9.1 Mechanical Testing

The gold standard to determine bone mechanical properties is through experimental mechanical testing. In itself, direct mechanical testing is a straightforward procedure. Yet, bone, and in particular trabecular bone, is a difficult material to test. Standard test geometries, like defined in mechanical testing standards, can rarely be used for trabecular bone, because it is often too fragile and too inhomogeneous to machine. As a consequence, sample preparation needs dedicated care. Compression testing is the most popular measurement technique, using test specimens that are cylindrical or cubic. Care must be taken in interpreting the outcomes of a mechanical test, as they are influenced by anatomic site and loading direction; furthermore, they can be influenced to a large extent by end artifacts. It also has to be realized that the quantification of bone strength is limited by its destructiveness; a sample can only be fractured once, making it physically impossible to assess the direction-dependent failure characteristics on single specimens.

Similar to mechanical testing of whole bones, the main outcome of a mechanical test on a bone specimen is a force-displacement curve (Fig. 9.1a). The stiffness of the specimen is derived as the slope of the initial linear regime of the force-displacement curve. The area under the curve represents the energy (also strain-energy or work) taken up by the specimen until fracture.

Given that the sample dimensions are known, the force-displacement curve can be transformed into a stress-strain curve (Fig. 9.1b) where stress is defined as force divided by the cross-sectional area of the specimen and strain as displacement divided by specimen length. Parameters that can be derived from the stress-strain curve are Young′s modulus, yield point, strength, and energy density. The yield point is defined as that particular stress or strain level at which the specimen deviates from the initial linear response; it is typically determined following the 0.2% offset rule (Fig. 9.1b). Strength is defined as the maximum stress level that can be sustained. Toughness can be determined by quantifying the area underneath the stress-strain curve; it represents the mechanical deformation energy per unit volume prior to fracture.

Note that the measures as derived from the stress-strain curve are representative of the bulk material; hence, they are independent of bone geometry. Yet, they include the effects of features with a smaller length scale, such as porosity, the three-dimensional arrangement of trabeculae, osteon composition, and their orientation. In order for the mechanical properties to be representative for the entire specimen, the specimen could be considered to be made up out of one homogeneous material. Trabecular bone can be considered as a continuum material when viewed at a length scale of 5 mm or more. 1 Thus, this finding puts a lower limit to the sample size, which should be at least 5 mm cubes. Ideally, the sample size should be larger because of boundary artifacts (next section); typically, specimen dimension is between 5 mm and 10 mm.

Mechanical testing is most commonly performed as a uniaxial test, performed in the direction of the main trabecular orientation, which is the stiffest direction. For that purpose, specimen preparation is typically performed according to the anatomic orientation. For anatomic sites with a complicated trabecular architecture, X-ray imaging prior to specimen preparation can serve as a guide in defining the proper cutting planes.

9.2 On Boundary Conditions and Preconditioning

Mechanical testing of trabecular bone is potentially subject to large systematic errors. 2 During specimen preparation, some of the trabeculae at the specimen surface might get damaged or even fractured. But even in the case of a perfect extraction of the specimen, substantial boundary artifacts will occur because the trabeculae at the boundaries of the specimens become “free” at one end, and will behave much more flexible than when contained in the trabecular architecture. This causes the boundary layer of the specimens to be softer than the inner portion of the sample; as a consequence the specimen as a whole will behave softer than the same bone specimen in situ. It will be obvious that this effect is larger for specimens with long, not well-connected trabeculae, hence, typically specimens with low bone volume fraction. The use of endcaps and/or polymethyl methacrylate embedding are good means in reducing this error. The use of a ball joint in the testing setup will reduce the error that could originate from the fact that the surfaces of the specimen are not precisely parallel.

When a sample is taken from bone and tested, it will generally not give the linear-elastic response for low strains, but will show a so-called toe-region (Fig. 9.2). This toe-region is an artifact, the origin of which lies in the creation process of the sample when surface irregularities can form. When the test is started, it is important to have good contact between the platens and the specimen in order to avoid artifacts from fluids on the surfaces and to allow for some alignment and seating of the specimen. The use of a number of preconditioning cycles in which the specimen is loaded within its linear elastic range (e.g., up to 0.1 to 0.2%) will largely remove the toe-region and variability associated with it. In addition, the final experimental test is typically started with a small preload, as to ensure contact between the specimen and the mechanical testing apparatus.

When a toe-region is present, a correction procedure should be applied in order to obtain proper values for the mechanical parameters. Specifically, the linear portion of the stress-strain curve is to be extended such that this line crosses the zero-stress axis. This point on the axis represents the “zero-strain” point from which all strains must be measured.