Fractal Properties of Cancellous Bone of the Iliac Crest in Vertebral Crush Fracture

Abstract

Fractal analysis is a method for describing complex shapes, including the cancellous structure of bone. It describes the surface texture and form of individual trabecular profiles and the overall cancellous structure. Sixty-four postmenopausal women with symptoms of back pain were referred for investigation for osteoporosis. The patients were divided into two groups for comparison: vertebral crush fracture (n = 31, mean age 68.58 ± 6.47 years), and no vertebral crush fracture (n = 33, mean age 63.36 ± 7.21 years). Cores of cancellous bone, 3 mm in diameter, were taken from the iliac crest and sectioned. A box-counting method implemented on an image analyzer was used to measure the fractal dimension. Three fractal dimensions describing trabecular surface texture (fractal 1), trabecular shape (fractal 2), and trabecular arrangement (fractal 3) were measured, indicating that cancellous bone has sectional self-similarity. Conventional histomorphometry was also performed on the samples. The results show that fractal 2 is significantly lower in the vertebral crush fracture group than in the nonfracture group (1.15 ± 0.10 < 1.23 ± 0.090, p < 0.0013). The histomorphometric analysis shows that bone surface total volume ( p < 0.0002), trabecular number ( p < 0.0001), and osteoid surface bone surface ( p < 0.028) are significantly lower in the fracture group than the nonfracture group. Eroded surface/bone surface ( p < 0.056) follows this trend, whereas trabecular separation ( p < 0.001) is significantly higher in the fracture group than in the nonfracture group. Fractal 1 and fractal 3 were not significantly different between study groups. The fractal dimension detects changes in the cancellous architecture and gives information about iliac bone transformation in postmenopausal women with vertebral fracture.