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Published in: Osteoporosis International 8/2010

Open Access 01-08-2010 | Original Article

A paediatric bone index derived by automated radiogrammetry

Authors: H. H. Thodberg, R. R. van Rijn, T. Tanaka, D. D. Martin, S. Kreiborg

Published in: Osteoporosis International | Issue 8/2010

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Abstract

Summary

Hand radiographs are obtained routinely to determine bone age of children. This paper presents a method that determines a Paediatric Bone Index automatically from such radiographs. The Paediatric Bone Index is designed to have minimal relative standard deviation (7.5%), and the precision is determined to be 1.42%.

Introduction

We present a computerised method to determine bone mass of children based on hand radiographs, including a reference database for normal Caucasian children.

Methods

Normal Danish subjects (1,867), of ages 7–17, and 531 normal Dutch subjects of ages 5–19 were included. Historically, three different indices of bone mass have been used in radiogrammetry all based on \( A = \pi {\text{ }}T{\text{ }}W\left( {{\text{1}} - T/W} \right) \), where T is the cortical thickness and W the bone width. The indices are the metacarpal index A/W 2, DXR-BMD = A/W, and Exton-Smith’s index A/(WL), where L is the length of the bone. These indices are compared with new indices of the form A/(W a L b ), and it is argued that the preferred index has minimal SD relative to the mean value at each bone age and sex. Finally, longitudinal series of X-rays of 20 Japanese children are used to derive the precision of the measurements.

Results

The preferred index is A/(W 1.33 L 0.33), which is named the Paediatric Bone Index, PBI. It has mean relative SD 7.5% and precision 1.42%.

Conclusions

As part of the BoneXpert method for automated bone age determination, our method facilitates retrospective research studies involving validation of the proposed index against fracture incidence and adult bone mineral density.
Footnotes
1
These paths are constructed using dynamic programming [15]. The original image has a resolution of 150 dpi, corresponding to a pixel size 170 × 170 μm. The algorithm first resamples the image in each ROI to an image with pixels aligned with the bone axis. The new pixel size is 850 μm along the bone axis and 186 μm across the bone axis. A typical ROI extends 1.5 mm along the bone axis or approximately 17 pixels (Fig. 1 shows the path at every second of these pixels inside each ROI). The outer and inner borders of the cortex are thus determined approximately 6 × 17 ≈ 100 times with a resolution of 186 μm in the six cortical areas of the three middle metacarpals, i.e. there are approximately 100 determinations of the cortical thickness. Since the precision SD error from rounding to an integer is approximately 0.3, the precision error from “pixelisation” of the cortex border is 0.3 × 186 μm = 56 μm, and the precision error on T from pixelisation is 56 × √2 μm = 79 μm. Averaging T over the 100 independent determinations yields a precision SD of about 8 μm. The observed precision on T is (as mentioned in the “Results” section) 27 μm. Using a finer pixel size would thus, at best, reduce the precision to 26 μm. This shows that the used image resolution is well adapted to the problem at hand.
 
2
If the three measurements are not taken with even intervals, e is defined as e = PBI2 − PBIinterpolate, where PBIinterpolate is the linear interpolation of PBI1 and PBI3 to the time of PBI2.
 
3
We considered using the term Bone Health Index (BHI) as an alternative name for PBI to reflect that this index is derived as the expression describing the bone balance in healthy children. However, that would perhaps suggest that there is evidence for a good relation between BHI and fracture risk; we do not yet have studies to support that, so we use the more neutral term PBI.
 
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Metadata
Title
A paediatric bone index derived by automated radiogrammetry
Authors
H. H. Thodberg
R. R. van Rijn
T. Tanaka
D. D. Martin
S. Kreiborg
Publication date
01-08-2010
Publisher
Springer-Verlag
Published in
Osteoporosis International / Issue 8/2010
Print ISSN: 0937-941X
Electronic ISSN: 1433-2965
DOI
https://doi.org/10.1007/s00198-009-1085-9

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