Three‐dimensional (3‐D) structural parameters derived from lower‐dimensional measurements using indirect morphometric methods may be strongly biased if the measured objects deviate from the assumed structure model. With the introduction of 3‐D microscopic measuring techniques it is possible to obtain a complete depiction of complex spatial structures. As a consequence, new 3‐D methods have recently been developed for the estimation of morphometric parameters such as volume, surface area and connectivity by direct processing of the 3‐D images. Structure thickness is an important morphometric parameter which is usually defined for specific structure models only. In this paper we propose a general thickness definition for arbitrary structures allowing us to calculate the mean structure thickness and the thickness distribution of 3‐D objects in a direct way and independently of an assumed structure model. Additionally, an efficient implementation for the practical usage of the method is described using distance transformation. The new method is applied to trabecular bone structures measured with a 3‐D micro‐computed tomography system.

The appearance of cancellous bone architecture is different for various skeletal sites and various disease states. During aging and disease, plates are perforated and connecting rods are dissolved. There is a continuous shift from one structural type to the other. So traditional histomorphometric procedures, which are based on a fixed model type, will lead to questionable results. The introduction of three-dimensional (3D) measuring techniques in bone research makes it possible to capture the actual architecture of cancellous bone without assumptions of the structure type. This requires, however, new methods that make direct use of the 3D information. Within the framework of a BIOMED I project of the European Union, we analyzed a total of 260 human bone biopsies taken from five different skeletal sites (femoral head, vertebral bodies L2 and L4, iliac crest, and calcaneus) from 52 donors. The samples were measured three-dimensionally with a microcomputed tomography scanner and subsequently evaluated with both traditional indirect histomorphometric methods and newly developed direct ones. The results show significant differences between the methods and in their relation to the bone volume fraction. Based on the direct 3D analysis of human bone biopsies, it appears that samples with a lower bone mass are primarily characterized by a smaller plate-to-rod ratio, and to a lesser extent by thinner trabecular elements. (J Bone Miner