Yusuf A. Bhagat

Micro–MR Imaging–based Computational Biomechanics Demonstrates Reduction in Cortical and Trabecular Bone Strength after Renal Transplantation

PURPOSE To examine the ability of three-dimensional micro-magnetic resonance (MR) imaging-based computational biomechanics to detect mechanical alterations in trabecular bone and cortical bone in the distal tibia of incident renal transplant recipients 6 months after renal transplantation and compare them with bone mineral density (BMD) outcomes. MATERIALS AND METHODS The study was approved by the institutional review board and complied with HIPAA guidelines. Written informed consent was obtained from all subjects. Micro-MR imaging of distal tibial metaphysis was performed within 2 weeks after renal transplantation (baseline) and 6 months later in 49 participants (24 female; median age, 44 years; range, 19-61 years) with a clinical 1.5-T whole-body imager using a modified three-dimensional fast large-angle spin-echo pulse sequence. Micro-finite-element models for cortical bone, trabecular bone, and whole-bone section were generated from each image by delineating the endosteal and periosteal boundaries. Mechanical parameters (stiffness and failure load) were estimated with simulated uniaxial compression tests on the micro-finite-element models. Structural parameters (trabecular bone volume fraction [BV/TV, bone volume to total volume ratio], trabecular thickness [TbTh], and cortical thickness [CtTh]) were computed from micro-MR images. Total hip and spine areal BMD were determined with dual-energy x-ray absorptiometry (DXA). Parameters obtained at the follow-up were compared with the baseline values by using parametric or nonparametric tests depending on the normality of data. RESULTS All mechanical parameters were significantly lower at 6 months compared with baseline. Decreases in cortical bone, trabecular bone, and whole-bone stiffness were 3.7% (P = .03), 4.9% (P = .03), and 4.3% (P = .003), respectively. Decreases in cortical bone, trabecular bone, and whole-bone failure strength were 7.6% (P = .0003), 6.0% (P = .004), and 5.6% (P = .0004), respectively. Conventional structural measures, BV/TV, TbTh, and CtTh, did not change significantly. Spine BMD decreased by 2.9% (P < .0001), while hip BMD did not change significantly at DXA. CONCLUSION MR imaging-based micro-finite-element analysis suggests that stiffness and failure strength of the distal tibia decrease over a 6-month interval after renal transplantation.

Cortical Bone Water Concentration: Dependence of MR Imaging Measures on Age and Pore Volume Fraction

PURPOSE To quantify bulk bone water to test the hypothesis that bone water concentration (BWC) is negatively correlated with bone mineral density (BMD) and is positively correlated with age, and to propose the suppression ratio (SR) (the ratio of signal amplitude without to that with long-T2 suppression) as a potentially stronger surrogate measure of porosity, which is evaluated ex vivo and in vivo. MATERIALS AND METHODS Human subject studies were conducted in compliance with institutional review board and HIPAA regulations. Healthy men and women (n = 72; age range, 20-80 years) were examined with a hybrid radial ultrashort echo time magnetic resonance (MR) imaging sequence at 3.0 T, and BWC was determined in the tibial midshaft. In a subset of 40 female subjects, the SR was measured with a similar sequence. Cortical volumetric BMD (vBMD) was measured by means of peripheral quantitative computed tomography (CT). The method was validated against micro-CT-derived porosity in 13 donor human cortical bone specimens. Associations among parameters were evaluated by using standard statistical tools. RESULTS BWC was positively correlated with age (r = 0.52; 95% confidence interval [CI]: 0.22, 0.73; P = .002) and negatively correlated with vBMD at the same location (r = -0.57; 95% CI: -0.76, -0.29; P < .001). Data were suggestive of stronger associations with SR (r = 0.64, 95% CI: 0.39, 0.81, P < .001 for age; r = -0.67, 95% CI: -0.82, -0.43, P < .001 for vBMD; P < .001 for both), indicating that SR may be a more direct measure of porosity. This interpretation was supported by ex vivo measurements showing SR to be strongly positively correlated with micro-CT porosity (r = 0.88; 95% CI: 0.64, 0.96; P < .001) and with age (r = 0.87; 95% CI: 0.62, 0.96; P < .001). CONCLUSION The MR imaging-derived SR may serve as a biomarker for cortical bone porosity that is potentially superior to BWC, but corroboration in larger cohorts is indicated.

Bone mineral (31)P and matrix-bound water densities measured by solid-state (31)P and (1)H MRI.

Bone is a composite material consisting of mineral and hydrated collagen fractions. MRI of bone is challenging because of extremely short transverse relaxation times, but solid‐state imaging sequences exist that can acquire the short‐lived signal from bone tissue. Previous work to quantify bone density via MRI used powerful experimental scanners. This work seeks to establish the feasibility of MRI‐based measurement on clinical scanners of bone mineral and collagen‐bound water densities, the latter as a surrogate of matrix density, and to examine the associations of these parameters with porosity and donors’ age.

Performance of μMRI-Based virtual bone biopsy for structural and mechanical analysis at the distal tibia at 7T field strength

To assess the performance of a 3D fast spin echo (FSE) pulse sequence utilizing out‐of‐slab cancellation through phase alternation and micro‐magnetic resonance imaging (μMRI)‐based virtual bone biopsy processing methods to probe the serial reproducibility and sensitivity of structural and mechanical parameters of the distal tibia at 7.0T.

Effects of Testosterone and Growth Hormone on the Structural and Mechanical Properties of Bone by Micro-MRI in the Distal Tibia of Men With Hypopituitarism

CONTEXT Severe deficiencies of testosterone (T) and GH are associated with low bone mineral density (BMD) and increased fracture risk. Replacement of T in hypogonadal men improves several bone parameters. Replacement of GH in GH-deficient men improves BMD. OBJECTIVE Our objective was to determine whether T and GH treatment together improves the structural and mechanical parameters of bone more than T alone in men with hypopituitarism. DESIGN AND SUBJECTS This randomized, prospective, 2-year study included 32 men with severe deficiencies of T and GH due to panhypopituitarism. INTERVENTION Subjects were randomized to receive T alone (n = 15) or T and GH (n = 17) for 2 years. MAIN OUTCOME MEASURES We evaluated magnetic resonance microimaging-derived structural (bone volume fraction [BVF] and trabecular thickness) and mechanical (axial stiffness [AS], a measure of bone strength) properties of the distal tibia at baseline and after 1 and 2 years of treatment. RESULTS Treatment with T and GH did not affect BVF, thickness, or AS differently from T alone. T treatment in all subjects for 2 years increased trabecular BVF by 9.6% (P < .0001), trabecular thickness by 2.6% (P < .001), and trabecular AS by 9.8% (P < .001). In contrast, testosterone treatment in all subjects significantly increased cortical thickness by 2.4% (P < .01) but decreased cortical BVF by -4.7% (P < .01) and cortical AS by -6.9% (P < .01). CONCLUSION Combined T and GH treatment of men with hypopituitarism for 2 years did not improve the measured structural or mechanical parameters of the distal tibia more than T alone. However, testosterone significantly increased the structural and mechanical properties of trabecular bone but decreased most of these properties of cortical bone, illustrating the potential importance of assessing trabecular and cortical bone separately in future studies of the effect of testosterone on bone.

Potential of in vivo MRI‐based nonlinear finite‐element analysis for the assessment of trabecular bone post‐yield properties

PURPOSE Bone strength is the key factor impacting fracture risk. Assessment of bone strength from high-resolution (HR) images have largely relied on linear micro-finite element analysis (μFEA) even though failure always occurs beyond the yield point, which is outside the linear regime. Nonlinear μFEA may therefore be more informative in predicting failure behavior. However, existing nonlinear models applied to trabecular bone (TB) have largely been confined to micro-computed tomography (μCT) and, more recently, HR peripheral quantitative computed tomography (HR-pQCT) images, and typically have ignored evaluation of the post-yield behavior. The primary purpose of this work was threefold: (1) to provide an improved algorithm and program to assess TB yield as well as post-yield properties; (2) to explore the potential benefits of nonlinear μFEA beyond its linear counterpart; and (3) to assess the feasibility and practicality of performing nonlinear analysis on desktop computers on the basis of micro-magnetic resonance (μMR) images obtained in vivo in patients. METHODS A method for nonlinear μFE modeling of TB yield as well as post-yield behavior has been designed where material nonlinearity is captured by adjusting the tissue modulus iteratively according to the tissue-level effective strain obtained from linear analysis using a computationally optimized algorithm. The software allows for images at in vivo μMRI resolution as input with retention of grayscale information. Associations between axial stiffness estimated from linear analysis and yield as well as post-yield parameters from nonlinear analysis were investigated from in vivo μMR images of the distal tibia (N = 20; ages: 58-84) and radius (N = 20; ages: 50-75). RESULTS All simulations were completed in 1 h or less for 61 strain levels using a desktop computer (dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM). Although yield stress and ultimate stress correlated strongly (R(2) > 0.95, p < 0.001) with axial stiffness, toughness correlated moderately at the distal tibia (R(2) = 0.81, p < 0.001) and only weakly at the distal radius (R(2) = 0.34, p = 0.007). Further, toughness was found to vary by up to 16% for bone of very similar axial stiffness (<2%). CONCLUSIONS The work demonstrates the practicality of nonlinear μFE simulations at in vivo μMRI resolution, as well as its potential for providing additional information beyond that obtainable from linear analysis. The data suggest that a direct assessment of toughness may provide information not captured by stiffness.

Helmholtz-pair transmit coil with integrated receive array for high-resolution MRI of trabecular bone in the distal tibia at 7T.

A Helmholtz-pair local transmit RF coil with an integrated four-element receive array RF coil and foot immobilization platform was designed and constructed for imaging the distal tibia in a whole-body 7T MRI scanner. Simulations and measurements of the B(1) field distribution of the transmit coil are described, along with SAR considerations for operation at 7T. Results of imaging the trabecular bone of three volunteers at 1.5T, 3T and 7T are presented, using identical 1.5T and 3T versions of the 7T four-element receive array. The spatially registered images reveal improved visibility for individual trabeculae and show average gains in SNR of 2.8× and 4.9× for imaging at 7T compared to 3T and 1.5T, respectively. The results thus display an approximately linear dependence of SNR with field strength and enable the practical utility of 7T scanners for micro-MRI of trabecular bone.

Predicting trabecular bone elastic properties from measures of bone volume fraction and fabric on the basis of micromagnetic resonance images

The relationship between fabric (a measure of structural anisotropy) and elastic properties of trabecular bone was examined by invoking morphology and homogenization theory on the basis of micromagnetic resonance images from the distal tibia in specimens (N = 30) and human subjects (N = 16) acquired at a 160 × 160 × 160 μm3 voxel size. The fabric tensor was mapped in 7.5 × 7.5 × 7.5 mm3 cubic subvolumes by a three‐dimensional mean‐intercept‐length method. Elastic constants (three Youngs and three shear moduli) were derived from linear microfinite element simulations of three‐dimensional grayscale bone volume fraction‐mapped images. In the specimen data, moduli fit power laws of bone volume fraction (bone volume/total volume) for all three test directions and subvolumes (R2 = 0.92–0.98) with exponents ranging from 1.3 to 1.8. Weaker linear relationships were found for the in vivo data because of a narrower range in bone volume/total volume. When pooling the data for all test directions and subvolumes, bone volume/total volume predicted elastic moduli less well in the specimens (mean R2 = 0.74) and not at all in vivo. A model of bone volume/total volume and fabric was highly predictive of microfinite element‐derived Youngs moduli: mean R2s of 0.98 and 0.82 (in vivo). The results show that fabric, an important predictor of bone mechanical properties, can be assessed in the limited resolution and signal‐to‐noise ratio regime of micromagnetic resonance images. Magn Reson Med, 2012.

On the Significance of Motion Degradation in High-Resolution 3D μMRI of Trabecular Bone

RATIONALE AND OBJECTIVES Subtle subject movement during high-resolution three-dimensional micro-magnetic resonance imaging of trabecular bone (TB) causes blurring, thereby rendering the data unreliable for quantitative analysis. In this work, the effects of translational and rotational motion displacements were evaluated qualitatively and quantitatively. MATERIALS AND METHODS In experiment 1, motion was induced by applying various simulated and previously observed in vivo trajectories as phase shifts to k-space or rotation angles to k-space segments of a virtually motion-free data set. In experiment 2, images that were visually free of motion artifacts from two groups of 10 healthy individuals, differing in age, were selected to probe the effects of motion on TB parameters. In both experiments, images were rated for motion severity, and the scores were compared to a focus criterion, the normalized gradient squared. RESULTS Strong correlations were observed between the motion quality scores and the corresponding normalized gradient squared values (R(2) = 0.52-0.64, P < .01). The results from experiment 1 demonstrated consistently lower image quality and alterations in structural parameters of 9% to 45% with increased amplitude of displacements. In experiment 2, the significant differences in structural parameter group means of the motion-free images were lost upon motion degradation. Autofocusing, a postprocessing correction method, partially recovered the sharpness of the original motion-free images in 13 of 20 subjects. CONCLUSIONS Quantitative TB structural measures are highly sensitive to subtle motion-induced degradation, which adversely affects precision and statistical power. The results underscore the influence of subject movement in high-resolution three-dimensional micro-magnetic resonance imaging and its correction for TB structure analysis.