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

Finite deformation elastography of articular cartilage and biomaterials based on imaging and topology optimization

Tissues and engineered biomaterials exhibit exquisite local variation in stiffness that defines their function. Conventional elastography quantifies stiffness in soft (e.g. brain, liver) tissue, but robust quantification in stiff (e.g. musculoskeletal) tissues is challenging due to dissipation of high frequency shear waves. We describe new development of finite deformation elastography that utilizes magnetic resonance imaging of low frequency, physiological-level (large magnitude) displacements, coupled to an iterative topology optimization routine to investigate stiffness heterogeneity, including spatial gradients and inclusions. We reconstruct 2D and 3D stiffness distributions in bilayer agarose hydrogels and silicon materials that exhibit heterogeneous displacement/strain responses. We map stiffness in porcine and sheep articular cartilage deep within the bony articular joint space in situ for the first time. Elevated cartilage stiffness localized to the superficial zone is further related to collagen fiber compaction and loss of water content during cyclic loading, as assessed by independent T2 measurements. We additionally describe technical challenges needed to achieve in vivo elastography measurements. Our results introduce new functional imaging biomarkers, which can be assessed nondestructively, with clinical potential to diagnose and track progression of disease in early stages, including osteoarthritis or tissue degeneration.

TENSCell: Imaging of Stretch-Activated Cells Reveals Divergent Nuclear Behavior and Tension

Mechanisms of cellular and nuclear mechanosensation are unclear, partially because of a lack of methods that can reveal dynamic processes. Here, we present a new concept for a low-cost, three-dimensionally printed device that enables high-magnification imaging of cells during stretch. We observed that nuclei of mouse embryonic skin fibroblasts underwent rapid (within minutes) and divergent responses, characterized by nuclear area expansion during 5% strain but nuclear area shrinkage during 20% strain. Only responses to low strain were dependent on calcium signaling, whereas actin inhibition abrogated all nuclear responses and increased nuclear strain transfer and DNA damage. Imaging of actin dynamics during stretch revealed similar divergent trends, with F-actin shifting away from (5% strain) or toward (20% strain) the nuclear periphery. Our findings emphasize the importance of simultaneous stimulation and data acquisition to capture mechanosensitive responses and suggest that mechanical confinement of nuclei through actin may be a protective mechanism during high mechanical stretch or loading.

In vivo articular cartilage deformation: noninvasive quantification of intratissue strain during joint contact in the human knee

The in vivo measurement of articular cartilage deformation is essential to understand how mechanical forces distribute throughout the healthy tissue and change over time in the pathologic joint. Displacements or strain may serve as a functional imaging biomarker for healthy, diseased, and repaired tissues, but unfortunately intratissue cartilage deformation in vivo is largely unknown. Here, we directly quantified for the first time deformation patterns through the thickness of tibiofemoral articular cartilage in healthy human volunteers. Magnetic resonance imaging acquisitions were synchronized with physiologically relevant compressive loading and used to visualize and measure regional displacement and strain of tibiofemoral articular cartilage in a sagittal plane. We found that compression (of 1/2 body weight) applied at the foot produced a sliding, rigid-body displacement at the tibiofemoral cartilage interface, that loading generated subject- and gender-specific and regionally complex patterns of intratissue strains, and that dominant cartilage strains (approaching 12%) were in shear. Maximum principle and shear strain measures in the tibia were correlated with body mass index. Our MRI-based approach may accelerate the development of regenerative therapies for diseased or damaged cartilage, which is currently limited by the lack of reliable in vivo methods for noninvasive assessment of functional changes following treatment.

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.

Comparison of intervertebral disc displacements measured under applied loading with MRI at 3.0 T and 9.4 T

The purpose of this study was to compare displacement behavior of cyclically loaded cadaveric human intervertebral discs as measured noninvasively on a clinical 3.0 T and a research 9.4 T MRI system. Intervertebral discs were cyclically compressed at physiologically relevant levels with the same MRI-compatible loading device in the clinical and research systems. Displacement-encoded imaging was synchronized to cyclic loading to measure displacements under applied loading with MRI (dual MRI). Displacements from the two systems were compared individually using linear regression and, across all specimens, using Bland-Altman analysis. In-plane displacement patterns measured at 3.0 T and 9.4 T were qualitatively comparable and well correlated. Bland-Altman analyses showed that over 90% of displacement values within the intervertebral disc regions of interest lay within the limits of agreement. Measurement of displacement using dual MRI using a 3.0 T clinical system is comparable to that of a 9.4 T research system. Additional refinements of software, technique implementation, and image processing have potential to improve agreement between different MRI systems. Despite differences in MRI systems in this initial implementation, this work demonstrates that dual MRI can be reliably implemented at multiple magnetic field strengths, permitting translation of dual MRI for a variety of applications in the study of tissue and biomaterial biomechanics.

Cell and tissue deformation measurements: texture correlation with third-order approximation of displacement gradients

Cells remarkably are capable of large deformations during motility and when subjected to mechanical force. Measurement of mechanical deformation (i.e. displacements, strain) is critical to understand functional changes in cells and biological tissues following disease, and to elucidate basic relationships between applied force and cellular biosynthesis. Microscopy-based imaging modalities provide the ability to noninvasively visualize small cell or tissue structures and track their motion over time, often using two-dimensional (2D) digital image (texture) correlation algorithms. For the measurement of complex and nonlinear motion in cells and tissues, implementation of texture correlation algorithms with high order approximations of displacement mapping terms are needed to minimize error. Here, we extend a texture correlation algorithm with up to third-order approximation of displacement mapping terms for the measurement of cell and tissue deformation. We additionally investigate relationships between measurement error and image texture, defined by subset entropy. Displacement measurement error is significantly reduced when the order of displacement mapping terms in the texture correlation algorithm matches or exceeds the order of the deformation observed. Displacement measurement error is also inversely proportional to subset entropy, with well-defined cell and tissue structures leading to high entropy and low error. For cell and tissue studies where complex or nonlinear displacements are expected, texture correlation algorithms with high order terms are required to best characterize the observed deformation.

Transient and microscale deformations and strains measured under exogenous loading by noninvasive magnetic resonance

Characterization of spatiotemporal deformation dynamics and material properties requires non-destructive methods to visualize mechanics of materials and biological tissues. Displacement-encoded magnetic resonance imaging (MRI) has emerged as a noninvasive and non-destructive technique used to quantify deformation and strains. However, the techniques are not yet applicable to a broad range of materials and load-bearing tissues. In this paper, we visualize transient and internal material deformation through the novel synchrony of external mechanical loading with rapid displacement-encoded MRI. We achieved deformation measurements in silicone gel materials with a spatial resolution of 100 µm and a temporal resolution (of 2.25 ms), set by the repetition time (TR) of the rapid MRI acquisition. Displacement and strain precisions after smoothing were 11 µm and 0.1%, respectively, approaching cellular length scales. Short (1/2 TR) echo times enabled visualization of in situ deformation in a human tibiofemoral joint, inclusive of multiple variable T(2) biomaterials. Moreover, the MRI acquisitions achieved a fivefold improvement in imaging time over previous technology, setting the stage for mechanical imaging in vivo. Our results provide a general approach for noninvasive and non-destructive measurement, at high spatial and temporal resolution, of the dynamic mechanical response of a broad range of load-bearing materials and biological tissues.

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.

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.

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.