Letter to the Editors (2010)

Dear Editor, I read with interest the recent article “Effect of Fracture Gap on Stability of Compression Plate Fixation: A Finite Element Study” by Oh et al.1 In their study, the authors validated a finite element model of a plated bone by comparing the model predictions for 4-point bending loading with actual experimental measurements of a plated bone analog. In Figure 3 of their article, the authors show two curves of bending moment versus bending angle, one for their finite element model and the other for their experiment. Referring to the bending stiffness (slope of the curves in their Fig. 3) the authors state: “The experimental results showed slightly lower values [of bending stiffness] at bending angles of >1.5° than those from the FEA, but this was thought to be caused by the difficulty in aligning the top and bottom epoxy cylinders in the same position during the plating onto the epoxy cylinder.” The difference in bending stiffness between their finite element model and their experiment is rather more substantial than the authors imply. For a bending moment of 20 Nm, the stiffness predicted by the finite element model is approximately 15.4 Nm/deg, whereas the stiffness from the experimental test is approximately 10.7 Nm. The model is therefore 44% stiffer than experiment. Another interesting difference between the finite element results and the experimental results is the basic shape of the curves in their Fig. 3. The response of the finite element model is linear over the range shown of the applied bending moment. The response of the experiment is clearly nonlinear. The nonlinear experimental results show that the bending stiffness decreases as the applied bending moment increases. Several previous studies suggest an alternative explanation for the observed nonlinear response that Oh et al. attribute to plate and bone mal-alignment. Using the same type of fixation plate (LC-DCP) attached to cadaveric femora, Borgeaud et al.2 showed that screw tightness can have a substantial influence on slippage between plate and bone, and this slippage is manifested as a nonlinear response between applied load and bone strain. In the study by Oh et al., slippage could be an additional contributor to the nonlinear experimental response between applied bending moment and bending angle. Beaupre et al.3 showed that slippage can also be simulated in a nonlinear finite element model using frictional interface conditions between screws and plate and between plate and bone in conjunction with a compressive preload in the screws. The compressive pre-load corresponded to different levels of screw tightness, which had a profound effect on the model predictions. The results of Beaupre et al. show that the same type of nonlinear response that is seen in experiments can be modeled with finite element analysis. In the study by Oh et al., the authors do not mention any details concerning the tightness of the screws in their experimental study, nor do they mention if screw tightness was modeled in their finite element analysis. The linear response of the finite element results in their Fig. 3 suggests that their model is not demonstrating the slippage and hysteresis that has been observed experimentally by Borgeaud et al. or seen in the finite element study by Beaupre et al. It would be helpful to readers if the authors would comment on the issue of screw tightness and the possibility of slippage at the plate-bone or screw-plate interface in both their experiments and their finite element analyses.