Fractal analysis of radiographs: Assessment of trabecular bone structure and prediction of elastic modulus and strength

The purpose of this study was to determine whether fractal dimension of rad iographs provide measures of trabecular bone structure which correlate with bone mineral density (BMD) and bane biomechanics, and whether these relati onships depend on the technique used to calculate the fractal dimension. Ei ghty seven cubic specimen of human trabecular bone were obtained from the v ertebrae and femur. The cubes were radiographed along all three orientation s-superior-inferior (SI), medial-lateral (ML), and anterior-posterior (AP), digitized, corrected for background variations, and fractal based techniqu es were applied to quantify trabecular structure. Three different technique s namely, semivariance, surface area, and power spectral methods were used. The specimens were tested in compression along three orientations and the Young's modulus-(YM) was determined. Compressive strength was measured alon g the SI direction. Quantitative computed tomography was used to measure tr abecular BMD. High-resolution magnetic-resonance images were used to obtain three-dimensional measures of trabecular architecture such as the apparent bone volume fraction, trabecular thickness, spacing, and number. The measu res of trabecular structure computed in the different directions showed sig nificant differences (p<0.05). The correlation between BMD, YM, strength, a nd the fractal dimension were direction and technique dependent. The trends of variation of the fractal dimension with BMD and biomechanical propertie s also depended On the technique and the range of resolutions over which th e data was analyzed. The fractal dimension showed varying trends with bone mineral density changes, and these trends also depended on the range of fre quencies over which the fractal dimension was measured. For example, using the power spectral method the fractal dimension increased with BMD when com puted over a lower range of spatial frequencies and decreased for higher ra nges. However, for the surface area technique the fractal dimension increas ed with increasing BMD. Fractal measures showed better correlation with tra becular spacing and number, compared to trabecular thickness. In a multivar iate regression model inclusion of some of the fractal measures in addition to BMD improved the prediction of strength and elastic modulus. Thus, frac tal based texture analysis of radiographs are technique dependent, but may be used to quantify trabecular structure and have, a potentially valuable i mpact in the study of osteoporosis. (C) 1999 American Association of Physic ists in Medicine. [S0094-2405(99)00207-2].