FRACTAL-BASED IMAGE-ANALYSIS OF HUMAN TRABECULAR BONE USING THE BOX-COUNTING ALGORITHM - IMPACT OF RESOLUTION AND RELATIONSHIP TO STANDARD MEASURES OF TRABECULAR BONE-STRUCTURE

An image texture measure based on the box counting algorithm is evalua ted for its potential to characterize human trabecular bone structure in medical images. Although bone images lack the self-similarity of th eoretical fractals, bone images are candidates for characterization us ing fractal analysis because of their highly complex structure. The fr actal based measure, herein called the box counting dimension (BCD), i s an effective dimension: and does not imply an underlying fractal geo metry. The importance of resolution in quantifying bone characteristic s using the BCD is addressed. The relationship of BCD to standard meas ures of trabecular bone structure is also analyzed. To evaluate the va riability of the BCD with change in resolution, the BCD is determined for two sections from each of seven 3D X-ray Tomographic Microscopy (X TM) images of human radius bone specimens, while the resolution is var ied using lowpass filtering. An automated method of choosing the range of scales for the fractal analysis curve regression is used. The rela tionship of BCD to trabecular bone width and spacing is analyzed both for the XTM images and for simulated images representing idealized str uctures. The range of BCD values is 1.21-1.54. Variation in BCD over a range of resolutions is found to be small compared to the variation i n BCD between different bone specimens. Maximum change in BCD over a l arge range of resolutions (17.60-176 microns per pixel) is 0.08. BCD d ecreases as space between trabeculae increases. Fractal based texture measures may potentially allow clinical monitoring of changes in bone structure - for example, using Magnetic Resonance Imaging at 150-200 m icron resolution.