1 Examples of the influence of cross-sectional geometry on the structural strength of three circular bars. This is essentially a measure of how the material is distributed about a given axis.įig. The second moment of inertia is determined by integrating small units of area (δA) across the bone’s cross-section with respect to distances from its centroid: I = ∫(y2 δA). Tubular structures have a larger moment of inertia both in bending and torsion than cylindrical structures with the same amount of mass (Fig. The second moment of inertia helps describe the mechanical consequences of cross-sectional shape and mass distribution of a cross-section from a tubular structure such as the diaphysis of a long limb bone. This includes the second moment of area, or inertia (I) as many also call it. Structural properties include features of a bone’s cross-sectional shape and robusticity (i.e., the amount and distribution of cortical area with respect to the total cross-sectional area) (Table 2). Measures of diaphyseal shape and robusticity: Moments and axes of inertia. (2001), there is currently no substitute for a mechanical test to measure whole-bone structural behavior no alternative parameter has been identified that is fully indicative of strength and can serve as a surrogate measure.

Therefore, both material and geometric properties are required to assess the structural integrity of a long bone, and neither material nor geometry alone is sufficient to predict the structural failure load. These two whole-bone measurements are structural properties and are influenced by both the material from which the structure is composed (the tissue material properties, see below) as well as how and where that material is distributed (the geometric form of the tissue). These data are represented in a “load-deformation curve” (in contrast to the “stress-strain curve” of a material test). The structural stiffness is a measure of the resistance to deformation under the applied load, and the structural strength is the load required to cause the whole bone to fail. What is a whole-bone structural test and what does it measure? Different types of loads, such as bending or torsion, can be applied to whole bones in vitro to determine the structure’s stiffness and failure load (structural strength). In their study, these investigators generally more strongly subscribe to the idea of structural/material synergism/compensation than the view that is conveyed below in this section. Much of the following paragraph is paraphrased from van der Meulen et al. Worksheet/checklist of important considerations for interpreting adaptation in the appendicular skeleton In fact, as argued below, regional material variations (e.g., patterns of predominant collagen fiber orientation and osteon morphotypes) are relatively more useful than structural characteristics (e.g., a bone’s cross-sectional shape or variations in its cortical thickness) for interpreting the load history of a bone region.

This is especially important because a bone’s structural requirements may have little to do with regional variations in its material/compositional requirements. material distinction’ is important for understanding the importance or regional material (e.g., collagen orientation) variations between regions of the same bone. These parameters are usually considered in terms of material properties, but to some degree can describe how well the whole bone can bear loads, which is measured via structural strength tests. For most studies of limb-bone adaptation, the following mechanical parameters are the most important to thoroughly understand: stiffness, strength, toughness, and fatigue resistance. material distinction.Ī sound understanding of basic mechanical concepts is necessary for accurately assessing many of the issues that must be considered (Table 1) when interpreting a bone’s load history through the examination of its structural and material characteristics. Basic Biomechanical Concepts: The Foundation for Interpreting Local Load History Using Bone Histomorphology 1.

Freemat randi with imax and imin