Invariant Characteristics of Networks and Patterns and Their Applications

University Of Houston, Houston TX

Investigators

Abstract

0201001 Gunaratne Osteoporosis is a major socio-economic problem in western societies. Since excessive use of therapeutic agents can have adverse consequences, non-invasive diagnostic tools to determine the need for intervention are essential for bones from older adults is the inner porous region whose structure is reminiscent of disordered cubic networks. The strength of a bone depends on several facets of this network, including its connectivity, the anisotropy, and the level of bone turnover. It is extremely difficult to account for these factors and complex interactions between them in clinical studies or in experiments on ex-vivo bone samples. We have introduced a model of porous bone, and propose to use it to develop a more comprehensive understanding of mechanical causes underlying bone decay. The insights gained from this study can be used to identify novel diagnostic tools to determine the need for therapeutic intervention. In particular, such properties cannot depend on most details of the porous bone; i.e., they need to be invariant characteristics. The model system was used to derive a new expression that relates the strength of a bone to its effective density. It will be tested using previously published data on human bone. Analysis of the model also provided a diagnostic (based on linear response) of the strength of networks. Tests will be conducted to determine how accurately it can predict the strength of bone samples. We also propose to study effects of factors like anisotropy on bone strength, and to develop methods to estimate these factors in-vivo. The second problem proposed is an application of a characteristic that quantifies the level of disorder in a pattern. The form of this measure was deduced by requiring its invariance under all rigid (i.e., Euclidean) motions of the pattern. We propose to use it to estimate the roughness of a surface on a nano-meter scale by characterizing the disorder in a speckle pattern formed by reflecting a laser beam from the surface. Such a characterization is expected find application in (for example) the auto industry.