stretched elastin fibers. The elastic moduli of elastase pretreated venous walls were in the order of 10(8) dynes/cm2, about 1000 times higher than those of the control. Accordingly, collagen fibers seemed not to play any appreciable role in the rheological behavior of venous walls under physiological conditions. This inference was supported by histological observations of venous walls under unstretched and stretched states. Models were proposed in regard to the architecture of the fibrous elements in the venous walls.     

Analysis of some effects of aortic smooth muscle on<Emphasis Type="Italic">in vivo</Emphasis> aortic pressure curves

When aortic pressure curves were predicted previously on the basis of a newly developed model of visco-elastic properties of the aorta, it was necessary to use published viscoelastic constants. These were usually obtained from longitudinal strips of blood vessels long removed from the animal, and therefore probably containing deteriorated smooth muscle. The predicted curves had the same form as actual tracings, substantiating the analysis somewhat, but the pressure levels were low. These low levels, if due to inadequate visco-elastic constants, could be attributed to the use of longitudinal rather than circumferential segments as well as to the use of segments with deteriorated muscle. The present analysis uses data collected by the author testing circumferential viscoelastic properties of fourteen different aortic regions in a way suggested by the author's model of an aortic wall. Moreover, the constants were measured on segments containing muscle relaxed by EDTA solutions and on similar segments containing muscle contracted by neosynephrine. These visco-elastic constants were used in the author's nonlinear differential equation of motion of the aortic wallin vivo to predictin vivo pressure curves. The predicted curves were low in any given aortic region if relaxed constants were used, but at normal levels with contracted constants. In fact, pressure curves predicted using constants obtained from aortic segments containing contracted muscle resembled actual tracings in form and pressure levels. Even the observed variations in the form of the systolic pressure curve down the aorta were predicted by this analysis.     

Effects of age on the anisotropy of the descending human thoracic aorta determined by uniaxial tensile testing and digestion by NaOH under load

Strips of human thoracic aortic wall taken at autopsy from 23 individuals aged 15-81 years have been tested in two ways: in uniaxial loading and by digestion in 0.1 M NaOH at 75 degrees C under a load of 50 g. The circumferentially oriented strips were more extensible in loading and took a longer time to fail while being digested under load than the longitudinal strips from the same location. The stress versus strain curve was fitted to an exponential equation of the form, stress = A[exp(B strain)]. For circumferentially oriented strips from 19 subjects, parameter A was independent of age. Parameter B increased by a factor of 2.75 from 19 to 81 years. For longitudinally oriented strips for 14 subjects, A was also independent of age and B increased by 2.4 times from 25 to 81. With digestion under load for 11 matched pairs of strips aged from 32 to 75 the circumferential strips failed in 117 +/- 23 min (standard error), while the longitudinal ones failed in 20.3 +/- 3.2 min (standard error) (p less than 0.003). The results have important implications for vessel attachments to the aorta in heart transplantation and in vascular surgery.     

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).     

Effects of organophosphate insecticides on mechanical properties of rat aorta

The present study was carried out to search whether organophosphate pesticides affect the mechanical properties of the thoracic aorta. Wistar female rats (aged 6-8 weeks) were assigned randomly to a control group and groups treated with either dichlorvos or chlorpyriphos for 90 days at a dose of 5 mg/kg/day. After that period, animals were killed and thoracic aorta strips in longitudinal direction were isolated. The stress, strain and elastic modulus were obtained from the strips. Our results showed that chronic administration of chlorpyriphos and dichlorvos caused downward shift of the stress-strain relations compared to the control curve. The elastic modulus-stress curve revealed distinct characteristics in the low and high stress regions. A power function was used to simulate the low stress region while a line was fit to the high stress region. Curve fitting procedure illustrated that both pesticides influenced mainly the high stress region, but they had diverse effects at the low stress region. The results also imply that chlorpyriphos and dichlorvos decrease the strength of the aorta and therefore might influence the response of the aorta to mechanical loading induced by blood pressure.     

Morphology and stress-strain properties along the small intestine in the rat

The stress-strain relationship is determined by the inherent mechanical properties of the intestinal wall, the geometric configurations, the loading conditions and the zero-stress state of the segment. The purpose of this project was to provide morphometric and biomechanical data for rat duodenum, jejunum and ileum. The circumferential strains were referenced to the zero-stress state. Large morphometric variations were found along the small intestine with an increase in the outer circumferential length and luminal area and a decrease in wall thickness in distal direction. The serosal residual strain was tensile and decreased in distal direction (P < 0.05). The mucosal residual strain was compressive and the absolute value decreased in distal direction (P < 0.001). The stress-strain experiments showed that the duodenum was stiffest. All segments were stiffest in longitudinal direction (P < 0.05). In conclusion, axial variation in morphometric and biomechanical properties was found in the small intestine. The zero-stress state must be considered in future biomechanical studies in the gastrointestinal tract.     

Mechanical properties in the human gastric antrum using B-mode ultrasonography and antral distension

The aims of this study were to investigate gastric antral geometry and stress-strain properties by using transabdominal ultrasound scanning during volume-controlled distensions in the human gastric antrum. Seven healthy volunteers underwent stepwise inflation of a bag located in the antrum with volumes up to 60 ml. The stretch ratio and Cauchy stress and strain were calculated from measurements of pressure, diameter, and wall thickness. A second distension series was conducted in three volunteers during administration of the anticholinergic drug butylscopolamine. Analysis of stretch ratios demonstrated positive strain in the circumferential direction, negative strain in the radial direction, and no strain in the longitudinal direction. The stress-strain relation was exponential and did not differ without or with the administration of butylscopolamine. The wall stress was decomposed into its active and passive components. The well-known length-tension diagram from in vitro studies of smooth muscle strips was reproduced. The maximum active tension appeared at a volume of 50 ml, corresponding to a stretch ratio of 1.5. We conclude that the method provides measures of antral biomechanical wall properties and can be used to reproduce the muscle length-tension diagram in humans.     

Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

We developed an extension-inflation experimental apparatus with a stereo vision system and a stress-strain analysis method to determine the regional mechanical properties of a blood vessel. Seven proximal descending thoracic aortas were investigated during the inflation test at a fixed longitudinal stretch ratio of 1.35 over a transmural pressure range from 1.33 to 21.33 kPa. Four circumferential regions of each aorta were designated as the anterior (A), left lateral (L), posterior (P), and right lateral (R) regions, and the inflation test was repeated for each region of the aortas. We used continuous functions to approximate the surfaces of the regional aortic wall in the reference configuration and the deformed configuration. Circumferential stretch and stress at the four circumferential regions of the aorta were computed. Circumferential stiffness, defined as the tangent of the stress-stretch curve, and physiological aortic stiffness, named pressure-strain elastic modulus, were also computed for each region. In the low pressure range, the stress increased linearly with increased stretch, but the mechanical response became progressively stiffer in the high-pressure range above a transition point. At a transmural pressure of 12.00 kPa, mean values of stiffness were 416±104 kPa (A), 523±99 kPa (L), 634±91 kPa (P), and 489±82 kPa (R). The stiffness of the posterior region was significantly higher than that of the anterior region, but no significant difference was found in pressure-strain elastic modulus.     

Effects of longitudinal stretch on VSM tone and distensibility of muscular conduit arteries

With progressing age, large arteries diminish their longitudinal stretch, which in extreme cases results in tortuosity. Increased age is also associated with loss of vessel distensibility. We measured pressure-diameter curves from muscular porcine carotid arteries ex vivo at different longitudinal stretch ratios (lambda(z) = 1.4 and 1.8) and under different vascular smooth muscle (VSM) conditions (fully relaxed, normal VSM tone, and maximally contracted). Distensibility was found to be halved by decreasing longitudinal stretch from lambda(z) = 1.8 to 1.4 at physiological pressures. This counterintuitive observation is possible because highly nonlinear elastic modulus of the artery and anisotropic properties. Furthermore, a significantly larger basal VSM contraction was observed at lambda(z) = 1.8 than 1.4, although this was clearly not related to a myogenic response during inflation. This dependence of VSM tone to longitudinal stretch may have possible implications on the functional characteristics of the arterial wall.     

Stomach stress and strain depend on location, direction and the layered structure

The stomach is as other parts of the gastrointestinal tract functionally subjected to dimensional change. Hence, the biomechanical properties are of functional importance. Our group has previously demonstrated that the stress–strain properties of the rat and rabbit stomach wall were species-, location- and direction-dependent. We further wanted to study the anisotropic biomechanical properties of the stomach wall in pigs. Furthermore, we made an in-depth biomechanical test on the layered wall of the stomach in different regions. Two stomach strips were cut both in longitudinal direction (parallel with the greater curvature) and circumferential direction (perpendicular to the greater curvature) from the gastric fundus, corpus and antrum. One strip was used for the non-separated (intact) wall test and the other one was separated for the test on the mucosa–submucosa and muscle layers individually. The length, thickness and width of each strip were measured from digital images. The uni-axial stress and strain were computed from the force generation and the tissue strip deformation during stretching. The muscle layer was the thickest in the antrum whereas the mucosal–submucosal layer was the thickest in the corpus of the stomach (P<0.01). The strips from the corpus were stiffest among the three regions in both longitudinal and circumferential directions (P<0.001). The longitudinal strips was stiffer than the circumferential strips in all three regions (P<0.001) and the mucosa–submucosa strips was stiffer than the intact wall and the muscle layer in both directions for the fundus and the corpus (P<0.001). The constant a of the intact wall and mucosa–submucosa layer was in both directions linearly associated with the mucosa–submucosa thickness. In conclusion, the uni-axial stress–strain curves of pig stomach were location-, direction- and layer-dependent. The stiffer wall in the corpus is likely due to its thicker mucosa, i.e., the stiffness of the mucosa–submucosa layer seems can explain the intact wall stiffness. Since the structure and function of the pig stomach are similar to the human stomach, we believe that the data obtained from this study can be extended to humans. Detailed biomechanical mapping of the stomach will likely help us to understand physiological functions of the different parts of the human stomach, such as gastric accommodation and mechanosensation.     

Increased production of prostacyclin (PGI2) by vascular intimal smooth muscle cells from atherosclerotic rabbit aorta

In vitro PGI2 synthesis by aortic strips obtained from thoracic aorta of rabbits fed a high cholesterol diet was examined and compared with that of control rabbits fed a normal diet. In this report, the amounts of PGI2 produced were shown as 6-keto-PGF1 alpha per microgram of aortic tissue DNA instead of per mg wet weight. We also investigated PGI2 synthesis by cultured smooth muscle cells (SMC) obtained from atherosclerotic intima. Basal PGI2 production by aortic strips from atherosclerotic rabbit aorta was significantly augmented compared with that of controls. Arachidonic acid (AA)-induced PGI2 production by atherosclerotic aorta was also significantly higher than that of controls. PGI2 producing capacities of intimal and medial layers, separated from atherosclerotic aorta, were examined and the intimal layer was found to elicit a significantly greater PGI2 production than the medial layer. Furthermore, cultured intimal SMC obtained from atherosclerotic rabbit aorta produced a greater amount of PGI2 than medial SMC from normal rabbit aorta at various cultured conditions. These results suggest that the possibility of enhanced PGI2 production by atherosclerotic aorta may well be considered as a defence mechanism of the vessel wall against damaging stimuli.     

A biophysical and histological analysis of factors that lead to aortic rupture in normal and lathyritic turkeys

These experiments were designed to determine if local differences in elastic properties or wall structure contributed to the development of aortic rupture in turkeys. Static elastic properties were measured from pressure-volume curves of cylindrical segments of upper and lower thoracic aorta and innominate artery in two groups of lathyritic birds and two age-matched control groups. The biggest changes were in the young lathyritic group that was on 0.04% beta-aminoproprionitrile at 3 weeks of age and continued for 2, 3, or 4 weeks. Much smaller changes were seen in the older group that started on 0.05% beta-aminoproprionitrile at 6 weeks of age for 10 days and then 0.02% beta-aminoproprionitrile for the next 9-12 weeks. The biggest changes were seen in the abdominal aorta, which ruptured spontaneously in 50% of the young lathyritic group. The birds had a marked decrease in the number of elastin layers per unit wall thickness. Analysis of the elastic diagrams showed that the elastance of both elastin and collagen were altered in the young lathyritic group. Rupture appeared to follow partial dissection of plaques, but true longitudinal dissection did not occur.     

In spontaneously hypertensive rats alterations in aortic wall properties precede development of hypertension

In hypertension arterial wall properties do not necessarily depend on increased blood pressure alone. The present study investigates the relationship between the development of hypertension and thoracic aortic wall properties in 1.5-, 3-, and 6-mo-old spontaneously hypertensive rats (SHR); Wistar-Kyoto rats (WKY) served as controls. During ketamine-xylazine anesthesia, compliance and distensibility were assessed by means of a noninvasive ultrasound technique combined with invasive blood pressure measurements. Morphometric measurements provided in vivo media cross-sectional area and thickness, allowing the calculation of the incremental elastic modulus. Extracellular matrix protein contents were determined as well. Blood pressure was not significantly different in 1.5-mo-old SHR and WKY, but compliance and distensibility were significantly lower in SHR. Incremental elastic modulus was not significantly different between SHR and WKY at this age. Media thickness and media cross-sectional area were significantly larger in SHR than in WKY, but there was no consistent difference in collagen density and content between the strains. Blood pressure was significantly higher in 3- and 6-mo-old SHR than in WKY, and compliance was significantly lower in SHR. The findings in this study show that in SHR, in which hypertension develops over weeks, alterations in functional aortic wall properties precede the development of hypertension. The decrease in compliance and distensibility at a young age most likely results from media hypertrophy rather than a change in intrinsic elastic properties.     

The effect of the elongation of the proximal aorta on the estimation of the aortic wall distensibility

The compliance of the proximal aortic wall is a major determinant of cardiac afterload. Aortic compliance is often estimated based on cross-sectional area changes over the pulse pressure, under the assumption of a negligible longitudinal stretch during the pulse. However, the proximal aorta is subjected to significant axial stretch during cardiac contraction. In the present study, we sought to evaluate the importance of axial stretch on compliance estimation by undertaking both an in silico and an in vivo approach. In the computational analysis, we developed a 3-D finite element model of the proximal aorta and investigated the discrepancy between the actual wall compliance to the value estimated after neglecting the longitudinal stretch of the aorta. A parameter sensitivity analysis was further conducted to show how increased material stiffness and increased aortic root motion might amplify the estimation errors (discrepancies between actual and estimated distensibility ranging from − 20 to − 62%). Axial and circumferential aortic deformation during ventricular contraction was also evaluated in vivo based on MR images of the aorta of 3 healthy young volunteers. The in vivo results were in good qualitative agreement with the computational analysis (underestimation errors ranging from − 26 to − 44%, with increased errors reflecting higher aortic root displacement). Both the in silico and in vivo findings suggest that neglecting the longitudinal strain during contraction might lead to severe underestimation of local aortic compliance, particularly in the case of women who tend to have higher aortic root motion or in subjects with stiff aortas.

     

Passive viscoelastic properties of the rabbit aorta in vitro

Tensile tests on longitudinal and circumferential strips of the rabbit aorta have been performed. Stress-strain and relaxation parameters have been estimated with respect to four stress levels and three positions on the aorta. Stress-strain data indicate that in longitudinal direction the aorta becomes more compliant with distance from the aortic arch. The opposite tendency is found for the circumferential direction. Stress-relaxation is found to be strongly dependent on the stress level. The results are discussed with regard to arterial dynamics.     

Assessment of the aortic stress-strain relation in uniaxial tension

The passive elastic characteristics of the abdominal aorta were investigated in two experimental animal models, aiming at assessing the stress-strain relation of the aortic wall. Twenty porcine and 15 rabbit healthy abdominal aortas were subjected to uniaxial stress-strain analysis, performed on a tensile-testing device, while immersed in a physiologic saline bath at body temperature. Measured parameters included original length, width and thickness, as well as axial force and extension. Based on these data, Kirchhoff stress and Green-St.Venant strain were computed and one-dimensional constitutive equations were defined, comprising of a power function and two exponential ones, in turn, for the low, physiologic and high-stress regions. The stress-strain curves were plotted as elastic modulus versus stress, displaying nonlinear part I and linear parts II and III. These were regressed, yielding parameters k, q (part I), a, b (part II) and c, d (part III). A detailed comparison of these constitutive parameters was undertaken between the two species, demonstrating variations in d (p<0.05). No statistical differences were found in parameters a, b, c, k and q, implying that the two aortas were equally stiff under low and physiologic stresses, whereas the porcine aorta was stiffer at higher stresses. In conclusion, a bi-exponential in addition to a power law was established, relating stress and strain in the aorta, which is advantageous in comparison with previous constitutive equations. Under passive conditions, the nonlinear nature of this constitutive law may account for the low, part I, physiologic, part II, and high-stress, part III of the stress-strain relationship, supporting the concept of the aortic wall as a biphasic material.