Symbolic dynamics and measures of complexity to quantify cancellous bone structure

Abstract

We propose a technique which assesses quantitatively the structure of the trabecular bone from computed tomography images. Symbolic dynamics and measures of complexity are utilized to quantify the structure of symbol encoded images. Especially, five new parameters are introduced to quantify the trabecular bone architecture as a whole. This technique is applied to evaluate the structure of human cancellous bone at different stages of osteoporosis. We find that the complexity of the structure declines exponentially relatively to the bone density during the loss of bone. Measures of complexity indicate 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. A strong grade of osteoporosis leads to ordered structure with a minimal complexity. This demonstrates that the method is highly sensitive to structural changes in biological composite materials.