Limitations of the continuum assumption in cancellous bone.
Most existing stress analyses of the skeleton which consider cancellous bone assume that it can be modelled as a continuum. In this paper we develop a criterion for the validity of this assumption. The limitations of the continuum assumption appear in two areas: near biologic interfaces, and in areas of large stress gradients. These limitations are explored using a probabilistic line scanning model for density measurement, resulting in an estimate of density accuracy as a function of line length which is experimentally verified. Within three to five trabeculae of an interface, a continuum model is suspect. When results as predicted using continuum analyses vary by more than 20-30% over a distance spanning three to five trabeculae, the results are suspect.
Harrigan
T P
TP
Department of Mechanical Engineering, Massachusetts Institute of Technology.
Jasty
M
M
Mann
R W
RW
Harris
W H
WH
D001696:Biomechanical Phenomena; D001842:Bone and Bones / Q000033:anatomy & histology* / Q000502:physiology; D003720:Densitometry; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D008954:Models, Biological; D011336:Probability