This paper deals with the application of the virtual fields method (VFM) to the identification of constants governing anisotropic constitutive equations. After a short recalling of the main features of the VFM, its sensitivity to noisy data is addressed. The study focuses on the random component of the noise which always adds to the actual fields in experimental full-field measurements. The uncertainty of the identified constants due to this random component is derived analytically. The obtained closedform expression is set as a criterion for grading virtual fields. The least sensitivity to noise leads to the best identification. The grading procedure is implemented directly in the VFM algorithm, providing systematically the virtual field which minimizes the sensitivity to random noises. Examples are provided for validating the approach with numerically simulated noisy data. Finally, the grading procedure is applied for adjusting the geometry which leads to an optimal use of the three-point bending test for identifying the elastic constants of a composite material. It shows that the criterion ''sensitivity to noise'' characterizes quantitatively the identifiability of one or several parameters. Future applications appear quite promising within the design of novel test methods for composites using the VFM.
In this paper, we present a new approach for the bi-axial characterization of in vitro human arteries and we prove its feasibility on an example. The specificity of the approach is that it can handle heterogeneous strain and stress distributions in arterial segments. From the full-field experimental data obtained in inflation/extension tests, an inverse approach, called the virtual fields method (VFM), is used for deriving the material parameters of the tested arterial segment. The obtained results are promising and the approach can effectively provide relevant values for the anisotropic hyperelastic properties of the tested sample.
Despite their medical importance, rupture properties of ascending thoracic aortic aneurysms (ATAA) subjected to biaxial tension were inexistent in the literature. In order to address this lack, our group developed a novel methodology based on bulge inflation and full-field optical measurements. Here we report rupture properties obtained with this methodology on 31 patients. It is shown for the first time that rupture occurs when the stretch applied to ATAAs reaches the maximum extensibility of the tissue and that this maximum extensibility correlates strongly with the elastic properties. The outcome is a better detection of at-risk individuals for elective surgical repair.
This study demonstrates the anisotropy of the aortic wall in ATAA and provides data on the mechanical behaviour in the physiological range of pressure.
Many vascular disorders, including aortic aneurysms and dissections, are characterized by localized changes in wall composition and structure. Notwithstanding the importance of histopathologic changes that occur at the microstructural level, macroscopic manifestations ultimately dictate the mechanical functionality and structural integrity of the aortic wall. Understanding structure-function relationships locally is thus critical for gaining increased insight into conditions that render a vessel susceptible to disease or failure. Given the scarcity of human data, mouse models are increasingly useful in this regard. In this paper, we present a novel inverse characterization of regional, nonlinear, anisotropic properties of the murine aorta. Full-field biaxial data are collected using a panoramic-digital image correlation (p-DIC) system. An inverse method, based on the principle of virtual power (PVP), is used to estimate values of material parameters regionally for a microstructurally motivated constitutive relation. We validate our experimental-computational approach by comparing results to those from standard biaxial testing. The results for the nondiseased suprarenal abdominal aorta from apolipoprotein-E null mice reveal material heterogeneities, with significant differences between dorsal and ventral as well as between proximal and distal locations, which may arise in part due to differential perivascular support and localized branches. Overall results were validated for both a membrane and a thick-wall model that delineated medial and adventitial properties. Whereas full-field characterization can be useful in the study of normal arteries, we submit that it will be particularly useful for studying complex lesions such as aneurysms, which can now be pursued with confidence given the present validation.
Endovascular repair of abdominal aortic aneurysms faces some adverse outcomes, such as kinks or endoleaks related to incomplete stent apposition, which are difficult to predict and which restrain its use although it is less invasive than open surgery. Finite element simulations could help to predict and anticipate possible complications biomechanically induced, thus enhancing practitioners' stent-graft sizing and surgery planning, and giving indications on patient eligibility to endovascular repair. The purpose of this work is therefore to develop a new numerical methodology to predict stent-graft final deployed shapes after surgery. The simulation process was applied on three clinical cases, using preoperative scans to generate patient-specific vessel models. The marketed devices deployed during the surgery, consisting of a main body and one or more iliac limbs or extensions, were modeled and their deployment inside the corresponding patient aneurysm was simulated. The numerical results were compared to the actual deployed geometry of the stent-grafts after surgery that was extracted from postoperative scans. We observed relevant matching between simulated and actual deployed stent-graft geometries, especially for proximal and distal stents outside the aneurysm sac which are particularly important for practitioners. Stent locations along the vessel centerlines in the three simulations were always within a few millimeters to actual stents locations. This good agreement between numerical results and clinical cases makes finite element simulation very promising for preoperative planning of endovascular repair.
We recently developed an approach to characterize local nonlinear, anisotropic mechanical properties of murine arteries by combining biaxial extension-distension testing, panoramic digital image correlation (pDIC), and an inverse method based on the principle of virtual power. This experimental-computational approach was illustrated for the normal murine abdominal aorta assuming uniform wall thickness. Here, however, we extend our prior approach by adding an optical coherence tomography (OCT) imaging system that permits local reconstructions of wall thickness. This multi-modality approach is then used to characterize spatial variations of material and structural properties in ascending thoracic aortic aneurysms (aTAA) from two genetically modified mouse models (fibrillin-1 and fibulin-4 deficient) and to compare them with those from angiotensin-II infused apolipoprotein-E deficient and wild-type control aortas. Local values of stored elastic energy and biaxial material stiffness, computed from spatial distributions of the bestfit material parameters, varied significantly with circumferential position (inner vs. outer curvature, ventral vs. dorsal sides) across genotypes and treatments. Importantly, these data reveal an inverse relationship between material stiffness and wall thickness that underlies a general linear relationship between stiffness and wall stress across aTAAs. OCT images also revealed sites of advanced medial degeneration, which were captured by the inverse material characterization. Quantification of histological data further provided high resolution local correlations amongst multiple mechanical metrics and wall microstructure. This is the first time that such structural defects and local properties have been characterized mechanically, which can better inform computational models of aortopathy that seek to predict where dissection or rupture may initiate.
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