Ekaterina Novitaskaya1, Po-Yu Chen3, Vlado Lubarda2, Joanna McKittrick1,2
1 Materials Science and Engineering Program, 2Department of Mechanical and Aerospace Engineering, University of California, San Diego, USA
3Department of Materials Science and Engineering, National Tsing Hua Universit
An analysis of osteoporotic degradation of elastic moduli of cancellous bone is presented. Two evolution equations are introduced, one for the rate of mass loss of the mineral content, and the other for the protein loss of cancellous bone. These losses are associated with the bone density and the volume changes, for which appropriate equations are proposed. With additional evolution equations for morphological parameters accounting for the trabecular microarchitecture, the evolution equations are derived for elastic moduli of deproteinated, demineralized and composite cancellous bone. An appealing special case is considered in which it is assumed that the relative ratios of the mineral and protein loss are equal to each other during progression of osteoporosis. The cellular mechanics approach is used to express the bulk moduli of elasticity in terms of trabecular moduli of elasticity, and the corresponding density ratios. An appropriate weight function is introduced to describe the mineral/protein interaction effects and the departure from an ideal mixture rule. The material parameters are specified from experimental results obtained by compressive testing of untreated, deproteinated, and demineralized cancellous bovine femur bone. This research is funded by the National Science Foundation, Division of Materials Research, Ceramics Program (Grant 1006931).
