The effect of parameters of equilibrium-based 3-D biomechanical models on extracted muscle synergies during isometric lumbar exertion

Abstract A hallmark of more advanced models is their higher details of trunk muscles represented by a larger number of muscles. The question is if in reality we control these muscles individually as independent agents or we control groups of them called “synergy”. To address this, we employed a 3-D biomechanical model of the spine with 18 trunk muscles that satisfied equilibrium conditions at L4/5, with different cost functions. The solutions of several 2-D and 3-D tasks were arranged in a data matrix and the synergies were computed by using non-negative matrix factorization (NMF) algorithms. Variance accounted for (VAF) was used to evaluate the number of synergies that emerged by the analysis, which were used to reconstruct the original muscle activations. It was showed that four and six muscle synergies were adequate to reconstruct the input data of 2-D and 3-D torque space analysis. The synergies were different by choosing alternative cost functions as expected. The constraints affected the extracted muscle synergies, particularly muscles that participated in more than one functional tasks were influenced substantially. The compositions of extracted muscle synergies were in agreement with experimental studies on healthy participants. The following computational methods show that the synergies can reduce the complexity of load distributions and allow reduced dimensional space to be used in clinical settings.