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.     

Zero-stress state of intra- and extraparenchymal airways from human, pig, rabbit, and sheep lung.

Alterations in airway wall anatomic properties and the consequential effects on airway narrowing have been assessed by use of computational models. In these models, it is generally assumed that at zero transmural pressure the airway wall exists in a zero-stress state. Many studies have shown that this is often not the case, as evidenced by a nonzero opening angle. In this study, we measured the opening angle of airway rings at zero transmural pressure to test this assumption. The airway tree was dissected from human, pig, sheep, and rabbit lungs. Airways were excised from the tree, and the opening angle was measured. There were obvious species and regional differences in opening angle. Rabbit airways from both extraparenchymal and intraparenchymal sites exhibited marked opening angles (7-82 degrees). Extraparenchymal airways from sheep had large opening angles (up to 50 degrees), but ovine intraparenchymal airways had small opening angles. Measurable opening angles were rarely observed in human and porcine airways of any size. The assumption of a stable zero-stress state at zero transmural pressure is therefore valid for human and porcine, but not rabbit and sheep, airways.     

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.     

Changes of opening angle in hypertensive and hypotensive arteries in 3-day organ culture

To study the effect of pressure changes on the opening angle of arteries in organ culture, tubular segments of porcine common carotid arteries were cultured with pulsatile flow perfusion under hypertensive (150+/-20 mmHg), normotensive (100+/-20 mmHg), or hypotensive (30+/-10 mmHg) pressure while maintaining the arteris at a physiological wall shear stress of approximately 15 dyn/cm(2) for up to 3 days. Arteries were then cut into short ring segments by sections perpendicular to the axis and then cut open radially to observe the opening angle in aerated phosphate buffered saline solution (37 degrees C). Norepinephrine (NE, 10 microM), carbacol (CCh, 100 microM), and sodium nitroprusside (SNP, 10 microM) were added after the radial cut at 30, 20, and 30 min intervals, the opening angles were measured, respectively. Results show that hypertensive arteries developed a significantly larger opening angle than normotensive and hypotensive arteries, associated with a significant increase in cell proliferation. In addition, with smooth muscle contraction activated by NE, the opening angle decreases significantly in hypertensive arteries but has little change in hypotensive and normotensive arteries, indicating an enhancement of smooth muscle contraction on the lumen side of the hypertensive arterial wall. In comparison, hypotensive pressure has little effect on arterial opening angle and cell proliferation.     

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.     

Postsurgical changes of the opening angle of canine autogenous vein graft.

The opening angles of 30 canine autogenous vein grafts were measured to determine the postsurgical change of residual strain in the vein graft. Canine femoral veins were grafted to femoral arteries in the end-to-end anastomosis fashion. When harvested, the vein grafts were cut into short segments and the segments were cut open radially. The opened-up configurations were taken as the zero-stress states of the vessels. Opening angle, defined as the angle between the two lines from the middle point to the tips of the inner wall, was used to describe the zero-stress states. Results show that the opening angles (mean +/- SD) are 63.0 +/- 30.6 deg for normal femoral veins, and -0.4 +/- 4.6, 6.1 +/- 19.4, 25.4 +/- 20.1, and 47.8 +/- 11.4 deg for vein grafts at 1 day, 1 week, 4 and 12 weeks postsurgery, respectively. The postsurgical changes in opening angle reveal nonuniform transmural tissue remodeling in the vascular wall. The relations between the changes in opening angle and the changes in the morphology of the vein grafts are discussed. Intimal hyperplasia is correlated to the opening angle and is suggested to be the main factor for the postsurgical increase in opening angle. The longitudinal strain in the vein graft is found to decrease postsurgically.     

Changes of zero-stress state of rat pulmonary arteries in hypoxic hypertension

Zero-stress state of the main pulmonary arteries, from the main trunk to a vessel with a lumen diameter approximately 60 microns, was determined in 25 normal control and 38 hypoxic pulmonary hypertensive rats. Pulmonary hypertension was induced by placing the rats in a hypoxic chamber with 10% O2-90% N2 at atmospheric pressure. The zero-stress state of each vessel was obtained by first cutting the vessel transversely into a series of rings and then cutting each ring radially, whereupon the ring opened into a sector, which is characterized by an opening angle defined as the angle subtended between two lines originating from the midpoint of the inner wall (endothelium) to the tips of the inner wall. Whereas the pulmonary blood pressure increased monotonically during the development of pulmonary hypertension, the opening angle followed a different course; e.g., the values (means +/- SD) of the opening angle at the pulmonary trunk at times 0 (control) and 2, 12, 28, 96, 144, 240, 480, and 720 h after exposure to hypoxia are, respectively, 294 +/- 30 degrees, 378 +/- 24 degrees, 385 +/- 12 degrees, 374 +/- 11 degrees, 246 +/- 63 degrees, 267 +/- 49 degrees, 193 +/- 19 degrees, 195 +/- 83 degrees, and 239 +/- 38 degrees. Trends at other places on the artery are similar, but the magnitudes differ. In this period of time, intimal edema and thickening were found. The intima media thickened rapidly from 48 to 240 h and then more slowly from 240 to 720 h. Adventitia thickened later; its thickness exceeded that of the intima media at approximately 96 h. Thus the changes of zero-stress state of the pulmonary arteries are seen to be related to the nonuniform remodeling of the vessel wall as revealed by the edema, blebs, and thickening of different layers.     

Composition of proteoglycans in the aortas of copper-deficient rats

Copper deficiency adversely affects the extracellular matrix of the arterial wall, leading to cardiovascular lesions. To study the lesions resulting from copper deficiency, the composition of proteoglycans from aortas of copper-deficient rats was compared with proteoglycans of aortas from copper-supplemented rats. Copper deficiency in rats was verified by copper levels in adrenal glands (mean +/- SE, 0.37 +/- 0.07 vs 1.03 +/- 0.17 micrograms/g wet wt in supplemented rats). The proteoglycans were isolated from the aorta by extraction with 4 M guanidine-HCl and by digestion of the tissue with elastase. The proteoglycans were purified by CsCl isopycnic centrifugation and fractionated by gel filtration. The fractions were characterized for molecular size and glycosaminoglycan composition. Total uronate in the aortas from copper-deficient rats was 25% greater than in aortas from copper-supplemented rats, and the proteoglycans from copper-deficient rat aortas were of greater molecular size. Among the glycosaminoglycans the concentration (microgram/mg tissue) of isomeric chondroitin sulfates, particularly dermatan sulfate, was greater in copper-deficient animals than in copper-supplemented animals. These observations are similar to earlier findings in experimental atherosclerosis and to a response of cardiovascular connective tissue to injury.     

Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction

Examination of changes occurring in the zero-stress state of an organ provides a way to study cellular growth in the organ due to change of physical stresses. The zero-stress state of the aorta is not a tube. It is a sector with an opening angle that varies with the location on the aorta and changes with cellular remodeling. Blood vessel remodeling can be induced by imposing a constriction on the abdominal aorta by a metal clip (aortic banding), which causes an increase of blood pressure, hypertrophy of the aortic wall, and large change of opening angle. The correlation of the opening angle with the blood vessel wall thickness and blood pressure changes in rat's aorta due to aortic banding is presented in this report. The opening angle changes daily following the aortic banding. Blood pressure rises in vessels of the upper body, but that in the lower body decreases at first and then rises to an asymptotic value. Blood vessel wall thickness increases in rough proportion to blood pressure. Vessel diameter changes also. But the most dramatic is the course of change of the zero-stress state. Typically, the time to reach 50 percent of asymptotic hypertrophy of blood vessel wall thickness is about 3-5 days. The corresponding time for blood pressure is about 7 days. The opening angle of the zero-stress state, however, increases rapidly at first, reaches a peak in about 2 to 4 days, then decreases gradually to a reduced asymptote. The exact values of the time constants depend on the location along the aortic tree. In general, the course of change of residual strain is very different from those of the blood pressure and the blood vessel wall thickness.     

Evidence for an interaction of lipoprotein lipase with artery wall proteoglycans

1. Artery wall proteoglycans-lipoprotein lipase binding characteristics were studied using bovine milk 125I-labelled lipoprotein lipase (LPL) and chondroitin sulphate-dermatan sulphate proteoglycans (PGs) purified from pig aorta. 2. The binding process was studied either by a soluble assay (gel filtration) or by an immobilized proteoglycan assay (ELISA). 3. The binding process was reversible, saturable and occurred at a stoichiometry 1:1. 4. The binding process involved ionic interactions between the positively charged groups of LPL and the negatively charged groups of PG carbohydrate chains. 5. The complex PG-LPL may lead to the production of remnant lipoproteins and, thereby, contribute to cholesteryl ester accumulation in the arterial wall.     

Alternate method for the analysis of residual strain in the arterial wall

If an artery is cut transversely into rings, and the rings are then cut radially, they spring open into sectors. This phenomenon implies the existence of residual stresses and strains in the arterial wall in the non-loaded state. In the present paper, we propose a new method to calculate the residual strain from the measured wall dimensions and a polar angle of a specimen in the stress-free state, assuming that the wall is homogeneous and incompressible, and that a radially cut, stress-free specimen forms a circular sector. For this analysis, edge angles were measured at the edges of the opened-up specimen. Residual strains were obtained for the descending thoracic aorta, the common carotid artery, and the femoral artery in the rabbit. The results obtained indicated that the magnitude of residual strain was largest in the femoral artery and smallest in the aorta among the three arteries. The opening angle did not depend upon the length of a ring specimen if the ratio of the length to the diameter was ≤ 3.     

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

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

Catalase overexpression in aortic smooth muscle prevents pathological mechanical changes underlying abdominal aortic aneurysm formation

The causality of the associations between cellular and mechanical mechanisms of abdominal aortic aneurysm (AAA) formation has not been completely defined. Because reactive oxygen species are established mediators of AAA growth and remodeling, our objective was to investigate oxidative stress-induced alterations in aortic biomechanics and microstructure during subclinical AAA development. We investigated the mechanisms of AAA in an angiotensin II (ANG II) infusion model of AAA in apolipoprotein E-deficient (apoE(-/-)) mice that overexpress catalase in vascular smooth muscle cells (apoE(-/-)xTg(SMC-Cat)). At baseline, aortas from apoE(-/-)xTg(SMC-Cat) exhibited increased stiffness and the microstructure was characterized by 50% more collagen content and less elastin fragmentation. ANG II treatment for 7 days in apoE(-/-) mice altered the transmural distribution of suprarenal aortic circumferential strain (quantified by opening angle, which increased from 130 ± 1° at baseline to 198 ± 8° after 7 days of ANG II treatment) without obvious changes in the aortic microstructure. No differences in aortic mechanical behavior or suprarenal opening angle were observed in apoE(-/-)xTg(SMC-Cat) after 7 days of ANG II treatment. These data suggest that at the earliest stages of AAA development H(2)O(2) is functionally important and is involved in the control of local variations in remodeling across the vessel wall. They further suggest that reduced elastin integrity at baseline may predispose the abdominal aorta to aneurysmal mechanical remodeling.     

Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study.

The dependence of local left ventricular (LV) mechanics on myocardial muscle fiber orientation was investigated using a finite element model. In the model we have considered anisotropy of the active and passive components of myocardial tissue, dependence of active stress on time, strain and strain rate, activation sequence of the LV wall and aortic afterload. Muscle fiber orientation in the LV wall is quantified by the helix fiber angle, defined as the angle between the muscle fiber direction and the local circumferential direction. In a first simulation, a transmural variation of the helix fiber angle from +60 degrees at the endocardium through 0 degrees in the midwall layers to -60 degrees at the epicardium was assumed. In this simulation, at the equatorial level maximum active muscle fiber stress was found to vary from about 110 kPa in the subendocardial layers through about 30 kPa in the midwall layers to about 40 kPa in the subepicardial layers. Next, in a series of simulations, muscle fiber orientation was iteratively adapted until the spatial distribution of active muscle fiber stress was fairly homogeneous. Using a transmural course of the helix fiber angle of +60 degrees at the endocardium, +15 degrees in the midwall layers and -60 degrees at the epicardium, at the equatorial level maximum active muscle fiber stress varied from 52 kPa to 55 kPa, indicating a remarkable reduction of the stress range. Moreover, the change of muscle fiber strain with time was more similar in different parts of the LV wall than in the first simulation. It is concluded that (1) the distribution of active muscle fiber stress and muscle fiber strain across the LV wall is very sensitive to the transmural distribution of the helix fiber angle and (2) a physiological transmural distribution of the helix fiber angle can be found, at which active muscle fiber stress and muscle fiber strain are distributed approximately homogeneously across the LV wall.     

Origin of axial prestretch and residual stress in arteries

The structural protein elastin endows large arteries with unique biological functionality and mechanical integrity, hence its disorganization, fragmentation, or degradation can have important consequences on the progression and treatment of vascular diseases. There is, therefore, a need in arterial mechanics to move from materially uniform, phenomenological, constitutive relations for the wall to those that account for separate contributions of the primary structural constituents: elastin, fibrillar collagens, smooth muscle, and amorphous matrix. In this paper, we employ a recently proposed constrained mixture model of the arterial wall and show that prestretched elastin contributes significantly to both the retraction of arteries that is observed upon transection and the opening angle that follows the introduction of a radial cut in an unloaded segment. We also show that the transmural distributions of elastin and collagen, compressive stiffness of collagen, and smooth muscle tone play complementary roles. Axial prestresses and residual stresses in arteries contribute to the homeostatic state of stress in vivo as well as adaptations to perturbed loads, disease, or injury. Understanding better the development of and changes in wall stress due to individual extracellular matrix constituents thus promises to provide considerable clinically important insight into arterial health and disease.     

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.     

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).     

Two qualitatively different structuro-functional states of mitochondria

Low (120 mosM) tonicity of incubation media of mitochondria was found to be associated with anomalous phase transition at 19--26 degrees C. A rise in temperature caused a decrease in the pyrene excitation in border lipids of the mitochondrial membrane. Within this temperature range the quenching of intrinsic protein fluorescence by pyrene was sharply decreased. It may be inferred from these data that at 100mosM tonicity and temperatures below 19 degrees C, mitochondrial membrane proteins are in an aggregated state. At temperatures above phase transition protein deaggregation takes place. It was shown that a decrease in tonicity from 300 to 120 mosM at 15 degrees C or a rise in temperature from 15 degrees to 37 degrees C at 300 mosM tonicity increased the phosphorylation of the 52 kDa mitochondrial protein. It was assumed that swelling of mitochondria in hypotonic media simulates one of the steps of the hormone-induced signal transfer in mitochondria in vivo.     

Hemodynamics simulation and identification of susceptible sites of atherosclerotic lesion formation in a model abdominal aorta

Employing the rabbit's abdominal aorta as a suitable atherosclerotic model, transient three-dimensional blood flow simulations and monocyte deposition patterns were used to evaluate the following hypotheses: (i) simulation of monocyte transport through a model of the rabbit abdominal aorta yields cell deposition patterns similar to those seen in vivo, and (ii) those deposition patterns are correlated with hemodynamic wall parameters related to atherosclerosis. The deposition pattern traces a helical shape down the aorta with local elevation in monocyte adhesion around vessel branches. The cell deposition pattern was altered by an exercise waveform with fewer cells attaching in the upper abdominal aorta but more attaching around the renal orifices. Monocyte deposition was correlated with the wall shear stress gradient and the wall shear stress angle gradient. The wall stress gradient, the wall shear stress angle gradient and the normalized monocyte deposition fraction were correlated with the distribution of monocytes along the abdominal aorta and monocyte deposition is correlated with the measured distribution of monocytes around the major abdominal branches in the cholesterol-fed rabbit. These results suggest that the transport and deposition pattern of monocytes to arterial endothelium plays a significant role in the localization of lesions.     

Residual strain in ischemic ventricular myocardium.

Structural remodeling during acute myocardial infarction affects ventricular wall stress and strain. To see whether acute myocardial infarction alters residual stress and strain in the left ventricle (LV), we measured opening angles in rat hearts after 30 minutes of left coronary artery occlusion. The mean opening angle in 18 ischemic hearts (51 +/- 20 deg) was significantly greater than in five sham-operated controls (29 +/- 11 deg, P < 0.05). To determine whether these alterations in residual strain may be associated with strain softening caused by systolic overstretch of the noncontracting ischemic tissue, we also measured opening angles in isolated hearts that had been passively inflated to high LV pressures (120 mmHg). The mean opening angle of the strain-softened hearts was not significantly different from the sham-operated hearts (34 +/- 27 deg, P = 0.74). Mean collagen area fractions in the myocardium were not significantly different between ischemic hearts (0.027 +/- 0.014) and the nonischemic group (0.022 +/- 0.011). Although there were significant differences in opening angles measured with ischemia, they do not appear to be a result of altered extracellular collagen content or softening associated with overstretch. Thus, there is a significant change in residual strain associated with acute ischemia that may be related to changes in collagen fiber structure, myocyte structure, or metabolic state.