Combining displacement field and grip force information to determine mechanical properties of planar tissue with complicated geometry

Appropriate Objective Functions for Quantifying Iris Mechanical Properties Using Inverse Finite Element Modeling

Quantifying the mechanical properties of the iris is important, as it provides insight into the pathophysiology of glaucoma. Recent ex vivo studies have shown that the mechanical properties of the iris are different in glaucomatous eyes as compared to normal ones. Notwithstanding the importance of the ex vivo studies, such measurements are severely limited for diagnosis and preclude development of treatment strategies. With the advent of detailed imaging modalities, it is possible to determine the in vivo mechanical properties using inverse finite element (FE) modeling. An inverse modeling approach requires an appropriate objective function for reliable estimation of parameters. In the case of the iris, numerous measurements such as iris chord length (CL) and iris concavity (CV) are made routinely in clinical practice. In this study, we have evaluated five different objective functions chosen based on the iris biometrics (in the presence and absence of clinical measurement errors) to determine the appropriate criterion for inverse modeling. Our results showed that in the absence of experimental measurement error, a combination of iris CL and CV can be used as the objective function. However, with the addition of measurement errors, the objective functions that employ a large number of local displacement values provide more reliable outcomes.

The role of the facet capsular ligament in providing spinal stability

Low back pain (LBP) is the most common type of pain in America, and spinal instability is a primary cause. The facet capsular ligament (FCL) encloses the articulating joints of the spine and is of particular interest due to its high innervation - as instability ensues, high stretch values likely are a cause of this pain. Therefore, this work investigated the FCL's role in providing stability to the lumbar spine. A previously validated finite element model of the L4-L5 spinal motion segment was used to simulate pure moment bending in multiple planes. FCL failure was simulated and the following outcome measures were calculated: helical axes of motion, range of motion (ROM), bending stiffness, facet joint space, and FCL stretch. ROM increased, bending stiffness decreased, and altered helical axis patterns were observed with the removal of the FCL. Additionally, a large increase in FCL stretch was measured with diminished FCL mechanical competency, providing support that the FCL plays an important role in spinal stability.

Isotropic Failure Criteria Are Not Appropriate for Anisotropic Fibrous Biological Tissues

The von Mises (VM) stress is a common stress measure for finite element models of tissue mechanics. The VM failure criterion, however, is inherently isotropic, and therefore may yield incorrect results for anisotropic tissues, and the relevance of the VM stress to anisotropic materials is not clear. We explored the application of a well-studied anisotropic failure criterion, the Tsai–Hill (TH) theory, to the mechanically anisotropic porcine aorta. Uniaxial dogbones were cut at different angles and stretched to failure. The tissue was anisotropic, with the circumferential failure stress nearly twice the axial (2.67 ± 0.67 MPa compared to 1.46 ± 0.59 MPa). The VM failure criterion did not capture the anisotropic tissue response, but the TH criterion fit the data well (R2 = 0.986). Shear lap samples were also tested to study the efficacy of each criterion in predicting tissue failure. Two-dimensional failure propagation simulations showed that the VM failure criterion did not capture the failure type, location, or propagation direction nearly as well as the TH criterion. Over the range of loading conditions and tissue geometries studied, we found that problematic results that arise when applying the VM failure criterion to an anisotropic tissue. In contrast, the TH failure criterion, though simplistic and clearly unable to capture all aspects of tissue failure, performed much better. Ultimately, isotropic failure criteria are not appropriate for anisotropic tissues, and the use of the VM stress as a metric of mechanical state should be reconsidered when dealing with anisotropic tissues.

A Novel Method for Repeatable Failure Testing of Annulus Fibrosus

Tears in the annulus fibrosus (AF) of the intervertebral disk can result in disk herniation and progressive degeneration. Understanding AF failure mechanics is important as research moves toward developing biological repair strategies for herniated disks. Unfortunately, failure mechanics of fiber-reinforced tissues, particularly tissues with fibers oriented off-axis from the applied load, is not well understood, partly due to the high variability in reported mechanical properties and a lack of standard techniques ensuring repeatable failure behavior. Therefore, the objective of this study was to investigate the effectiveness of midlength (ML) notch geometries in producing repeatable and consistent tissue failure within the gauge region of AF mechanical test specimens. Finite element models (FEMs) representing several notch geometries were created to predict the location of bulk tissue failure using a local strain-based criterion. FEM results were validated by experimentally testing a subset of the modeled specimen geometries. Mechanical testing data agreed with model predictions (∼90% agreement), validating the model's predictive power. Two of the modified dog-bone geometries (“half” and “quarter”) effectively ensured tissue failure at the ML for specimens oriented along the circumferential-radial and circumferential-axial directions. The variance of measured mechanical properties was significantly lower for notched samples that failed at the ML, suggesting that ML notch geometries result in more consistent and reliable data. In addition, the approach developed in this study provides a framework for evaluating failure properties of other fiber-reinforced tissues, such as tendons and meniscus.

Image-based multiscale mechanical modeling shows the importance of structural heterogeneity in the human lumbar facet capsular ligament

The lumbar facet capsular ligament (FCL) primarily consists of aligned type I collagen fibers that are mainly oriented across the joint. The aim of this study was to characterize and incorporate in-plane local fiber structure into a multiscale finite element model to predict the mechanical response of the FCL during in vitro mechanical tests, accounting for the heterogeneity in different scales. Characterization was accomplished by using entire-domain polarization-sensitive optical coherence tomography to measure the fiber structure of cadaveric lumbar FCLs ([Formula: see text]). Our imaging results showed that fibers in the lumbar FCL have a highly heterogeneous distribution and are neither isotropic nor completely aligned. The averaged fiber orientation was [Formula: see text] ([Formula: see text] in the inferior region and [Formula: see text] in the middle and superior regions), with respect to lateral-medial direction (superior-medial to inferior-lateral). These imaging data were used to construct heterogeneous structural models, which were then used to predict experimental gross force-strain behavior and the strain distribution during equibiaxial and strip biaxial tests. For equibiaxial loading, the structural model fit the experimental data well but underestimated the lateral-medial forces by [Formula: see text]16% on average. We also observed pronounced heterogeneity in the strain field, with stretch ratios for different elements along the lateral-medial axis of sample typically ranging from about 0.95 to 1.25 during a 12% strip biaxial stretch in the lateral-medial direction. This work highlights the multiscale structural and mechanical heterogeneity of the lumbar FCL, which is significant both in terms of injury prediction and microstructural constituents' (e.g., neurons) behavior.

An imaged-based inverse finite element method to determine in-vivo mechanical properties of the human trabecular meshwork

AIM

Previous studies have shown that the trabecular meshwork (TM) is mechanically stiffer in glaucomatous eyes as compared to normal eyes. It is believed that elevated TM stiffness increases resistance to the aqueous humor outflow, producing increased intraocular pressure (IOP). It would be advantageous to measure TM mechanical properties in vivo, as these properties are believed to play an important role in the pathophysiology of glaucoma and could be useful for identifying potential risk factors. The purpose of this study was to develop a method to estimate in-vivo TM mechanical properties using clinically available exams and computer simulations.

DESIGN

Inverse finite element simulation.

METHODS

A finite element model of the TM was constructed from optical coherence tomography (OCT) images of a healthy volunteer before and during IOP elevation. An axisymmetric model of the TM was then constructed. Images of the TM at a baseline IOP level of 11, and elevated level of 23 mmHg were treated as the undeformed and deformed configurations, respectively. An inverse modeling technique was subsequently used to estimate the TM shear modulus (G). An optimization technique was used to find the shear modulus that minimized the difference between Schlemm's canal area in the in-vivo images and simulations.

RESULTS

Upon completion of inverse finite element modeling, the simulated area of the Schlemm's canal changed from 8,889 µm² to 2,088 µm², similar to the experimentally measured areal change of the canal (from 8,889 µm² to 2,100 µm²). The calculated value of shear modulus was found to be 1.93 kPa, (implying an approximate Young's modulus of 5.75 kPa), which is consistent with previous ex-vivo measurements.

CONCLUSION

The combined imaging and computational simulation technique provides a unique approach to calculate the mechanical properties of the TM in vivo without any surgical intervention. Quantification of such mechanical properties will help us examine the mechanistic role of TM biomechanics in the regulation of IOP in healthy and glaucomatous eyes.

Design Requirements for Annulus Fibrosus Repair: Review of Forces, Displacements, and Material Properties of the Intervertebral Disk and a Summary of Candidate Hydrogels for Repair

There is currently a lack of clinically available solutions to restore functionality to the intervertebral disk (IVD) following herniation injury to the annulus fibrosus (AF). Microdiscectomy is a commonly performed surgical procedure to alleviate pain caused by herniation; however, AF defects remain and can lead to accelerated degeneration and painful conditions. Currently available AF closure techniques do not restore mechanical functionality or promote tissue regeneration, and have risk of reherniation. This review determined quantitative design requirements for AF repair materials and summarized currently available hydrogels capable of meeting these design requirements by using a series of systematic PubMed database searches to yield 1500+ papers that were screened and analyzed for relevance to human lumbar in vivo measurements, motion segment behaviors, and tissue level properties. We propose a testing paradigm involving screening tests as well as more involved in situ and in vivo validation tests to efficiently identify promising biomaterials for AF repair. We suggest that successful materials must have high adhesion strength (∼0.2 MPa), match as many AF material properties as possible (e.g., approximately 1 MPa, 0. 3 MPa, and 30 MPa for compressive, shear, and tensile moduli, respectively), and have high tensile failure strain (∼65%) to advance to in situ and in vivo validation tests. While many biomaterials exist for AF repair, few undergo extensive mechanical characterization. A few hydrogels show promise for AF repair since they can match at least one material property of the AF while also adhering to AF tissue and are capable of easy implantation during surgical procedures to warrant additional optimization and validation.

Planar biaxial extension of the lumbar facet capsular ligament reveals significant in-plane shear forces

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.

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

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.