Scott N. Hwang

Digital topological analysis of in vivo magnetic resonance microimages of trabecular bone reveals structural implications of osteoporosis.

Osteoporosis is a disease characterized by bone volume loss and architectural deterioration. The majority of work aimed at evaluating the structural implications of the disease has been performed based on stereologic analysis of histomorphometric sections. Only recently noninvasive imaging methods have emerged that provide sufficient resolution to resolve individual trabeculae. In this article, we apply digital topological analysis (DTA) to magnetic resonance microimages (μ‐MRI) of the radius obtained at 137 × 137 × 350 μm3 voxel size in a cohort of 79 women of widely varying bone mineral density (BMD) and vertebral deformity status. DTA is a new method that allows unambiguous determination of the three‐dimensional (3D) topology of each voxel in a trabecular bone network. The analysis involves generation of a bone volume fraction map, which is subjected to subvoxel processing to alleviate partial volume blurring, followed by thresholding and skeletonization. The skeletonized images contain only surfaces, profiles, curves, and their mutual junctions as the remnants of trabecular plates and rods after skeletonization. DTA parameters were compared with integral BMD in the lumbar spine and femur as well as MR‐derived bone volume fraction (BV/TV). Vertebral deformities were determined based on sagittal MRIs of the spine with a semiautomatic method and the number of deformities counted after threshold setting. DTA structural indices were found the strongest discriminators of subjects with deformities from those without deformities. Subjects with deformities (n = 29) had lower topological surface (SURF) density (p < 0.0005) and surface‐to‐curve ratio (SCR; a measure of the ratio of platelike to rodlike trabeculae; p < 0.0005) than those without. Profile interior (PI) density, a measure of intact trabecular rods, was also lower in the deformity group (p < 0.0001). These data provide the first in vivo evidence for the structural implications inherent in postmenopausal osteoporosis accompanying bone loss, that is, the conversion of trabecular plates to rods and disruption of rods due to repeated osteoclastic resorption.

Topological analysis of trabecular bone MR images

Recently, imaging techniques have become available which permit nondestructive analysis of the three-dimensional (3-D) architecture of trabecular bone (TB), which forms a network of interconnected plates and rods. Most osteoporotic fractures occur at locations rich in TB, which has spurred the search for architectural parameters as determinants of bone strength. Here, the authors present a new approach to quantitative characterization of the 3-D microarchitecture of TB, based on digital topology. The method classifies each voxel of the 3-D structure based on the connectivity information of neighboring voxels. Following conversion of the 3-D digital image to a skeletonized surface representation containing only one-dimensional (1-D) and two-dimensional (2-D) structures, each voxel is classified as a curve, surface, or junction. The method has been validated by means of synthesized images and has subsequently been applied to TB images from the human wrist. The topological parameters were found to predict Youngs modulus (YM) for uniaxial loading, specifically, the surface-to-curve ratio was found to be the single strongest predictor of YM (r/sup 2/=0.69). Finally, the method has been applied to TB images from a group of patients showing very large variations in topological parameters that parallel much smaller changes in bone volume fraction (BVF).

Indirect Measurement of Regional Axon Diameter in Excised Mouse Spinal Cord with Q-space Imaging: Simulation and Experimental Studies

Q-space imaging (QSI), a diffusion MRI technique, can provide quantitative tissue architecture information at cellular dimensions not amenable by conventional diffusion MRI. By exploiting regularities in molecular diffusion barriers, QSI can estimate the average barrier spacing such as the mean axon diameter in white matter (WM). In this work, we performed ex vivo QSI on cervical spinal cord sections from healthy C57BL/6 mice at 400 MHz using a custom-designed uniaxial 50T/m gradient probe delivering a 0.6 microm displacement resolution capable of measuring axon diameters on the scale of 1 microm. After generating QSI-derived axon diameter maps, diameters were calculated using histology from seven WM tracts (dorsal corticospinal, gracilis, cuneatus, rubrospinal, spinothalamic, reticulospinal, and vestibulospinal tracts) each with different axon diameters. We found QSI-derived diameters from regions drawn in the seven WM tracts (1.1 to 2.1 microm) to be highly correlated (r(2)=0.95) with those calculated from histology (0.8 to 1.8 microm). The QSI-derived values overestimated those obtained by histology by approximately 20%, which is likely due to the presence of extra-cellular signal. Finally, simulations on images of synthetic circular axons and axons from histology suggest that QSI-derived diameters are informative despite diameter and axon shape variation and the presence of intra-cellular and extra-cellular signal. QSI may be able to quantify nondestructively changes in WM axon architecture due to pathology or injury at the cellular level.

Biexponential diffusion attenuation in the rat spinal cord: Computer simulations based on anatomic images of axonal architecture

Water diffusion in neurological tissues is known to possess multicomponent diffusion behavior. The fractions of fast and slow apparent diffusion components have often been attributed to the volume fractions of extracellular space (ECS) and intracellular space (ICS) although diffusion fractions are at variance with the tissue compartment volume ratios. In this article this puzzle was examined with a finite difference diffusion simulation model on the basis of optical images from sectioned rat spinal cord. Here the results show that assignment of fractions obtained from biexponential fits of fast and slow diffusion attenuation to ECS and ICS volume ratios is not correct. Rather, the observed multicomponent diffusion behavior is caused by motional restriction and limited intercompartmental water exchange in that at long diffusion times diffusion attenuation is shown to become monoexponential. Although the measured apparent diffusion fractions also depend on T2 relaxation time of water protons in the various compartments, the sensitivity to T2 is small and thus T2 differences are unlikely to explain the mismatch between apparent diffusion fractions and cellular volume fractions. Magn Reson Med 47:455–460, 2002.

Probability-based structural parameters from three-dimensional nuclear magnetic resonance images as predictors of trabecular bone strength

The mechanical competence of trabecular bone is a function of its apparent density and three-dimensional (3D) distribution. Three-dimensional structure is typically inferred from histomorphometry and stereology on a limited number of two-dimensional anatomic sections. In this work 3D nuclear magnetic resonance (NMR) images of anisotropic trabecular bone from the distal radius were analyzed in terms of a series of new structural parameters which are obtainable at relatively crude resolution, i.e., in the presence of substantial partial volume blurring. Unlike typical feature extraction techniques requiring image segmentation, the method relies on spatial autocorrelation analysis, which is based on the probability of finding bone at specified locations. The structural parameters were measured from high-resolution images (78x78x78 microm3 voxels) of 23 trabecular bone specimens from the distal radius. Maximum-likelihood bone volume fractions (BVF) were calculated for each voxel and a resolution achievable in vivo (156x156x391 microm3 voxels) was simulated by averaging BVFs from neighboring voxels. The parameters derived from the low-resolution images were found to account for 91% of the variation in Youngs modulus. The results suggest that noninvasive assessment of the mechanical competence of trabecular bone in osteoporotic patients may be feasible.

Genomic Mapping and Survival Prediction in Glioblastoma: Molecular Subclassification Strengthened by Hemodynamic Imaging Biomarkers

PURPOSE To correlate tumor blood volume, measured by using dynamic susceptibility contrast material-enhanced T2*-weighted magnetic resonance (MR) perfusion studies, with patient survival and determine its association with molecular subclasses of glioblastoma (GBM). MATERIALS AND METHODS This HIPAA-compliant retrospective study was approved by institutional review board. Fifty patients underwent dynamic susceptibility contrast-enhanced T2*-weighted MR perfusion studies and had gene expression data available from the Cancer Genome Atlas. Relative cerebral blood volume (rCBV) (maximum rCBV [rCBV(max)] and mean rCBV [rCBV(mean)]) of the contrast-enhanced lesion as well as rCBV of the nonenhanced lesion (rCBV(NEL)) were measured. Patients were subclassified according to the Verhaak and Phillips classification schemas, which are based on similarity to defined genomic expression signature. We correlated rCBV measures with the molecular subclasses as well as with patient overall survival by using Cox regression analysis. RESULTS No statistically significant differences were noted for rCBV(max), rCBV(mean) of contrast-enhanced lesion or rCBV(NEL) between the four Verhaak classes or the three Phillips classes. However, increased rCBV measures are associated with poor overall survival in GBM. The rCBV(max) (P = .0131) is the strongest predictor of overall survival regardless of potential confounders or molecular classification. Interestingly, including the Verhaak molecular GBM classification in the survival model clarifies the association of rCBV(mean) with patient overall survival (hazard ratio: 1.46, P = .0212) compared with rCBV(mean) alone (hazard ratio: 1.25, P = .1918). Phillips subclasses are not predictive of overall survival nor do they affect the predictive ability of rCBV measures on overall survival. CONCLUSION The rCBV(max) measurements could be used to predict patient overall survival independent of the molecular subclasses of GBM; however, Verhaak classifiers provided additional information, suggesting that molecular markers could be used in combination with hemodynamic imaging biomarkers in the future.

Outcome Prediction in Patients with Glioblastoma by Using Imaging, Clinical, and Genomic Biomarkers: Focus on the Nonenhancing Component of the Tumor

PURPOSE To correlate patient survival with morphologic imaging features and hemodynamic parameters obtained from the nonenhancing region (NER) of glioblastoma (GBM), along with clinical and genomic markers. MATERIALS AND METHODS An institutional review board waiver was obtained for this HIPAA-compliant retrospective study. Forty-five patients with GBM underwent baseline imaging with contrast material-enhanced magnetic resonance (MR) imaging and dynamic susceptibility contrast-enhanced T2*-weighted perfusion MR imaging. Molecular and clinical predictors of survival were obtained. Single and multivariable models of overall survival (OS) and progression-free survival (PFS) were explored with Kaplan-Meier estimates, Cox regression, and random survival forests. RESULTS Worsening OS (log-rank test, P = .0103) and PFS (log-rank test, P = .0223) were associated with increasing relative cerebral blood volume of NER (rCBVNER), which was higher with deep white matter involvement (t test, P = .0482) and poor NER margin definition (t test, P = .0147). NER crossing the midline was the only morphologic feature of NER associated with poor survival (log-rank test, P = .0125). Preoperative Karnofsky performance score (KPS) and resection extent (n = 30) were clinically significant OS predictors (log-rank test, P = .0176 and P = .0038, respectively). No genomic alterations were associated with survival, except patients with high rCBVNER and wild-type epidermal growth factor receptor (EGFR) mutation had significantly poor survival (log-rank test, P = .0306; area under the receiver operating characteristic curve = 0.62). Combining resection extent with rCBVNER marginally improved prognostic ability (permutation, P = .084). Random forest models of presurgical predictors indicated rCBVNER as the top predictor; also important were KPS, age at diagnosis, and NER crossing the midline. A multivariable model containing rCBVNER, age at diagnosis, and KPS can be used to group patients with more than 1 year of difference in observed median survival (0.49-1.79 years). CONCLUSION Patients with high rCBVNER and NER crossing the midline and those with high rCBVNER and wild-type EGFR mutation showed poor survival. In multivariable survival models, however, rCBVNER provided unique prognostic information that went above and beyond the assessment of all NER imaging features, as well as clinical and genomic features.

Subvoxel processing: A method for reducing partial volume blurring with application to in vivo MR images of trabecular bone

Partial volume blurring precludes accurate measurement of structural dimensions in the limited‐resolution regime in which image voxel size is larger than the typical structural element to be resolved. Since acquiring images at increased resolution often exacts an unacceptable signal‐to‐noise ratio (SNR) penalty, methods to alleviate the adverse effects of partial volume blurring are instrumental for the accurate measurement of architectural parameters in applications such as predicting the mechanical competence of trabecular bone networks. In the current work, a novel post‐processing method, referred to as “subvoxel processing,” is described for increasing apparent image resolution. The method is applicable to volumes of interest containing material phases of two discrete signal intensities. The principal strategy consists of subdividing voxels and assigning voxel intensities to each subvoxel on the basis of local neighborhood criteria and strict mass conservation. In the current work, the methods accuracy has been evaluated using microcomputed tomography images (22 × 22 × 22 μm3 voxel size) of human trabecular bone. The results demonstrate that subvoxel processing is significantly more accurate than trilinear interpolation in decreasing apparent voxel size, especially in the presence of noise. In addition, the methods effectiveness is illustrated with MR images of human trabecular bone acquired in vivo at 137 × 137 × 350 μm3 voxel size. The subvoxel‐processed images are shown to have architectural features characteristic of images acquired at higher spatial resolution. Magn Reson Med 47:948–957, 2002.

An image‐based finite difference model for simulating restricted diffusion

Water diffusion in tissues is generally restricted and often anisotropic. Neural tissue is of particular interest, since it is well known that injury alters diffusion in a characteristic manner. Both Monte Carlo simulations and approximate analytical models have previously been reported in attempts to predict water diffusion behavior in the central nervous system. These methods have relied on axonal models, which assume simple geometries (e.g., ellipsoids, cylinders, and square prisms) and ignore the thickness of the myelin sheath. The current work describes a method for generating models using synthetic images. The computations are based on a 3D finite difference (FD) approximation of the diffusion equation. The method was validated with known analytic solutions for diffusion in a cylindrical pore and in a hexagonal array of cylinders. Therefore, it is envisioned that, by exploiting histologic images of neuronal tissues as input model, current method allows investigating the water diffusion behavior inside biological tissues and potentially assessing the status of neural injury and regeneration. Magn Reson Med 50:373–382, 2003.

ESTIMATING VOXEL VOLUME FRACTIONS OF TRABECULAR BONE ON THE BASIS OF MAGNETIC RESONANCE IMAGES ACQUIRED IN VIVO

A method is described for extracting information from images acquired in the limited spatial resolution regime in which the structures to be identified are smaller than the image voxel size. Under these conditions and in the presence of noise, the voxel intensity histogram is monomodal; therefore, segmenting the image with an intensity threshold is inaccurate. The present method, which is applicable to two‐phase materials of discrete intensity, relies on iterative deconvolution to obtain a noiseless histogram. A noiseless image is then generated on the basis of the noiseless histogram and the unprocessed image. In the current work, the method is referred to as bone volume fraction (BVF) mapping, since it has been applied to determine the spatial distribution of trabecular bone. BVF computed from maps generated on the basis of in vivo magnetic resonance images of the human radius has been shown to compare well with bone mineral density (R2 = 0.8). The accuracy and precision of BVF measurements have been further evaluated by using a BVF map of the radius as a gold standard and then adding different levels of noise to generate test images. The results suggest that the error in BVF is <0.01 for SNR > 8.