Letter to the Editor: In Response to “Consistency Among Musculoskeletal Models: Caveat Utilitor”

To the Editor, We read with great interest the paper ‘‘Consistency Among Musculoskeletal Models: Caveat Utilitor’’ by Wagner et al. The paper compares eight musculoskeletal models by scaling them to the same dimensions in order to evaluate differences in the quadriceps moment arms,muscle forces and tibio-femoral contact forces for a standardized knee flexion task. We would like to comment on the methods and interpretation of results presented in the paper, particularly with regard to the London Lower Limb Model (LLLM). As the authors of that paper, we note that the muscle force distribution between the quadriceps muscles reported in Figure 4 of Wagner et al. for the LLLMand described as the result of ‘‘a potential modelling error’’ arises from an unintended use of the model.We have not assessed the results reported by Wagner et al. for other models used in their study and so only comment on the use of our model. The publicly availableLLLMmodelwas implemented in OpenSim, assessed and used for hip joint applications, with specific conditions and limitations associated with implementation and use of the model, reported in the documentation accompanying the model (uploaded as part of the model release pack on 3rd July 2011 available at https://simtk.org/home/low_limb_london). In particular, the publicly available model is meant to be used for estimating muscle forces by using the static optimization technique without including the force– length–velocity relationship. For this reason in our original publication we explicitly stated that ‘‘neither contraction dynamics nor force–length–velocity relationships were implemented for the muscle actuators’’. The simplification we adopted is commonly accepted in studies dealing with research questions similar to ours, as the inclusion of muscle contraction dynamics does not significantly affect the simulation results in terms of muscle forces for level walking. Using the model as intended, the relative load share of the quadriceps muscles to equilibrate 90 Nm of torque applied at the knee (Fig. 4 of Ref. 11) calculated by minimizing the sum of muscle activation squared would have been the one reported in Fig. 1 of this letter. In order to validate results found through appropriate use of the model, we solved the static optimization problem in two independent ways for the LLLM scaled as described by Wagner et al.: