Tensile Yield Strain of Human Cortical Bone from the Femoral Diaphysis Is Constant among Healthy Adults and across the Anatomical Quadrants.

The literature suggests that the yield strain of cortical bone is invariant to its stiffness (elastic modulus) and strength (yield stress). However, data about intra-individual variations, e.g., the influence of different collagen/mineral organisations observed in bone aspects withstanding different habitual loads, are lacking. The hypothesis that the yield strain of human cortical bone tissue, retrieved from femoral diaphyseal quadrants subjected to different habitual loads, is invariant was tested. Four flat dumbbell-shaped specimens were machined from each quadrant of the proximal femoral diaphysis of five adult donors for a total of 80 specimens. Two extensometers attached to the narrow specimen region were used to measure deformation during monotonic tensile testing. The elastic modulus (linear part of the stress-strain curve) and yield strain/stress at a 0.2% offset were obtained. Elastic modulus and yield stress values were, respectively, in the range of 12.2-20.5 GPa and 75.9-136.6 MPa and exhibited a positive linear correlation. All yield strain values were in the narrow range of 0.77-0.87%, regardless of the stiffness and strength of the tissue and the anatomical quadrant. In summary, the results corroborate the hypothesis that tensile yield strain in cortical bone is invariant, irrespective also of the anatomical quadrant. The mean yield strain value found in this study is similar to what was reported by inter-species and evolution studies but slightly higher than previous reports in humans, possibly because of the younger age of our subjects. Further investigations are needed to elucidate a possible dependence of yield strain on age.

Measurement of apparent mechanical properties of trabecular bone tissue: Accuracy and limitation of digital image correlation technique.

Trabecular bone surface is distant from the ideal non-reflecting, continuous, regular, flat surface suitable for accurate digital image correlation (DIC) measurements. We tested the feasibility of DIC to accurately measure surface displacements on trabecular microstructures, using four-extensometer technique as gold standard measurement. Thirty cylindrical human trabecular bone specimens were obtained. Ten were used to evaluate if pattern creation, required for DIC, had any effect on the apparent elastic modulus (Eapp) of trabecular bone, the remaining twenty were used to assess DIC accuracy in measuring Eapp. All specimens underwent a loading scheme including i) 10 preconditioning cycles, ii) 8 monotonic compressive ramps up to 0.5% nominal deformation, and iii) a second compressive series identical to the first. Changes in Eapp, due to pattern created between the two series, were assessed using the four-extensometer techniques. Pattern quality was also evaluated. DIC and four-extensometer technique were then used in the remaining twenty specimens to measure local axial displacements and compute global axial deformation during the first and second series, respectively. DIC accuracy was assessed comparing Eapp values calculated using axial deformation determined with the two techniques. Achieved pattern had on average a speckle size of 2.8 pixels, and 42% coverage. Pattern creation did not alter significantly Eapp values (median difference=-0.6%; Wilcoxon p=0.76). DIC technique was not applicable on the most porous specimens. DIC-extensometer comparison was not possible in three low-density specimens with Eapp < 0.4 GPa because of progressive trabecular damage over test repetitions. Good agreement in Eapp values was found in the remaining sixteen specimens (median difference=-1.5%; 10th percentile=-7.5%; 90th percentile=6.9%; max difference < 10%). Four-extensometer and DIC are interchangeable techniques: the former is the most straightforward to measure the axial deformation of trabecular bone tissue under monotonic compression, the latter is a useful alternative whenever surface displacement maps are needed.

Experimentally Achievable Accuracy Using a Digital Image Correlation Technique in measuring Small-Magnitude (<0.1%) Homogeneous Strain Fields.

Measuring small-magnitude strain fields using a digital image correlation (DIC) technique is challenging, due to the noise-signal ratio in strain maps. Here, we determined the level of accuracy achievable in measuring small-magnitude (<0.1%) homogeneous strain fields. We investigated different sets of parameters for image processing and imaging pre-selection, based on single-image noise level. The trueness of DIC was assessed by comparison of Young’s modulus (E) and Poisson’s ratio (ν) with values obtained from strain gauge measurements. Repeatability was improved, on average, by 20⁻25% with experimentally-determined optimal parameters and image pre-selection. Despite this, the intra- and inter-specimen repeatability of strain gauge measurements was 5 and 2.5 times better than DIC, respectively. Moreover, although trueness was also improved, on average, by 30⁻45%, DIC consistently overestimated the two material parameters by 1.8% and 3.2% for E and ν, respectively. DIC is a suitable option to measure small-magnitude homogeneous strain fields, bearing in mind the limitations in achievable accuracy.

Elastic properties and strain-to-crack-initiation of calcium phosphate bone cements: Revelations of a high-resolution measurement technique.

Calcium phosphate cements (CPCs) should ideally have mechanical properties similar to those of the bone tissue the material is used to replace or repair. Usually, the compressive strength of the CPCs is reported and, more rarely, the elastic modulus. Conversely, scarce or no data are available on Poisson's ratio and strain-to-crack-initiation. This is unfortunate, as data on the elastic response is key to, e.g., numerical model accuracy. In this study, the compressive behaviour of brushite, monetite and apatite cements was fully characterised. Measurement of the surface strains was done using a digital image correlation (DIC) technique, and compared to results obtained with the commonly used built-in displacement measurement of the materials testers. The collected data showed that the use of fixed compression platens, as opposed to spherically seated ones, may in some cases underestimate the compressive strength by up to 40%. Also, the built-in measurements may underestimate the elastic modulus by up to 62% as compared to DIC measurements. Using DIC, the brushite cement was found to be much stiffer (24.3 ± 2.3GPa) than the apatite (13.5 ± 1.6GPa) and monetite (7.1 ± 1.0GPa) cements, and elastic moduli were inversely related to the porosity of the materials. Poisson's ratio was determined to be 0.26 ± 0.02 for brushite, 0.21 ± 0.02 for apatite and 0.20 ± 0.03 for monetite. All investigated CPCs showed low strain-to-crack-initiation (0.17-0.19%). In summary, the elastic modulus of CPCs is substantially higher than previously reported and it is concluded that an accurate procedure is a prerequisite in order to properly compare the mechanical properties of different CPC formulations. It is recommended to use spherically seated platens and measuring the strain at a relevant resolution and on the specimen surface.