MRI-based technique for determining nonuniform deformations throughout the volume of articular cartilage explants

Nondestructive Techniques to Evaluate the Characteristics and Development of Engineered Cartilage

In this review, methods for evaluating the properties of tissue engineered (TE) cartilage are described. Many of these have been developed for evaluating properties of native and osteoarthritic articular cartilage. However, with the increasing interest in engineering cartilage, specialized methods are needed for nondestructive evaluation of tissue while it is developing and after it is implanted. Such methods are needed, in part, due to the large inter- and intra-donor variability in the performance of the cellular component of the tissue, which remains a barrier to delivering reliable TE cartilage for implantation. Using conventional destructive tests, such variability makes it near-impossible to predict the timing and outcome of the tissue engineering process at the level of a specific piece of engineered tissue and also makes it difficult to assess the impact of changing tissue engineering regimens. While it is clear that the true test of engineered cartilage is its performance after it is implanted, correlation of pre and post implantation properties determined non-destructively in vitro and/or in vivo with performance should lead to predictive methods to improve quality-control and to minimize the chances of implanting inferior tissue.

Application of Elastography for the Noninvasive Assessment of Biomechanics in Engineered Biomaterials and Tissues

The elastic properties of engineered biomaterials and tissues impact their post-implantation repair potential and structural integrity, and are critical to help regulate cell fate and gene expression. The measurement of properties (e.g., stiffness or shear modulus) can be attained using elastography, which exploits noninvasive imaging modalities to provide functional information of a material indicative of the regeneration state. In this review, we outline the current leading elastography methodologies available to characterize the properties of biomaterials and tissues suitable for repair and mechanobiology research. We describe methods utilizing magnetic resonance, ultrasound, and optical coherent elastography, highlighting their potential for longitudinal monitoring of implanted materials in vivo, in addition to spatiotemporal limits of each method for probing changes in cell-laden constructs. Micro-elastography methods now allow acquisitions at length scales approaching 5-100 μm in two and three dimensions. Many of the methods introduced in this review are therefore capable of longitudinal monitoring in biomaterials and tissues approaching the cellular scale. However, critical factors such as anisotropy, heterogeneity and viscoelasity-inherent in many soft tissues-are often not fully described and therefore require further advancements and future developments.

Ultrasound Elastography for Estimation of Regional Strain of Multilayered Hydrogels and Tissue-Engineered Cartilage

Tissue-engineered (TE) cartilage constructs tend to develop inhomogeneously, thus, to predict the mechanical performance of the tissue, conventional biomechanical testing, which yields average material properties, is of limited value. Rather, techniques for evaluating regional and depth-dependent properties of TE cartilage, preferably non-destructively, are required. The purpose of this study was to build upon our previous results and to investigate the feasibility of using ultrasound elastography to non-destructively assess the depth-dependent biomechanical characteristics of TE cartilage while in a sterile bioreactor. As a proof-of-concept, and to standardize an assessment protocol, a well-characterized three-layered hydrogel construct was used as a surrogate for TE cartilage, and was studied under controlled incremental compressions. The strain field of the construct predicted by elastography was then validated by comparison with a poroelastic finite-element analysis (FEA). On average, the differences between the strains predicted by elastography and the FEA were within 10%. Subsequently engineered cartilage tissue was evaluated in the same test fixture. Results from these examinations showed internal regions where the local strain was 1-2 orders of magnitude greater than that near the surface. These studies document the feasibility of using ultrasound to evaluate the mechanical behaviors of maturing TE constructs in a sterile environment.

Functional imaging in OA: role of imaging in the evaluation of tissue biomechanics

Functional imaging refers broadly to the visualization of organ or tissue physiology using medical image modalities. In load-bearing tissues of the body, including articular cartilage lining the bony ends of joints, changes in strain, stress, and material properties occur in osteoarthritis (OA), providing an opportunity to probe tissue function through the progression of the disease. Here, biomechanical measures in cartilage and related joint tissues are discussed as key imaging biomarkers in the evaluation of OA. Emphasis will be placed on the (1) potential of radiography, ultrasound, and magnetic resonance imaging to assess early tissue pathomechanics in OA, (2) relative utility of kinematic, structural, morphological, and biomechanical measures as functional imaging biomarkers, and (3) improved diagnostic specificity through the combination of multiple imaging biomarkers with unique contrasts, including elastography and quantitative assessments of tissue biochemistry. In comparison to other modalities, magnetic resonance imaging provides an extensive range of functional measures at the tissue level, with conventional and emerging techniques available to potentially to assess the spectrum of preclinical to advance OA.

Mechanical characterization of tissue-engineered cartilage using microscopic magnetic resonance elastography

Knowledge of mechanical properties of tissue-engineered cartilage is essential for the optimization of cartilage tissue engineering strategies. Microscopic magnetic resonance elastography (μMRE) is a recently developed MR-based technique that can nondestructively visualize shear wave motion. From the observed wave pattern in MR phase images the tissue mechanical properties (e.g., shear modulus or stiffness) can be extracted. For quantification of the dynamic shear properties of small and stiff tissue-engineered cartilage, μMRE needs to be performed at frequencies in the kilohertz range. However, at frequencies greater than 1 kHz shear waves are rapidly attenuated in soft tissues. In this study μMRE, with geometric focusing, was used to overcome the rapid wave attenuation at high frequencies, enabling the measurement of the shear modulus of tissue-engineered cartilage. This methodology was first tested at a frequency of 5 kHz using a model system composed of alginate beads embedded in agarose, and then applied to evaluate extracellular matrix development in a chondrocyte pellet over a 3-week culture period. The shear stiffness in the pellet was found to increase over time (from 6.4 to 16.4 kPa), and the increase was correlated with both the proteoglycan content and the collagen content of the chondrocyte pellets (R(2)=0.776 and 0.724, respectively). Our study demonstrates that μMRE when performed with geometric focusing can be used to calculate and map the shear properties within tissue-engineered cartilage during its development.

Direct noninvasive measurement and numerical modeling of depth-dependent strains in layered agarose constructs

Biomechanical factors play an important role in the growth, regulation, and maintenance of engineered biomaterials and tissues. While physical factors (e.g. applied mechanical strain) can accelerate regeneration, and knowledge of tissue properties often guide the design of custom materials with tailored functionality, the distribution of mechanical quantities (e.g. strain) throughout native and repair tissues is largely unknown. Here, we directly quantify distributions of strain using noninvasive magnetic resonance imaging (MRI) throughout layered agarose constructs, a model system for articular cartilage regeneration. Bulk mechanical testing, giving both instantaneous and equilibrium moduli, was incapable of differentiating between the layered constructs with defined amounts of 2% and 4% agarose. In contrast, MRI revealed complex distributions of strain, with strain transfer to softer (2%) agarose regions, resulting in amplified magnitudes. Comparative studies using finite element simulations and mixture (biphasic) theory confirmed strain distributions in the layered agarose. The results indicate that strain transfer to soft regions is possible in vivo as the biomaterial and tissue changes during regeneration and maturity. It is also possible to modulate locally the strain field that is applied to construct-embedded cells (e.g. chondrocytes) using stratified agarose constructs.

Probing articular cartilage damage and disease by quantitative magnetic resonance imaging

Osteoarthritis (OA) is a debilitating disease that reflects a complex interplay of biochemical, biomechanical, metabolic and genetic factors, which are often triggered by injury, and mediated by inflammation, catabolic cytokines and enzymes. An unmet clinical need is the lack of reliable methods that are able to probe the pathogenesis of early OA when disease-rectifying therapies may be most effective. Non-invasive quantitative magnetic resonance imaging (qMRI) techniques have shown potential for characterizing the structural, biochemical and mechanical changes that occur with cartilage degeneration. In this paper, we review the background in articular cartilage and OA as it pertains to conventional MRI and qMRI techniques. We then discuss how conventional MRI and qMRI techniques are used in clinical and research environments to evaluate biochemical and mechanical changes associated with degeneration. Some qMRI techniques allow for the use of relaxometry values as indirect biomarkers for cartilage components. Direct characterization of mechanical behaviour of cartilage is possible via other specialized qMRI techniques. The combination of these qMRI techniques has the potential to fully characterize the biochemical and biomechanical states that represent the initial changes associated with cartilage degeneration. Additionally, knowledge of in vivo cartilage biochemistry and mechanical behaviour in healthy subjects and across a spectrum of osteoarthritic patients could lead to improvements in the detection, management and treatment of OA.

A three-dimensional finite element analysis of finger joint stresses in the MCP joint while performing common tasks

The goal of this study was to develop a three-dimensional finite element model of the metacarpophalangeal (MCP) joint to characterize joint contact stresses incurred during common daily activities. The metacarpal and proximal phalanx were modeled using a COMSOL-based finite element analysis. Muscle forces determined from a static force analysis of two common activities (pen grip and carrying a weight) were applied to the simulation to characterize the surface stress distributions at the MCP joint. The finite element analysis predicted that stresses as high as 1.9 MPa, similar in magnitude to stresses experienced at the hip, may be experienced by the subchondral bone in the MCP joint. The internal structure and material properties of the phalanges were found to play a significant role in both the magnitude and distribution of stresses, but the dependence on cancellous bone modulus was not as severe as predicted by previous two dimensional models.

The acute effect of running on knee articular cartilage and meniscus magnetic resonance relaxation times in young healthy adults

BACKGROUND

Understanding the acute response of healthy knee cartilage to running may provide valuable insight into functional properties. In recent years, quantitative magnetic resonance (MR) imaging techniques (T1(ρ) and T2 relaxation measurement) have shown tremendous potential and unique ability to noninvasively and quantitatively determine cartilage response to physiologic levels of loading occurring with physiologic levels of exercise.

PURPOSE

To measure the short-term changes in MR T1(ρ) and T2 relaxation times of knee articular cartilage and meniscus in healthy individuals immediately after 30 minutes of running.

STUDY DESIGN

Descriptive laboratory study.

METHODS

Twenty young healthy volunteers, aged 22 to 35 years, underwent 3T MR imaging of the knee before and immediately after 30 minutes of running. Quantitative assessment of the cartilage and menisci was performed using MR images with a T1(ρ) and T2 mapping technique. After adjusting for age, sex, and body mass index, repeated-measures analysis of variance was used to determine the effects of running on MR relaxation times.

RESULTS

The post-run T1(ρ) and T2 measurement showed significant reduction in all regions of cartilage except the lateral tibia when compared with the pre-run condition. The medial tibiofemoral (T1(ρ): 9.4%, P < .0001; T2: 5.4%, P = .0049) and patellofemoral (T1(ρ): 12.5%, P < .0001; T2: 5.7%, P = .0007) compartments experienced the greatest reduction after running. The superficial layer of the articular cartilage showed significantly higher change in relaxation times than the deep layer (T1(ρ): 9.6% vs 8.2%, P = .050; T2: 6.0% vs 3.5%, P = .069). The anterior and posterior horns of the medial meniscus (9.7%, P = .016 and 11.4%, P = .001) were the only meniscal subregions with significant changes in T1(ρ) after running.

CONCLUSION

Shorter T1(ρ) and T2 values after running suggest alteration in the water content and collagen fiber orientation of the articular cartilage. Greater changes in relaxation times of the medial compartment and patellofemoral joint cartilage indicate greater load sharing by these areas during running.

Association of MR relaxation and cartilage deformation in knee osteoarthritis

We assessed the relationship between cartilage MR relaxation times and biomechanical response of tibiofemoral articular cartilage to physiological loading in healthy subjects and patients with osteoarthritis (OA). Female subjects above 40 years of age with (N(1)  = 20) and without (N(2)  = 10) OA were imaged on a 3T MR scanner using a custom made loading device. MR images were acquired with the knee flexed at 20° with and without a compressive load of 50% of the subject's bodyweight. The subjects were categorized based on the clinical MRI scoring of medial and lateral cartilage surfaces. Data were stratified twice into two equal groups (low and high) at the median value of T(1ρ) and T(2) relaxation time. The change in contact area and cartilage deformation was measured within these groups. Paired Student's t-test (α = 0.05) was used to analyze the effect of loading on contact area and deformation. The average area of the contact region in the medial compartment was significantly higher in OA subjects compared with normal subjects in both unloaded (314 ± 112 mm(2) vs. 227 ± 106 mm(2), p = 0.023) and loaded (425 ± 128 mm(2) vs. 316 ± 107 mm(2), p = 0.01) conditions. The overall relative change of cartilage thickness in the medial compartment was significantly higher than the lateral compartment (-5.3 ± 9.9% vs. -1.9 ± 9.2%, p = 0.042). When cartilage was divided into deep and superficial layers, superficial layers showed higher changes in relaxation time (T(1ρ) and T(2)) than the changes in relaxation time of whole cartilage (Normal: 12.5% vs. 6.9%; OA: 10.9% vs. 4.6%). The average T(1ρ) and T(2) times, change in area of contact region, and change in cartilage thickness in subjects with OA were higher when compared to normal subjects. This study provides support for a relationship between the mechanical response of cartilage to physiological loading (cartilage-on-cartilage contact area and cartilage deformation) and MR relaxation times (T(1ρ) and T(2)) in both OA patients and normal subjects.

Noninvasive high resolution mechanical strain maps of the spine intervertebral disc using nonrigid registration of magnetic resonance images

High resolution strain measurements are of particular interest in load bearing tissues such as the intervertebral disc (IVD), permitting characterization of biomechanical conditions which could lead to injury and degenerative outcomes. Magnetic resonance (MR) imaging produces excellent image contrast in cartilaginous tissues, allowing for image-based strain determination. Nonrigid registration (NRR) of MR images has previously demonstrated sub-voxel registration accuracy although its accuracy and precision in determining strain has not been evaluated. Accuracy and precision of NRR-derived strain measurements were evaluated using computer generated deformations applied to both computer generated images and MR images. Two different measures of registration similarity--the cost function which drives the registration algorithm--were compared: Mutual Information (MI) and Least Squares (LS). Strain error was evaluated with respect to signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and strain heterogeneity. Additionally, the creep strain response from an in vitro loaded porcine IVD is shown and comparisons between similarity measures are presented. MI showed a decrease in strain precision with increasing CNR and decreasing SNR while LS was insensitive to both. Both similarity measures showed a decrease in strain precision with increasing strain heterogeneity. When computer generated heterogeneous strains were applied to MR images of the IVD, LS showed substantially lower strain error in comparison to MI. Results suggest that LS-driven NRR provides a more accurate image-based method for mapping large and heterogeneous strain fields and this method can be applied to studies of the IVD and, potentially, other soft tissues which present sufficient image texture.

Displacement smoothing for the precise MRI-based measurement of strain in soft biological tissues

Displacement and strain are fundamental quantities that describe the normal and pathological mechanical function of soft biological materials. Non-invasive imaging techniques, including displacement-encoded magnetic resonance imaging (MRI), enable the direct calculation of biomaterial displacements during the application of extrinsic mechanical forces. However, because strain is derived from measured MRI-based displacements, data processing must be accomplished to minimise the propagation and amplification of errors. Here, we evaluate smoothing methods (including averaging filters, splines, finite impulse response filters and wavelets) that enable the calculation of strain in biomaterials from MRI-based displacements for minimal error, defined in terms of bias and precision. Displacement and strain precisions were improved using all smoothing methods studied. Precision generally increased with the number of smoothing iterations (i.e. repeated applications) of a chosen smoothing method. The bias depended on the smoothing method and tended to increase with the number of smoothing iterations. A Gaussian filter characterised complex and heterogeneous strain fields with maximum precision and minimum bias. The results suggest that the optimal choice of smoothing method to compute strain for a given biomaterial or tissue application depends on a careful consideration of trade-offs between the improved precision (with increased data smoothing) and the trending increase in bias.

Elastography: modality-specific approaches, clinical applications, and research horizons

Manual palpation has been used for centuries to provide a relative indication of tissue health and disease. Engineers have sought to make these assessments increasingly quantitative and accessible within daily clinical practice. Since many of the developed techniques involve image-based quantification of tissue deformation in response to an applied force (i.e., "elastography"), such approaches fall squarely within the domain of the radiologist. While commercial elastography analysis software is becoming increasingly available for clinical use, the internal workings of these packages often remain a "black box," with limited guidance on how to usefully apply the methods toward a meaningful diagnosis. The purpose of the present review article is to introduce some important approaches to elastography that have been developed for the most widely used clinical imaging modalities (e.g., ultrasound, MRI), to provide a basic sense of the underlying physical principles, and to discuss both current and potential (musculoskeletal) applications. The article also seeks to provide a perspective on emerging approaches that are rapidly developing in the research laboratory (e.g., optical coherence tomography, fibered confocal microscopy), and which may eventually gain a clinical foothold.

In-vivo time-dependent articular cartilage contact behavior of the tibiofemoral joint

OBJECTIVE

The purpose of this study was to investigate the in-vivo time-dependent contact behavior of tibiofemoral cartilage of human subjects during the first 300 s after applying a constant full body weight loading and determine whether there are differences in cartilage contact responses between the medial and lateral compartments.

DESIGN

Six healthy knees were investigated in this study. Each knee joint was subjected to full body weight loading and the in-vivo positions of the knee were captured by two orthogonal fluoroscopes during the first 300 s after applying the load. Three-dimensional models of the knee were created from MR images and used to reproduce the in-vivo knee positions recorded by the fluoroscopes. The time-dependent contact behavior of the cartilage was represented using the peak cartilage contact deformation and the cartilage contact area as functions of time under the constant full body weight.

RESULTS

Both medial and lateral compartments showed a rapid increase in contact deformation and contact area during the first 20s of loading. After 50s of loading, the peak contact deformation values were 10.5+/-0.8% (medial) and 12.6+/-3.4% (lateral), and the contact areas were 223.9+/-14.8 mm(2) (medial) and 123.0+/-22.8 mm(2) (lateral). Thereafter, the peak cartilage contact deformation and contact area remained relatively constant. The respective changing rates of cartilage contact deformation were 1.4+/-0.9%/s (medial) and 3.1+/-2.5%/s (lateral); and of contact areas were 40.6+/-20.8 mm(2)/s (medial) and 24.0+/-11.4 mm(2)/s (lateral), at the first second of loading. Beyond 50 s, both changing rates approached zero.

CONCLUSIONS

The peak cartilage contact deformation increased rapidly within the first 20s of loading and remained relatively constant after approximately 50 s of loading. The time-dependent response of cartilage contact behavior under constant full body weight loading was significantly different in the medial and lateral tibiofemoral compartments, with greater peak cartilage contact deformation on the lateral side and greater contact area on the medial side. These data can provide insight into normal in-vivo cartilage function and provide guidelines for the improvement of ex-vivo cartilage experiments and the validation of computational models that simulate human knee joint contact.

Characterization of engineered tissue construct mechanical function by magnetic resonance imaging

Non-invasive magnetic resonance imaging (MRI) is a technology that enables the characterization of multiple physical phenomena in living and engineered tissues. The mechanical function of engineered tissues is a primary endpoint for the successful regeneration of many biological tissues, such as articular cartilage, spine and heart. Here we demonstrate the application of MRI to characterize the mechanical function of engineered tissue. Phase contrast-based methods were demonstrated to characterize detailed deformation fields throughout the interior of native and engineered tissue, using an articular cartilage defect model as a study system. MRI techniques revealed that strain fields varied non-uniformly, depending on spatial position. Strains were highest in the tissue constructs compared to surrounding native cartilage. Tissue surface geometry corresponded to strain fields observed within the tissue interior near the surface. Strain fields were further evaluated with respect to the spatial variation in the concentration of glycosaminoglycans ([GAG]), critical proteoglycans in the extracellular matrix of cartilage, as determined by gadolinium-enhanced imaging. [GAG] also varied non-uniformly, depending on spatial position and was lowest in the tissue constructs compared to the surrounding cartilage. The use of multiple MRI techniques to assess tissue mechanical function provides complementary data and suggests that deformation is related to tissue geometry, underlying extracellular matrix constituents and the lack of tissue integration in the model system studied. Specialized and advanced MRI phase contrast-based methods are valuable for the detailed characterization and evaluation of mechanical function of tissue-engineered constructs.

Quasi-steady-state displacement response of whole human cadaveric knees in a MRI scanner

It is important to determine the three-dimensional nonuniform deformation of articular cartilage in its native environment. A new magnetic resonance imaging (MRI)-based technique (cartilage deformation by tag registration (CDTR)) has been developed, which can determine such deformations provided that the compressive load-displacement response of the knee reaches a quasi-steady state during cyclic loading. The objectives of this study were (1) to design and construct an apparatus to cyclically compress human cadaveric knees to physiological loads in a MRI scanner, (2) to determine the number of load cycles required to reach a quasi-steady-state load-displacement response for cyclic loading of human cadaveric knees, and (3) to collect sample MR images of undeformed and deformed states of tibiofemoral cartilage free of artifact while using the apparatus within a MRI scanner. An electropneumatic MRI-compatible apparatus was constructed to fit in a clinical MRI scanner, and a slope criterion was defined to indicate the point at which a quasi-steady-state load-displacement response, which would allow the use of CDTR, occurred during cyclic loading of a human knee. The average number of cycles required to reach a quasi-steady-state load-displacement response according to the slope criterion defined herein for three cadaveric knee joints was 356+/-69. This indicates that human knee joint specimens can be cyclically loaded such that deformation is repeatable according to MRI requirements of CDTR. Sample images of tibiofemoral cartilage were obtained for a single knee joint. These images demonstrate the usefulness of the apparatus in a MRI scanner. Thus the results of this study are a crucial step toward developing a MRI-based method to determine the deformations of articular cartilage in whole human cadaveric knees.

Two-dimensional strain fields on the cross-section of the bovine humeral head under contact loading

The objective of this study was to provide a detailed experimental assessment of the two-dimensional cartilage strain distribution on the cross-section of immature and mature bovine humeral heads subjected to contact loading at a relatively rapid physiological loading rate. Six immature and six mature humeral head specimens were loaded against glass and strains were measured at the end of a 5s loading ramp on the textured articular cross-section using digital image correlation analysis. The primary findings indicate that elevated tensile and compressive strains occur near the articular surface, around the center of the contact region. Few qualitative or quantitative differences were observed between mature and immature joints. Under an average contact stress of approximately 1.7 MPa, the peak compressive strains averaged -0.131+/-0.048, which was significantly less than the relative change in cartilage thickness, -0.104+/-0.032 (p<0.05). The peak tensile strains were significantly smaller in magnitude, at 0.0325+/-0.013. These experimental findings differ from a previous finite element analysis of articular contact, which predicted peak strains at the cartilage-bone interface even when accounting for the porous-hydrated nature of the tissue, its depth-dependent inhomogeneity, and the disparity between its tensile and compressive properties. These experimental results yield new insights into the local mechanical environment of the tissue and cells, and suggest that further refinements are needed in the modeling of contacting articular layers.

In vivo cartilage contact deformation in the healthy human tibiofemoral joint

OBJECTIVES

In vivo cartilage contact deformation is instrumental for understanding human joint function and degeneration. This study measured the total deformation of contacting articular cartilage in the human tibiofemoral joint during in vivo weight-bearing flexion.

METHODS

Eleven healthy knees were magnetic resonance (MR) scanned and imaged with a dual fluoroscopic system while the subject performed a weight-bearing single-leg lunge. The tibia, femur and associated articulating cartilage were constructed from the MR images and combined with the dual fluoroscopic images to determine in vivo cartilage contact deformation from full extension to 120 degrees of flexion.

RESULTS

In both compartments, minimum peak compartmental contact deformation occurred at 30 degrees of flexion (24 +/- 6% medial, 17 +/- 7% lateral) and maximum peak compartmental deformation occurred at 120 degrees of flexion (30 +/- 13% medial, 30 +/- 10% lateral) during the weight-bearing flexion from full extension to 120 degrees. Average medial contact areas and peak contact deformations were significantly greater than lateral compartment values (P < 0.05). In addition, cartilage thickness in regions of contact was on average 1.4- and 1.1-times thicker than the average thickness of the tibial and femoral cartilage surfaces, respectively (P < 0.05).

CONCLUSIONS

These data may provide base-line knowledge for investigating the effects of various knee injuries on joint contact biomechanics and the aetiology of cartilage degeneration.

Characterization of the dynamic shear properties of hyaline cartilage using high-frequency dynamic MR elastography

This work evaluated the feasibility of dynamic MR Elastography (MRE) to quantify structural changes in bovine hyaline cartilage induced by selective enzymatic degradation. The ability of the technique to quantify the frequency-dependent response of normal cartilage to shear in the kilohertz range was also explored. Bovine cartilage plugs of 8 mm in diameter were used for this study. The shear stiffness (mu(s)) of each cartilage plug was measured before and after 16 hr of enzymatic treatments by dynamic MRE at 5000 Hz of shear excitation. Collagenase and trypsin were used to selectively affect the collagen and proteoglycans contents of the matrix. Additionally, normal cartilage plugs were tested by dynamic MRE at shear-excitations of 3000-7000 Hz. Measured micro(s) of cartilage plugs showed a significant decrease (-37%, P < 0.05) after collagenase treatment and a significant decrease (-28%, P < 0.05) after trypsin treatment. Furthermore, a near-linear increase (R(2) = 0.9141) in the speed of shear wave propagation with shear-excitation frequency was observed in cartilage, indicating that wave speed is dominated by viscoelastic effects. These experiments suggest that dynamic MRE can provide a sensitive quantitative tool to characterize the degradation process and viscoelastic behavior of cartilage.

Coupled motions under compressive load in intact and ACL-deficient knees: a cadaveric study

Knowledge of the coupled motions, which develop under compressive loading of the knee, is useful to determine which degrees of freedom should be included in the study of tibiofemoral contact and also to understand the role of the anterior cruciate ligament (ACL) in coupled motions. The objectives of this study were to measure the coupled motions of the intact knee and ACL-deficient knee under compression and to compare the coupled motions of the ACL-deficient knee with those of the intact knee. Ten intact cadaveric knees were tested by applying a 1600 N compressive load and measuring coupled internal-external and varus-valgus rotations and anterior-posterior and medial-lateral translations at 0 deg, 15 deg, and 30 deg of flexion. Compressive loads were applied along the functional axis of axial rotation, which coincides approximately with the mechanical axis of the tibia. The ACL was excised and the knees were tested again. In the intact knee, the peak coupled motions were 3.8 deg internal rotation at 0 deg flexion changing to -4.9 deg external rotation at 30 deg of flexion, 1.4 deg of varus rotation at 0 deg flexion changing to -1.9 deg valgus rotation at 30 deg of flexion, 1.4 mm of medial translation at 0 deg flexion increasing to 2.3 mm at 30 deg of flexion, and 5.3 mm of anterior translation at 0 deg flexion increasing to 10.2 mm at 30 deg of flexion. All changes in the peak coupled motions from 0 deg to 30 deg flexion were statistically significant (p<0.05). In ACL-deficient knees, there was a strong trend (marginally not significant, p=0.07) toward greater anterior translation (12.7 mm) than that in intact knees (8.0 mm), whereas coupled motions in the other degrees of freedom were comparable. Because the coupled motions in all four degrees of freedom in the intact knee and ACL-deficient knee are sufficiently large to substantially affect the tibiofemoral contact area, all degrees of freedom should be included when either developing mathematical models or designing mechanical testing equipment for study of tibiofemoral contact. The increase in coupled anterior translation in ACL-deficient knees indicates the important role played by the ACL in constraining anterior translation during compressive loading.

An MRI-based method to align the compressive loading axis for human cadaveric knees

There is a need to align the mechanical axis of the tibia with the axis of loading for studies involving tibiofemoral compression to interpret results and to ensure repeatability of loading within and among specimens. Therefore, the objectives of this study were (1) to develop a magnetic resonance imaging (MRI)-based alignment method for use with apparatuses applying tibiofemoral joint compression, (2) to demonstrate the usefulness of the method by aligning cadaveric knees in an apparatus that could apply tibiofemoral joint compression, and (3) to quantify the error associated with the alignment method. A four degree-of-freedom adjustable device was constructed to allow determination and alignment of the mechanical axis of the tibia of cadaveric knee joints with the axis of loading of an apparatus applying tibiofemoral joint compression. MRI was used to determine the locations of bony landmarks in three dimensions defining the mechanical axis of the tibia relative to an initial orientation of the four degree-of-freedom device. Adjustment values of the device were then computed and applied to the device to align the mechanical axis of the tibia with the axis of a compressive loading apparatus. To demonstrate the usefulness of the method, four cadaveric knees were aligned in the compressive loading apparatus. The vectors describing the mechanical axis of the tibia and the loading axis of the apparatus before and after adjustment of the four degree-of-freedom device were computed for each cadaveric knee. After adjustment of the four degree-of-freedom device, the mechanical axis of the tibia was collinear with the loading axis of the apparatus for each cadaveric knee. The errors in the adjustment values introduced by inaccuracies in the MR images were quantified using the Monte Carlo technique. The precisions in the translational and rotational adjustments were 1.20 mm and 0.90 deg respectively. The MR-based alignment method will allow consistent interpretation of results obtained during tibiofemoral compressive studies conducted using the apparatus described in this paper by providing a well-defined loading axis. The alignment method can also be adapted for use with other apparatuses applying tibiofemoral compression.

Displacement encoding for the measurement of cartilage deformation

Articular cartilage is a load bearing and lubricating tissue in animal joints. Heterogeneous deformations arise in the structured and zonal tissue under the application of mechanical load. The character of these deformations is altered by degenerative joint disease. Here, we document an MRI-based technique for determining deformations throughout the volume of the tissue based on displacement encoding with stimulated echoes (DENSE) and a fast spin echo (FSE) readout. A DENSE-FSE technique was designed to image cartilage at 9.4 Tesla in a deformed state during the application of cyclic mechanical loading. Artifact elimination arising from stimulated echoes and FSE was accomplished by radio frequency pulse phase cycling. The error of the technique was random and was quantified in terms of precision as better than 0.17% strain. Heterogeneous deformation field patterns in axial, transverse, and shear directions were quantified in a single tissue explant loaded in simple uniaxial compression. The technique is appropriate for documenting tissue deformations during applied physiologically relevant stress levels and loading rates. It may also be applied to characterize the micromechanical strain environment in normal, diseased, or regenerated cartilage in response to applied mechanical loading.

Optimal methods for the preservation of cartilage samples in MRI and correlative biochemical studies

MRI studies of cartilage require the prevention of sample degradation before and during scanning and during shipment for correlative studies. Methods to achieve this include immersion in protease inhibitors (PIs), refrigeration, and freezing. In this study, bovine nasal cartilage (BNC) samples were stored in Dulbecco's phosphate-buffered saline (DPBS), DPBS with standard PIs, or PI solution with GM6001, a potent metalloproteinase inhibitor. For each buffer, three samples were scanned at +4 degrees C and stored at +4 degrees C or at -20 degrees C with thawing prior to imaging. T2 and magnetization transfer (MT) rate, km, were measured weekly over 4 months, after which time water and glycosaminoglycan (GAG) contents were compared with those of matching tissue excised pre-storage. Samples in DPBS exhibited increased T2 (+33.6% after 1 month at +4 degrees C, P = 0.040) and decreased km (-20.6%, P = 0.004), while refrigeration in DPBS with PI and GM6001 yielded good stability (T2: +2.7%, P = 0.874; km: -4.2%, P = 0.654 after 108 days at +4 degrees C). Water content increased while GAG content markedly decreased in all samples. Thus, stability in cartilage MRI parameters can be optimized with appropriate storage conditions, but storage time should nonetheless be minimized.

Noninvasive determination of ligament strain with deformable image registration

Ligament function and propensity for injury are directly related to regional stresses and strains. However, noninvasive techniques for measurement of strain are currently limited. This study validated the use of Hyperelastic Warping, a deformable image registration technique, for noninvasive strain measurement in the human medial collateral ligament using direct comparisons with optical measurements. Hyperelastic Warping determines the deformation map that aligns consecutive images of a deforming material, allowing calculation of strain. Diffeomorphic deformations are ensured by representing the deformable image as a hyperelastic material. Ten cadaveric knees were subjected to six loading scenarios each. Tissue deformation was documented with magnetic resonance imaging (MRI) and video-based experimental measurements. MRI datasets were analyzed using Hyperelastic Warping, representing the medial collateral ligament (MCL) with a hexahedral finite element (FE) model projected to a manually segmented ligament surface. The material behavior was transversely isotropic hyperelastic. Warping predictions of fiber stretch were strongly correlated with experimentally measured strains (R (2) = 0.81). Both sets of measurements were in agreement with previous ex vivo studies. Warping predictions of fiber stretch were insensitive to bulk:shear modulus ratio, fiber stiffness, and shear modulus in the range of +2.5SD to -1.0SD. Correlations degraded when the shear modulus was decreased to 2.5SD below the mean (R (2) = 0.56), and when an isotropic constitutive model was substituted for the transversely isotropic model (R (2) = 0.65). MCL strains in the transitional region near the joint line, where the material behavior and material symmetry are more complex, showed the most sensitivity to changes in shear modulus. These results demonstrate that Hyperelastic Warping requires the use of a constitutive model that reflects the material symmetry, but not subject-specific material properties for accurate strain predictions for this application. Hyperelastic Warping represents a powerful technique for noninvasive strain measurement of musculoskeletal tissues and has many advantages over other image-based strain measurement techniques.

Developments in dynamic MR elastography for in vitro biomechanical assessment of hyaline cartilage under high-frequency cyclical shear

The design, construction, and evaluation of a customized dynamic magnetic resonance elastography (MRE) technique for biomechanical assessment of hyaline cartilage in vitro are described. For quantification of the dynamic shear properties of hyaline cartilage by dynamic MRE, mechanical excitation and motion sensitization were performed at frequencies in the kilohertz range. A custom electromechanical actuator and a z-axis gradient coil were used to generate and image shear waves throughout cartilage at 1000-10,000 Hz. A radiofrequency (RF) coil was also constructed for high-resolution imaging. The technique was validated at 4000 and 6000 Hz by quantifying differences in shear stiffness between soft ( approximately 200 kPa) and stiff ( approximately 300 kPa) layers of 5-mm-thick bilayered phantoms. The technique was then used to quantify the dynamic shear properties of bovine and shark hyaline cartilage samples at frequencies up to 9000 Hz. The results demonstrate that one can obtain high-resolution shear stiffness measurements of hyaline cartilage and small, stiff, multilayered phantoms at high frequencies by generating robust mechanical excitations and using large magnetic field gradients. Dynamic MRE can potentially be used to directly quantify the dynamic shear properties of hyaline and articular cartilage, as well as other cartilaginous materials and engineered constructs.

Spatially varying material properties of the rat caudal intervertebral disc

STUDY DESIGN

The use of a microscopy based material testing technique to assess the local material properties of rat caudal intervertebral discs under uniaxial compression.

OBJECTIVES

To better understand the cell environment of rat caudal intervertebral discs during mechanical loading and elucidate better the role of the nucleus pulposus to the overall disc material properties.

SUMMARY OF BACKGROUND DATA

Rat tail models of disc degeneration have been widely used for their similarity with the degeneration phenomena in human beings. Degenerative patterns in the disc are often inhomogeneous, however, only average material properties of rodent discs have been studied. Knowledge of the spatially varying properties within the disc is necessary to understand the disc cell milieu during tissue loading.

METHODS

Rat caudal motion segments were tested intact, sectioned, and with alterations of nucleus pulposus using microscopy based techniques. Local displacements and strains were obtained using digital image correlation. Strains and load measurements were used to get the average apparent Young's modulus, peak stress, local Young's modulus, and local Poisson's ratio.

RESULTS

There was no difference observed in the average apparent Young's modulus among experimental groups. Peak stresses decreased significantly when the nucleus pulposus was replaced with extremely fluid-like materials. The axial displacement field showed 3 distinct linear distributions in samples which were sectioned. The center region in all groups had significantly smaller axial strain and showed a higher local Young's modulus.

CONCLUSIONS

The average equilibrium Young's modulus may be dependent on short-range ultrastructural organization. Spatially varying material properties within the intervertebral disc may be caused by orientation of fiber bundles in the different regions of the anulus fibrosus. The fiber bundles are better able to resist compressive loads when oriented parallel rather than perpendicular to the loading direction. At equilibrium, the anulus fibrosus also appears to have a shielding effect independent of the material filling up the nucleus pulposus space.

Error optimization of a three-dimensional magnetic resonance imaging tagging-based cartilage deformation technique

Three-dimensional strain fields in articular cartilage subjected to compressive loading can be determined using a recently developed MRI-based cartilage deformation by tag registration technique. The objective of this study was to determine the experimental variables that minimize the technique error, which has not been previously reported. Error (strain bias and precision) was determined using direct experiments and Monte Carlo simulations for four variables: spatial resolution, tag line spacing, applied nominal strain, and number of control points used to describe tag lines in a B-spline model. The important results include the following: (1) bias was not significantly different from zero, (2) precision increased with image resolution and with tag line spacing, (3) precision was independent of applied nominal strain, and (4) error was a minimum (absolute precision = 0.41% strain) for the following values: spatial resolution = 0.05 x 0.05 mm2; tag line spacing = 2.0 mm; control points = 6. With these results the technique can now be used in various applications while minimizing error.

Heterogeneous three-dimensional strain fields during unconfined cyclic compression in bovine articular cartilage explants

Articular cartilage provides critical load-bearing and tribological properties to the normal function of diarthrodial joints. The unique properties of cartilage, as well as heterogeneous deformations during mechanical compression, are due to the nonuniform microstructural organization of tissue components such as collagens and proteoglycans. A new cartilage deformation by tag registration (CDTR) technique has been developed by the authors to determine heterogeneous deformations in articular cartilage explants. The technique uses a combination of specialized MRI methods, a custom cyclic loading apparatus, and image processing software. The objective of this study was to use the CDTR technique to document strain patterns throughout the volume of normal bovine articular cartilage explants during cyclic unconfined compression at two physiologically-relevant applied normal stress levels (1.29 and 2.57 MPa). Despite simple uniaxial cyclic compressive loading with a flat, nonporous indenter, strain patterns were heterogeneous. Strains in the thickness direction (E(yy)) were compressive, varied nonlinearly with depth from the articular surface from a maximum magnitude of 11% at the articular surface, and were comparable despite a 2-fold increase in applied normal stress. Strains perpendicular to the thickness direction (E(xx) and E(zz)) were tensile, decreased linearly with depth from the articular surface from a maximum of 7%, and increased in magnitude 2.5-fold with a 2-fold increase in applied normal stress. Shear strains in the transverse plane (E(xz)) were approximately zero while shear strains in the other two planes were much larger and increased in magnitude with depth from the articular surface, reaching maximum magnitudes of 2% at the articular cartilage-subchondral bone interface. In general, strain patterns indicated that cartilage osteochondral explants exhibited depth-dependent nonisotropic behavior during uniaxial cyclic loading. These results are useful in verifying constitutive formulations of articular cartilage during cyclic unconfined compression and in characterizing the micromechanical environment likely experienced by individual chondrocytes throughout the tissue volume.