## INTRODUCTION

Microstructural organization plays an important role in defining the mechanical properties of trabecular bone.^{(1–4)} Moreover, trabecular morphology adapts to changes in mechanical environment and to aging and disease.^{(5–8)} Understanding this adaptive behavior as well as the influences of aging and disease on trabecular properties requires characterization of the three-dimensional (3D) architecture of trabecular bone.

The traditional method for imaging trabecular bone is two-dimensional (2D) optical microscopy.^{(9)} From these images, morphologic parameters can be determined using a technique such as the secant method.^{(10)} This method is equivalent to scanning a 2D matrix of bone and marrow with an array of parallel test lines with a uniform spacing. The average number of intersections of the test lines with the bone–marrow interface are counted for several different test line orientations. Based on the area fraction, the number of intersections, and stereology principles and models, 3D structural parameters can be estimated from the planar sections.^{(9)} These techniques are well established and allow estimation of basic morphometric measures such as bone volume fraction (BV/TV), trabecular number (Tb.N), thickness (Tb.Th), and separation (Tb.Sp).

More recent imaging techniques, such as microcomputed tomography,^{(11)} micromagnetic resonance imaging,^{(12,13)} optical serial reconstruction,^{(14)} and X-ray tomographic microscopy^{(15)} produce 3D images of trabecular bone. These images allow 3D morphology measurements using a 3D version of the directed secant method. These methods can be automated and have been applied routinely to describe the microstructure of trabecular bone. However, there are no standardized implementations of an automated 3D directed secant method. Furthermore, the directed secant method requires the user to define certain analysis parameters such as the test grid spacing, the number of test grid rotations, and how the bone–marrow interface is identified. The effect of varying these parameters on basic morphometric measures has not been described previously. Variations between laboratories in the implementation of morphological analysis algorithms or the selection of analysis parameters could result in significant differences that would preclude accurate comparison of morphometry data.

Thus, the objective of this study was to examine the relative effect of varying the implementation of the directed secant method on measurements of trabecular bone microstructure. Specifically, we asked whether basic morphologic parameters (Tb.N, Tb.Th, and Tb.Sp) were significantly affected by variations in: (1) the algorithm to determine when a test line crossed the bone–marrow interface; (2) the algorithm to classify a particular point as bone or marrow; (3) the number of test grid rotations; and (4) the spacing of the test grid lines.