Radiographic texture analysis of densitometer-generated calcaneus images differentiates postmenopausal women with and without fractures

Abstract

Introduction

Bone fragility is determined by bone mass, measured as bone mineral density (BMD), and by trabecular structure, which cannot be easily measured using currently available noninvasive methods. In previous studies, radiographic texture analysis (RTA) performed on the radiographic images of the spine, proximal femur, and os calcis differentiated subjects with and without osteoporotic fractures. The present cross-sectional study was undertaken to determine whether such differentiation could also be made using high-resolution os calcis images obtained on a peripheral densitometer.

Methods

In 170 postmenopausal women (42 with and 128 without prevalent vertebral fractures) who had no secondary causes of osteoporosis and were not receiving treatment for osteoporosis, BMD of the lumbar spine, proximal femur, and os calcis was measured using dual energy x-ray absorptiometry. Vertebral fractures were diagnosed on densitometric spine images. RTA, including Fourier-based and fractal analyses, was performed on densitometric images of os calcis.

Results

BMD at all three sites and all texture features was significantly different in subjects with and without fractures, with the most significant differences observed for the femoral neck and total hip measurements and for the RTA feature Minkowski fractal (p<0.001). In univariate logistic regression analysis, Minkowski fractal predicted the presence of vertebral fractures as well as femoral neck BMD (p<0.001). In multivariate logistic regression analysis, both femoral neck BMD and Minkowski fractal yielded significant predictive effects (p=0.001), and when age was added to the model, the effect of RTA remained significant (p=0.002), suggesting that RTA reflects an aspect of bone fragility that is not captured by age or BMD. Finally, when RTA was compared in 42 fracture patients and 42 nonfracture patients matched for age and BMD, the RTA features were significantly different between the groups (p=0.003 to p=0.04), although BMD and age were not.

Conclusion

This study suggests that RTA of densitometer-generated calcaneus images provides an estimate of bone fragility independent of and complementary to BMD measurement and age.

Appendix

Formulas used to calculate RTA features

The Fourier-based texture analysis features are given by the following formulas:

$$RMS = {\sqrt {{\sum\limits_m {{\sum\limits_n {{\left| {Fm,n} \right|}^{2} } }} }} }$$

$$FMP = \frac{{{\sum {_{m} } }{\sum {_{n} {\sqrt {m^{2} n^{2} } }{\left| {Fm,n} \right|}^{2} } }}} {{{\sum {_{m} } }{\sum {_{n} {\left| {Fm,n} \right|}^{2} } }}}$$

F _m,n corresponds to the Fourier transform of the background corrected ROI of the trabecular pattern, and m and n are the indices of the ROI array.

Global Minkowski dimension, D[f], is computed for each ROI as given by

$${{D}}_{{{M}}} {\left[ {{f}} \right]} = {\mathop {\lim }\limits_{{\text{ $ \varepsilon $ }} \to 0} }\frac{{\log {\left[ {{{V}}_{{{g}}} {\left( {\text{ $ \varepsilon $ }} \right)}/{\text{ $ \varepsilon $ }}^{3} } \right]}}}{{\log {\left( {1/{\text{ $ \varepsilon $ }}} \right)}}},$$

where f corresponds to the ROI image data. For a structuring element g at scale ε, V _g(ε) is the “volume” between two processed versions of f obtained using morphological operators.

The volume V _g(ε) is computed by

$$V_{G} {\left( \varepsilon \right)} = {\sum\limits_{M = 0}^{64} {{\sum\limits_{N = 0}^{64} {{\left\{ {{\left( {F \oplus \varepsilon G} \right)} - {\left( {F \otimes \varepsilon G} \right)}} \right\}}} }} },$$

where ${\left( {F \oplus \varepsilon G} \right)}$ and ${\left( {F \otimes \varepsilon G} \right)}$ are the dilated version and the eroded version, respectively, of the image obtained using a structuring element g at scale ε. Finding the slope of the least-squares fitted line between log[V _g(ε)/ε³] and log(1/ε) gives the estimated Minkowski fractal dimension.