title: Theoretical bounds for the influence of tissue-level ductility on the apparent-level strength of human trabecular bone.
abstract: The role of tissue-level post-yield behavior on the apparent-level strength of trabecular bone is a potentially important aspect of bone quality. To gain insight into this issue, we compared the apparent-level strength of trabecular bone for the hypothetical cases of fully brittle versus fully ductile failure behavior of the trabecular tissue. Twenty human cadaver trabecular bone specimens (5mm cube; BV/TV=6-36%) were scanned with micro-CT to create 3D finite element models (22-micron element size). For each model, apparent-level strength was computed assuming either fully brittle (fracture with no tissue ductility) or fully ductile (yield with no tissue fracture) tissue-level behaviors. We found that the apparent-level ultimate strength for the brittle behavior was only about half the value of the apparent-level 0.2%-offset yield strength for the ductile behavior, and the ratio of these brittle to ductile strengths was almost constant (mean±SD=0.56±0.02; n=20; R(2)=0.99 between the two measures). As a result of this small variation, although the ratio of brittle to ductile strengths was positively correlated with the bone volume fraction (R(2)=0.44, p=0.01) and structure model index (SMI, R(2)=0.58, p<0.01), these effects were small. Mechanistically, the fully ductile behavior resulted in a much higher apparent-level strength because in this case about 16-fold more tissue was required to fail than for the fully brittle behavior; also, there was more tensile- than compressive-mode of failure at the tissue level for the fully brittle behavior. We conclude that, in theory, the apparent-level strength behavior of human trabecular bone can vary appreciably depending on whether the tissue fails in a fully ductile versus fully brittle manner, and this effect is largely constant despite appreciable variations in bone volume fraction and microarchitecture.
authors.affiliation: Orthopaedic Biomechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA. shashank@berkeley.edu
authors.forename: Shashank
authors.initials: S
authors.lastname: Nawathe
authors.forename: Frédéric
authors.initials: F
authors.lastname: Juillard
authors.forename: Tony M
authors.initials: TM
authors.lastname: Keaveny
mesh_terms: D000368:Aged; D001842:Bone and Bones / Q000473:pathology / Q000503:physiopathology*; D019245:Compressive Strength; D005260:Female; D020342:Finite Element Analysis; D050723:Fractures, Bone / Q000473:pathology / Q000503:physiopathology*; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D055114:X-Ray Microtomography