A new device and method for measuring the elastic modulus of single trabeculae

The smallest functional unit of cancellous bone is the single trabecula. To investigate its influence at the macroscopic level, a mechanical characterization is required. The aim of this work is to present a new procedure for measuring the elastic behavior of a single trabecula, assumed as an isotropic material, by means of a bending protocol. Our experimental setup permits the measurement of the bending force and deflection of a single trabecula within the natural network. The exact geometry of the trabecula is attained by using a laser scanning microscopy of the labeled sample and subsequently using it as the input for FE simulation. The results between the FE analysis and experimental data are compared in order to determine an isotropic elastic modulus of the trabecula. The system uncertainty has been estimated using the propagation of uncertainty method based on the analytical bending function for a fixed beam. Variables are force, deflection, radius and length and their relative uncertainties. It results in a total uncertainty of 13%, dominated by the influence of radius uncertainty, which is related to the exact determination of the real geometry of the trabecula. The system has been subsequently validated using samples with known geometry and elastic modulus. Finally, the proposed new method consists of sample preparation, a newly designed sample positioning system, an experimental bending test on a single trabecula within the trabecular network, labeling of the bone with a fluorescent marker, 3D imaging of the trabecula and FE analysis of the bending test.