Quantification of cancellous bone structure using symbolic dynamics and measures of complexity

Abstract

In this study we generalize symbolic dynamics to analyze two-dimensional objects and utilize measures of complexity to quantify the structure of symbol-encoded images. This technique is applied to study quantitatively the structure of human cancellous bone by analyzing computed tomography images. First, the preprocessed images are transformed into symbols, applying a mixture of static and dynamic encoding. Next, the spatial distribution of cancellous bone is evaluated using measures of complexity. New parameters are introduced to quantify the cancellous bone architecture as a whole. The results exhibit that the complexity of the structure declines more rapidly than density during the loss of bone in osteoporosis, strongly suggesting an exponential relationship between bone mass and architecture. It is found that normal bone has complex ordered structure, while the structure during the initial stage of bone loss is characterized by lower complexity and a significantly higher level of disorder, which is maximal there. A strong grade of the bone loss leads again to ordered structure, however its complexity is minimal. In addition, this method is significantly sensitive to changes in structure of natural composite materials.