Unbiased stereologic estimation of surface density in bone using vertical sections

Abstract

The conventional stereologic procedure for estimating bone surface densities in iliac crest biopsies gives biased estimates because bone substructure is anisotropic and the sectioning of the biopsies is intended to be parallel to the cylindrical axis of the iliac crest biopsy. It has recently been shown that random anisotropic sections with an identifiable axis or direction that is arbitrary but fixed can be used for unbiased estimates of surface areas. The arbitrary axis is called “vertical,” which does not imply anything about its relation to direction of gravity. To describe the methodology and the practical sampling procedure for vertical sections, surface density of trabecular bone was estimated in 16 bone samples obtained at autopsy from eight persons (mean age 64 years) using an anisotropic cycloid test system designed for vertical sections. In addition, variation in the estimation procedure was quantitated. The average surface density of trabecular bone was 2.8 ± 0.4 mm −1 (± SD). No systematic difference was observed between the two bone specimens from each of the eight persons. Estimation of the variance at each level of sampling showed that the majority of the total observed variance was due to true variance between individuals. Vertical section is, in general, the method of choice when dealing with surfaces not known to have an isotropic orientation distribution. The cycloid test system is easy and fast to use and the estimate is truely unbiased. The requirements are (1) all sections must be parallel to the vertical axis, (2) the rotation around this axis must be random, (3) the position of the section or of the biopsy must be random, and (4) the vertical axis must be identified in the section.