Markovianity of trabecular networks
Clinically established methods to diagnose osteoporosis, a systemic disease with multiple implications to the human's well being are bound to the bone mineral density. Since it is well known, that the bone structure changes under osteoporosis, this thesis investigates, whether structural changes represent information independent of bone mineral density, and whether this structural information, obtained by innovative mathematical techniques improves first the ability to distinguish between osteoporotic and healthy structures, second the measurement of a risk to belong to the osteoporotic group, and third the prediction of a biomechanical measure, the failure load, compared to existing standard structural measures. By building a bridge between natural patterns of human cancellous bone to mathematical and stochastic algorithms capable of modeling complex structures this in vitro study proposed a successful way to catch the specifics of these natural patterns and to improve the current structural analysis methods. Methods investigated included Markov point processes, hidden Markov models and conditional entropie.