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).     

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.     

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.     

Some unusual considerations about vessel walls and wall stresses

The "zero-stress state" of blood vessels is usually defined with respect to the atmospheric pressure p(a) ( approximately 750 mmHg). As a consequence, circumferential and axial wall stresses due to a positive transmural pressure can only be positive and thus, by definition, only tensile. If the zero-stress state were defined with respect to vacuum pressure (0 mmHg), the compressive stress -p(a) generated by p(a) everywhere in the wall would, however, be included so that negative (=compressive) wall stresses would formally become possible. In order to examine the consequences this alternative definition would have for arteries, we have compared radial, circumferential, and axial stresses calculated "conventionally" to the values they take when the zero-stress state is defined "correctly" by reference to the vacuum pressure. It turns out that, under normal physiologic conditions, axial stress and perhaps also circumferential stress might well be compressive in many elastic and conductance arteries, contrary to the intuitive conviction of many people. Since the type of stresses a vessel wall is submitted to may be highly relevant for its structure and mechanical properties, this unconventional way of considering wall stresses may reveal unsuspected relationships between wall stresses on one side, and wall structure, vessel growth, adaptation and repair processes, atherosclerosis, angioplasty or stenting on the other side. Similar considerations might also prove useful with regard to cardiac hypertrophy.     

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.     

Transmural strain distribution in the blood vessel wall

The transmural distributions of stress and strain at the in vivo state have important implications for the physiology and pathology of the vessel wall. The uniform transmural strain hypothesis was proposed by Takamyzawa and Hayashi (Takamizawa K and Hayashi K. J Biomech 20: 7-17, 1987; Biorheology 25: 555-565, 1988) as describing the state of arteries in vivo. From this hypothesis, they derived the residual stress and strain at the no-load condition and the opening angle at the zero-stress state. However, the experimental evidence cited by Takamyzawa and Hayashi (J Biomech 20: 7-17, 1987; and Biorheology 25: 555-565, 1988) to support this hypothesis was limited to arteries whose opening angles (theta) are <180 degrees. It is well known, however, that theta > 180 degrees do exist in the cardiovascular system. Our hypothesis is that the transmural strain distribution cannot be uniform when theta; is >180 degrees. We present both theoretical and experimental evidence for this hypothesis. Theoretically, we show that the circumferential stretch ratio cannot physically be uniform across the vessel wall when theta; exceeds 180 degrees and the deviation from uniformity will increase with an increase in theta; beyond 180 degrees. Experimentally, we present data on the transmural strain distribution in segments of the porcine aorta and coronary arterial tree. Our data validate the theoretical prediction that the outer strain will exceed the inner strain when theta > 180 degrees. This is the converse of the gradient observed when the residual strain is not taken into account. Although the strain distribution may not be uniform when theta exceeds 180 degrees, the uniformity of stress distribution is still possible because of the composite nature of the blood vessel wall, i.e., the intima-medial layer is stiffer than the adventitial layer. Hence, the larger strain at the adventitia can result in a smaller stress because the adventitia is softer at physiological loading.     

Distribution of stress and strain along the porcine aorta and coronary arterial tree

The existence of a homeostatic state of stresses and strains has been axiomatic in the cardiovascular system. The objective of this study was to determine the distribution of circumferential stress and strain along the aorta and throughout the coronary arterial tree to test this hypothesis. Silicone elastomer was perfused through the porcine aorta and coronary arterial tree to cast the arteries at physiological pressure. The loaded and zero-stress dimensions of the vessels were measured. The aorta (1.8 cm) and its secondary branches were considered down to 1.5 mm diameter. The left anterior descending artery (4.5 mm) and its branches down to 10 microm were also measured. The Cauchy mean circumferential stress and midwall stretch ratio were calculated. Our results show that the stretch ratio and Cauchy stress were lower in the thoracic than in the abdominal aorta and its secondary branches. The opening angle (theta) and midwall stretch ratio (lambda) showed a linear variation with order number (n) as follows: theta = 10.2n + 63.4 (R(2) = 0.989) and lambda = 4.47 x 10(-2)n + 1.1 (R(2) = 0.995). Finally, the stretch ratio and stress varied between 1.2 and 1.6 and between 10 and 150 kPa, respectively, along the aorta and left anterior descending arterial tree. The relative uniformity of strain (50% variation) from the proximal aorta to a 10-microm arteriole implies that the vascular system closely regulates the degree of deformation. This suggests a homeostasis of strain in the cardiovascular system, which has important implications for mechanotransduction and for vascular growth and remodeling.     

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.     

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

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

3d Mechanical properties of the partially obstructed guinea pig small intestine

Background and aimsPartial obstruction of the small intestine results in severe hypertrophy of smooth muscle cells, dilatation and functional denervation. Hypertrophy of the small intestine is associated with alteration of the wall structure and the mechanical properties. The aims of this study were to determine three dimensional material properties of the obstructed small intestine in guinea pigs and to obtain the 3D stress–strain distributions in the small intestinal wall.MethodsPartial obstruction of mid-jejunum was created surgically in five guinea pigs that were euthanized 2 weeks after the surgery. Ten-cm-long segments proximal to the obstruction site were used for the stretch-inflation mechanical test using a tri-axial test machine. The outer diameter, longitudinal force and the luminal pressure during the test were recorded simultaneously. An anisotropic exponential pseudo-strain energy density function was used as the constitutive equation to fit the experimental loading curve and for computation of the stress–strain distribution.ResultsThe wall thickness and the wall area increased significantly in the obstructed jejunum (P<0.001). The pressure—outer radius curves in the obstructed segments were translated to the left of the normal segments, indicating wall stiffening after the obstruction. The circumferential stress and the longitudinal stress through the wall were higher in the obstructed segments (P<0.02). This was independent of whether the zero-stress state or the no-load states were used as the reference state.ConclusionThe mechanical behaviour of the obstructed small intestine can be described using a 3D constitutive model. The obstruction-induced biomechanical properties change was characterized by higher circumferential and longitudinal stresses in the wall and altered material constants in the 3D constitutive model.     

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.     

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.     

Effect of residual stress and heterogeneity on circumferential stress in the arterial wall

Quantifying the stress distribution through the arterial wall is essential to studies of arterial growth and disease. Previous studies have shown that both residual stress, as measured by opening angle, and differing material properties for the media-intima and the adventitial layers affect the transmural circumferential stress (sigma theta) distribution. Because a lack of comprehensive data on a single species and artery has led to combinations from multiple sources, this study determined the sensitivity of sigma theta to published variations in both opening angle and layer thickness data. We fit material properties to previously published experimental data for pressure-diameter relations and opening angles of rabbit carotid artery, and predicted sigma theta through the arterial wall at physiologic conditions. Using a one-layer model, the ratio of sigma theta at the internal wall to the mean sigma theta decreased from 2.34 to 0.98 as the opening angle increased from 60 to 130 deg. In a two-layer model using a 95 deg opening angle, mean sigma theta in the adventitia increased (112 percent for 25 percent adventitia) and mean sigma theta in the media decreased (47 percent for 25 percent adventitia). These results suggest that both residual stress and wall layers have important effects on transmural stress distribution. Thus, experimental measurements of loading curves, opening angles, and wall composition from the same species and artery are needed to accurately predict the transmural stress distribution in the arterial wall.     

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

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

A constitutive formulation of arterial mechanics including vascular smooth muscle tone

A pseudo-strain energy function (pseudo-SEF) describing the biomechanical properties of large conduit arteries under the influence of vascular smooth muscle (VSM) tone is proposed. In contrast to previous models that include the effects of smooth muscle contraction through generation of an active stress, in this study we consider the vascular muscle as a structural element whose contribution to load bearing is modulated by the contraction. This novel pseudo-SEF models not only arterial mechanics at maximal VSM contraction but also the myogenic contraction of the VSM in response to local increases in stretch. The proposed pseudo-SEF was verified with experimentally obtained pressure-radius curves and zero-stress state configurations from rat carotid arteries displaying distinct differences in VSM tone: arteries from normotensive rats displaying minimal VSM tone and arteries from hypertensive rats exhibiting significant VSM tone. The pressure-radius curves were measured in three different VSM states: fully relaxed, maximally contracted, and normal VSM tone. The model fitted the experimental data very well (r2 > 0.99) in both the normo- and hypertensive groups for all three states of VSM activation. The pseudo-SEF was used to illustrate the localized reduction of circumferential stress in the arterial wall due to normal VSM tone, suggesting that the proposed pseudo-SEF can be of general utility for describing stress distribution not only under passive VSM conditions, as most SEFs proposed so far, but also under physiological and pathological conditions with varying levels of VSM tone.     

Postnatal changes in the rheological properties of the aorta in Sprague-Dawley rats.

Postnatal changes in the rheological properties of the aortic wall were investigated in relation to morphological development of the wall in Sprague-Dawley (SD) rats at 3, 8 and 20 weeks old. The mechanical tensile characteristics of the longitudinal wall strip excised from the proximal thoracic aorta were assessed with stress-strain and stress-relaxation tests. Wall tension in the low and medium strain ranges was significantly lower in 3-week-old rats than in 8-week-old rats and in 8-week-old rats than in 20-week-old rats. Wall stress was significantly lower in 3-week-old rats than in 8- and 20-week-old rats mainly in the medium strain range, but was significantly greater in 3-week-old rats than in 8- and 20-week-old rats in the high strain range. The value of incremental elastic modulus at 3 weeks old was significantly smaller than that at 8 and 20 weeks old at a strain of 0.25 and significantly larger than that at 8 and 20 weeks old at a strain of 0.50. The value of relaxation strength at 5 min after the stretching was significantly greater at 3 weeks old than that at 8 and 20 weeks old. The wall was viscoelastic in the low and medium strain ranges at 3 weeks though large wall stress was generated in the high strain range. Histological investigation revealed that the smooth muscle layer, fine elastin fiber connecting thick elastin fibers and wall thickness were thin at 3 weeks old in comparison with those at 8 and 20 weeks old, though there was no significant difference in number of nuclei of the smooth muscle cells among the three age groups. Changes in the tensile characteristics of the wall reflected well those of the microstructure of the wall with growth. The rheological properties and microstructure of the aortic wall were close to maturation at 8 weeks in SD rats.     

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.     

A model of stress-induced geometrical remodeling of vessel segments adjacent to stents and artery/graft anastomoses

The mismatch between the elastic properties and initial geometry of a host artery and an implanted stent or graft cause significant stress concentration at the zones close to junctions. This may contribute to the often observed intimal hyperplasia, resulting in late lumen loss and eventual restenosis. This study proposes a mathematical model for stress-induced thickening of the arterial wall at the zones close to an implanted stent or graft. The host artery was considered initially as a cylindrical shell with constant thickness that was clamped to the stent or graft, which was assumed to be non-deformable in the circumferential direction. It was assumed that the abnormal circumferential and axial stresses due to the bending of the arterial wall cause wall thickening that tends to restore the stress state close to that existing far from the junction. The linear equations of a cylindrical shell with variable thickness were coupled to an evolution equation for the wall thickness. These equations were solved numerically and a parametric study was performed using finite difference method and explicit time step. The results show that the remodeling process is self-limiting and leads to local thickening that gradually decreases with distance from the edge of the stent/graft. Model predictions were tested against morphological findings existing in the literature. Recommendations on stent designs that reduce stress concentrations are discussed.     

Regional distribution of axial strain and circumferential residual strain in the layered rabbit oesophagus

The oesophagus is subjected to large axial strains in vivo and the zero-stress state is not a closed cylinder but an open circular cylindrical sector. The closed cylinder with no external loads applied is called the no-load state and residual strain is the difference in strain between the no-load state and zero-stress state. To understand oesophageal physiology and pathophysiology, it is necessary to know the distribution of axial strain, the zero-stress state, the stress-strain relations of oesophageal tissue, and the changes of these states and relationships due to biological remodeling of the tissue under stress. This study is addressed to such biomechanical properties in normal rabbits. The oesophagi were marked on the surface in vivo, photographed, excised (in vitro state), photographed again, and sectioned into rings (no-load state) in an organ bath containing calcium-free Kreb's solution with dextran and EGTA added. The rings were cut radially to obtain the zero-stress state for the non-separated wall and further dissected to separate the muscle and submucosa layers. Equilibrium was awaited for 30min in each state and the specimens were photographed in no-load and the zero-stress states. The oesophageal length, circumferences, layer thicknesses and areas, and openings angle were measured from the digitised images. The oesophagus shortened axially by 35% after excision. The in vivo axial strain showed a significant variation with the highest values in the mid-oesophagus (p<0.001). Luminal area, circumferences, and wall and layer thicknesses and areas varied in axial direction (in all tests p<0.05). The residual strain was compressive at the mucosal surface and tensile at the serosal surface. The dissection studies demonstrated shear forces between the two layers in the non-separated wall in the no-load and zero-stress states. In conclusion, our data show significant axial variation in passive morphometric and biomechanical properties of the oesophagus. The oesophagus is a layered composite structure with nonlinear and anisotropic mechanical behaviour.     

A novel arterial constitutive model in a commercial finite element package: Application to balloon angioplasty

Recently, a novel linearized constitutive model with a new strain measure that absorbs the material nonlinearity was validated for arteries. In this study, the linearized arterial stress-strain relationship is implemented into a finite element method package, ANSYS, via the user subroutine USERMAT. The reference configuration is chosen to be the closed cylindrical tube (no-load state) rather than the open sector (zero-stress state). The residual strain is taken into account by analytic calculation and the incompressibility condition is enforced with Lagrange penalty method. Axisymmetric finite element analyses are conducted to demonstrate potential applications of this approach in a complex boundary value problem where angioplasty balloon interacts with the vessel wall. The model predictions of transmural circumferential and compressive radial stress distributions were also validated against an exponential-type Fung model, and the mean error was found to be within 6%.