Collapse and viscoelasticity of diseased human arteries

A laboratory study of the hydrostatic collapse of diseased tibial arteries demonstrated hysteresis in the pressure-flow behaviour which resembled that seen in the stress-strain relations of the arterial tissue. The pressures at which the vessels collapsed were found to be considerably lower than expected on the basis of theoretical elastic models. Also, the pressures at which the vessels reopened were consistently lower than the pressures at which they collapsed. These findings were explained on the basis of viscoelasticity. The difference between collapse and opening pressure may provide insight into the mechanical properties of vessels, and a clue to errors in non-invasive measurements of blood pressure which depend upon collapse of arteries.     

A biomechanical analysis of venous tissue in its normal and post-phlebitic conditions

Although biomechanical studies of the normal rat vein wall have been reported (Weizsacker, 1988, Plante, 2002), there are no published studies that have investigated the mechanical effects of thrombus formation on murine venous tissue. In response to the lack of knowledge concerning the mechanical consequences of thrombus resolution, distinct thrombus-induced changes in the biomechanical properties of the murine vena cava were measured via biaxial stretch experiments. These data served as input for strain energy function (SEF) fitting and modeling (Gasser et al., 2006). Statistical differences were observed between healthy and diseased tissue with respect to the structural coefficient that represents the response of the non-collagenous, isotropic ground substance. Alterations following thrombus formation were also noted for the SEF coefficient which describes the anisotropic contribution of the fibers. The data indicate ligation of the vena cava leads to structural alterations in the ground substance and collagen fiber network.     

Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation

Computational implementation of physical and physiologically realistic constitutive models is critical for numerical simulation of soft biological tissues in a variety of biomedical applications. It is well established that the highly nonlinear and anisotropic mechanical behaviors of soft tissues are an emergent behavior of the underlying tissue microstructure. In the present study, we have implemented a structural constitutive model into a finite element framework specialized for membrane tissues. We noted that starting with a single element subjected to uniaxial tension, the non-fibrous tissue matrix must be present to prevent unrealistic tissue deformations. Flexural simulations were used to set the non-fibrous matrix modulus because fibers have little effects on tissue deformation under three-point bending. Multiple deformation modes were simulated, including strip biaxial, planar biaxial with two attachment methods, and membrane inflation. Detailed comparisons with experimental data were undertaken to insure faithful simulations of both the macro-level stress–strain insights into adaptations of the fiber architecture under stress, such as fiber reorientation and fiber recruitment. Results indicated a high degree of fidelity and demonstrated interesting microstructural adaptions to stress and the important role of the underlying tissue matrix. Moreover, we apparently resolve a discrepancy in our 1997 study (Billiar and Sacks, 1997. J. Biomech. 30 (7), 753–756) where we observed that under strip biaxial stretch the simulated fiber splay responses were not in good agreement with the experimental results, suggesting non-affine deformations may have occurred. However, by correctly accounting for the isotropic phase of the measured fiber splay, good agreement was obtained. While not the final word, these simulations suggest that affine fiber kinematics for planar collagenous tissues is a reasonable assumption at the macro level. Simulation tools such as these are imperative in the design and simulation of native and engineered tissues.     

A gimbal-mounted pressurization chamber for macroscopic and microscopic assessment of ocular tissues

The biomechanical model of glaucoma considers intraocular pressure-related stress and resultant strain on load bearing connective tissues of the optic nerve and surrounding peripapillary sclera as one major causative influence that effects cellular, vascular, and axonal components of the optic nerve. By this reasoning, the quantification of variations in the microstructural architecture and macromechanical response of scleral shells in glaucomatous compared to healthy populations provides an insight into any variations that exist between patient populations. While scleral shells have been tested mechanically in planar and pressure-inflation scenarios the link between the macroscopic biomechanical response and the underlying microstructure has not been determined to date. A potential roadblock to determining how the microstructure changes based on pressure is the ability to mount the spherical scleral shells in a method that does not induce unwanted stresses to the samples (for instance, in the flattening of the spherical specimens), and then capturing macroscopic and microscopic changes under pressure. Often what is done is a macroscopic test followed by sample fixation and then imaging to determine microstructural organization. We introduce a novel device and method, which allows spherical samples to be pressurized and macroscopic and microstructural behavior quantified on fully hydrated ocular specimens. The samples are pressurized and a series of markers on the surface of the sclera imaged from several different perspectives and reconstructed between pressure points to allow for mapping of nonhomogenous strain. Pictures are taken from different perspectives through the use of mounting the pressurization scheme in a gimbal that allows for positioning the sample in several different spherical coordinate system configurations. This ability to move the sclera in space about the center of the globe, coupled with an upright multiphoton microscope, allows for collecting collagen, and elastin signal in a rapid automated fashion so the entire globe can be imaged.     

Characterization of evolving biomechanical properties of tissue engineered vascular grafts in the arterial circulation

We used a murine model to assess the evolving biomechanical properties of tissue engineered vascular grafts (TEVGs) implanted in the arterial circulation. The initial polymeric tubular scaffold was fabricated from poly(lactic acid)(PLA) and coated with a 50:50 copolymer of poly(caprolactone) and poly(lactic acid)(P[PC/LA]). Following seeding with syngeneic bone marrow derived mononuclear cells, TEVGs (n=50) were implanted as aortic interposition grafts in wild-type mice and monitored serially using ultrasound. A custom biaxial mechanical testing device was used to quantify the in vitro circumferential and axial mechanical properties of grafts explanted at 3 or 7 months. At both times, TEVGs were much stiffer than native tissue in both directions. Repeated mechanical testing of some TEVGs treated with elastase or collagenase suggested that elastin did not contribute significantly to the overall stiffness whereas collagen did contribute. Traditional histology and immunostaining revealed smooth muscle cell layers, significant collagen deposition, and increasing elastin production in addition to considerable scaffold at both 3 and 7 months, which likely dominated the high stiffness seen in mechanical testing. These results suggest that PLA has inadequate in vivo degradation, which impairs cell-mediated development of vascular neotissue having properties closer to native arteries. Assessing contributions of individual components, such as elastin and collagen, to the developing neovessel is needed to guide computational modeling that may help to optimize the design of the TEVG.     

Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms

A fluid–solid-growth (FSG) model of saccular cerebral aneurysm evolution is developed. It utilises a realistic two-layered structural model of the internal carotid artery and explicitly accounts for the degradation of the elastinous constituents and growth and remodelling (G&R) of the collagen fabric. Aneurysm inception is prescribed: a localised degradation of elastin results in a perturbation in the arterial geometry; the collagen fabric adapts, and the artery achieves a new homeostatic configuration. The perturbation to the geometry creates an altered haemodynamic environment. Subsequent degradation of elastin is explicitly linked to low wall shear stress (WSS) in a confined region of the arterial domain. A sidewall saccular aneurysm develops, the collagen fabric adapts and the aneurysm stabilises in size. A quasi-static analysis is performed to determine the geometry at diastolic pressure. This enables the cyclic stretching of the tissue to be quantified, and we propose a novel index to quantify the degree of biaxial stretching of the tissue. Whilst growth is linked to low WSS from a steady (systolic) flow analysis, a pulsatile flow analysis is performed to compare steady and pulsatile flow parameters during evolution. This model illustrates the evolving mechanical environment for an idealised saccular cerebral aneurysm developing on a cylindrical parent artery and provides the guidance to more sophisticated FSG models of aneurysm evolution which link G&R to the local mechanical stimuli of vascular cells.     

Improved prediction of the collagen fiber architecture in the aortic heart valve

Living tissues show an adaptive response to mechanical loading by changing their internal structure and morphology. Understanding this response is essential for successful tissue engineering of load-bearing structures, such as the aortic valve. In this study, mechanically induced remodeling of the collagen architecture in the aortic valve was investigated. It was hypothesized that, in uniaxially loaded regions, the fibers aligned with the tensile principal stretch direction. For biaxial loading conditions, on the other hand, it was assumed that the collagen fibers aligned with directions situated between the principal stretch directions. This hypothesis has already been applied successfully to study collagen remodeling in arteries. The predicted fiber architecture represented a branching network and resembled the macroscopically visible collagen bundles in the native leaflet. In addition, the complex biaxial mechanical behavior of the native valve could be simulated qualitatively with the predicted fiber directions. The results of the present model might be used to gain further insight into the response of tissue engineered constructs during mechanical conditioning.     

A finite element model of stress-mediated vascular adaptation: application to abdominal aortic aneurysms

Despite rapid expansion of our knowledge of vascular adaptation, developing patient-specific models of diseased arteries is still an open problem. In this study, we extend existing finite element models of stress-mediated growth and remodelling of arteries to incorporate a medical image-based geometry of a healthy aorta and, then, simulate abdominal aortic aneurysm. Degradation of elastin initiates a local dilatation of the aorta while stress-mediated turnover of collagen and smooth muscle compensates the loss of elastin. Stress distributions and expansion rates during the aneurysm growth are studied for multiple spatial distribution functions of elastin degradation and kinetic parameters. Temporal variations of the degradation function are also investigated with either direct time-dependent degradation or stretch-induced degradation as possible biochemical and biomechanical mechanisms for elastin degradation. The results show that this computational model has the capability to capture the complexities of aneurysm progression due to variations of geometry, extent of damage and stress-mediated turnover as a step towards patient-specific modelling.     

A finite element model of stress-mediated vascular adaptation: application to abdominal aortic aneurysms

Despite rapid expansion of our knowledge of vascular adaptation, developing patient-specific models of diseased arteries is still an open problem. In this study, we extend existing finite element models of stress-mediated growth and remodelling of arteries to incorporate a medical image-based geometry of a healthy aorta and, then, simulate abdominal aortic aneurysm. Degradation of elastin initiates a local dilatation of the aorta while stress-mediated turnover of collagen and smooth muscle compensates the loss of elastin. Stress distributions and expansion rates during the aneurysm growth are studied for multiple spatial distribution functions of elastin degradation and kinetic parameters. Temporal variations of the degradation function are also investigated with either direct time-dependent degradation or stretch-induced degradation as possible biochemical and biomechanical mechanisms for elastin degradation. The results show that this computational model has the capability to capture the complexities of aneurysm progression due to variations of geometry, extent of damage and stress-mediated turnover as a step towards patient-specific modelling.     

Progressive structural and biomechanical changes in elastin degraded aorta

Aortic aneurysm is an important clinical condition characterized by common structural changes such as the degradation of elastin, loss of smooth muscle cells, and increased deposition of fibrillary collagen. With the goal of investigating the relationship between the mechanical behavior and the structural/biochemical composition of an artery, this study used a simple chemical degradation model of aneurysm and investigated the progressive changes in mechanical properties. Porcine thoracic aortas were digested in a mild solution of purified elastase (5 U/mL) for 6, 12, 24, 48, and 96 h. Initial size measurements show that disruption of the elastin structure leads to increased artery dilation in the absence of periodic loading. The mechanical properties of the digested arteries, measured with a biaxial tensile testing device, progress through four distinct stages termed (1) initial-softening, (2) elastomer-like, (3) extensible-but-stiff, and (4) collagen-scaffold-like. While stages 1, 3, and 4 are expected as a result of elastin degradation, the S-shaped stress versus strain behavior of the aorta resulting from enzyme digestion has not been reported previously. Our results suggest that gradual changes in the structure of elastin in the artery can lead to a progression through different mechanical properties and thus reveal the potential existence of an important transition stage that could contribute to artery dilation during aneurysm formation.     

Live en face imaging of aortic valve leaflets under mechanical stress

Soft tissues, such as tendons, skin, arteries, or lung, are constantly subject to mechanical stresses in vivo. None more so than the aortic heart valve that experiences an array of forces including shear stress, cyclic pressure, strain, and flexion. Anisotropic biaxial cyclic stretch maintains valve homeostasis; however, abnormal forces are implicated in disease progression. The response of the valve endothelium to deviations from physiological levels has not been fully characterized. Here, we show the design and validation of a novel stretch apparatus capable of applying biaxial stretch to viable heart valve tissue, while simultaneously allowing for live en face endothelial cell imaging via confocal laser scanning microscopy (CLSM). Real-time imaging of tissue is possible while undergoing highly characterized mechanical conditions and maintaining the native extracellular matrix. Thus, it provides significant advantages over traditional cell culture or in vivo animal models. Planar biaxial tissue stretching with simultaneous live cell imaging could prove useful in studying the mechanobiology of any soft tissue.     

Micromechanical modelling of cortical bone

Cortical bone is a heterogeneous material with a complex hierarchical microstructure. In this work, unit cell finite element models were developed to investigate the effect of microstructural morphology on the macroscopic properties of cortical bone. The effect of lacunar and vascular porosities, percentage of osteonal bone and orientation of the Haversian system on the macroscopic elastic moduli and Poisson's ratios was investigated. The results presented provide relationships for applying more locally accurate material properties to larger scale and whole bone models of varying porosity. Analysis of the effect of the orientation of the Haversian system showed that its effects should not be neglected in larger scale models. This study also provides insight into how microstructural features effect local distributions and cause a strain magnification effect. Limitations in applying the unit cell methodology approach to bone are also discussed.     

Calcifications in atherosclerotic plaques and impact on plaque biomechanics

The catastrophic mechanical rupture of an atherosclerotic plaque is the underlying cause of the majority of cardiovascular events. The infestation of vascular calcification in the plaques creates a mechanically complex tissue composite. Local stress concentrations and plaque tissue strength properties are the governing parameters required to predict plaque ruptures. Advanced imaging techniques have permitted insight into fundamental mechanisms driving the initiating inflammatory-driven vascular calcification of the diseased intima at the (sub-) micron scale and up to the macroscale. Clinical studies have potentiated the biomechanical relevance of calcification through the derivation of links between local plaque rupture and specific macrocalcification geometrical features. The clinical implications of the data presented in this review indicate that the combination of imaging, experimental testing, and computational modelling efforts are crucial to predict the rupture risk for atherosclerotic plaques. Specialised experimental tests and modelling efforts have further enhanced the knowledge base for calcified plaque tissue mechanical properties. However, capturing the temporal instability and rupture causality in the plaque fibrous caps remains elusive. Is it necessary to move our experimental efforts down in scale towards the fundamental (sub-) micron scales in order to interpret the true mechanical behaviour of calcified plaque tissue interactions that is presented on a macroscale in the clinic and to further optimally assess calcified plaques in the context of biomechanical modelling.     

Biaxial vasoactivity of porcine coronary artery

The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K(+)-induced vasoconstriction, the mean ± SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 ± 0.17 and 3.28 ± 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca(2+)-free-induced vasodilated state (i.e., 4.01 ± 0.16 and 3.75 ± 0.20 mm, respectively). The mean ± SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 ± 0.04 mm and 2.25 ± 0.08 mm and 126 ± 22°, respectively. The active stresses have a maximal value at the passive pressure of 80-100 mmHg and at the active pressure of 140-160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.     

Site specific inelasticity of arterial tissue

Understanding the mechanical behaviour of arterial tissue is vital to the development and analysis of medical devices targeting diseased vessels. During angioplasty and stenting, stress softening and permanent deformation of the vessel wall occur during implantation of the device, however little data exists on the inelastic behaviour of cardiovascular tissue and how this varies through the arterial tree. The aim of this study was to characterise the magnitude of stress softening and inelastic deformations due to loading throughout the arterial tree and to investigate the anisotropic inelastic behaviour of the tissue. Cyclic compression tests were used to investigate the differences in inelastic behaviour for carotid, aorta, femoral and coronary arteries harvested from 3-4 month old female pigs, while the anisotropic behaviour of aortic and carotid tissue was determined using cyclic tensile tests in the longitudinal and circumferential directions. The differences in inelastic behaviour were correlated to the ratio of collagen to elastin content of the arteries. It was found that larger inelastic deformations occurred in muscular arteries (coronary), which had a higher collagen to elastin ratio than elastic arteries (aorta), where the smallest inelastic deformations were observed. Lower magnitude inelastic deformations were observed in the circumferential tensile direction than in the longitudinal tensile direction or due to radial compression. This may be as a result of non-collagenous components in the artery becoming more easily damaged than the collagen fibres during loading. Stress softening was also found to be dependent on artery type. In the future, computational models should consider such site dependant, anisotropic inelastic behaviour in order to better predict the outcomes of interventional procedures such as angioplasty and stenting.     

Age-related properties at the microscale affect crack propagation in cortical bone

The increased risk for fracture with age is associated not only with reduced bone mass but also with impaired bone quality. At the microscale, bone quality is related to porosity, microstructural organization, accumulated microdamage and intrinsic material properties. However, the link between these characteristics and fracture behavior is still missing. Bone tissue has a complex structure and as age-related compositional and structural changes occur at all hierarchical length scales it is difficult to experimentally identify and discriminate the effect of each mechanism. The aim of this study was therefore to use computational models to analyze how microscale characteristics in terms of porosity, intrinsic toughness properties and microstructural organization affect the mechanical behavior of cortical bone. Tensile tests were simulated using realistic microstructural geometries based on microscopy images of human cortical bone. Crack propagation was modelled using the extended finite element method where cement lines surrounding osteons were modelled with an interface damage law to capture crack deflections along osteon boundaries. Both increased porosity and impaired material integrity resulted in straighter crack paths with cracks penetrating osteons, similar to what is seen experimentally for old cortical bone. However, only the latter predicted a more brittle failure behavior. Furthermore, the local porosity influenced the crack path more than the macroscopic porosity. In conclusion, age-related changes in cortical bone affect the crack path and the mechanical response. However, increased porosity alone was not driving damage in old bone, but instead impaired tissue integrity was required to capture brittle failure in aging bone.     

A multiaxial computer-controlled organ culture and biomechanical device for mouse carotid arteries

Much of our understanding of vascular mechanotransduction has come from studies using either cell culture or in vivo animal models, but the recent success of organ culture systems offers an exciting alternative. In studying cell-mediated vascular adaptations to altered loading, organ culture allows one to impose well-controlled mechanical loads and to perform multiaxial mechanical tests on the same vessel throughout the culture period, and thereby to observe cell-mediated vascular adaptations independent of neural and hormonal effects. Here, we present a computer-controlled perfused organ culture and biomechanical testing device designed for small caliber (50-5000 micron) blood vessels. This device can control precisely the pulsatile pressure, luminal flow, and axial load (or stretch) and perform intermittent biaxial (pressure-diameter and axial load-length) and functional tests to quantify adaptations in mechanical behavior and cellular function, respectively. Device capabilities are demonstrated by culturing mouse carotid arteries for 4 days.