The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

Comparative analysis of endothelial cell and sub-endothelial cell elastic moduli in young and aged mice: Role of CD36

ObjectiveTo perform comparative analysis of the role of scavenger receptor CD36 on endothelial vs. sub-endothelial elastic modulus (stiffness) in the aortas of young and aged mice.Approaches and ResultsElastic moduli of endothelial and sub-endothelial layers of freshly isolated mouse aortas were quantified using atomic force microscopy. In young mice (4–6 months old), we found that while endothelial stiffness is markedly reduced in aortas of CD36^−/−mice, as compared to WT controls, no difference between CD36^−/− and WT aortas is observed in the stiffness of the sub-endothelial layer in denuded arteries. Additionally, inhibition of myosin phosphorylation also decreases the elastic modulus in the EC, but not the sub-EC layer in WT mice. Moreover, inhibiting CD36 mediated uptake of oxLDL in intact WT aortas abrogated oxLDL-induced endothelial stiffening. Further analysis of aged mice (22–25 months) revealed that aging resulted not only in significant stiffening of the denuded arteries, as was previously known, but also a comparable increase in the elastic modulus of the endothelial layer. Most significantly, this stiffening in the EC layer is dependent on CD36, whereas the denuded layer is not affected.ConclusionsOur results show that the role CD36 in stiffening of cellular components of intact aortas is endothelial-specific and that genetic deficiency of CD36 protects against endothelial stiffening in aged mice. Moreover, these data suggest that endothelial stiffness in intact mouse aortas depends more on the expression of CD36 than on the stiffness of the sub-endothelial layer.     

Forces and deformations of the abdominal wall--a mechanical and geometrical approach to the linea alba

Force-elongation responses of the human abdominal wall in the linea alba region were determined by tensile tests in which the linea alba was seen to exhibit a nonlinear elastic, anisotropic behavior as is frequently observed in soft biological tissues. In addition, the geometry of the abdominal wall was determined, based on MRI data. The geometry can be specified by principal radii of curvature in longitudinal of approximately 470 mm and in the transverse direction of about 200 mm. The determined radii agree with values found in other studies. Mechanical stresses, deformations and abdominal pressures for load cases above 6% elongation can be related using Laplace's formula and our constitutive and geometrical findings. Results from uni- and biaxial tensile tests can thus be compared using this model. Calculations confirm that abdominal pressures of approximately 20 kPa correspond to related biaxial forces of about 3.4N/mm in the transverse and 1.5 N/mm in the longitudinal direction. Young's moduli can be calculated with respect to the uniaxial as well as the biaxial loading. At these physiological loadings, a compliance ratio of about 2:1 between the longitudinal and transversal directions is found. Young's moduli of about 50 kPa occur in transversal direction and of about 20 kPa in longitudinal direction at transverse and longitudinal strains both in the order of 6%. These findings coincide with results from other investigations in which the properties of the abdominal wall have been examined.     

Rheological properties of the thoracic aorta in normal and WHHL rabbits

The tension-strain, stress-strain and stress relaxation curves of longitudinal and circumferential strips of proximal thoracic aortas in normal and WHHL rabbits of different ages were determined using a tensile testing instrument. Wall distensibility of longitudinal and circumferential strips was the greatest in the normal aorta and decreased with advancing age in the atherosclerotic aorta. The wall thickness of the atherosclerotic aorta was positively related to age with a correlation coefficient of 0.66(p less than 0.01). The incremental elastic moduli calculated from the stress-strain curves increased with advancing age in the atherosclerotic aorta. Accordingly, the decreased distensibility of the atherosclerotic wall may be due to the increased wall thickness caused by the intimal thickening as well as to the increase in wall stiffness caused by the increased elastic modulus. The viscoelasticity of the atherosclerotic aorta was larger than that of the normal aorta. This reflects the mechanical effect of atherosclerotic changes that occurred in the thickened intima.     

Shear modulus of porcine coronary artery: contributions of media and adventitia

The epicardial coronary arteries experience significant torsion in the axial direction due to changes in the shape of the heart during the cardiac cycle. The objective of this study was to determine the torsional mechanical properties of the coronary arteries under various circumferential and longitudinal loadings. The coronary artery was treated as a two-layer composite vessel consisting of intima-medial and adventitial layers, and the shear modulus of each layer was determined. Eight porcine hearts were obtained at a local abattoir, and their right coronary and left anterior descending arteries were isolated and tested in vitro with a triaxial torsion machine (inflation, longitudinal stretch, and circumferential twist). After the intact vessel was tested, the adventitia was dissected away, leaving an intact media that was then tested under identical triaxial loading conditions. We proposed a biomechanical analysis to compute the shear modulus of the adventitia from the measured shear moduli of the intact vessel and the media. To validate our predictions, we used four additional hearts in which the shear modulus of the adventitia was measured after dissection of media. Our results show that the shear modulus does not depend on the shear stress or strain but varies linearly with circumferential and longitudinal stresses and in a nonlinear way with the corresponding strains. Furthermore, we found that the shear modulus of the adventitia is larger than that of the intact vessel, which is larger than the vessel media. These results may have important implications for baroreceptor sensitivity, circulation of the vasa vasorum, and coronary dissection.     

A comparison of the size of fenestrations in the internal elastic lamina of young and old porcine aortas as seen with the scanning electron microscope.

The size of the fenestrations (windows) in the internal elastic lamina (IEL) of arteries may be important in the functioning of the blood vessel wall. The fenestrations are filled with collagen, muscle, and (or) ground substance, which must be removed to make the fenestration visible with the scanning electron microscope. All of the nonelastic components are removed with a hot alkali solution. Our experiments were designed to compare the fenestration size in the IEL of the thoracic aorta of young (6-8 weeks) and old (6-9 months) pigs. A protocol for digestion of young pig tissue was developed and showed that fresh young aortas should be digested in 0.1 M NaOH at 75 degrees C for 2 h and fixed tissue should be digested for 5 h. The average area of the fenestrations for young pig thoracic aortas digested for 2 h was 1.8 +/- 0.29 (SE) microns 2 and for the old pig aortas digested for 2 h was 1.7 +/- 0.11 (SE) microns 2. These values were not significantly different (p greater than 0.05), but the IEL from young pigs appeared rougher than the previously reported smooth IEL of the adult pigs.     

Analysis of the passive mechanical properties of rat carotid arteries

The passive mechanical properties of rat carotid arteries were studied in vitro. Using a tensile testing machine and a piston pump, intact segments of carotid arteries were subjected to large deformations both in the longitudinal and circumferential directions. Internal pressure, external diameter, length and longitudinal force were measured during the experiment and compared with the in vivo dimensions of the segments prior to excision. The anisotropic mechanical properties of the vessel wall material were analyzed using incremental elastic moduli and incremental Poisson's ratios. The results suggest that there is a characteristic deformation pattern common to all vessels investigated which is highly correlated with the conditions of loading that occur in vivo. That is, under average physiological deformation of the vessel, the longitudinal force is nearly independent of internal pressure. In this range of loading the circumferential incremental elastic modulus is nearly independent of longitudinal strain. However, the longitudinal and radial incremental elastic moduli vary significantly with deformation in this direction. The values of the moduli in all three directions increase with raising internal pressure. The weak coupling between circumferential and longitudinal direction in the wall material of carotid arteries is shown by the small value of the corresponding incremental Poisson's ratios.     

Age-related changes of elements in thoracic and abdominal aortas and coronary, common carotid, pulmonary, splenic, common iliac, and uterine arteries and relationships in elements among their arteries

To elucidate whether the accumulation of elements occurred simultaneously in the various arteries with aging, the authors investigated age-related changes of elements in the eight arteries, such as the thoracic and abdominal aortas and the coronary, common carotid, pulmonary, splenic, common iliac, and uterine arteries, and the relationships in the element contents among their arteries. After ordinary dissection by medical students was finished, the thoracic and abdominal aortas and the coronary, common carotid, pulmonary, splenic, common iliac, and uterine arteries were resected from the subjects, who ranged in age from 58 to 94 yr. The element contents were analyzed by inductively coupled plasma-atomic emission spectrometry. It was found that the accumulation of Ca was the highest in the common iliac artery and decreased in the order of the uterine artery, abdominal aorta, coronary artery, thoracic aorta, splenic artery, common carotid artery, and pulmonary artery. Regarding the relationships in the element contents among the eight arteries, it was found that there were significant direct correlations in the contents of Ca, P, Mg, Zn, Fe, and Na between the coronary and splenic arteries, and there were significant correlations in the contents of Ca, P, and Mg between the abdominal aorta and pulmonary artery.     

Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

We developed an extension-inflation experimental apparatus with a stereo vision system and a stress-strain analysis method to determine the regional mechanical properties of a blood vessel. Seven proximal descending thoracic aortas were investigated during the inflation test at a fixed longitudinal stretch ratio of 1.35 over a transmural pressure range from 1.33 to 21.33 kPa. Four circumferential regions of each aorta were designated as the anterior (A), left lateral (L), posterior (P), and right lateral (R) regions, and the inflation test was repeated for each region of the aortas. We used continuous functions to approximate the surfaces of the regional aortic wall in the reference configuration and the deformed configuration. Circumferential stretch and stress at the four circumferential regions of the aorta were computed. Circumferential stiffness, defined as the tangent of the stress-stretch curve, and physiological aortic stiffness, named pressure-strain elastic modulus, were also computed for each region. In the low pressure range, the stress increased linearly with increased stretch, but the mechanical response became progressively stiffer in the high-pressure range above a transition point. At a transmural pressure of 12.00 kPa, mean values of stiffness were 416±104 kPa (A), 523±99 kPa (L), 634±91 kPa (P), and 489±82 kPa (R). The stiffness of the posterior region was significantly higher than that of the anterior region, but no significant difference was found in pressure-strain elastic modulus.     

Is location a significant parameter in the layer dependent dissection properties of the aorta?

Proper characterisation of biological tissue is key to understanding the effect of the biomechanical environment in the physiology and pathology of the cardiovascular system. Aortic dissection in particular is a prevalent and sometimes fatal disease that still lacks a complete comprehension of its progression. Its development and outcome, however, depend on the location in the vessel. Dissection properties of arteries are frequently studied via delamination tests, such as the T-peel test and the mixed-mode peel test. So far, a study that performs both tests throughout different locations of the aorta, as well as dissecting several interfaces, is missing. This makes it difficult to extract conclusions in terms of vessel heterogeneity, as a standardised experimental procedure cannot be assured for different studies in literature. Therefore, both dissection tests have been here performed on healthy porcine aortas, dissecting three interfaces of the vessels, i.e., the intima-media, the media-adventitia and the media within itself, considering different locations of the aorta, the ascending thoracic aorta (ATA), the descending thoracic aorta and the infrarenal abdominal aorta (IAA). Significant differences were found for both, layers and location. In particular, dissection forces in the ATA were the highest and the separation of the intima-media interface required significantly the lowest force. Moreover, dissection in the longitudinal direction of the vessel generally required more force than in the circumferential one. These results emphasise the need to characterise aortic tissue considering the specific location and dissected layer of the vessel.

     

Bi-directional mechanical properties of the posterior region of the glenohumeral capsule

The objective of this study was to determine the mechanical properties of the posterior region of the glenohumeral capsule in the directions perpendicular (transverse) and parallel (longitudinal) to the longitudinal axis of the posterior band of the inferior glenohumeral ligament. A punch was used to excise one transverse and one longitudinal tissue sample from the posterior capsule of 11 cadaveric shoulders. All tissue samples exhibited the typical nonlinear behavior reported for ligaments and tendons. Significant differences (p < 0.05) were detected between the transverse and longitudinal tissue samples for ultimate stress (1.5+/-1.4 and 4.9+/-2.9 MPa, respectively) and tangent modulus (10.3+/-6.6 and 31.5+/-12.7 MPa, respectively). No significant differences (p > 0.05) were observed between the ultimate strain (transverse: 22.3+/-12.5%, longitudinal: 22.8+/-11.1%) and strain energy density (transverse: 27.2+/-52.8 MPa, longitudinal: 67.5+/-88.2 MPa) of the transverse and longitudinal tissue samples. The ratio of the longitudinal to transverse moduli (4.8+/-4.2) was similar to that found for the axillary pouch (3.3+/-2.8) in a previous study. Thus, both the axillary pouch and the posterior capsule function to stabilize the joint multi-axially. Future analytical models of the glenohumeral joint should consider the properties of the posterior capsule in its transverse and longitudinal directions to fully describe the behavior of the glenohumeral capsule. These models will be clinically important by providing a more accurate representation of the intact capsule as well as simulated capsular injuries and surgical repair procedures.     

Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation

High-resolution architecture-based finite element models are commonly used for characterizing the mechanical behavior of cancellous bone. The vast majority of studies use homogeneous material properties to model trabecular tissue. The objectives of this study were to demonstrate that inhomogeneous finite element models that account for microcomputed tomography-measured tissue modulus variability more accurately predict the apparent stiffness of cancellous bone than homogeneous models, and to examine the sensitivity of an inhomogeneous model to the degree of tissue property variability. We tested five different material cases in finite element models of ten cancellous cubes in simulated uniaxial compression. Three of these cases were inhomogeneous and two were homogeneous. Four of these cases were unique to each specimen, and the remaining case had the same tissue modulus for all specimens. Results from all simulations were compared with measured elastic moduli from previous experiments. Tissue modulus variability for the most accurate of the three inhomogeneous models was then artificially increased to simulate the effects of non-linear CT-attenuation-modulus relationships. Uniqueness of individual models was more critical for model accuracy than level of inhomogeneity. Both homogeneous and inhomogeneous models that were unique to each specimen had at least 8% greater explanatory power for apparent modulus than models that applied the same material properties to all specimens. The explanatory power for apparent modulus of models with a tissue modulus coefficient of variation (COV) range of 21-31% was 13% greater than homogeneous models (COV=0). The results of this study indicate that inhomogenous finite element models that have tissue moduli unique to each specimen more accurately predict the elastic behavior of cancellous cubic specimens than models that have common tissue moduli between all specimens.     

Method for characterizing viscoelasticity of human gluteal tissue

Characterizing compressive transient large deformation properties of biological tissue is becoming increasingly important in impact biomechanics and rehabilitation engineering, which includes devices interfacing with the human body and virtual surgical guidance simulation. Individual mechanical in vivo behaviour, specifically of human gluteal adipose and passive skeletal muscle tissue compressed with finite strain, has, however, been sparsely characterised. Employing a combined experimental and numerical approach, a method is presented to investigate the time-dependent properties of in vivo gluteal adipose and passive skeletal muscle tissue. Specifically, displacement-controlled ramp-and-hold indentation relaxation tests were performed and documented with magnetic resonance imaging. A time domain quasi-linear viscoelasticity (QLV) formulation with Prony series valid for finite strains was used in conjunction with a hyperelastic model formulation for soft tissue constitutive model parameter identification and calibration of the relaxation test data. A finite element model of the indentation region was employed. Strong non-linear elastic but linear viscoelastic tissue material behaviour at finite strains was apparent for both adipose and passive skeletal muscle mechanical properties with orthogonal skin and transversal muscle fibre loading. Using a force-equilibrium assumption, the employed material model was well suited to fit the experimental data and derive viscoelastic model parameters by inverse finite element parameter estimation. An individual characterisation of in vivo gluteal adipose and muscle tissue could thus be established. Initial shear moduli were calculated from the long-term parameters for human gluteal skin/fat: G(∞,S/F)=1850 Pa and for cross-fibre gluteal muscle tissue: G(∞,M)=881 Pa. Instantaneous shear moduli were found at the employed ramp speed: G(0,S/F)=1920 Pa and G(0,M)=1032 Pa.     

A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear.

Brainstem trauma occurs frequently in severe head injury, often resulting in fatal lesions due to importance of brainstem in crucial neural functions. Structurally, the brainstem is composed of bundles of axonal fibers distinctly oriented in a longitudinal direction surrounded by an extracellular matrix. We hypothesize that the oriented structure and architecture of the brainstem dictates this mechanical response and results in its selective vulnerability in rotational loading. In order to understand the relationship between the biologic architecture and the mechanical response and provide further insight into the high vulnerability of this region, a structural and mathematical model was created. A fiber-reinforced composite model composed of viscoelastic fibers surrounded by a viscoelastic matrix was used to relate the biological architecture of the brainstem to its anisotropic mechanical response. Relevant model parameters measured include the brainstem's composite complex moduli and relative fraction of matrix and fiber. The model predicted that the fiber component is three times stiffer and more viscous than the matrix. The fiber modulus predictions were compared with experimental tissue measurements. The optic nerve, a bundle of tightly packed longitudinally arranged myelinated fibers with little matrix, served as a surrogate for the brainstem fiber component. Model predictions agreed with experimental measures, offering a validation of the model. This approach provided an understanding of the relationship between the specific biologic architecture of the brainstem and the anisotropic mechanical response and allowed insight into reasons for the selective vulnerability of this region in rotational head injury.     

Simultaneous accumulation of calcium, phosphorus, and magnesium in various human arteries

To elucidate compositional changes of the arteries with aging, the authors investigated the relationships among average contents of calcium, phosphorus, sulfur, and magnesium in the arteries by inductively coupled plasma-atomic emission spectrometry. The arteries used were the thoracic and abdominal aortas, coronary, common carotid, anterior, middle and posterior cerebral, vertebral, basilar, internal thoracic, axillary, radial, truncus celiacus, common, internal and external iliac, femoral, popliteal, and umbilical arteries. It was found that high correlations were found between the average contents of calcium and phosphorus, between the average contents of calcium and magnesium, and between the average contents of phosphorus and magnesium in the arteries, but not between the average contents of sulfur and the other elements. These correlations revealed that as the content of calcium and phosphorus increased in the arteries, the magnesium content increased simultaneously in the arteries, but the sulfur content did not. It is likely that magnesium forms compounds with phosphorus in the arteries.     

Vascular function in rats with adenine-induced chronic renal failure

The aim of the present study was to characterize the function of resistance arteries, and the aorta, in rats with adenine-induced chronic renal failure (A-CRF). Sprague-Dawley rats were randomized to chow with or without adenine supplementation. After 6-10 wk, mesenteric arteries and thoracic aortas were analyzed ex vivo by wire myography. Plasma creatinine concentrations were elevated twofold at 2 wk, and eight-fold at the time of death in A-CRF animals. Ambulatory systolic and diastolic blood pressures measured by radiotelemetry were significantly elevated in A-CRF animals from week 3 and onward. At death, A-CRF animals had anemia, hyperphosphatemia, hyperparathyroidism, and elevated plasma levels of asymmetric dimethylarginine and oxidative stress markers. There were no significant differences between groups in the sensitivity, or maximal response, to ACh, sodium nitroprusside (SNP), norepinephrine, or phenylephrine in either mesenteric arteries or aortas. However, in A-CRF animals, the rate of aortic relaxation was significantly reduced following washout of KCl (both in intact and endothelium-denuded aorta) and in response to ACh and SNP. Also the rate of contraction in response to KCl was significantly reduced in A-CRF animals both in mesenteric arteries and aortas. The media of A-CRF aortas was thickened and showed focal areas of fragmented elastic lamellae and disorganized smooth muscle cells. No vascular calcifications could be detected. These results indicate that severe renal failure for a duration of less than 10 wk in this model primarily affects the aorta and mainly slows the rate of relaxation.     

Multiphoton microscopy observations of 3D elastin and collagen fiber microstructure changes during pressurization in aortic media

Elastin and collagen fibers play important roles in the mechanical properties of aortic media. Because knowledge of local fiber structures is required for detailed analysis of blood vessel wall mechanics, we investigated 3D microstructures of elastin and collagen fibers in thoracic aortas and monitored changes during pressurization. Using multiphoton microscopy, autofluorescence images from elastin and second harmonic generation signals from collagen were acquired in media from rabbit thoracic aortas that were stretched biaxially to restore physiological dimensions. Both elastin and collagen fibers were observed in all longitudinal–circumferential plane images, whereas alternate bright and dark layers were observed along the radial direction and were recognized as elastic laminas (ELs) and smooth muscle-rich layers (SMLs), respectively. Elastin and collagen fibers are mainly oriented in the circumferential direction, and waviness of collagen fibers was significantly higher than that of elastin fibers. Collagen fibers were more undulated in longitudinal than in radial direction, whereas undulation of elastin fibers was equibiaxial. Changes in waviness of collagen fibers during pressurization were then evaluated using 2-dimensional fast Fourier transform in mouse aortas, and indices of waviness of collagen fibers decreased with increases in intraluminal pressure. These indices also showed that collagen fibers in SMLs became straight at lower intraluminal pressures than those in EL, indicating that SMLs stretched more than ELs. These results indicate that deformation of the aorta due to pressurization is complicated because of the heterogeneity of tissue layers and differences in elastic properties of ELs, SMLs, and surrounding collagen and elastin.     

Mechanical properties of porcine femoral cortical bone measured by nanoindentation

This study uses a nanoindentation technique to examine variations in the local mechanical properties of porcine femoral cortical bone under hydrated conditions. Bone specimens from three age groups (6, 12 and 42 months), representing developing bone, ranging from young to mature animals, were tested on the longitudinal and transverse cross-sectional surfaces. Elastic modulus and hardness of individual lamellae within bone's microstructure: laminar bone, interstitial bone, and osteons, were measured. Both the elastic modulus and hardness increased with age. However, the magnitudes of these increases were different for each microstructural component. The longitudinal moduli were higher than the transverse moduli. Dehydrated samples were also tested to allow a comparison with hydrated samples and these resulted in higher moduli and hardness than the hydrated samples. Again, the degree of variation was different for each microstructural component. These results indicate that the developmental changes in bone have different rates of mechanical change within each microstructural component.     

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.