Binary Local Fractal Dimension: a Precise Structure Parameter for 3D High Resolution Computed Tomography Images of the Human Spongiosa

Abstract

We present the Binary Local Fractal Dimension (LFD) to analyze osteoporosis induced fracture risk with clinical 3D high resolution quantitative computed tomographic (HRCT) images of human vertebrae. We test if LFD parameters provide precise additional information besides bone mineral density (BMD) and standard descriptors of bone quality, for example bone surface ratio (BS/BV). We define a weighted LFD (wLFD) using the ¯R2 of the H¨older exponents. We compare the LFD with standard methods (distance transform, direct secant method and run-length method) on 5 vertebrae × 8 volumes of interest and 5 repeated scans. The wLFD contains the highest direct and BMD-independent precision (R2 = 0.985 and R2 = 0.949), followed by BS/BV (R2 = 0.977 and R2 = 0.920) including low correlation with BMD (wLFD: R2 = 0.704, BS/BV: R2 = 0.814). LFD improves the translation from reference μCT- to clinical HRCT-resolution. In conclusion, LFD provides a strong diagnostic tool to characterize bone quality to predict osteoporosis induced fracture risk.