Collaborative Research: Novel mathematical methods for retrieving mechanical properties and microstructural information of cancellous bones

Bob Gilbert collaborative with Philippe Guyenne, Yvonne Ou at the Oakridge National Laboratory and Mathew Lewis at the University of Texas Medical School

The aim of this proposal is to provide a mathematical background for understanding the use of ultrasound methodology for osteoporosis diagnosis and to begin the investigations of the dynamics of osteoporosis. To understand exactly what mechanical information of cancellous bone can be extracted from ultrasound measurement, especially in the lower frequency range (< 100 kHz) where effective theory applies, this project proposes to 1) develop accurate both low (< 100 kHz) and high (1-2 MHz) frequency ultrasound models for the isonification of cancellous bone, 2) test these models by solving the inverse acoustic model for the e ective bone parameters and compare with experimental results and 3) correlate microscopic bone parameters with macroscopic parameters using the methods of dehomogenization. Two different mathematical approaches are applied in order to go beyond periodic microstructure: one by variant of Tartar's method of oscillating test functions, the other by stochastic-two-scale homogenization.

Article created: August 28, 2009