A method has recently been introduced to analyze cancellous bone in planar sections with four axes; however, the computational method itself has not yet been published. This paper presents a new method and numerical analysis of the results by using a computer-assisted technique to decompose the linear-nonlinear matrix of cancellous bone in planar sections into three components that describe the shape of the material. Computational results reveal structural insights that were not apparent by surface inspection, such as the presence of longitudinal bone on the midfacial bones of mummified animals and the existence of cancellous bone on the skull of humans as well as an uncharacteristically large concentration of cancellous bone on and near the base of the human mandible. It will be the purpose of this paper to develop this method and to analyze experimental data pertaining to cancellous bone, including human mummies, from five regions of the world. Results for the other regions of the world, including Egypt, Israel, North America, Europe, Africa, and Asia, will be studied by use of standard geometric methods (topology) and by analyzing the relationships between the shape of the cancellous bone, its morphology, and its distribution. Finally, the method will be applied to evaluate bone samples from mummified and nonmummified animals, using the results of bone and soft tissue analyzes to determine if the materials have been damaged by burial or use. Introduction: The development of stereo lithographic (SL) machinery for scanning materials, particularly bones, at high resolution has resulted in a new field of computational biology involving the analysis of the structure of biological material (1, 2). Recently, a new computational approach was used to characterize anisotropic cancellous bone, a material with four axes of orientation in the natural environment (3–7, 8, 9). Analysis of this material requires a computational technique that can decompose the linear-nonlinear matrix of anisotropic bone in planar sections into three components, describing the shape of the material; these components are expressed on two planes and can be measured. If bone material is composed of six axes of orientation with orientation in two planes and a spatial resolution of 1.0 nm in the axial plane, then the decomposition of the matrix in planar sections is 4 × 16 × 12 = 3.
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Journal of Ortiz opted Research 9:91&931 Raven Press, Ltd., New York O 1991 Orthopedic Research Society Computational Methods for Analyzing the Structure of Cancellous Bone in Planar Sections Arthur
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