Zero-stress State Research Articles

Mechanism of theB3toB1transformation in cubic AlN under uniaxial stress

Using ab initio calculations, we model the $B3$ to $B1$ phase transformation of cubic AlN in both tensile and shear deformations in order to obtain detailed information about the structure and the movement of the atoms within the cell. It is shown that, during that transformation, the strained $B3$ $(Imm2)$ structure changes to strained $B1$ $(I4∕mmm)$ structure as a result of a collective antiparallel movement of the Al and N atoms along the ⟨001⟩ crystallographic axis. The transition is discontinuous under uniaxial stress and the zero-stress transition state corresponds to a hypothetical state with a sudden lattice reconstruction.

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.

Computational modeling of morphogenesis regulated by mechanical feedback

Mechanical forces cause changes in form during embryogenesis and likely play a role in regulating these changes. This paper explores the idea that changes in homeostatic tissue stress (target stress), possibly modulated by genes, drive some morphogenetic processes. Computational models are presented to illustrate how regional variations in target stress can cause a range of complex behaviors involving the bending of epithelia. These models include growth and cytoskeletal contraction regulated by stress-based mechanical feedback. All simulations were carried out using the commercial finite element code ABAQUS, with growth and contraction included by modifying the zero-stress state in the material constitutive relations. Results presented for bending of bilayered beams and invagination of cylindrical and spherical shells provide insight into some of the mechanical aspects that must be considered in studying morphogenetic mechanisms.

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

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

Biomechanical and morphometric colon remodelling in STZ‐induced diabetic rats

Diabetes mellitus may affect the whole GI tract and cause severe symptoms. The morphometric and passive biomechanical properties were studied in the mid-colon in 6 non-diabetic and 12 streptozotocin-induced diabetic rats. The diabetic rats were divided into two equal groups living 4 weeks and 8 weeks after the induction of diabetes. The test was done as ramp distension. The diameter and length were obtained from digitised images of the segments at pre-selected pressures and at no-load and zero-stress states. Circumferential and longitudinal stresses and strains were computed from the length, diameter and pressure data and from the zero-stress state geometry. The following was found for the non-diabetic and 4 and 8 weeks diabetic groups, respectively: the blood glucose (mmol/L) (6.7±1.8, 23.6±4.4, 24.5±3.6, P< 0.001); weight (g) per cm length of the colon (0.097±0.023, 0.123±0.022, 0.144±0.031, P<0.05), wall thickness (mm) (0.39±0.08, 0.52±0.11, 0.67±0.15, P<0.05); the opening angle (degree) (118±23, 152±24, 178±34, P<0.01) and absolute values of residual strain (inner, −0.07±0.02, −0.11±0.02, −0.15±0.03; outer 0.05±0.01, 0.09±0.02, 0.13±0.03, P<0.01). Furthermore, the circumferential and longitudinal stiffness of the wall increased during diabetes (P<0.01). In conclusion, diabetic rats showed changes of morphometry and biomechanics in the colon. The study was supported by Aalborg Hospital.

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

Previous studies have indicated that intestinal mucosa is compressed in vivo. The present study investigated the contribution of the villi to the biomechanical properties in circumferential direction in the guinea pig jejunum. Eight segments were used in this study. Each 20 cm long segment was excised and separated into two 10 cm long segments. The mucosal villi were scraped off from half the segments. Then the segments were pressurized in vitro with Krebs solution from 0–10 cmH2O 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 villi from the mucosa resulted in small opening angles (139±16 vs 189±27 with villi) and absolute value 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 stress-strain curve of the segment without villi was located at the left compared to the segment with villi, indicating the wall was stiffer without villi. However, if the villi were not taken into account in the computation of the stress-strain in the intact segment, the curve was only partly shifted to the left. In conclusion, the villi not only affect the zero-stress state conformation but also affect circumferential stresses and strains in the guinea pig jejunum. The research was supported by Aalborg Hospital.

The oesophageal zero-stress state and mucosal folding from a GIOME perspective.

The oesophagus is a cylindrical organ with a collapsed lumen and mucosal folds. The mucosal folding may serve to advance the function of the oesophagus, i.e. the folds have a major influence on the flow of air and bolus through the oesophagus. Experimental studies have demonstrated oesophageal mucosal folds in the no-load state. This indicates that mucosal buckling must be considered in the analysis of the mechanical reference state since the material stiffness drops dramatically after tissue collapse. Most previous work on the oesophageal zero-stress state and mucosal folding has been experimental. However, numerical analysis offers a promising alternative approach, with the additional ability to predict the mucosal buckling behaviour and to calculate the regional stress and strain in complex structures. A numerical model used for describing the mechanical behaviour of the mucosal-folded, three-layered, two-dimensional oesophageal model is reviewed. GIOME models can be used in the future to predict the tissue function physiologically and pathologically.

Biomechanical and histomorphometric esophageal remodeling in type 2 diabetic GK rats

Diabetes mellitus induces remodeling of the morphology and mechanical properties in the gastrointestinal tract. This study aimed to investigate the histomorphometric and biomechanical remodeling of esophagus in the diabetic type 2 model Goto-Kakizaki (GK) rats. Five male diabetic GK rats and five male nondiabetic Wistar rats were used in this study. The mechanical test was performed in vitro where the whole esophagus was stretched to its in situ length and distended with pressures up to 10 cm H 2O using a ramp distension protocol. The pressure and outer diameter were recorded. Circumferential stress (force per area) and strain (deformation) were computed from the diameter and pressure data using the zero-stress state as reference. The zero-stress state was obtained by cutting esophageal rings radially. This caused the rings to open up into a sector. The thickness, area, and the opening angle were measured from the digitized images. The layer circumference, thickness, and area were measured from histological slides. The collagen fraction was determined from histological slides with Van Gieson stain. Diabetes induced pronounced morphometric changes, e.g., the wall thickness and wall cross-sectional area significantly increased in the GK rats ( P<.01). Histologically, the circumference, thickness, and area of the muscle layer and the collagen fraction of mucosa–submucosa layer were significantly increased in the GK rats ( P<.01). The opening angle, outer residual strain, and residual strain difference to wall thickness ratio decreased significantly in the GK rats ( P<.05 and P<.01). Furthermore, the circumferential stiffness of the esophagus is significantly higher in the GK rats than in the normal rats ( P<.01). In conclusion, histomorphometric and biomechanical remodeling is a feature of the esophageal wall in GK rats.

Manual pressure distension of the human saphenous vein changes its biomechanical properties—implication for coronary artery bypass grafting

Patency rates of saphenous vein grafts following coronary artery bypass grafting (CABG) depend on multiple factors. Information regarding the impact of biomechanical properties of vein grafts on patency rates is not available. The objective of the present study was to evaluate whether uncontrolled manual pressure distension during routine preparation of the saphenous vein in CABG-induced changes in the biomechanical properties of the vein. The morphometric and stress–strain properties were studied in isolated segments of the saphenous vein from 12 patients undergoing elective CABG. Six segments were manually distended without pressure control and six were not distended. The mechanical test was performed as a ramp inflation using syringe pump. The vein dimensions were obtained from digitised images at different pressures as well as at the no-load and zero-stress states. The circumferences, the wall and lumen area, the wall thickness, and the outer diameter as function of the applied pressure were largest in the segments with uncontrolled manual distension compared to those without distension ( P < 0.05 ) . The opening angle and the absolute value of the residual strains were lower ( P < 0.01 ) and the circumferential stress–strain curve shifted to the left, indicating the wall became stiffer with uncontrolled manual distension compared to those without distension ( P < 0.05 ) . In conclusion, manual pressure distension changed the morphometric and biomechanical properties of the saphenous vein. The perspective is that studies on biomechanical properties on the saphenous vein may guide surgeons how to handle graft material without causing major changes of the biomechanical properties during harvesting and preparation.

Longitudinal residual strain and stress-strain relationship in rat small intestine

BackgroundTo obtain a more detailed description of the stress-free state of the intestinal wall, longitudinal residual strain measurements are needed. Furthermore, data on longitudinal stress-strain relations in visceral organs are scarce. The present study aims to investigate the longitudinal residual strain and the longitudinal stress-strain relationship in the rat small intestine.MethodsThe longitudinal zero-stress state was obtained by cutting tissue strips parallel to the longitudinal axis of the intestine. The longitudinal residual stress was characterized by a bending angle (unit: degrees per unit length and positive when bending outwards). Residual strain was computed from the change in dimensions between the zero-stress state and the no-load state. Longitudinal stresses and strains were computed from stretch experiments in the distal ileum at luminal pressures ranging from 0–4 cmH2O.ResultsLarge morphometric variations were found between the duodenum and ileum with the largest wall thickness and wall area in the duodenum and the largest inner circumference and luminal area in the distal ileum (p < 0.001). The bending angle did not differ between the duodenum and ileum (p > 0.5). The longitudinal residual strain was tensile at the serosal surface and compressive at the mucosal surface. Hence, the neutral axis was approximately in the mid-wall. The longitudinal residual strain and the bending angle was not uniform around the intestinal circumference and had the highest values on the mesenteric sides (p < 0.001). The stress-strain curves fitted well to the mono-exponential function with determination coefficients above 0.96. The α constant increased with the pressure, indicating the intestinal wall became stiffer in longitudinal direction when pressurized.ConclusionLarge longitudinal residual strains reside in the small intestine and showed circumferential variation. This indicates that the tissue is not uniform and cannot be treated as a homogenous material. The longitudinal stiffness of the intestinal wall increased with luminal pressure. Longitudinal residual strains must be taken into account in studies of gastrointestinal biomechanical properties.

A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries

A multiscale model was proposed to calculate the circumferential stress (CS) and wall shear stress (WSS) and analyze the effects of global and local factors on the CS, WSS and their synergy on the arterial endothelium in large straight arteries. A parameter pair [Zs,SPA] (defined as the ratio of CS amplitude to WSS amplitude and the phase angle between CS and WSS for different harmonic components, respectively) was proposed to characterize the synergy of CS and WSS. The results demonstrated that the CS or WSS in the large straight arteries is determined by the global factors, i.e. the preloads and the afterloads, and the local factors, i.e. the local mechanical properties and the zero-stress states of arterial walls, whereas the Zs and SPA are primarily determined by the local factors and the afterloads. Because the arterial input impedance has been shown to reflect the physiological and pathological states of whole downstream arterial beds, the stress amplitude ratio Zs and the stress phase difference SPA might be appropriate indices to reflect the influences of the states of whole downstream arterial beds on the local blood flow-dependent phenomena such as angiogenesis, vascular remodeling and atherosgenesis.

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.

Effect of Kaiyu Qingwei Jianji on the morphometry and residual strain distribution of small intestine in experimental diabetic rats

To investigate the effect of a Chinese medicine, Kaiyu Qingwei Jianji (KYQWJJ) used for diabetic treatment, on the morphometry and residual strain distribution of the small intestine in streptozotocin (STZ) -induced diabetic rats. Correlation analysis was also performed between the opening angle and residual strain with the blood glucose level. Forty-two male Wistar rats weighing 220-240 g were included in this study. Thirty-two STZ-induced diabetic rats were subdivided into four groups (n = 8 in each group), i.e. diabetic control group (DM); high dose of KYQWJJ (T1, 36 g/kg per day); low dose of KYQWJJ (T2, 17 g/kg per day) and Gliclazide (T3, 50 mg/kg per day). Another ten rats were used as non-diabetic control (CON). The medicines were poured directly into stomach lumen by gastric lavage twice daily. The rats of CON and DM groups were only poured the physiological saline. Blood glucose and plasma insulin levels were measured. Experimental period was 35 d. At the end of experiment, three 5-cm long segments were harvested from the duodenum, jejunum and ileum. Three rings of 1-2 mm in length for no-load and zero-stress state tests were cut from the middle of different segments. The morphometric data, such as the circumferential length, the wall thickness and the opening angle were measured from the digitized images of intestinal segments in the no-load state and zero-stress state. The residual strain was computed from the morphometry data. Furthermore, the linear regression analysis was performed between blood glucose level with morphometric and biomechanical data in the different intestinal segments. The blood glucose level of DM group was consistent 4-fold to 5-fold higher than those in CON group during the experiment (16.89+/-1.11 vs 3.44+/-0.15 mmol/L, P < 0.001). The blood glucose level in the T1 (16.89+/-1.11 vs 11.08+/-2.67 mmol/L, P < 0.01) and T3 groups (16.89+/-1.11 vs 13.54+/-1.73 mmol/L, P < 0.05), but not in T2 group (P > 0.05) was significantly lower than those in DM group. The plasma insulin levels of DM, T1, T2 and T3 groups were significantly lower than those in CON group (10.98+/-1.02, 12.52+/-1.42,13.54+/-1.56,10.96+/-0.96 vs 17.84+/-2.34 pmol/L respectively, P < 0.05), but no significantly difference among the groups with exception of CON group. The wet weight/cm and total wall thickness of duodenum, jejunum and ileum in DM group were significantly higher than those in CON group (wet weight (g/cm): duodenum 0.209+/-0.012 vs 0.166+/-0.010, jejunum 0.149+/-0.008 vs 0.121+/-0.004, ileum 0.134+/-0.013 vs 0.112+/-0.007; Wall thickness (mm): duodenum 0.849+/-0.027 vs 0.710+/-0.026, jejunum 0.7259+/-0.034 vs 0.627+/-0.025, ileum 0.532+/-0.023 vs 0.470+/-0.010, all P < 0.05), T1 and T3 treatment could partly restore change of wall thickness, but T2 could not. The opening angle and absolute value of inner and outer residual stain were significantly smaller in duodenal segment (188+/-11 degrees, -0.31+/-0.02 and 0.35+/-0.03 vs 259+/-15 degrees, -0.40+/-0.02 and 0.43+/-0.05) and larger in jejunal (215+/-20 degrees, -0.30+/-0.03 and 0.36+/-0.06 vs 172+/-19 degrees, -0.25+/-0.02 and 0.27+/-0.02) and ileal segments (183+/-20 degrees, -0.28+/-0.01 and 0.34+/-0.05 vs 153+/-14 degrees, -0.23+/-0.03 and 0.29+/-0.04) in DM group than in CON group (P < 0.01). T1 and T3 treatment could partly restore this biomechanical alteration, but strong effect was found in T1 treatment (duodenum 243+/-14 degrees, -0.36+/-0.02 and 0.42+/-0.06, jejunum 180+/-15 degrees, -0.26+/-0.03 and 0.30+/-0.06 and ileum 163+/-17 degrees, -0.23+/-0.03 and 0.30+/-0.05, compared with DM, P < 0.05). The linear association was found between the glucose level with most morphometric and biomechanical data. KYQWJJ (high dose) treatment could partly restore the changes of blood glucose level and the remodeling of morphometry and residual strain of small intestine in diabetic rats. The linear regression analysis demonstrated that the effect of KYQWJJ on intestinal opening angle and residual strain is partially through its effect on the blood glucose level.

Biomechanical remodeling of obstructed guinea pig jejunum with reference to the zero-stress state

Biomechanical remodeling of obstructed guinea pig jejunum with reference to the zero-stress state

First approximation of the zero-stress state of arterial wall and contraction of SMC

First approximation of the zero-stress state of arterial wall and contraction of SMC

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.

The Effect of Digestion of Collagen and Elastin on Histomorphometry and the Zero-Stress State in Rat Esophagus

To understand the physiology and pathology of the esophagus, it is necessary to know the mechanical properties and their dependence on the structural components. The aim of this study was to investigate the effect of collagenase and elastase on the morphological and biomechanical properties in the no-load and zero-stress states in the rat esophagus. Twenty tissue rings from each esophagus of seven normal rats were sectioned in an organ bath containing calcium-free Krebs solution with dextran and EGTA. After the rings were photographed in the no-load state, 8 of the 20 rings were separated into mucosa-submucosa and muscle rings and the rings were transferred to four different solutions containing collagenase, elastase, or corresponding control solutions. The rings were cut radially to obtain the zero-stress state and photographed again. The thickness, area, and opening angle were measured from the digitized images. The collagen and elastin area fractions were determined from histological slides with Van Gieson and Weigert's elastic stain. The opening angles and residual strain did not differ in the nonseparated enzyme-treated rings and control rings. However, in the separated mucosa-submucosa ring the opening angle was significantly smaller after treatment than that in control rings (P < 0.01). Collagenase and elastase reduced collagen and elastin in the mucosa-submucosa layer about 40% in the nonseparated wall and 54% in the separated mucosa-submucosa layer (P < 0.01). Collagenase and elastase increased the thickness in the separated mucosa-submucosa layer compared to the control (P < 0.05). Disconnection between the epithelia and the lamina propria was histologically observed after elastase digestion. In conclusion, collagenase and elastase caused the opening angle and the residual strain in the separated mucosa-submucosa layer to decrease. The opening angle of the separated mucosa-submucosa layer depended to some extent on the fraction of collagen and elastin.

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.

Tension and stress in the rat and rabbit stomach are location‐ and direction‐dependent

Distension studies in the stomach are very common. It is assumed in pressure-volume (barostat) studies of tone and tension in the gastric fundus that the fundus is a sphere, i.e. that the tension in all directions is identical. However, the complex geometry of the stomach indicates a more complex mechanical behaviour. The aim of this study was to determine uniaxial stress-strain properties of gastric strips obtained from rats (n=12) and rabbits (n=10). Furthermore, we aimed to study the gastric zero-stress state since the stomach is one of the remaining parts of the gastrointestinal tract where residual strain studies have not been conducted. Longitudinal strips (in parallel with the lesser curvature) and circumferential strips (perpendicular to the lesser curvature) were cut from the gastric fundus (glandular part) and forestomach (non-glandular part). The residual stress was evaluated as bending angles (unit: degree per unit length and negative when bending outwards). The residual strain was computed from the change in length between the zero-stress state and no-load state. The stress-strain test was performed using a tensile test machine. The thickness and width of each strip were measured from digital images. The strips data were compared with data obtained in the intact stomach in vitro. Most residual stresses and strains were bigger in the glandular part than in the forestomach, and in general the rat stomach had higher values than the rabbit stomach. The glandular strips were stiffer than the forestomach strips and the longitudinal glandular strips were stiffer than the circumferential glandular strips (P<0.05). The gastric strips were stiffer in rats than in rabbits (P<0.01). The data obtained in the intact rat stomach confirmed the strips data and indicated that those were obtained in the physiological range. In conclusion, the biomechanical properties of the gastric strips from the rat and rabbit are location-dependent, direction-dependent and species-dependent. The assumption in physiological pressure-volume studies that the stomach is a sphere with uniform tension is not valid. Three-dimensional geometric data obtained using imaging technology and mechanical data are needed for evaluation of the stomach function.

A two-layered mechanical model of the rat esophagus. Experiment and theory

BackgroundThe function of esophagus is to move food by peristaltic motion which is the result of the interaction of the tissue forces in the esophageal wall and the hydrodynamic forces in the food bolus. The structure of the esophagus is layered. In this paper, the esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We developed a model and experimental setup for determination of elastic moduli in the two layers in circumferential direction and related the measured elastic modulus of the intact esophagus to the elastic modulus computed from the elastic moduli of the two layers.MethodsInflation experiments were done at in vivo length and pressure-diameters relations were recorded for the rat esophagus. Furthermore, the zero-stress state was taken into consideration.ResultsThe radius and the strain increased as function of pressure in the intact as well as in the individual layers of the esophagus. At pressures higher than 1.5 cmH2O the muscle layer had a larger radius and strain than the mucosa-submucosa layer. The strain for the intact esophagus and for the muscle layer was negative at low pressures indicating the presence of residual strains in the tissue. The stress-strain curve for the submucosa-mucosa layer was shifted to the left of the curves for the muscle layer and for the intact esophagus at strains higher than 0.3. The tangent modulus was highest in the submucosa-mucosa layer, indicating that the submucosa-mucosa has the highest stiffness. A good agreement was found between the measured elastic modulus of the intact esophagus and the elastic modulus computed from the elastic moduli of the two separated layers.