Carotid artery mechanical properties and stresses quantified using in vivo data from normotensive and hypertensive humans

The goal of this study was to model the in vivo non-linear mechanical behavior of human common carotid arteries (CCAs) and then to compare wall stresses and associated contributions of micro-constituents in normotensive (NT) and treated hypertensive (HT) subjects. We used an established theoretical model of 3D arterial mechanics that assumes a hyperelastic, anisotropic, active–passive, and residually stressed wall. In vivo data were obtained non-invasively from CCAs in 16 NT (21–64 years old) and 25 treated HT (44–69 years old) subjects. The associated quasi-static boundary value problem was solved semi-analytically over a cardiac cycle while accounting for surrounding perivascular tissue. Best-fit values of model parameters, including those describing contributions by intramural elastin, fibrillar collagen, and vascular smooth muscle, were estimated by a non-linear least-squares method. The model (1) captured temporal changes in intraluminal pressure, (2) estimated wall stress fields that appeared to reflect the presence or absence of age and disease, and (3) suggested changes in mechanical characteristics of wall micro-constituents despite medical treatment of hypertension. For example, age was positively correlated with residual stresses and altered fibrillar collagen in NT subjects, which indirectly validated the modeling, and HT subjects had higher levels of stresses, increased smooth muscle tone, and a stiffer elastin-dominated matrix despite treatment. These results are consistent with prior reports on effects of age and hypertension, but provide increased insight into evolving contributions of cell and matrix mechanics to arterial behavior in vivo.     

Initial stress and nonlinear material behavior in patient-specific AAA wall stress analysis

Rupture risk estimation of abdominal aortic aneurysms (AAA) is currently based on the maximum diameter of the AAA. A more critical approach is based on AAA wall stress analysis. For that, in most cases, the AAA geometry is obtained from CT-data and treated as a stress free geometry. However, during CT imaging, the AAA is subjected to a time-averaged blood pressure and is therefore not stress free. The aim of this study is to evaluate the effect of neglecting these initial stresses (IS) on the patient-specific AAA wall stress as computed by finite element analysis. Additionally, the contribution of the nonlinear material behavior of the AAA wall is evaluated.Thirty patients with maximum AAA diameters below the current surgery criterion were scanned with contrast-enhanced CT and the AAA's were segmented from the image data. The mean arterial blood pressure (MAP) was measured immediately after the CT-scan and used to compute the IS corresponding with the CT geometry and MAP. Comparisons were made between wall stress obtained with and without IS and with linear and nonlinear material properties.On average, AAA wall stresses as computed with IS were higher than without IS. This was also the case for the stresses computed with the nonlinear material model compared to the linear material model. However, omitting initial stress and material nonlinearity in AAA wall stress computations leads to different effects in the resulting wall stress for each AAA. Therefore, provided that other assumptions made are not predominant, IS cannot be discarded and a nonlinear material model should be used in future patient-specific AAA wall stress analyses.     

Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation

The pulsatile flow in an anatomically realistic compliant human carotid bifurcation was simulated numerically. Pressure and mass flow waveforms in the carotid arteries were obtained from an individual subject using non-invasive techniques. The geometry of the computational model was reconstructed from magnetic resonance angiograms. Maps of time-average wall shear stress, contours of velocity in the flow field as well as wall movement and tensile stress on the arterial wall are all presented. Inconsistent with previous findings from idealised geometry models, flow in the carotid sinus is dominated by a strong helical flow accompanied by a single secondary vortex motion. This type of flow is induced primarily by the asymmetry and curvature of the in vivo geometry. Flow simulations have been carried out under the rigid wall assumption and for the compliant wall, respectively. Comparison of the results demonstrates the quantitative influence of the vessel wall motion. Generally there is a reduction in the magnitude of wall shear stress, with its degree depending on location and phase of the cardiac cycle. The region of slow or reversed flow was greater, in both spatial and temporal terms in the compliant model, but the global characteristics of the flow and stress patterns remain unchanged. The analysis of mechanical stresses on the vessel surface shows a complicated stress field. Stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb. These are also regions of low wall shear stress. The comparison of computed and measured wall movement generally shows good agreement.     

Patient-specific initial wall stress in abdominal aortic aneurysms with a backward incremental method

Patient-specific wall stress simulations on abdominal aortic aneurysms may provide a better criterion for surgical intervention than the currently used maximum transverse diameter. In these simulations, it is common practice to compute the peak wall stress by applying the full systolic pressure directly on the aneurysm geometry as it appears in medical images. Since this approach does not account for the fact that the measured geometry is already experiencing a substantial load, it may lead to an incorrect systolic aneurysm shape. We have developed an approach to compute the wall stress on the true diastolic geometry at a given pressure with a backward incremental method. The method has been evaluated with a neo-Hookean material law for several simple test problems. The results show that the method can predict an unloaded configuration if the loaded geometry and the load applied are known. The effect of incorporating the initial diastolic stress has been assessed by using three patient-specific geometries acquired with cardiac triggered MR. The comparison shows that the commonly used approach leads to an unrealistically smooth systolic geometry and therefore provides an underestimation for the peak wall stress. Our backward incremental modelling approach overcomes these issues and provides a more plausible estimate for the systolic aneurysm volume and a significantly different estimate for the peak wall stress. When the approach is applied with a more complex material law which has been proposed specifically for abdominal aortic aneurysm similar effects are observed and the same conclusion can be drawn.     

Flow-pressure drop measurement and calculation in a tapered femoral artery of a dog

This study describes the in vivo measurement of pressure drop and flow during the cardiac cycle in the femoral artery of a dog, and the computer simulation of the experiment based on the use of the measured flow, vessel dimensions and blood viscosity. In view of the experimental uncertainty in obtaining the accurate velocity profile at the wall region, the velocity pulse at the center was measured and numerical calculations were performed for the center Une instantaneous velocity and within the two limits of spatial distribution of inlet flow conditions: uniform and parabolic. Temporal and spatial variations of flow parameters, i.e., velocity profile, shear rate, non-Newtonian viscosity, wall shear stress, and pressure drop were calculated. There existed both positive and negative shear rates during a pulse cycle, i.e., the arterial wall experiences zero shear three times during a cardiac cycle. For the parabolic inlet condition, the taper of the artery not only increased the magnitude of the positive and negative shear rates, but caused a steep gradient in shear rate, a phenomenon which in turn affects wall shear stress and pressure. In contrast, for the uniform inlet condition, the flow through the tapered artery was predominantly the developing type, which resulted in reduction in magnitude of wall shear rate along the axial direction.     

Candidate mechanical stimuli for hypertrophy during volume overload.

A myocyte system that senses and responds to mechanical inputs might be activated by any number of features of the time-varying length or force signals experienced by the myocytes. We therefore characterized left ventricular volume and wall stress signals during early volume overload with high spatial and temporal resolution. Left ventricular pressure and volume were measured in open-chest isoflurane-anesthetized male Sprague-Dawley rats 4 and 7 days after surgical creation of an infrarenal arteriovenous fistula or sham operation. Mean wall stresses were calculated by using a simple thick-walled ellipsoidal model. Consistent with previous reports, this surgical model produced a 66% increase in cardiac output and a 10% increase in left ventricular mass by day 7. A number of features of the time-varying volume signal (maximum, mean, amplitude, rates of rise and fall) were significantly altered during early volume overload, whereas many other proposed hypertrophic stimuli, including peak systolic wall stress and diastolic strain, were not. Treating hemodynamic variables more generally as time-varying signals allowed us to identify a wider range of candidate mechanical stimuli for hypertrophy (including some not previously proposed in the literature) than focusing on standard time points in the cardiac cycle. We conclude that features of the time-varying ventricular volume signal and related local deformations may drive hypertrophy during volume overload and propose that those features of the volume signal that also change during pressure overload might be the most interesting candidates for further exploration.     

Flow measurements in an atherosclerotic curved, tapered femoral artery model of man

Flow visualization and pressure measurements were made for physiological conditions in a model derived from a femoral angiogram of a patient with lesion localization on the inner curvature wall and with vessel taper. Effects of curvature and taper were evaluated separately in other curved, tapered, smooth and straight, tapered, smooth models. Double helical secondary flow patterns were modified by plaque on the inner wall, and flow separations were observed between plaques at higher flow rates and Reynolds numbers. Pressure drop data for the plaque simulation model were similar in trend with Reynolds number as for the smooth model, but flow resistances were 25 to 40 percent higher. Significant pressure drops were measured due to the mild taper which could be estimated from momentum considerations, and smaller increased pressure drops were found due to curvature effects at the higher Dean numbers. Flow resistances for in vivo pulsatile flow simulation were about 10 percent higher than for steady flow for the plaque model, whereas no differences were observed for the smooth model.     

Quantifying whole bladder biomechanics using the novel pentaplanar reflected image macroscopy system

Optimal bladder compliance is essential to urinary bladder storage and voiding functions. Calculated as the change in filling volume per change in pressure, bladder compliance is used clinically to characterize changes in bladder wall biomechanical properties that associate with lower urinary tract dysfunction. But because this method calculates compliance without regard to wall structure or wall volume, it gives little insight into the mechanical properties of the bladder wall during filling. Thus, we developed Pentaplanar Reflected Image Macroscopy (PRIM): a novel ex vivo imaging method to accurately calculate bladder wall stress and stretch in real time during bladder filling. The PRIM system simultaneously records intravesical pressure, infused volume, and an image of the bladder in five distinct visual planes. Wall thickness and volume were then measured and used to calculate stress and stretch during filling. As predicted, wall stress was nonlinear; only when intravesical pressure exceeded ~ 15 mmHg did bladder wall stress rapidly increase with respect to stretch. This method of calculating compliance as stress vs stretch also showed that the mechanical properties of the bladder wall remain similar in bladders of varying capacity. This study demonstrates how wall tension, stress and stretch can be measured, quantified, and used to accurately define bladder wall biomechanics in terms of actual material properties and not pressure/volume changes. This method is especially useful for determining how changes in bladder biomechanics are altered in pathologies where profound bladder wall remodeling occurs, such as diabetes and spinal cord injury.

     

Computation of hemodynamics in the left coronary artery with variable angulations

The purpose of this study was to investigate the hemodynamic effect of variations in the angulations of the left coronary artery, based on simulated and realistic coronary artery models. Twelve models consisting of four realistic and eight simulated coronary artery geometries were generated with the inclusion of left main stem, left anterior descending and left circumflex branches. The simulated models included various coronary artery angulations, namely, 15°, 30°, 45°, 60°, 75°, 90°, 105° and 120°. The realistic coronary angulations were based on selected patient's data with angles ranging from narrow angles of 58° and 73° to wide angles of 110° and 120°. Computational fluid dynamics analysis was performed to simulate realistic physiological conditions that reflect the in vivo cardiac hemodynamics. The wall shear stress, wall shear stress gradient, velocity flow patterns and wall pressure were measured in simulated and realistic models during the cardiac cycle. Our results showed that a disturbed flow pattern was observed in models with wider angulations, and wall pressure was found to reduce when the flow changed from the left main stem to the bifurcated regions, based on simulated and realistic models. A low wall shear stress gradient was demonstrated at left bifurcations with wide angles. There is a direct correlation between coronary angulations and subsequent hemodynamic changes, based on realistic and simulated models. Further studies based on patients with different severities of coronary artery disease are required to verify our results.     

Inter-individual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans

Fluid shear stress and mechanical wall stress may play a role in the formation of early atherosclerotic lesions, but these quantities are difficult to measure in vivo. Our objective was to quantify these parameters in normal subjects in a clinical setting, and to define regions of low wall shear stress and high mechanical stress. The right carotid bifurcations of five healthy male volunteers were investigated using a novel non-invasive technique which integrates magnetic resonance angiography, ultrasonography, tonometry and state-of-the-art computational fluid dynamics and solid mechanics models. Significant inter-subject variations in patterns as well as magnitude of wall shear stress and mechanical stress were found. In spite of individual variabilities, this study revealed that some regions of the artery wall are exposed simultaneously to low wall shear stress and high mechanical stress and that these regions correspond to areas where atherosclerotic plaque develops. The coexistence of regions of low wall shear stress and high tensile stress may be an important determinant of the formation of atheroma in human arteries.     

Evaluating patient-specific abdominal aortic aneurysm wall stress based on flow-induced loading

In this paper, we develop a physiologic wall stress analysis procedure by incorporating experimentally measured, non-uniform pressure loading in a patient-based finite element simulation. First, the distribution of wall pressure is measured in a patient-based lumen cast at a series of physiologically relevant steady flow rates. Then, using published equi-biaxial stress-deformation data from aneurysmal tissue samples, a nonlinear hyperelastic constitutive equation is used to describe the mechanical behavior of the aneurysm wall. The model accounts of the characteristic exponential stiffening due to the rapid engagement of nearly inextensible collagen fibers and assumes, as a first approximation, an isotropic behavior of the arterial wall. The results show a complex wall stress distribution with a localized maximum principal stress value of 660 kPa on the inner surface of the posterior surface of the aneurysm bulge, a considerably larger value than has generally been reported in calculations of wall stress under the assumption of uniform loading. This is potentially significant since the posterior wall has been suggested as a common site of rupture, and the aneurysmal tensile strength reported by other authors is of the same order of magnitude as the maximum stress value found here.     

Nonlinear ultrasound can detect accumulated damage in human bone

Bone micro-damage is commonly accepted as a relevant parameter for fracture risk assessment, but there is no available technique for its non-invasive characterization. The objective of this work is to study the potential of nonlinear ultrasound for damage detection in human bone. Ultrasound is particularly desirable due to its non-invasive and non-ionizing characteristics. We show results illustrating the correlation of progressive fatigue of human bone samples to their nonlinear dynamical response. In our experiments, damage was induced in 30 samples of diaphyseal human femur using fatigue cycling. At intervals in the cycling, the nonlinear response of the samples was assessed applying Nonlinear Resonant Ultrasound Spectroscopy (NRUS). The nonlinear parameter alpha, which in other materials correlates with the quantity of damage, dramatically increased with the number of mechanical testing cycles. We find a large spread in alpha in the pristine samples and infer that the spread is due to damage differences in the sample population. As damage accumulates during cycling, we find that alpha is much more sensitive to damage than other quantities measured, including the slope and hysteresis of the load/displacement curve, and the dynamic wavespeed. To our knowledge, this study represents the first application of the concept of nonlinear dynamic elasticity to human bone. The results are promising, suggesting the value of further work on this topic. Ultimately, the approach may have merit for in vivo bone damage characterization.     

Measurement of oscillatory flow pressure gradient in an elastic artery model

In vitro experiments were conducted to measure the oscillatory flow pressure gradient along an elastic tube in order to assess the recent nonlinear theory of Wang and Tarbell. According to this theory, in an elastic tube with oscillatory flow, the mean (time-averaged) pressure gradient cannot be calculated using Poiseuille's law. The effect of wall motion creates a nonlinear convective acceleration, and an induced mean pressure gradient is required to balance the convective acceleration. The induced mean pressure gradient depends on the diameter variation over a cycle, the pulsatility and unsteadiness of the flow, and the phase difference between the pressure wave form and the flow wave form. The amplitude of the pressure gradient also depends on these parameters and may deviate significantly from Womersley's rigid tube theory. A flow loop was constructed to produce oscillatory flow in an elastic tube. Flow wave forms were measured with an ultrasonic flow probe, and ultrasonic diameter crystals were used to measure wall movement. A special device for pressure drop measurement was constructed using Millar catheter tip transducers to obtain both forward and backward pressure drops that were then averaged. This averaging method eliminated the static error of the pressure transducers. The pressure-flow phase angle was varied by clamping a distal elastic section at various locations. Pressure gradients were obtained for a range of phase angles between −55 ° and +49 °. The mean and amplitude of the measured pressure gradient were compared to theoretical values. Both positive and negative induced mean pressure gradients were measured over the range of phase angles. The measured pressure gradient amplitudes were always lower than predicted by Womersley's rigid tube theory. The experimental means and amplitudes are in good agreement with the elastic tube theoretical values. Thus, the experiments verify the theory of Wang and Tarbell.     

A viscoelastic model for use in predicting arterial pulse waves

In nonlinear mathematical models of the arterial circulation, the viscoelasticity of the vessel walls has generally been neglected or only taken into account in a highly approximate manner. A new method is proposed to simulate the nonlinear viscoelastic properties of the wall material with the aid of a convolution integral of the creep function and the pressure history. With this simulation it is possible to properly describe the measured characteristics of arterial viscoelasticity. Moreover, it is utilized in a mathematical model of arterial pulse propagation to study the influence of the internal wall friction on the shape, amplitude and mean value of pressure and flow pulses. The corresponding predictions are in much better agreement with in-vivo measurements, especially for the distal part of the circulation, than those obtained without viscoelasticity.     

Biomechanical response of arterial wall to DOCA-salt hypertension in growing and middle-aged rats

To study arterial remodeling in response to hypertension, Deoxycortico-sterone acetate (DOCA)-salt hypertension was induced in immature (aged 16 weeks) and middle-aged (48 weeks) rats, and biomechanical properties and wall dimensions of common carotid arteries were determined. Arterial segments were excised at 10 or 16 weeks postoperatively from the immature rats and at 16 weeks from the middle-aged ones. In vitro pressure-diameter tests were performed under normal (in Krebs-Ringer solution), active (norepinephrine), and passive (papaverine) conditions. Non-treated, age-matched rats (26, 32, and 64 weeks) were used to obtain control data. Wall thickness at in vivo blood pressure level was increased by hypertension at all ages; however, there were no significant changes in inner diameter. In hypertensive rats, arterial outer diameter was smaller under normal condition than under passive condition, indicating the increase of smooth muscle tone by hypertension. Diameter reduction developed by norepinephrine was increased by hypertension, which was significant above 100 mmHg; however, there were no significant differences between hypertensive and normotensive arteries, if compared at respective in vivo blood pressures. No significant differences were observed in wall stiffness at in vivo pressure. Wall hoop stress at in vivo blood pressure had a significant positive correlation with the pressure in 26-week old arteries. However, there were no differences in the stress between hypertension and normotension in 32- and 64-week old arteries. These results were essentially similar to previous ones observed in Goldblatt hypertension and in younger animals. Age-related differences in arterial wall remodeling were not clearly observed.     

A model of the structural and functional development of the normal human fetal left ventricle based on a global growth law

The purpose of this research is to study the growth of the normal human left ventricle (LV) during the fetal period from 14 to 40 weeks of gestation. A new constitutive law for the active myocardium describing the mechanical properties of the active muscle during the whole cardiac cycle has been proposed. The LV model is a thick-walled, incompressible, hyperelastic cylinder, with families of helicoidal fibers running on cylindrical surfaces [1]. Based on the works of Lin and Taber [2] done on the embryonic chick heart, we use for the human fetal heart a growth law in which the growth rate depends on the wall stresses. The parameters of the growth law are adapted to agree with sizes and volumes inferred from two dimensional ultrasound measurements performed on 18 human fetuses.Then calculations are performed to extrapolate the cardiac performance during normal growth of the fetal LV. The results presented support the idea that a growth law in which the growth rate depends linearly on the mean wall stresses averaged through the space and during whole cardiac cycle, is adapted to the normal human fetal LV development.     

Relation of B-type natriuretic peptide to left ventricular wall stress as assessed by cardiac magnetic resonance imaging in patients with dilated cardiomyopathy

Ventricular loading conditions are crucial determinants of cardiac function and prognosis in heart failure. B-type natriuretic peptide (BNP) is mainly stored in the ventricular myocardium and is released in response to an increased ventricular filling pressure. We examined, therefore, the hypothesis that BNP serum concentrations are related to ventricular wall stress. Cardiac magnetic resonance imaging (MRI) was used to assess left ventricular (LV) mass and cardiac function of 29 patients with dilated cardiomyopathy and 5 controls. Left ventricular wall stress was calculated by using a thick-walled sphere model, and BNP was assessed by immunoassay. LV mass (r = 0.73, p < 0.001) and both LV end-diastolic (r = 0.54, p = 0.001) and end-systolic wall stress (r = 0.66, p < 0.001) were positively correlated with end-diastolic volume. LV end-systolic wall stress was negatively related to LV ejection fraction (EF), whereas end-diastolic wall stress was not related to LVEF. BNP concentration correlated positively with LV end-diastolic wall stress (r = 0.50, p = 0.002). Analysis of variance revealed LV end-diastolic wall stress as the only independent hemodynamic parameter influencing BNP (p < 0.001). The present approach using a thick-walled sphere model permits determination of mechanical wall stress in a clinical routine setting using standard cardiac MRI protocols. A correlation of BNP concentration with calculated LV stress was observed in vivo. Measurement of BNP seems to be sufficient to assess cardiac loading conditions. Other relations of BNP with various hemodynamic parameters (e.g., EF) appear to be secondary. Since an increased wall stress is associated with cardiac dilatation, early diagnosis and treatment could potentially prevent worsening of the outcome.     

MECHANICAL BEHAVIOR OF PLANT TISSUES AS INFERRED FROM THE THEORY OF PRESSURIZED CELLULAR SOLIDS

The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete “cell” walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive (“cell wall”) material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of “cell walls” and the magnitude of internal “cell” pressure. Analyses indicate that two “stiffening” agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or “densifying” material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material.     

Determination of human arterial wall parameters from clinical data

This study suggests a method to compute the material parameters for arteries in vivo from clinically registered pressure-radius signals. The artery is modelled as a hyperelastic, incompressible, thin-walled cylinder and the membrane stresses are computed using a strain energy. The material parameters are determined in a minimisation process by tuning the membrane stress to the stress obtained by enforcing global equilibrium. In addition to the mechanical model, the study also suggests a preconditioning of the pressure-radius signal. The preconditioning computes an average pressure-radius cycle from all consecutive cycles in the registration and removes, or reduces, undesirable disturbances. The effect is a robust parameter identification that gives a unique solution. The proposed method is tested on clinical data from three human abdominal aortas and the results show that the material parameters from the proposed method do not differ significantly (p < 0.01) from the corresponding parameters obtained by averaging the result from consecutive cycles.     

Non-invasive Evaluation of Aortic Stiffness Dependence with Aortic Blood Pressure and Internal Radius by Shear Wave Elastography and Ultrafast Imaging

Background

Elastic properties of arteries have long been recognized as playing a major role in the cardiovascular system. However, non-invasive in vivo assessment of local arterial stiffness remains challenging and imprecise as current techniques rely on indirect estimates such as wall deformation or pulse wave velocity. Recently, Shear Wave Elastography (SWE) has been proposed to non-invasively assess the intrinsic arterial stiffness.