Calculating the probability that microcracks initiate resorption spaces

Abstract

This paper explores the assumptions and limitations of the probability calculation that led to the conclusion by Burr et al. (1985) that microcracks initiate new remodeling events. It also corrects several minor errors in the calculation in the original manuscript. The results show that the probability that cracks and resorption spaces are associated depends heavily on a factor, F, that accounts for the possibility that some osteons that contain both a crack and a resorption space share a cement line with an adjacent osteon to which the crack more properly ‘belongs.’ F in turn depends on (1) the measurement criteria for cracks and resorption spaces, (2) the osteon population density in the bone, and (3) the mechanism by which cracks initiate remodeling. The theoretical maximum number of osteons that can contain both a crack and a resorption space ( n max) increases as the number of resorption spaces ( r), the number of cracks ( c), and F increase, but decreases as the osteon population density ( d) increases. A larger n max makes a direct association between cracks and resorption spaces more difficult to demonstrate experimentally.