Internal three-dimensional strains in human intervertebral discs under axial compression quantified noninvasively by magnetic resonance imaging and image registration

Age and gender differences in lumbar intervertebral disk strain using mechanical loading magnetic resonance imaging

The objective of the current study was to investigate age- and gender-related differences in lumbar intervertebral disk (IVD) strain with the use of static mechanical loading and continuous three-dimensional (3D) golden-angle radial sparse parallel (GRASP) MRI. A continuous 3D-GRASP stack-of-stars trajectory of the lumbar spine was performed on a 3-T scanner with static mechanical loading. Compressed sensing reconstruction, motion deformation maps, and Lagrangian strain maps during loading and recovery in the X-, Y-, and Z-directions were calculated for segmented IVD segments from L1/L2 to L5/S1. Mean IVD height was measured at rest. Spearman coefficients were used to evaluate the associations between age and global IVD height and global IVD strain. Mann-Whitney tests were used to compare global IVD height and global IVD strain in males and females. The prospective study enrolled 20 healthy human volunteers (10 males, 10 females; age 34.6 ± 11.4 [mean ± SD], range 22-56 years). Significant increases in compressive strain were observed with age, as evidenced by negative correlations between age and global IVD strain during loading (ρ = -0.76, p = 0.0046) and recovery (ρ = -0.68, p = 0.0251) in the loading X-direction. There was no significant correlation between age and global IVD height, global IVD strain during loading and recovery in the Y-direction, and global IVD strain during loading and recovery in the Z-direction. There were no significant differences between males and females in global IVD height and global IVD strain during loading and recovery in the X-, Y-, and Z-directions. It was concluded that our study demonstrated the significant role aging plays in internal dynamic strains in the lumbar IVD during loading and recovery. Older healthy individuals have reduced IVD stiffness and greater IVD compression during static mechanical loading of the lumbar spine. The GRASP-MRI technique demonstrates the feasibility to identify changes in IVD mechanical properties with early IVD degeneration due to aging.

Quantifying internal intervertebral disc strains to assess nucleus replacement device designs: a digital volume correlation and ultra-high-resolution MRI study

Introduction: Nucleus replacement has been proposed as a treatment to restore biomechanics and relieve pain in degenerate intervertebral discs (IVDs). Multiple nucleus replacement devices (NRDs) have been developed, however, none are currently used routinely in clinic. A better understanding of the interactions between NRDs and surrounding tissues may provide insight into the causes of implant failure and provide target properties for future NRD designs. The aim of this study was to non-invasively quantify 3D strains within the IVD through three stages of nucleus replacement surgery: intact, post-nuclectomy, and post-treatment. Methods: Digital volume correlation (DVC) combined with 9.4T MRI was used to measure strains in seven human cadaveric specimens (42 ± 18 years) when axially compressed to 1 kN. Nucleus material was removed from each specimen creating a cavity that was filled with a hydrogel-based NRD. Results: Nucleus removal led to loss of disc height (12.6 ± 4.4%, p = 0.004) which was restored post-treatment (within 5.3 ± 3.1% of the intact state, p > 0.05). Nuclectomy led to increased circumferential strains in the lateral annulus region compared to the intact state (-4.0 ± 3.4% vs. 1.7 ± 6.0%, p = 0.013), and increased maximum shear strains in the posterior annulus region (14.6 ± 1.7% vs. 19.4 ± 2.6%, p = 0.021). In both cases, the NRD was able to restore these strain values to their intact levels (p ≥ 0.192). Discussion: The ability of the NRD to restore IVD biomechanics and some strain types to intact state levels supports nucleus replacement surgery as a viable treatment option. The DVC-MRI method used in the present study could serve as a useful tool to assess future NRD designs to help improve performance in future clinical trials.

Intervertebral Disc Elastography to Relate Shear Modulus and Relaxometry in Compression and Bending

Intervertebral disc degeneration is the most recognized cause of low back pain, characterized by the decline of tissue structure and mechanics. Image-based mechanical parameters (e.g., strain, stiffness) may provide an ideal assessment of disc function that is lost with degeneration but unfortunately remains underdeveloped. Moreover, it is unknown whether strain or stiffness of the disc may be predicted by MRI relaxometry (e.g. T1 or T2), an increasingly accepted quantitative measure of disc structure. In this study, we quantified T1 and T2 relaxation times and in-plane strains using displacement-encoded MRI within the disc under physiological levels of compression and bending. We then estimated shear modulus in orthogonal image planes and compared these values to relaxation times and strains within regions of the disc. Intratissue strain depended on the loading mode, and shear modulus in the nucleus pulposus was typically an order of magnitude lower than the annulus fibrosis, except in bending, where the apparent stiffness depended on the loading. Relative shear moduli estimated from strain data derived under compression generally did not correspond with those from bending experiments, with no correlations in the sagittal plane and only 4 of 15 regions correlated in the coronal plane, suggesting that future inverse models should incorporate multiple loading conditions. Strain imaging and strain-based estimation of material properties may serve as imaging biomarkers to distinguish healthy and diseased discs. Additionally, image-based elastography and relaxometry may be viewed as complementary measures of disc structure and function to assess degeneration in longitudinal studies.

A swelling-based biphasic analysis on the quasi-static biomechanical behaviors of healthy and degenerative intervertebral discs

BACKGROUND AND OBJECTIVE

The degeneration of intervertebral discs is significantly dependent of the changes in tissue composition ratio and tissue structure. Up to the present, the effects of degeneration on the quasi-static biomechanical responses of discs have not been well understood. The goal of this study is to quantitatively analyze the quasi-static responses of healthy and degenerative discs.

METHODS

Four biphasic swelling-based finite element models are developed and quantitatively validated. Four quasi-static test protocols, including the free-swelling, slow-ramp, creep and stress-relaxation, are implemented. The double Voigt and double Maxwell models are further used to extract the immediate (or residual), short-term and long-term responses of these tests.

RESULTS

Simulation results show that both the swelling-induced pressure in the nucleus pulposus and the initial modulus decrease with degeneration. In the free-swelling test of discs possessing healthy cartilage endplates, simulation results show that over 80% of the total strain is contributed by the short-term response. The long-term response is dominant for discs with degenerated permeability in cartilage endplates. For the creep test, over 50% of the deformation is contributed by the long-term response. In the stress-relaxation test, the long-term stress contribution occupies approximately 31% of total response and is independent of degeneration. Both the residual and short-term responses vary monotonically with degeneration. In addition, both the glycosaminoglycan content and permeability affect the engineering equilibrium time constants of the rheologic models, in which the determining factor is the permeability.

CONCLUSIONS

The content of glycosaminoglycan in intervertebral soft tissues and the permeability of cartilage endplates are two critical factors that affect the fluid-dependent viscoelastic responses of intervertebral discs. The component proportions of the fluid-dependent viscoelastic responses depend also strongly on test protocols. In the slow-ramp test, the glycosaminoglycan content is responsible for the changes of the initial modulus. Since existing computational models simulate disc degenerations only by altering disc height, boundary conditions and material stiffness, the current work highlights the significance of biochemical composition and cartilage endplates permeability in the biomechanical behaviors of degenerated discs.

A novel tool to quantify in vivo lumbar spine kinematics and 3D intervertebral disc strains using clinical MRI

Medical imaging modalities that calculate tissue morphology alone cannot provide direct information regarding the mechanical behaviour of load-bearing musculoskeletal organs. Accurate in vivo measurement of spine kinematics and intervertebral disc (IVD) strains can provide important information regarding the mechanical behaviour of the spine, help to investigate the effects of injuries on the mechanics of the spine, and assess the effectiveness of treatments. Additionally, strains can serve as a functional biomechanical marker for detecting normal and pathologic tissues. We hypothesised that combining digital volume correlation (DVC) with 3T clinical MRI can provide direct information regarding the mechanics of the spine. Here, we have developed a novel non-invasive tool for in vivo displacement and strain measurement within the human lumbar spine and we used this tool to calculate lumbar kinematics and IVD strains in six healthy subjects during lumbar extension. The proposed tool enabled spine kinematics and IVD strains to be measured with errors that did not exceed 0.17 mm and 0.5%, respectively. The findings of the kinematics study identified that during extension the lumbar spine of healthy subjects experiences total 3D translations ranging from 1 mm to 4.5 mm for different vertebral levels. The findings of strain analysis identified that the average of the maximum tensile, compressive, and shear strains for different lumbar levels during extension ranged from 3.5% to 7.2%. This tool can provide base-line data that can be used to describe the mechanical environment of healthy lumbar spine, which can help clinicians manage preventative treatments, define patient-specific treatments, and to monitor the effectiveness of surgical and non-surgical interventions.

MRI ‐based measurement of in vivo disc mechanics in a young population due to flexion, extension, and diurnal loading

Background

Intervertebral disc degeneration is often implicated in low back pain; however, discs with structural degeneration often do not cause pain. It may be that disc mechanics can provide better diagnosis and identification of the pain source. In cadaveric testing, the degenerated disc has altered mechanics, but in vivo, disc mechanics remain unknown. To measure in vivo disc mechanics, noninvasive methods must be developed to apply and measure physiological deformations.

Aim

Thus, this study aimed to develop methods to measure disc mechanical function via noninvasive MRI during flexion and extension and after diurnal loading in a young population. This data will serve as baseline disc mechanics to later compare across ages and in patients.

Materials & Methods

To accomplish this, subjects were imaged in the morning in a reference supine position, in flexion, in extension, and at the end of the day in a supine position. Disc deformations and vertebral motions were used to quantify disc axial strain, changes in wedge angle, and anterior-posterior (A-P) shear displacement. T₂ weighted MRI was also used to evaluate disc degeneration via Pfirrmann grading and T₂ time. All measures were then tested for effect of sex and disc level.

Results

We found that flexion and extension caused level-dependent strains in the anterior and posterior of the disc, changes in wedge angle, and A-P shear displacements. Flexion had higher magnitude changes overall. Diurnal loading did not cause level-dependent strains but did cause small level-dependent changes in wedge angle and A-P shear displacements.

Discussion

Correlations between disc degeneration and mechanics were largest in flexion, likely due to the smaller contribution of the facet joints in this condition.

Conclusion

In summary, this study established methods to measure in vivo disc mechanical function via noninvasive MRI and established a baseline in a young population that may be compared to older subjects and clinical disorders in the future.

Regional variations in discrete collagen fibre mechanics within intact intervertebral disc resolved using synchrotron computed tomography and digital volume correlation

Many soft tissues, such as the intervertebral disc (IVD), have a hierarchical fibrous composite structure which suffers from regional damage. We hypothesise that these tissue regions have distinct, inherent fibre structure and structural response upon loading. Here we used synchrotron computed tomography (sCT) to resolve collagen fibre bundles (∼5μm width) in 3D throughout an intact native rat lumbar IVD under increasing compressive load. Using intact samples meant that tissue boundaries (such as endplate-disc or nucleus-annulus) and residual strain were preserved; this is vital for characterising both the inherent structure and structural changes upon loading in tissue regions functioning in a near-native environment. Nano-scale displacement measurements along >10,000 individual fibres were tracked, and fibre orientation, curvature and strain changes were compared between the posterior-lateral region and the anterior region. These methods can be widely applied to other soft tissues, to identify fibre structures which cause tissue regions to be more susceptible to injury and degeneration. Our results demonstrate for the first time that highly-localised changes in fibre orientation, curvature and strain indicate differences in regional strain transfer and mechanical function (e.g. tissue compliance). This included decreased fibre reorientation at higher loads, specific tissue morphology which reduced capacity for flexibility and high strain at the disc-endplate boundary.

Statement of significance

The analyses presented here are applicable to many collagenous soft tissues which suffer from regional damage. We aimed to investigate regional intervertebral disc (IVD) structural and functional differences by characterising collagen fibre architecture and linking specific fibre- and tissue-level deformation behaviours. Synchrotron CT provided the first demonstration of tracking discrete fibres in 3D within an intact IVD. Detailed analysis of regions was performed using over 200k points, spaced every 8 μm along 10k individual fibres. Such comprehensive structural characterisation is significant in informing future computational models. Morphological indicators of tissue compliance (change in fibre curvature and orientation) and fibre strain measurements revealed localised and regional differences in tissue behaviour.

Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.

Measurement of Three-Dimensional Internal Dynamic Strains in the Intervertebral Disc of the Lumbar Spine With Mechanical Loading and Golden-Angle Radial Sparse Parallel-Magnetic Resonance Imaging

BACKGROUND

Noninvasive measurement of internal dynamic strain can be potentially useful to characterize spine intervertebral disc (IVD) in the setting of injury or degenerative disease.

PURPOSE

To develop and demonstrate a noninvasive technique to quantify three-dimensional (3D) internal dynamic strains in the IVD using a combination of static mechanical loading of the IVD using a magnetic resonance imaging (MRI)-compatible ergometer.

STUDY TYPE

Prospective.

SUBJECTS

Silicone gel phantom studies were conducted to assess strain variation with load and repeatability. Mechanical testing was done on the phantoms to confirm MR results. Eight healthy human volunteers (four men and four woman, age = 29 ± 5 years) underwent MRI using a rest, static loading, and recovery paradigm. Repeatability tests were conducted in three subjects.

FIELD STRENGTH/SEQUENCE

MRI (3 T) with 3D continuous golden-angle radial sparse parallel (GRASP) and compressed sensing (CS) reconstruction.

ASSESSMENT

CS reconstruction of the images, motion deformation, and Lagrangian strain maps were calculated for five IVD segments from L1/L2 to L5/S1.

STATISTICAL TESTS

Ranges of displacement and strain in each subject and the resulting mean and standard deviation were calculated. Student t-tests were used to calculate changes in strain from loading to recovery. The correlation coefficient (CC) in the repeatability study was calculated.

RESULTS

The most compressive strain experienced by the IVD segments under loaded conditions was in the L4/L5 segment (-7.5 ± 2.9%). The change in minimum strain from load to recovery was the most for the L4/L5 segment (-7.5% to -5.0%, P = 0.026) and the least for the L1/L2 segment (-4.4% to -3.9%, P = 0.51). In vivo repeatability in three subjects shows strong correlation between scans in subjects done 6 months apart, with CCs equal to 0.86, 0.94, and 0.94 along principal directions.

DATA CONCLUSION

This study shows the feasibility of using static mechanical loading with continuous GRASP-MRI acquisition with CS reconstruction to measure 3D internal dynamic strains in the spine IVD.

LEVEL OF EVIDENCE

2 TECHNICAL EFFICACY STAGE: 1.

The Effect of Degeneration on Internal Strains and the Mechanism of Failure in Human Intervertebral Discs Analyzed Using Digital Volume Correlation (DVC) and Ultra-High Field MRI

The intervertebral disc (IVD) plays a main role in absorbing and transmitting loads within the spinal column. Degeneration alters the structural integrity of the IVDs and causes pain, especially in the lumbar region. The objective of this study was to investigate non-invasively the effect of degeneration on human 3D lumbar IVD strains (n = 8) and the mechanism of spinal failure (n = 10) under pure axial compression using digital volume correlation (DVC) and 9.4 Tesla magnetic resonance imaging (MRI). Degenerate IVDs had higher (p < 0.05) axial strains (58% higher), maximum 3D compressive strains (43% higher), and maximum 3D shear strains (41% higher), in comparison to the non-degenerate IVDs, particularly in the lateral and posterior annulus. In both degenerate and non-degenerate IVDs, peak tensile and shear strains were observed close to the endplates. Inward bulging of the inner annulus was observed in all degenerate IVDs causing an increase in the AF compressive, tensile, and shear strains at the site of inward bulge, which may predispose it to circumferential tears (delamination). The endplate is the spine's “weak link” in pure axial compression, and the mechanism of human vertebral fracture is associated with disc degeneration. In non-degenerate IVDs the locations of failure were close to the endplate centroid, whereas in degenerate IVDs they were in peripheral regions. These findings advance the state of knowledge on mechanical changes during degeneration of the IVD, which help reduce the risk of injury, optimize treatments, and improve spinal implant designs. Additionally, these new data can be used to validate computational models.

Quantifying deformations and strains in human intervertebral discs using Digital Volume Correlation combined with MRI (DVC-MRI)

Physical disruptions to intervertebral discs (IVDs) can cause mechanical changes that lead to degeneration and to low back pain which affects 75% of us in our lifetimes. Quantifying the effects of these changes on internal IVD strains may lead to better preventative strategies and treatments. Digital Volume Correlation (DVC) is a non-invasive technique that divides volumetric images into subsets, and measures strains by tracking the internal patterns within them under load. Applying DVC to MRIs may allow non-invasive strain measurements. However, DVC-MRI for strain measurements in IVDs has not been used previously. The purpose of this study was to quantify the strain and deformation errors associated with DVC-MRI for measurements in human IVDs. Eight human lumbar IVDs were MRI scanned (9.4 T) for a 'zero-strain study' (multiple unloaded scans to quantify noise within the system), and a loaded study (2 mm axial compression). Three DVC methodologies: Fast-Fourier transform (FFT), direct correlation (DC), and a combination of both FFT and DC approaches were compared with subset sizes ranging from 8 to 88 voxels to establish the optimal DVC methodology and settings which were then used in the loaded study. FFT + DC was the optimal method and a subset size of 56 voxels (2520 µm) was found to be a good compromise between errors and spatial resolution. Displacement and strain errors did not exceed 28 µm and 3000 microstrain, respectively. These findings demonstrate that DVC-MRI can quantify internal strains within IVDs non-invasively and accurately. The method has unique potential for assessing IVD strains within patients.

Human Disc Nucleotomy Alters Annulus Fibrosus Mechanics at Both Reference and Compressed Loads

Nucleotomy is a common surgical procedure and is also performed in ex vivo mechanical testing to model decreased nucleus pulposus (NP) pressurization that occurs with degeneration. Here, we implement novel and noninvasive methods using magnetic resonance imaging (MRI) to study internal 3D annulus fibrosus (AF) deformations after partial nucleotomy and during axial compression by evaluating changes in internal AF deformation at reference loads (50 N) and physiological compressive loads (∼10% strain). One particular advantage of this methodology is that the full 3D disc deformation state, inclusive of both in-plane and out-of-plane deformations, can be quantified through the use of a high-resolution volumetric MR scan sequence and advanced image registration. Intact grade II L3-L4 cadaveric human discs before and after nucleotomy were subjected to identical mechanical testing and imaging protocols. Internal disc deformation fields were calculated by registering MR images captured in each loading state (reference and compressed) and each condition (intact and nucleotomy). Comparisons were drawn between the resulting three deformation states (intact at compressed load, nucleotomy at reference load, nucleotomy at compressed load) with regard to the magnitude of internal strain and direction of internal displacements. Under compressed load, internal AF axial strains averaged -18.5% when intact and -22.5% after nucleotomy. Deformation orientations were significantly altered by nucleotomy and load magnitude. For example, deformations of intact discs oriented in-plane, whereas deformations after nucleotomy oriented axially. For intact discs, in-plane components of displacements under compressive loads oriented radially outward and circumferentially. After nucleotomy, in-plane displacements were oriented radially inward under reference load and were not significantly different from the intact state at compressed loads. Re-establishment of outward displacements after nucleotomy indicates increased axial loading restores the characteristics of internal pressurization. Results may have implications for the recurrence of pain, design of novel therapeutics, or progression of disc degeneration.

New Findings Confirm Regional Internal Disc Strain Changes During Simulation of Repetitive Lifting Motions

To understand the mechanisms of disc injuries that result from repetitive loading, it is important to measure disc deformations and use MRI to quantify disc damage. The aim of this study was to measure internal disc strains during simulated repetitive lifting and their relation to disc injury. Eight cadaveric lumbar segments underwent a pre-test MRI and 20,000 cycles of loading under combined compression (1.0 MPa), hyperflexion, and right axial rotation (2°), which simulated bending and twisting while lifting a 20 kg box. The remaining eight segments had a grid of tantalum wires inserted and used stereoradiography to calculate maximum shear strain (MSS) at increasing cycles. Post-test MRI revealed that 73% of specimens were injured after repetitive loading (annular protrusion, endplate failure, or lumbar disc herniation). MSS at cycle 20,000 was significantly larger than all earlier cycles (p < 0.003). MSS in the anterior, left posterolateral, and left lateral regions was significantly greater than the nucleus region (p < 0.006). Large strains, annular protrusion and herniation in the posterolateral regions were found in this study, which is consistent with clinical observations. In vitro strains can be used to develop more-robust computational models for understanding of the specimen-specific effects of repetitive lifting on disc tissue.

Relative Nucleus Pulposus Area and Position Alters Disc Joint Mechanics

Aging and degeneration of the intervertebral disc are noted by changes in tissue composition and geometry, including a decrease in nucleus pulposus (NP) area. The NP centroid is positioned slightly posterior of the disc's centroid, but the effect of NP size and location on disc joint mechanics is not well understood. We evaluated the effect of NP size and centroid location on disc joint mechanics under dual-loading modalities (i.e., compression in combination with axial rotation or bending). A finite element model was developed to vary the relative NP area (NP:Disc area ratio range = 0.21 - 0.60). We also evaluated the effect of NP position by shifting the NP centroid anteriorly and posteriorly. Our results showed that compressive stiffness and average first principal strains increased with NP size. Under axial compression, stresses are distributed from the NP to the annulus, and stresses were redistributed towards the NP with axial rotation. Moreover, peak stresses were greater for discs with a smaller NP area. NP centroid location had a greater impact on intradiscal pressure during flexion and extension, where peak pressures in the posterior annulus under extension was greater for discs with a more posteriorly situated NP. In conclusion, the findings from this study highlight the importance of closely mimicking NP size and location in computational models that aim to understand stress/strain distribution during complex loading and for developing repair strategies that aim to recapitulate the mechanical behavior of healthy discs.

Viscoelastic heating of insulated bovine intervertebral disc

Back pain is the leading cause of disability globally and the second most common cause of doctors' visits. Despite extensive research efforts, the underlying mechanism of back pain has not been fully elucidated. The intervertebral disc (IVD) is a viscoelastic tissue that provides flexibility to the spinal column and acts as a shock absorber in the spine. When viscoelastic materials like the IVD are cyclically loaded, they dissipate energy as heat. Thus, diurnal, regular movements of the vertebral column that deform the IVD could increase disc temperature through viscoelastic heating. This temperature rise has the potential to influence cell function, drive cell death and induce nociception in innervating nociceptive neurons within the IVD. The present study was conducted to investigate the capacity of IVD to increase in temperature due to viscoelastic heating. Insulated caudal bovine IVD were subjected to physiological cyclic uniaxial compression over a range of frequencies (0.1-15 Hz) and loading durations (1-10 min) ex vivo, and the temperature rise in the tissue was recorded. According to our findings, the IVD can experience a temperature rise of up to 2.5°C under cyclic loading. Furthermore, under similar conditions, the inner nucleus pulposus exhibits more viscoelastic heating than the outer annulus fibrosis, likely due to its more viscous composition. The measured temperature rise of the disc has physiological relevance as degenerative IVD tissue has been shown to produce a sensitization of nociceptive neurons that spontaneously fire at 37°C, with a T50 response at 37.3°C and a maximum response at 38°C. Our results suggest that viscoelastic heating of IVD could interact with sensitized nociceptive neurons in the degenerative IVD to play a role in back pain.

Automated Bone Segmentation and Surface Evaluation of a Small Animal Model of Post-Traumatic Osteoarthritis

MicroCT imaging allows for noninvasive microstructural evaluation of mineralized bone tissue, and is essential in studies of small animal models of bone and joint diseases. Automatic segmentation and evaluation of articular surfaces is challenging. Here, we present a novel method to create knee joint surface models, for the evaluation of PTOA-related joint changes in the rat using an atlas-based diffeomorphic registration to automatically isolate bone from surrounding tissues. As validation, two independent raters manually segment datasets and the resulting segmentations were compared to our novel automatic segmentation process. Data were evaluated using label map volumes, overlap metrics, Euclidean distance mapping, and a time trial. Intraclass correlation coefficients were calculated to compare methods, and were greater than 0.90. Total overlap, union overlap, and mean overlap were calculated to compare the automatic and manual methods and ranged from 0.85 to 0.99. A Euclidean distance comparison was also performed and showed no measurable difference between manual and automatic segmentations. Furthermore, our new method was 18 times faster than manual segmentation. Overall, this study describes a reliable, accurate, and automatic segmentation method for mineralized knee structures from microCT images, and will allow for efficient assessment of bony changes in small animal models of PTOA.

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.

MRI quantification of human spine cartilage endplate geometry: Comparison with age, degeneration, level, and disc geometry

Geometry is an important indicator of disc mechanical function and degeneration. While the geometry and associated degenerative changes in the nucleus pulposus and the annulus fibrosus are well-defined, the geometry of the cartilage endplate (CEP) and its relationship to disc degeneration are unknown. The objectives of this study were to quantify CEP geometry in three dimensions using an MRI FLASH imaging sequence and evaluate relationships between CEP geometry and age, degeneration, spinal level, and overall disc geometry. To do so, we assessed the MRI-based measurements for accuracy and repeatability. Next, we measured CEP geometry across a larger sample set and correlated CEP geometric parameters to age, disc degeneration, level, and disc geometry. The MRI-based measures resulted in thicknesses (0.3-1 mm) that are comparable to prior measurements of CEP thickness. CEP thickness was greatest at the anterior/posterior (A/P) margins and smallest in the center. The CEP A/P thickness, axial area, and lateral width decreased with age but were not related to disc degeneration. Age-related, but not degeneration-related, changes in geometry suggest that the CEP may not follow the progression of disc degeneration. Ultimately, if the CEP undergoes significant geometric changes with aging and if these can be related to low back pain, a clinically feasible translation of the FLASH MRI-based measurement of CEP geometry presented in this study may prove a useful diagnostic tool. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1410-1417, 2016.

Novel human intervertebral disc strain template to quantify regional three-dimensional strains in a population and compare to internal strains predicted by a finite element model

Tissue strain is an important indicator of mechanical function, but is difficult to noninvasively measure in the intervertebral disc. The objective of this study was to generate a disc strain template, a 3D average of disc strain, of a group of human L4-L5 discs loaded in axial compression. To do so, magnetic resonance images of uncompressed discs were used to create an average disc shape. Next, the strain tensors were calculated pixel-wise by using a previously developed registration algorithm. Individual disc strain tensor components were then transformed to the template space and averaged to create the disc strain template. The strain template reduced individual variability while highlighting group trends. For example, higher axial and circumferential strains were present in the lateral and posterolateral regions of the disc, which may lead to annular tears. This quantification of group-level trends in local 3D strain is a significant step forward in the study of disc biomechanics. These trends were compared to a finite element model that had been previously validated against the disc-level mechanical response. Depending on the strain component, 81-99% of the regions within the finite element model had calculated strains within one standard deviation of the template strain results. The template creation technique provides a new measurement technique useful for a wide range of studies, including more complex loading conditions, the effect of disc pathologies and degeneration, damage mechanisms, and design and evaluation of treatments. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1264-1273, 2016.

Theory of MRI contrast in the annulus fibrosus of the intervertebral disc

OBJECTIVE

Here we develop a three-dimensional analytic model for MR image contrast of collagen lamellae in the annulus fibrosus of the intervertebral disc of the spine, based on the dependence of the MRI signal on collagen fiber orientation.

MATERIALS AND METHODS

High-resolution MRI scans were performed at 1.5 and 7 T on intact whole disc specimens from ovine, bovine, and human spines. An analytic model that approximates the three-dimensional curvature of the disc lamellae was developed to explain inter-lamellar contrast and intensity variations in the annulus. The model is based on the known anisotropic dipolar relaxation of water in tissues with ordered collagen.

RESULTS

Simulated MRI data were generated that reproduced many features of the actual MRI data. The calculated inter-lamellar image contrast demonstrated a strong dependence on the collagen fiber angle and on the circumferential location within the annulus.

CONCLUSION

This analytic model may be useful for interpreting MR images of the disc and for predicting experimental conditions that will optimize MR image contrast in the annulus fibrosus.

A comparison of stress in cracked fibrous tissue specimens with varied crack location, loading, and orientation using finite element analysis

Cracks in fibrous soft tissue, such as intervertebral disc annulus fibrosus and knee meniscus, cause pain and compromise joint mechanics. A crack concentrates stress at its tip, making further failure and crack extension (fracture) more likely. Ex vivo mechanical testing is an important tool for studying the loading conditions required for crack extension, but prior work has shown that it is difficult to reproduce crack extension. Most prior work used edge crack specimens in uniaxial tension, with the crack 90° to the edge of the specimen. This configuration does not necessarily represent the loading conditions that cause in vivo crack extension. To find a potentially better choice for experiments aiming to reproduce crack extension, we used finite element analysis to compare, in factorial combination, (1) center crack vs. edge crack location, (2) biaxial vs. uniaxial loading, and (3) crack-fiber angles ranging from 0° to 90°. The simulated material was annulus fibrosus fibrocartilage with a single fiber family. We hypothesized that one of the simulated test cases would produce a stronger stress concentration than the commonly used uniaxially loaded 90° crack-fiber angle edge crack case. Stress concentrations were compared between cases in terms of fiber-parallel stress (representing risk of fiber rupture), fiber-perpendicular stress (representing risk of matrix rupture), and fiber shear stress (representing risk of fiber sliding). Fiber-perpendicular stress and fiber shear stress concentrations were greatest in edge crack specimens (of any crack-fiber angle) and center crack specimens with a 90° crack-fiber angle. However, unless the crack is parallel to the fiber direction, these stress components alone are insufficient to cause crack opening and extension. Fiber-parallel stress concentrations were greatest in center crack specimens with a 45° crack-fiber angle, either biaxially or uniaxially loaded. We therefore recommend that the 45° center crack case be tried in future experiments intended to study crack extension by fiber rupture.

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress-strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model's nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean ± 95% confidence interval) of the disc's nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc's full nonlinear response in multiple loading scenarios.