Testing Two Predictions for Fracture Load Using Computer Models of Trabecular Bone

¹ Rice University
² University of Zurich
³ University of Houston
⁴ Robert Wood Johnson Medical School

^* To whom correspondence should be addressed. E-mail: gemunu{at}uh.edu.

Submitted on December 3, 2004
Revised on March 1, 2005
Accepted on 8 April 2005

	Abstract

Aging induces several types of architectural changes in trabecular bone including thinning, increased levels of anisotropy, and perforation. It has been determined, on the basis of analysis of mathematical models, that reduction in fracture load caused by perforation is significantly higher than those due to equivalent levels of thinning or anisotropy. The analysis has also provided an expression which relates the fractional reduction of strength to the fraction of elements that have been removed from a network. Further, it was proposed that the ratio of the elastic constant of a sample and its linear response at resonance can be used as a surrogate for . Experimental validation of these predictions requires following architectural changes in a given sample of trabecular bone; techniques to study such changes using micro computed tomography are just beginning to be available. In the present study, we use anatomically accurate computer models constructed from digitized images of bone samples for the purpose. Images of healthy bone are subjected to successive levels of synthetic degradation via surface erosion. Computer models constructed from these images are used to calculate their fracture load and other mechanical properties. Results from these computations are shown to be consistent with predictions derived from the analysis of mathematical models. Although the form of is known, parameters in the expression are expected to be sample specific, and hence is not a reliable predictor of strength. We provide an example to demonstrate this. In contrast, analysis of model networks shows that the linear part of depends only on the structure of trabecular bone. Computations on models constructed from samples of iliac crest trabecular bone are shown to be in agreement with this assertion. Since can be computed from a vibrational assessment of bone, we argue that the latter can be used to introduce new surrogates for bone strength and hence diagnostic tools for osteoporosis.

Key Words: bone strength, linear response, networks, osteoporosis