Measuring the shape and size of microcracks in bone

Abstract

Microcracks in bone are normally measured from two-dimensional, transverse sections but this provides incomplete information about their three-dimensional shape and size. The methods of stereology can usefully be applied in such a case. This problem has been addressed using a theoretical model and a numerical simulation. Results show that the data are consistent with a crack shape which is elliptical, with axis ratio approximately 4.5:1 and with size variation (expressed as the ratio of standard deviation to mean length) of at least 0.1. Measured lengths will, on average, be smaller and have more scatter than true lengths. Errors caused by omitting small cracks are relatively unimportant. Knowledge of the true crack dimensions, and their variability, is important for the analysis of damage, stress fracture, remodelling and adaptation.