Comparison between different methods for biomechanical assessment of ex vivo fracture callus stiffness in small animal bone healing studies

Abstract

For ex vivo measurements of fracture callus stiffness in small animals, different test methods, such as torsion or bending tests, are established. Each method provides advantages and disadvantages, and it is still debated which of those is most sensitive to experimental conditions (i.e. specimen alignment, directional dependency, asymmetric behavior). The aim of this study was to experimentally compare six different testing methods regarding their robustness against experimental errors. Therefore, standardized specimens were created by selective laser sintering (SLS), mimicking size, directional behavior, and embedding variations of respective rat long bone specimens. For the latter, five different geometries were created which show shifted or tilted specimen alignments. The mechanical tests included three-point bending, four-point bending, cantilever bending, axial compression, constrained torsion, and unconstrained torsion. All three different bending tests showed the same principal behavior. They were highly dependent on the rotational direction of the maximum fracture callus expansion relative to the loading direction (creating experimental errors of more than 60%), however small angular deviations (<15°) were negligible. Differences in the experimental results between the bending tests originate in their respective location of maximal bending moment induction. Compared to four-point bending, three-point bending is easier to apply on small rat and mouse bones under realistic testing conditions and yields robust measurements, provided low variation of the callus shape among the tested specimens. Axial compressive testing was highly sensitive to embedding variations, and therefore cannot be recommended. Although it is experimentally difficult to realize, unconstrained torsion testing was found to be the most robust method, since it was independent of both rotational alignment and embedding uncertainties. Constrained torsional testing showed small errors (up to 16.8%, compared to corresponding alignment under unconstrained torsion) due to a parallel offset between the specimens' axis of gravity and the torsional axis of rotation.

Fig 1. Standardized test specimens representing simplified substitutes for healed rat femurs.

A) Variation of the rotational alignment for bending tests in seven increments of 15° between 0°- and 90°-rotational alignment. Model designs showing different relations between the axis of the “fixture cylinders” and the axis of the “cortical cylinders “: B) Design S0 with perfect alignment C) Design S1 with 1.25 mm parallel offset. D) Design S2 with 2.5 mm parallel offset, E) Design T7 with 7° angulation, E) Design T14 with 14° angulation.

Fig 2. Test setups and boundary conditions for four different experiments: A) and E) three-point bending, B) and F) four-point bending, C) and G) cantilever bending, D) and H) axial compression.

Fig 3. Torsional testing.

A) Test set-up for torsional testing in the multi-axial flexibility testing machine. B) boundary conditions for constrained torsional testing (CT) and C) boundary conditions for the unconstrained torsional testing (UT).

Fig 4. Results for the bending stiffness (mean±SD) (left) and the respective errors of the means (right) in relation to the reference mean value (i.e. respective mean stiffness of S0 at 0° axial rotational alignment) for three different bending experiments: A) Three-point bending stiffness EI _3P, B) four-point bending stiffness EI _4P, and C) cantilever bending stiffness EI _CB.

Results are shown for the five different model designs (S0, S1, S2, T7, and T14) and for the seven different axial rotational angular alignments (0°-90° in 15° increments). *p<0.05, **p<0.01, ***p<0.001, ****p<0.0001.

Fig 5. Axial compressive stiffness k _ax (mean±SD) (left) and the respective errors of the means (right) in relation to the reference mean value (i.e. respective mean axial stiffness of S0) for the five different model designs S0, S1, S2, T7, and T14).

Fig 6. Results of the torsional testing.

A) Torsional stiffness GI for the five different model designs S0, S1, S2, T7, and T14, under unconstrained (UT-left) and constrained (CT-right) axial torsion. B) The respective errors of the means in relation to the reference mean value (i.e. stiffness of S0 under unconstrained torsion). C) Reaction forces F at the gimbal in axial direction (z) and the secondary directions (x and y). D) Reaction moments M at the gimbal in axial direction (z) and the secondary directions (x and y). *p<0.05, ***p<0.001, ****p<0.0001.