Local Wall Stress Research Articles

Quantifying differences in local wall stress between carotid and femoral arteries

ObjectiveArterial remodeling after vascular procedures are mediated by pulsatile stress, but arterial wall biomechanics likely contribute; this study defines differences in arterial wall stress between healthy femoral and carotid arteries.MethodHealthy nonhuman primate arteries were tested on a custom‐made device to determine biaxial mechanical responses. A custom LABVIEW program was using for data acquisition and processing. Local wall stress was calculated based on a nonlinear, finite deformation framework utilizing an orthotropic material model. Residual stresses were considered in the analysis through quantifying circumferential and longitudinal opening angles. Heteroscedastic t‐tests were used to analyze the results.ResultsThe pressure‐diameter response of the arteries at the in vivo stretch demonstrate that femoral are stiffer than the carotid arteries (P=0.05); Fig. 1. Circumferential opening angle results (Fig. 2) also show a trend toward a greater opening angle in the femoral arteries (P=0.3).ConclusionsThese results support baseline biomechanical differences between femoral and carotid arteries in nonhuman primates. A better understanding of the matricellular differences between arteries may provide improved compatibility strategies for future therapies.(RLG:GTEC Foundation Endowment; NIH, NSF)

Shear stresses and mass transfer at the base of a stirred filtration cell and corresponding conditions in narrow channels with spacers

This study aims to adequately characterize shear stresses and mass transfer coefficients at the membrane surface of a high pressure stirred filtration cell, and to determine equivalent conditions for flow in narrow channels with spacers. Employing electro-chemical techniques, measurements were made of local wall stresses and transfer coefficients, and of space-average mass transfer rates, at various Schmidt numbers and Reynolds numbers 6500–39,000. The local measurements revealed salient features of momentum and mass transfer at the cell base, and the average quantities were successfully correlated with the respective Reynolds numbers. Furthermore, from detailed numerical and experimental studies of cross-flow in narrow spacer-filled channels (simulating conditions in spiral-wound membrane modules), relevant data on wall shear stress and mass transfer were selected for comparison with the new results from the stirred-cell. This comparative data analysis allows estimation of the stirrer rotational speed ω which corresponds to equal area-average shear stress (or mass transfer coefficient) at the membrane surface of stirred cell and of spacer-filled channel (for specific cross flow velocity U). The range of ω values, corresponding to a certain U range, is different for the cases of matching mean shear stress or mass transfer rates in the two flow systems.

Pathogenesis of Acute Aortic Dissections: A Finite Element Stress Analysis

Conclusion: Wall stress in the thoracic aorta peaks above the sinotubular junction and distal to the left subclavian artery origin. Wall stress may contribute to the pathophysiology of thoracic aortic dissection. Summary: In most cases, type A and type B thoracic aortic dissections originate with entry tears, respectively, above the sinotubular junction or distal to the left subclavian artery origin. Although thoracic dissection is influenced by many components, including aortic diameter, hypertension, and decreases in wall strength associated with Marfan syndrome or Ehlers-Danlos syndrome, the precise mechanistic rationale for origin of thoracic type A and type B dissections is not understood. The authors hypothesized that a biomechanical approach to predicting thoracic aortic walls stress may better define the risk of thoracic aortic dissection in individual patients. They mapped patterns of wall stress in the thoracic aorta in normal individuals, extrapolating wall stress patterns from normal individuals to those with potential dissection. They identified 47 patients whose thoracic aorta was normal by electrocardiogram-gated computed tomography angiography. The thoracic aorta was segmentally reconstructed and triangulated to create a geometric mesh with the ABAQUS/Explicit 6.3 program (HKS Inc, Pawtucket, RI). A systolic pressure load of 120 mm Hg was then used to construct a finite element analysis and to predict regional thoracic aortic wall stress. Local maximum wall stress was highest in the sinotubular junction in the ascending aorta and distal to the origins of the supra-aortic vessels, including the left subclavian artery, in the aortic arch. No errors of maximum wall stress were identified in the descending thoracic aorta. A comparison of areas of mean peak wall stress above the sinotubular junction (0.43 ± 0.77 MPa), distal to the left subclavian artery origin (0.021 ± 0.77 MPa), and in the descending thoracic aorta (0.06 ± 0.01 MPa) demonstrated significant levels of wall stress by aortic region (P < .001). Comment: The data indicate that there are peaks in wall stress in the normal thoracic aorta above the sinotubular junction and just distal to the origin of the left subclavian artery. The implication that peaks in wall stress may contribute to aortic dissection is a bit of “guilt by association.” Preventing thoracic aortic dissection is likely to be a multifaceted task. Diameter, according to Laplace's Law, is currently used as a noninvasive surrogate of aortic wall stress. Surgical intervention is timed to occur before wall stress exceeds the maximal tensile strength of the aorta, estimated at about 800 kPs. Although the risk of acute aortic events is currently correlated roughly with size, even small aortas can have fatal dissections and ruptures. Improving wall strength of the aorta, decreasing expansion rates, and calculations of wall sheer stress will all likely, in the future, be used in the management of patients with thoracic and abdominal aortic disease.

Drag reduction by microbubbles in a turbulent boundary layer

An experimental characterization of the turbulent boundary layer over a flat plate in the presence of small amounts of microbubbles is performed. The average diameter of the injected bubbles is comparable with the local Kolmogorov lengthscale, and the bulk void fraction C¯ is approximately 0.1%. The velocity field of the liquid phase, as well as the bubble characteristics, is acquired by optical techniques. Even at the small void fraction typical of this investigation, the interaction between microbubbles and turbulence leads to significant modifications of the underlying flow field. In accordance with previous investigations, the main global effect consists in a reduction of the magnitude of the viscous drag. This has been checked with preliminary tests conducted in a towing tank, as well as by inferring the wall stress from the boundary layer velocity profile measured in a laboratory facility at the same conditions. Here, the local wall stress is found to drop by approximately 25%. An analysis of the turbulent statistics shows that the reduction in drag is accompanied by a substantial reduction of the momentum flux throughout most of the inner region and by a decrease of the characteristic dimension of the turbulent scales involved in the production of kinetic energy. The distribution of turbulent kinetic energy among different scales is found to be substantially altered in the two flows. In particular, an enhancement of the energy content at smaller scales is observed in the bubbly case. These effects are discussed in relation with the decrease of the coherence of near-wall flow structures induced by the bubble forcing.

Comments regarding ‘The Influence of Wall Stress on AAA Growth and Biomarkers’

This is a complex study of 37 patients with abdominal aortic aneurysms that range from 40 to 55 mm in diameter, sizes that are normally followed closely and considered for intervention at the upper end of the diameter range. The authors examined the relationship between maximum aneurysm diameter (Dm), maximum aneurysm wall stress (Sm), aneurysm diameter growth rate and several circulating biomarkers of inflammation and/or degeneration. While Dm is the accepted AAA variable for size classification and management recommendations, the advent of computational methods for determining local wall stresses from CT scans has emerged in the past decade as a potentially powerful tool for predicting aneurysm rupture. However, Sm is only half of the AAA rupture equation. The other half is the degree of damage to the aneurysm wall due to several factors which lower wall rupture strength including atherosclerosis and deformation associated with growth. Mechanical failure or rupture occurs when arterial pressure induced wall stress exceeds the ability of the damaged wall to remain intact. While determination of aneurysm wall rupture strength in vivo is an elusive and complex problem, serum biomarker concentrations may indirectly provide an estimate of the degree of AAA wall damage. This study gives a glimpse of the relationships between these variables. The potential value of Sm over Dm in predicting aneurysm rupture is illustrated in Figure 2. While the positive correlation of maximum stress with maximum diameter is expected and not a new finding, Figure 2 illustrates both the wide variability of Sm in aneurysms of similar Dm and the potential value of maximum stress relative to maximum diameter, that is, the ratio of Sm to Dm, or Sm/Dm. AAAs develop from near cylindrical aortas with low and relatively similar Sm/Dm values. With growth aneurysm geometries vary considerably between patients and Sm is rarely located in the plane of Dm, resulting in the wide variability of Sm/Dm. Figure 3 shows that the diameter growth rates of the one third of aneurysms with the lowest Sm/Dm values have significantly lower growth rates than that of the two thirds with higher Sm/Dm values. This means that maximum stress relative to maximum diameter (Sm/Dm) may be a valuable index for predicting AAA growth. Unfortunately circulating biomarkers were measured in only 18 of the 37 patients. However, in this subset, aneurysm growth rates correlate significantly with levels of matrix metalloproteinase-9 and both MMP-9 and CPR tended to increase with increasing values of Sm/Dm. These findings support the author's hypothesis that AAAs in patients with high Sm/Dm values may undergo more rapid growth and wall damage than those with low Sm/Dm values. The shortcomings of this study are the small number of patients with serum biomarker analysis, the restriction of data to AAAs with diameters of 40 to 55 mm and the utilization of repeated measurement of aneurysm growth in a number of patients. Never the less, this study serves as a model for future investigations into the role of AAA wall stress, growth rate and serum biomarkers in estimating the probability of AAA rupture. The Influence of Wall Stress on AAA Growth and BiomarkersEuropean Journal of Vascular and Endovascular SurgeryVol. 39Issue 4PreviewThis study investigated the relation between abdominal aortic aneurysm (AAA) wall stress, AAA growth rate and biomarker concentrations. With increasing wall stress, more damage may be caused to the AAA wall, possibly leading to progression of the aneurysm and reflection in up- or downregulation of specific circulating biomarkers. Levels of matrix metalloproteinase-9, tissue inhibitor of matrix metalloproteinase-1, C-reactive protein and alpha 1-antitrypsin were therefore evaluated. Full-Text PDF Open Archive

Pulmonary artery calcification in racehorses may be related to transient and repeated increases in arterial pressure during exercise

Calcification of the pulmonary artery has been found in a large number of racing horses. The majority of calcified lesions are found immediately distal to the primary arterial bifurcation. Increased arterial wall stress levels have been previously demonstrated at these locations, with the wall stress levels increasing under intra-luminal pressures associated with exercise. We hypothesize therefore that the formation of calcified lesions is mediated by transient and repeated increases in pulmonary artery intra-luminal pressure. The presence of calcified lesions would likely further exacerbate the levels of wall stress, leading to growth of the lesions. A level of wall stress may exist above which calcified lesions form, and a second level may exist above which the calcified lesions grow at an increased rate. A computer model of pulmonary artery wall stress with calcified lesions was created, and wall stress levels were found to be greatest at the periphery of the calcified lesions. Osteo/chondrocyte-like cells have also been found at the periphery of the calcified lesions and could be responsible for collagen deposition and lesion growth, mediated by local wall stress levels. These increased levels of wall stress could place racehorses at a greater risk of acute pulmonary arterial rupture at the site of the calcified lesions, due to the high levels of intra-luminal pressure within the pulmonary artery during exercise. The hypothesis may also have implications in the etiology of human vascular diseases.

Stress analysis of carotid atheroma in a transient ischaemic attack patient using the MRI-based fluid–structure interaction method

Rupture of atherosclerotic plaque is a major cause of mortality. Plaque stress analysis, based on patient-specific multisequence in vivo MRI, can provide critical information for the understanding of plaque rupture and could eventually lead to plaque rupture prediction. However, the direct link between stress and plaque rupture is not fully understood. In the present study, the plaque from a patient who recently experienced a transient ischaemic attack (TIA) was studied using a fluid-structure interaction method to quantify stress distribution in the plaque region based on in vivo MR images. The results showed that wall shear stress is generally low in the artery with a slight increase at the plaque throat owing to minor luminal narrowing. The oscillatory shear index is much higher in the proximal part of the plaque. Both local wall stress concentrations and the relative stress variation distribution during a cardiac cycle indicate that the actual plaque rupture site is collocated with the highest rupture risk region in the studied patient.

Personalised imaging and biomechanical modelling of large vessels

The large blood vessels are crucial for blood flow distribution in the body but they may be subjected to disease processes like atherosclerosis, and consequences thereof like aneurysm formation, stroke, and myocardial infarction. These diseases are associated to a majority of the mortality of cardiovascular disease, which may be as high as 33% of overall disease related mortality. The function of these blood vessels has successfully been studied in the framework of biology, physics, and imaging. While a decade ago vessel function was merely described in terms of average blood flow, overall compliance and distensibility, the turbulent development of computational resources and numerical modelling has enabled calculations of local wall stress, local blood flow, and local wall deformation. Especially the methods to solve the non-linear Navier‐ Stokes equations and the equations that describe non-linear solid mechanics have evolved over the last decade and currently enable shear stress distributions in complex vessel geometries. Furthermore, the development of invasive and non-invasive imaging enables imaging the 3D geometry of blood vessels and thereby to develop personalised and segmental calculations of the wall stress and shear stress fields. This Special Issue is focussed upon the development and improvement of methods to obtain personalised information of the arterial tree in terms of vascular geometry, pressure distribution, shear stress distribution and wall stress distribution, in order to predict better interventions for individual patients. The first paper in this issue [9] gives an overview of developments in diagnostic tests for carotid and coronary disease, and aortic aneurysms and dissection. It is concluded that improved diagnostics by applying biophysics based mathematical model eventually will lead to improved patient management. In the second series of papers the technical description of automated methods for image reconstruction is presented. In the first of the series, Peiro [8] describe methods

A numerical model to predict abdominal aortic aneurysm expansion based on local wall stress and stiffness

Aneurysms of the abdominal aorta enlarge until rupture occurs. We assume that this is the result of remodelling to restore wall stress. We developed a numerical model to predict aneurysm expansion based on this assumption. In addition, we obtained aneurysm geometry of 11 patients from computed tomography angiographic images to obtain patient specific calculations. The assumption of a wall stress related expansion indeed resulted in a series of local expansions, adjusting global geometry in an exponential fashion similar as in patients. Furthermore, it revealed that location of peak wall stress changed over time. The assumptions of this model are discussed in detail in this manuscript, and the implications are related to literature findings.

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes. The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation. In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola–Kirchhoff active stress tensor. As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.

A volumetric model for growth of arterial walls with arbitrary geometry and loads

Stress and deformation in arterial wall tissue are factors which may influence significantly its response and evolution. In this work we develop models based on nonlinear elasticity and finite element numerical solutions for the mechanical behaviour and the remodelling of the soft tissue of arteries, including anisotropy induced by the presence of collagen fibres. Remodelling and growth in particular constitute important features in order to interpret stenosis and atherosclerosis. The main object of this work is to model accurately volumetric growth, induced by fluid shear stress in the intima and local wall stress in arteries with patient-specific geometry and loads. The model is implemented in a nonlinear finite element setting which may be applied to realistic 3D geometries obtained from in vivo measurements. The capabilities of this method are demonstrated in several examples. Firstly a stenotic process on an idealised geometry induced by a non-uniform shear stress distribution is considered. Following the growth of a right coronary artery from an in vivo reconstructed geometry is presented. Finally, experimental measurements for growth under hypertension for rat carotid arteries are modelled.

Fluid structure interaction of patient specific abdominal aortic aneurysms: a comparison with solid stress models

BackgroundAbdominal aortic aneurysm (AAA) is a dilatation of the aortic wall, which can rupture, if left untreated. Previous work has shown that, maximum diameter is not a reliable determinant of AAA rupture. However, it is currently the most widely accepted indicator. Wall stress may be a better indicator and promising patient specific results from structural models using static pressure, have been published. Since flow and pressure inside AAA are non-uniform, the dynamic interaction between the pulsatile flow and wall may influence the predicted wall stress. The purpose of the present study was to compare static and dynamic wall stress analysis of patient specific AAAs.MethodPatient-specific AAA models were created from CT scans of three patients. Two simulations were performed on each lumen model, fluid structure interaction (FSI) model and static structural (SS) model. The AAA wall was created by dilating the lumen with a uniform 1.5 mm thickness, and was modeled as a non-linear hyperelastic material. Commercial finite element code Adina 8.2 was used for all simulations. The results were compared between the FSI and SS simulations.ResultsResults are presented for the wall stress patterns, wall shear stress patterns, pressure, and velocity fields within the lumen. It is demonstrated that including fluid flow can change local wall stresses slightly. However, as far as the peak wall stress is concerned, this effect is negligible as the difference between SS and FSI models is less than 1%.ConclusionThe results suggest that fully coupled FSI simulation, which requires considerable computational power to run, adds little to rupture risk prediction. This justifies the use of SS models in previous studies.

Effects of Stenting on Blood Flow in a Coronary Artery Network Model

The effect of stenting on blood flow is investigated using a model of the coronary artery network. The parameters in a generic non-linear pressure–radius relationship are varied in the stented region to model the increase in stiffness of the vessel due to the presence of the stent. A computationally efficient form of the Navier–Stokes equation is solved using a Lax–Wendroff finite difference method. Pressure, vessel radius and flow velocity are computed along the vessel segments. Results show negative pressure gradients at the ends of the stent and increased velocity through the middle of the stented region. Changes in local flow patterns and vessel wall stresses due to the presence of the stent have been shown to be important in restenosis of vessels. Local and global pressure gradients affect local flow patterns and vessel wall stresses, and therefore may be an important factor associated with restenosis. The model presented in this study can be easily extended to solve flows for stented vessels in a full, anatomically realistic coronary network. The framework to allow for the effects of the deformation of the myocardium on the coronary network is also in place.

Effects of blood flow and vessel geometry on wall stress and rupture risk of abdominal aortic aneurysms

Sudden rupture of abdominal aortic aneurysm (AAA), often without prior medical warning, is the 13th leading cause of mortality in the US. The local rupture is triggered when the elusive maximum local wall stress exceeds the patient's yield stress. Employing a validated fluid – structure interaction code, the coupled blood flow and AAA wall dynamics were simulated and analysed for two representative asymmetric AAAs with different neck angles and iliac bifurcations. It turned out that the AAA morphology plays an important role in wall deformation and stress distribution, and hence possible rupture. The neck angle substantially impacts flow fields. A large neck angle may cause strong irregular vortices in the AAA cavity and may influence the wall stress distribution remarkably. The rupture risk of lateral asymmetric AAAs is higher than for the anterior – posterior asymmetric types. The most likely rupture site is located near the anterior distal side for the anterior – posterior asymmetric AAA and the left distal side in the lateral asymmetric AAA.

Nonuniformity of axial and circumferential remodeling of large coronary veins in response to ligation

The pressure-induced remodeling of coronary veins is important in coronary venous retroperfusion. Our hypothesis is that the response of the large coronary veins to pressure overload will depend on the degree of myocardial support. Eleven normal Yorkshire swine from either sex, weighing 31-39 kg, were studied. Five pigs underwent ligation of the left anterior descending (LAD) vein, and six served as sham-operated controls. The ligation of the coronary vein caused an increase in pressure intermediate to arterial and venous values. After 2 wk of ligation, the animals were euthanized and the coronary vessels were perfusion-fixed with glutaraldehyde. The LAD vein was sectioned, and detailed morphometric measurements were made along its length from the point of ligation near the base down to the apex of the heart. The structural remodeling of the vein was circumferentially nonuniform because the vein is partially embedded in the myocardium; it was also axially nonuniform because it is tethered to the myocardium to different degrees along its axial length. The wall area was significantly larger in the experimental group, whereas luminal area in the proximal LAD vein was significantly smaller in the same group compared with sham-operated controls. The wall thickness-to-radius ratio was also significantly larger in the experimental group in proportion to the increase in pressure. The major conclusion of this study is that the response of the vein depends on the local wall stress, which is, in part, determined by the surrounding tissue. Furthermore, the geometric remodeling of the coronary vein restores the circumferential stress to the homeostatic value.

Effect of endovascular stent strut geometry on vascular injury, myointimal hyperplasia, and restenosis

Purpose: Early restenosis and the development of myointimal hyperplasia in stented blood vessels have been attributed to deep vascular injury with fracture of the internal elastic lamina (IEL). The purpose of this study was the evaluation of the vascular wall response to superficial injury (without IEL rupture) after balloon angioplasty and intravascular stent placement in porcine arteries and the determination of the effect of stent strut geometry on the degree of vessel injury and early restenosis. Methods: Balloon-expandable stainless-steel stents were placed into the iliac arteries of 10 Sinclair miniature swine that had been fed an atherogenic diet. A Palmaz stent, with rectangular struts and smooth corners, was randomly assigned to one iliac artery (group 1), and a novel stent, which was designed and manufactured in the laboratory with thicker struts and sharper corners specifically to induce large wall stress concentrations, was placed in the contralateral iliac artery (group 2). Intravascular ultrasound scan was used in all deployments to ensure accurate balloon sizing and to avoid stent overexpansion and deep vascular injury. At 90 days after implantation, the animals were killed, the stented vessels harvested, and histomorphometric analysis performed. Results: Deployment of novel stents in group 2 resulted in a statistically higher incidence rate of deep vascular injury (fracture of the IEL) compared with group 1, despite identical balloon size used for deployment (with Student t test, P < .05). Vessels with deep injury showed a 10-fold increase in myointimal thickening compared with those vessels in which the IEL remained intact. A statistically higher restenosis rate was observed for group 2 (33.5% ± 19.90%) compared with group 1 (20.39% ± 14.70%). For both stent designs, there was a trend toward lower degrees of restenosis within the mid-portion of the stent. For superficially injured arteries in both groups, no correlation was observed between the amount of vessel wall/medial layer compression and the development of restenosis from myointimal hyperplasia. Conclusion: Maintenance of an intact IEL is an important factor in the prevention of myointimal hyperplasia and restenosis in stented porcine iliac arteries. The alteration of stent strut height and geometry does not significantly affect restenosis and the development of myointimal hyperplasia in vessels with superficial injury. Superficial injury elicits a response that is independent of stent strut geometry and vessel wall compression. Stent strut profile may, however, increase local vessel wall stress concentrations, leading to IEL rupture and an exaggerated response to injury. (J Vasc Surg 2002;36:143-9.)

Effects of Stenting on Blood Flow in a Coronary Artery Network Model

The effect of stenting on blood flow is investigated using a model of the coronary artery network. The parameters in a generic non‐linear pressure–radius relationship are varied in the stented region to model the increase in stiffness of the vessel due to the presence of the stent. A computationally efficient form of the Navier–Stokes equation is solved using a Lax–Wendroff finite difference method. Pressure, vessel radius and flow velocity are computed along the vessel segments. Results show negative pressure gradients at the ends of the stent and increased velocity through the middle of the stented region. Changes in local flow patterns and vessel wall stresses due to the presence of the stent have been shown to be important in restenosis of vessels. Local and global pressure gradients affect local flow patterns and vessel wall stresses, and therefore may be an important factor associated with restenosis. The model presented in this study can be easily extended to solve flows for stented vessels in a full, anatomically realistic coronary network. The framework to allow for the effects of the deformation of the myocardium on the coronary network is also in place.

Estimation of regional left ventricular wall stresses in intact canine hearts.

Left ventricular (LV) wall stress is an important element in the assessment of LV systolic function; however, a reproducible technique to determine instantaneous local or regional wall stress has not been developed. Fourteen dogs underwent placement of twenty-six myocardial markers into the ventricle and septum. One week later, marker images were obtained using high-speed biplane videofluoroscopy under awake, sedated, atrially paced baseline conditions and after inotropic stimulation (calcium). With a model taking into account LV pressure, regional wall thickness, and meridional and circumferential regional radii of curvature, we computed average midwall stress for each of nine LV sites. Regional end-systolic and maximal LV wall stress were heterogeneous and dependent on latitude (increasing from apex to base, P < 0.001) and specific wall (anterior > lateral and posterior wall stresses; P = 0. 002). Multivariate ANOVA demonstrated only a trend (P = 0.056) toward increased LV stress after calcium infusion; subsequent univariate analysis isolated significant increases in end-systolic LV wall stress with increased inotropic state at all sites except the equatorial regions. The model used in this analysis incorporates local geometric factors and provides a reasonable estimate of regional LV wall stress compared with previous studies. LV wall stress is heterogeneous and dependent on the particular LV site of interest. Variation in wall stress may be caused by anatomic differences and/or extrinsic interactions between LV sites, i.e., influences of the papillary muscles and the interventricular septum.

Stress Distributions in Vascular Aneurysms: Factors Affecting Risk of Aneurysm Rupture

Aneurysm rupture occurs when local wall stresses exceed the tensile strength of vascular tissues. Knowledge of vascular wall stresses, and insight into the factors that change wall stresses, will lead to a better understanding of how aneurysms grow and rupture. In this study, stress distributions in the walls of small aneurysms were calculated using finite element analysis (FEA), a numerical technique able to predict stress distributions with greater accuracy than the Law of Laplace. Stresses were calculated for an initial small aneurysm and compared to stresses produced by increasing the aneurysm diameter, decreasing the wall thickness, and changing the material properties of the aneurysm wall. FEA calculations indicate that wall stresses are generally greatest on the inner surface of an aneurysm, and decrease nonlinearly as the outer wall is approached. Maximum wall stresses occur along the region of greatest diameter, and circumferential stresses tend to be significantly greater than longitudinal stresses. Doubling the diameter of an aneurysm produced a twofold increase in the maximum wall stress. Decreasing the wall thickness by half also produced a doubling of the maximum wall stress. Changing material properties produced no appreciable change in wall stresses. However, weaker materials fail at lower stresses, thus halving material strength would be equivalent to doubling wall stresses. We conclude that the Law of Laplace is inaccurate in predicting the complicated stress distributions that exist in aneurysm walls, and that more sophisticated tools, such as FEA, will be needed to understand this complex phenomenon. We also conclude that proportional changes in the diameter, wall thickness, or aneurysm tissue strength have roughly equivalent effects on aneurysm growth and rupture.

Hypertrophy of surviving myocytes overlying the infarct in human old myocardial infarctions with abnormal Q waves

The time course of hypertrophy of surviving myocytes overlying the infarct after the onset was examined and the hypertrophy was analyzed in relation to the transmural extent of infarct in 34 autopsied hearts with Q wave infarction. The 34 hearts were divided into 4 groups according to the length of time between the onset of infarction and death. This was less than 5 days in group 1 ( n = 10), 20–30 days in group 2 ( n = 7), 40–60 days in group 3 ( n = 7), and 12–24 months in group 4 ( n = 10). To clarify the regional hypertrophy of myocytes overlying the infarct, the size of the surviving myocytes in the outer third of the left ventricular wall in the 1-cm wide central zone of the infarct was compared with that of the myocytes in the outer third of the left ventricular wall without infarction (control wall) in the same heart. To exclude factors which stimulate the hypertrophy of the whole left ventricle, the ratio of the myocyte diameter in the infarcted wall to that in the control wall was examined. It was 1.0 ± 0.0 (mean ± SD) in group 1, 1.0 ± 0.1 in group 2, 1.2 ± 0.1 in group 3, and 1.3 ± 0.1 in group 4. The ratio was significantly higher in group 3 than in groups 1 and 2, and was highest in group 4. In group 4, the corrected percentage transmural extent of infarct indicating the original transmural extent of infarct at the acute stage was 63 + 8%, and this transmural extent correlated positively with the ratio of myocyte diameter. It was concluded that the hypertrophy of surviving myocytes becomes detectable more than one month after the onset of infarction, probably due to compensation for increased local wall stress after the loss of myocytes.