After obtaining an MR image, pre-processing of the image is usually required in order to improve the signal-to-noise ratio and image quality and make it possible to differentiate marrow from bone trabeculae. Pre-processing may include coil correction, noise reduction, motion correction, and thresholding. Coil correction is required to correct spatial variations in the sensitivity of the detection coil as tissue close to the coil usually appears brighter than tissue further away from the coil. Coil correction algorithms depend on the structure of the specific coil. Coils that completely surround the object being scanned (e.g. bird-cage coil) provide sufficient in-plane homogeneity, making longitudinal correction sufficient. In surface coils, which may not provide in-plane homogeneity, a low-pass filter (LPF)- based coil correction scheme is necessary (Figure 4). Noise reduction improves the signal-to-noise ratio and may be accomplished using a median low pass filter, in which the median of the pixels in a certain kernel size (e.g. 3×3 pixels) surrounding a pixel becomes the new filtered value for the pixel. A low pass filter removes high signal noise, while preserving the low signal data. The kernel median allows edge detection, whereas the kernel mean would smooth the data and blur the edges. Hwang et al. proposed a histogram deconvolution method in order to obtain a noiseless histogram for trabecular bone. In this method a probability distribution of the noise (e.g. Gaussian) and an initial estimate of the noiseless histogram are assumed in order to predict a histogram. The predicted histogram is iteratively improved by comparing it to the measured histogram. The noiseless histogram and raw image are used to produce a noiseless image. Others have proposed wavelet-based thresholding that allows more local noise reduction while retaining relevant detail information. Imaging trabeculae on the order of 100 ^m means that a small amount of motion will affect the image. Various techniques have been devised to correct for motion artifacts. Navigator correction alters the echo sequence, adding echos to sense small displacements. The data is corrected in k-space by analyzing the phase shift and adjusting for translational motions. Studies have shown that navigator correction improves reproducibility and accuracy of trabecular bone parameters. Retrospective motion correction can also be performed with autofocusing (Figure 5). This technique applies trial phase shifts to the data and compares the resulting image with the original. An entropy focusing criterion is applied to minimize the amount of entropy in the image and obtain maximum contrast.
Perhaps the most critical pre-processing step is thresholding, which allows delineation of the trabeculae and the marrow. Because the resolution of in vivo MR images is on the same scale as the trabecular width, partial volume effects occur. In partial voluming, a single voxel may contain signals from multiple tissue types. The voxel intensity is the average signal from the various tissues. The histogram of trabecular bone, therefore, is not bi-modal with marrow and bone peaks, but rather mono modal with a peak intensity between the values of marrow and bone. Various thresholding methods have been established in order to segment the bone from the marrow where partial volume effects are an issue. Majumdar et al. proposed a dual thresholding method in which the threshold for bone was a mean pixel value taken in the cortical shell and the threshold for marrow was the lower signal intensity at which the histogram reached half its peak.
Link et al. compared global and local thresholding methods. Global thresholding applies the same threshold throughout the entire image. The disadvantage of global thresholding is that images of with a dense trabecular structure appear completely black, while images with a sparse trabecular structure appear white. Using local thresholding the intesity of a square region surrounding a pixel is averaged. If the central pixel has an intensity lower than the average, it is considered bone; higher than average pixels are considered marrow. Local thresholding is not affected by bone density, but is dependent on noise in the image. It was found that global thresholding was more accurate in calculating trabecular thickness and local thresholding was more accurate in predicting trabecular spacing.
Figure 4 – Effects of coil correction on sagittal images of the calcaneus. Coil correction equalizes the fat and marrow intensities throughout the visible bone.
Wu et al. introduced a Bayesian approach to segment bone from marrow in which each voxel was divided into subvoxels. The local tissue environment influenced the distribution of bone and marrow within the subvoxels with a Gibbs distribution modeling the interaction between subvoxels. This approach improves segmentation but has only been performed on images from small-bore NMR microscopy machines and has yet to be applied to clinical scans. Hwang et al. proposed a spatial autocorrelation analysis which also used the local tissue environment to determine the probability of finding bone at specified locations. This method was used to analyze images at in vivo resolution (voxel size of 156x156x391 |im3). Similarly, a relaxation labeling process that takes into account the spatial context, in particular local contextual information (as in Markov fields) was used by Antoniadis et al. to segment trabecular bone. Each pixel was assigned a probability of being bone or marrow and then iteratively updated according to the local and surrounding segments until the probability of each pixel was either 1 or 0. Thresholding using one of these techniques results in a binarized image that consists of only bone or marrow voxels. Beat the drug companies and
Figure 5 – Coronal images of the shoulder. A. Original image corrupted by motion. B. After motion correction (From Atkinson et al., Magnetic Resonance in Medicine 1999;41:169. Reprinted with permission of Wiley-Liss Inc., a subsidiary of John Wiley & Sons Inc., Copyright 1999).