Abstract:Performing planar biaxial testing and using nominal stress-strain curves for soft-tissue characterization is most suitable when (1) the test produces homogeneous strain fields, (2) fibers are aligned with the coordinate axes, and (3) strains are measured far from boundaries. Some tissue types [such as lamellae of the annulus fibrosus (AF)] may not allow for these conditions to be met due to their natural geometry and constitution. The objective of this work was to develop and test a method utilizing a surface … Show more
“…The overall stress within the tissue is the sum of all the fiber stresses. Strength of alignment ( κ = 1.5 ), stiffness ( A = 5 kPa ), and nonlinearity ( B = 12 ) were selected based on previous fits of the NFSM to data from rat myocardium (Witzenburg et al 2012), cadaveric bladder wall (Raghupathy 2011), and cadaveric annulus fibrosus lamellae (Nagel et al 2014). For the remainder of this article, we use the term “simulated experiment” to refer specifically to the results of the simulation using the closed-form nonlinear fiber-based structural model, including results that would be measurable experimentally (e.g., grip forces) and results that could not be measured but are available from the simulation and used for comparison with NGAIM calculations (e.g., stress or strain energy).…”
Section: Methodsmentioning
confidence: 99%
“…In addition, precise levels of preload and preconditioning must be applied carefully. For experimental data obtained using the biaxial tester (Instron 1 ), load cells (JR3 Inc. (Nagel et al 2014)) and digital camera (Cannon, 24 fps, 1080p HD resolution) available at the University of Minnesota, a step size of 0.5 seconds is reasonable.
Figure A.1
Final step size fits for the equibiaxial and right-arm-only extensions for the simulated sample containing an inclusion in which the fiber orientation is rotated, shown in Figure 2. Ten steps were utilized to describe the force behavior.
Figure A.2
Displacement field for equibiaxial and right-arm-only extensions for the representative simulation at the end of each step.
…”
Section: Figure A1mentioning
confidence: 99%
“…In addition, precise levels of preload and preconditioning must be applied carefully. For experimental data obtained using the biaxial tester (Instron 1 ), load cells (JR3 Inc. (Nagel et al 2014)) and digital camera (Cannon, 24 fps, 1080p HD resolution) available at the University of Minnesota, a step size of 0.5 seconds is reasonable.…”
Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the “computational dissection” of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.
“…The overall stress within the tissue is the sum of all the fiber stresses. Strength of alignment ( κ = 1.5 ), stiffness ( A = 5 kPa ), and nonlinearity ( B = 12 ) were selected based on previous fits of the NFSM to data from rat myocardium (Witzenburg et al 2012), cadaveric bladder wall (Raghupathy 2011), and cadaveric annulus fibrosus lamellae (Nagel et al 2014). For the remainder of this article, we use the term “simulated experiment” to refer specifically to the results of the simulation using the closed-form nonlinear fiber-based structural model, including results that would be measurable experimentally (e.g., grip forces) and results that could not be measured but are available from the simulation and used for comparison with NGAIM calculations (e.g., stress or strain energy).…”
Section: Methodsmentioning
confidence: 99%
“…In addition, precise levels of preload and preconditioning must be applied carefully. For experimental data obtained using the biaxial tester (Instron 1 ), load cells (JR3 Inc. (Nagel et al 2014)) and digital camera (Cannon, 24 fps, 1080p HD resolution) available at the University of Minnesota, a step size of 0.5 seconds is reasonable.
Figure A.1
Final step size fits for the equibiaxial and right-arm-only extensions for the simulated sample containing an inclusion in which the fiber orientation is rotated, shown in Figure 2. Ten steps were utilized to describe the force behavior.
Figure A.2
Displacement field for equibiaxial and right-arm-only extensions for the representative simulation at the end of each step.
…”
Section: Figure A1mentioning
confidence: 99%
“…In addition, precise levels of preload and preconditioning must be applied carefully. For experimental data obtained using the biaxial tester (Instron 1 ), load cells (JR3 Inc. (Nagel et al 2014)) and digital camera (Cannon, 24 fps, 1080p HD resolution) available at the University of Minnesota, a step size of 0.5 seconds is reasonable.…”
Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the “computational dissection” of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.
“…Data from an equibiaxial extension in the middle of the protocol were used for all further analyses; remaining data from the extensive protocol can be used for future study. The amount of grip strain (12%) was selected to be large enough to stretch the tissue out of the toe region and produce a significant nonlinear response, but no so large as to compromise tissue integrity, based on the observations of Little and Khalsa (2005) and Nagel et al (2014). The ligament surface was speckled with Working Elastic Stain Solution from a Verhoeff's stain kit (Sigma HT25A) for displacement tracking, and the full test protocol was video recorded at 24 frames/second.…”
Section: Methodsmentioning
confidence: 99%
“…In this work, however, we introduce biaxial tests that provide complementary information, including coupling between the two directions and shear forces during loading. Previously, we performed equibiaxial tests on a lumbar FCL as part of a study on fitting methods (Nagel et al, 2014), but the study was primarily methodological and did not generate detailed information on the tissue’s biaxial response.…”
The lumbar facet capsular ligament (FCL) articulates with six degrees of freedom during spinal motions of flexion/extension, lateral bending, and axial rotation. The lumbar FCL is composed of highly aligned collagen fiber bundles on the posterior surface (oriented primarily laterally between the rigid articular facets) and irregularly oriented elastin on the anterior surface. Because the FCL is a capsule, it has multiple insertion sites across the lumbar facet joint, which, along with its material structure, give rise to complicated deformations in vivo. We performed planar equibiaxial mechanical tests on excised healthy cadaveric lumbar FCLs (n = 6) to extract normal and shear reaction forces, and fit sample-specific two-fiber-family finite element models to the experimental force data. An eight-parameter anisotropic, hyperelastic model was used. Shear forces at maximum extension (mean values of 1.68N and 3.01N in the two directions) were of comparable magnitude to the normal forces perpendicular to the aligned collagen fiber bundles (4.67N) but smaller than normal forces in the fiber direction (16.11N). Inclusion of the experimental shear forces in the model optimization yielded fits with highly aligned fibers oriented at a specific angle across all samples, typically with one fiber population aligned nearly horizontally and the other at an oblique angle. Conversely, models fit to only the normal force data resulted in a broad range of fiber angles with low specificity. We found that shear forces generated through planar equibiaxial extension aided the model fit in describing the anisotropic nature of the FCL surface.
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