Fractal analysis of radiographs: Assessment of trabecular bone structure and prediction of elastic modulus and strength

1999 ◽  
Vol 26 (7) ◽  
pp. 1330-1340 ◽  
Author(s):  
Sharmila Majumdar ◽  
John Lin ◽  
Thomas Link ◽  
Jacob Millard ◽  
Peter Augat ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Bone Structure ◽  
Trabecular Bone Structure

In vivoassessment of trabecular bone structure using fractal analysis of distal radius radiographs

2000 ◽  
Vol 27 (11) ◽  
pp. 2594-2599 ◽  
Author(s):  
Sharmila Majumdar ◽  
Thomas M. Link ◽  
Jacob Millard ◽  
John C. Lin ◽  
Peter Augat ◽  
...  
Keyword(s):  
Trabecular Bone ◽  
Distal Radius ◽  
Fractal Analysis ◽  
Bone Structure ◽  
Trabecular Bone Structure

The computed tomography-based fractal analysis of trabecular bone structure may help in detecting decreased quality of bone before urgent spinal procedures

2017 ◽  
Vol 17 (8) ◽  
pp. 1156-1162 ◽  
Author(s):  
Marcin Czyz ◽  
Arion Kapinas ◽  
James Holton ◽  
Renata Pyzik ◽  
Bronek M. Boszczyk ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Bone Structure ◽  
Trabecular Bone Structure

Fractal Based Image Analysis of Human Trabecular Bone using the Box Counting Algorithm

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 275-283 ◽  
Author(s):  
Daniel Osman ◽  
David Newitt ◽  
Alice Gies ◽  
Thomas Budinger ◽  
Vu Hao Truong ◽  
...  
Keyword(s):  
Trabecular Bone ◽  
Fractal Analysis ◽  
Bone Structure ◽  
Trabecular Bone Structure ◽  
Human Trabecular Bone ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Relationship Of ◽  
The Relationship ◽  
Counting Algorithm

An image texture measure based on the box counting algorithm is evaluated for its potential to characterize human trabecular bone structure in medical images. Although bone images lack the self-similarity of theoretical fractals, bone images are candidates for characterization using fractal analysis because of their highly complex structure. The fractal based measure, herein called the box counting dimension (BCD), is an effective dimension, and does not imply an underlying fractal geometry. The importance of resolution in quantifying bone characteristics using the BCD is addressed. The relationship of BCD to standard measures of trabecular bone structure is also analyzed. To evaluate the variability of the BCD with change in resolution, the BCD is determined for two sections from each of seven 3D X-ray Tomographic Microscopy (XTM) images of human radius bone specimens, while the resolution is varied using lowpass filtering. An automated method of choosing the range of scales for the fractal analysis curve regression is used. The relationship of BCD to trabecular bone width and spacing is analyzed both for the XTM images and for simulated images representing idealized structures. The range of BCD values is 1.21–1.54. Variation in BCD over a range of resolutions is found to be small compared to the variation in BCD between different bone specimens. Maximum change in BCD over a large range of resolutions (17.60–176 microns per pixel) is 0.08. BCD decreases as space between trabeculae increases. Fractal based texture measures may potentially allow clinical monitoring of changes in bone structure — for example, using Magnetic Resonance Imaging at 150–200 micron resolution.

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