Three-dimensional multifractal analysis of trabecular bone under clinical computed tomography

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An adequate understanding of bone structural properties is critical for predicting fragility conditions caused by diseases such as osteoporosis, and in gauging the success of fracture prevention treatments. In this work we aim to develop multiresolution image analysis techniques to extrapolate high-resolution images predictive power to images taken in clinical conditions.


We performed multifractal analysis (MFA) on a set of 17 ex vivo human vertebrae clinical CT scans. The vertebræ failure loads (Symbol) were experimentally measured. We combined bone mineral density (BMD) with different multifractal dimensions, and BMD with multiresolution statistics (e.g., skewness, kurtosis) of MFA curves, to obtain linear models to predict Symbol. Furthermore we obtained short- and long-term precisions from simulated in vivo scans, using a clinical CT scanner. Ground-truth data — high-resolution images — were obtained with a High-Resolution Peripheral Quantitative Computed Tomography (HRpQCT) scanner.


At the same level of detail, BMD combined with traditional multifractal descriptors (Lipschitz–Hölder exponents), and BMD with monofractal features showed similar prediction powers in predicting Symbol (87%, adj. R2). However, at different levels of details, the prediction power of BMD with multifractal features raises to 92% (adj. Symbol) of Symbol. Our main finding is that a simpler but slightly less accurate model, combining BMD and the skewness of the resulting multifractal curves, predicts 90% (adj. Symbol) of Symbol.


Compared to monofractal and standard bone measures, multifractal analysis captured key insights in the conditions leading to Symbol. Instead of raw multifractal descriptors, the statistics of multifractal curves can be used in several other contexts, facilitating further research.

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