A measure of intrinsic strength, not nominal strength, reflects effects of ex-vivo cortical bone matrix modulation by raloxifene

Abstract

Understanding bone strength is important when assessing bone diseases and their treatment. Bending experiments are often used to determine strength. Then, flexural stresses are calculated from elastic bending theory. With a brittle failure criterion, the maximum flexural tensile stress is equated to (nominal) strength. However, bone is not a perfectly brittle material. A quasi-brittle failure criterion is more appropriate. Such an approach allows for material failure to occur before full fracture. The extent of the subcritical damage domain then introduces a length scale. The intrinsic strength of the bone is calculated from the critical load at fracture and the failure process zone dimensions relative to the specimen size. We apply this approach to human cortical bone specimens extracted from a femur. We determine strength measures in the untreated reference state and after treatment with the selective estrogen receptor modulator raloxifene. We find that the common nominal strength measure does not distinguish between treatments. However, the dimensions of the failure process zone differ between treatments. Intrinsic strength measures then are demonstrated as descriptors of bone strength sensitive to treatment. An extrapolation of laboratory data to whole bone is demonstrated.