Lacunarity analysis of spatial pattern in CT images of vertebral trabecular bone for assessing osteoporosis

Abstract

The structural integrity of vertebral trabecular bone is determined by the continuity of its trabecular network and the size of the holes comprising its marrow space, both of which determine the apparent size of the marrow spaces in a transaxial CT image. A model-independent assessment of the trabeculation pattern was determined from the lacunarity of thresholded CT images. Using test images of lumbar vertebrae from human cadavers, acquired at different slice thicknesses, we determined that both median thresholding and local adaptive thresholding (using a 7×7 window) successfully segmented the grey-scale images. Lacunarity analysis indicated a multifractal nature to the images, and a range of marrow space sizes with significant structure around 14–18 mm2. Preliminary studies of in vivo images from a clinical CT scanner indicate that lacunarity analysis can follow the pattern of bone loss in osteoporosis by monitoring the homogeneity of the marrow spaces, which is related to the connectivity of the trabecular bone network and the marrow space sizes. Although the patient sample was small, derived parameters such as the maximum deviation of the lacunarity from a neutral (fractal) model, and the maximum derivative of this deviation, seem to be sufficiently sensitive to distinguish a range of bone conditions. Our results suggest that these parameters, used with bone mineral density values, may have diagnostic value in characterizing osteoporosis and predicting fracture risk.

The structural integrity of vertebral trabecular bone is determined by the continuity of its trabecular network and the size of the holes comprising its marrow space, both of which determine the apparent size of the marrow spaces in a transaxial CT image. A model-independent assessment of the trabeculation pattern was determined from the lacunarity of thresholded CT images. Using test images of lumbar vertebrae from human cadavers, acquired at different slice thicknesses, we determined that both median thresholding and local adaptive thresholding (using a 7×7 window) successfully segmented the grey-scale images. Lacunarity analysis indicated a multifractal nature to the images, and a range of marrow space sizes with significant structure around 14–18 mm2. Preliminary studies of in vivo images from a clinical CT scanner indicate that lacunarity analysis can follow the pattern of bone loss in osteoporosis by monitoring the homogeneity of the marrow spaces, which is related to the connectivity of the trabecular bone network and the marrow space sizes. Although the patient sample was small, derived parameters such as the maximum deviation of the lacunarity from a neutral (fractal) model, and the maximum derivative of this deviation, seem to be sufficiently sensitive to distinguish a range of bone conditions. Our results suggest that these parameters, used with bone mineral density values, may have diagnostic value in characterizing osteoporosis and predicting fracture risk.