Trabecular networks of cancellous bone show complex and stochastic characteristics, which have to be modelled in an adequate way to determine pathological changes of the network induced by osteoporosis. The analysis of complexity may be handled by the use of the Markov Theory, which is based on local interactions of a set of
elements and thus can be applied to trabecular networks. The conditional entropy which is investigated as a potential measure of complexity, estimates the order of a structure and thus provides a means for classification of healthy versus osteoporotic bone structures. Since the conditional entropy is based on transition probabilities, stochastic characteristics are modelled, too. From a set of 29 female human vertebra T12, classified into two groups of 18 non-osteoporotic and 11 osteoporotic vertebrae axial biopsies were excised from the centre of the vertebral body. A digital model of the trabecular network was extracted with a Micro-CT device (FanBeam Microscope, Stratec, Pforzheim, Germany). Transition probabilities between neighboured voxels were coded as a set of 18 symbols describing the local dimension of a voxel and its relationship to its neighbours within a certain distance. A tree graph of the symbolic transitions coded the transition probabilities and founded a basis
for the calculation of the local conditional entropy as a measure of order. The estimated local entropy for a distance at and above 10 voxels showed significantly higher values for the non-osteoporotic subjects than for the osteoporotic ones. This difference indicates, that non-osteoporotic trabecular networks show a higher degree of
disorder compared to the osteoporotic ones.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.