Reply to the Comments on the Effect of an Orthogonal Locking Plate and Primary Plate Working Length on Construct Stiffness and Plate Strain in an In vitro Fracture-Gap Model

We thank you for your interest in our research. Please see our responses to your specific concerns below:

The abstract sentence “strain was significantly, incrementally, higher as working length was extended” remains true. Strain was higher in the long working length (LWL) constructs than the short (SWL) and medium working length (MWL) constructs. Higher measured strain at a longer working length in our study can be described as a direct relationship. We specifically used the term incremental in our results to highlight that we have measured at three distinct working lengths and have not made inferences about strain assessment between these measured working lengths.

We selected the axial plate region between the central screw holes of the 3.5-mm LCP as the area of interest for surface strain assessment as this represented a consistent region across all working lengths and allowed for relative comparison. The application of flexure formula theory to this region of the plate in isolation is flawed. Flexure formula is true for a uniform beam and would be true if the plate alone was subjected to a bending moment. The term constructs used in our study describes the combined bone model, screws, plates, and loading apparatus, and therefore has the biomechanical properties of a composite beam. The bending stiffness of a composite beam is influenced by the combined area moment of inertia of the materials, their modulus of elasticity, and the mechanical connection between the beams.[1] A composite beam of bone and bone plate (i.e., Delrin rod + bone plate in our study) is stiffer than a bone plate alone. The stiffness of such a composite beam in a fracture-gap model is dependent on how much of the construct is combined plate and Delrin, and how much is plate alone. The long working length constructs therefore had shorter regions of combined plate and Delrin and a longer region of plate alone resulting in a less stiff construct. The less stiff construct deformed more under the constant bending moment applied through four-point bending and, as such, measured strain was higher, as would be expected.[2] [3] [4] [5] [6] Higher strain, and by inference stress, in LWL constructs is supported by shorter fatigue life in longer working length constructs.[2] [7] Based on this reasoning and the results of our biomechanical testing, we accepted our second research hypothesis that strain would be higher as working length was extended.

The results by Chao et al[8] are confounded by their loading conditions. They applied femoral locking plates in direct contact with the lateral aspect of a femoral bone model and tested under axial compression. The resultant bending moment caused contact between the bone plate and the bone model at the fracture-gap, which means the effective working length was equal to the fracture-gap length for all screw configurations.[8] Studies investigating locking plate constructs where plate-bone standoff is maintained and where loading is applied in a direction such that screw configuration defines the effective working length consistently show lower stiffness and correspondingly higher strain with longer working lengths and support the findings of our research.[3] [4] [5] [6] [9] [10] Additionally, the bending moment applied during axial compression is not constant, as discussed by the authors. The magnitude of the moment arm increases during construct deformation so constructs of varying stiffness will therefore be subjected to different bending moments; a less stiff construct will deform more resulting in a larger moment arm and larger bending moment than a stiffer construct that deforms less during testing. This further confounds the results of their study and makes interpretation of some of their results difficult. Were changes in stiffness and strain due to altered loading conditions? or due to screw configuration? or both?[8] We deliberately chose a synthetic bone model with low expected variance to be tested under four-point bending so that measured differences in stiffness and strain could be confidently attributed to screw configuration.

Thank you again for your interest in our research. We are confident that our construct configuration and biomechanical testing setup were appropriate for testing our research hypotheses. Flexure formula for a uniform beam is not directly applicable to our composite constructs, as discussed. Our results are supported by other studies using similar testing methodology and would be expected to be repeatable. Our conclusions have remained within the confines of our study, and we feel they are appropriate for the in vitro testing performed.

Authors' contribution

All authors contributed to drafting and revising this letter.

Publication History

Article published online:
27 December 2024

• References

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