Three-dimensional quantification of structures in trabecular bone using measures of complexity.
The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high-resolution three-dimensional (3D) imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D microarchitecture of trabecular bone. We introduce an approach based on spatial geometrical properties and define structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organization and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high-resolution microcomputed tomography (microCT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analyzed geometrical features of trabecular bone and loss of bone density, but also indicate that the measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the microCT data sets.
Marwan
Norbert
N
Interdisciplinary Center for Dynamics of Complex Systems, University of Potsdam, 14415 Potsdam, Germany. marwan@pik-potsdam.de
Kurths
Jürgen
J
Thomsen
Jesper Skovhus
JS
Felsenberg
Dieter
D
Saparin
Peter
P
D000465:Algorithms; D015519:Bone Density; D001842:Bone and Bones / Q000000981:diagnostic imaging* / Q000503:physiopathology*; D003198:Computer Simulation; D006801:Humans; D008953:Models, Anatomic; D008954:Models, Biological; D010024:Osteoporosis / Q000000981:diagnostic imaging* / Q000503:physiopathology*; D014057:Tomography, X-Ray Computed / Q000379:methods*