The effect of parameters of equilibrium-based 3-D biomechanical models on extracted muscle synergies during isometric lumbar exertion A.H. Eskandari a , E. Sedaghat-Nejad a,b,n , E. Rashedi c , A. Sedighi c , N. Arjmand a , M. Parnianpour a,d a Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran b Department of Biomedical Engineering, Johns Hopkins School of Medicine, Baltimore, USA c Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, USA d Department of Industrial and Manufacturing Engineering, University of Wisconsin-Milwaukee, USA article info Article history: Accepted 14 December 2015 Keywords: Spine model Muscle synergy Motor control Optimization Biomechanics 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 ade- quate 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. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction A significant number of muscles, which are comprised of thousands of motor units, become activated at the same time when the central nervous system (CNS) coordinates voluntary movements. Many investigators since Bernstein (1967) have stu- died how the CNS's burden is reduced by controlling a much smaller set of variables. This fundamental complex problem has been the center of focus of many computational, experimental and theoretical researchers. Given the complexity of trunk control, a large number of muscles, and degrees of freedom that must be coordinated to produce functional activities, especially in combined movements, new approaches are required to investigate and interpret activity patterns of trunk muscles (Parnianpour, 2013; Hadizadeh et al., 2014; Christophy et al., 2012; Rupp et al., 2015). Muscle synergies are simple basic modules employed by the central nervous system (CNS), which simplify task generation (Bizzi and Cheung, 2013). Thus, the CNS potentially controls muscle synergies or groups of co-activated muscles instead of individual muscles during move- ments. Muscle synergies provide a map between task-level goals and execution-level commands for task achievement (Ting and Mckay, 2007). In this case, a group of muscles is activated to generate torque and force during task execution and also to con- trol the biomechanical properties, such as joint stiffness or impe- dance (Moghadam et al., 2011; Rashedi et al., 2010). However, the existence and function of muscle synergies are still unclear (Tresch and Jarc, 2009). Steele et al. (2015, 2013) evaluated the effect of biomechanically constrained tasks, the number of muscles, and choice of muscles on synergy analysis. Their results demonstrated that the accuracy of estimated syner- gies can be reduced by a biomechanically constrained task. In addition, the structure of estimated synergies is affected by the number and choice of muscles included in the analysis. They Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics http://dx.doi.org/10.1016/j.jbiomech.2015.12.024 0021-9290/& 2015 Elsevier Ltd. All rights reserved. n *Corresponding author at: Johns Hopkins University, 720 Rutland Ave, 416 Traylor Building, Baltimore, MD 21205-2195. Tel.: +1 410 340 0078. E-mail address: e.sedaghatnejad@jhmi.edu (E. Sedaghat-Nejad). Journal of Biomechanics 49 (2016) 967–973