## 2 Materials and Methods
### Simulation Procedure  
In OpenSim, the standard simulation procedure was followed, as discussed in the papers by [PERSON] et al. [24] and [PERSON] et al. [25], to predict the muscle force. In the first step, a forward dynamics simulation for 1 s was performed to obtain the motion file (.mot file) for the CBA and HBB test by defining the kinematics presented in Tables 1 and 2. In this step, coordinates were locked so they do not move; instead, they hold the set coordinate angle for the CBA and HBB test. So, the motion file will give us the joint angles that are just the constant value for each discrete time step for the entire duration of the simulation. The duration of the forward simulation, whether 0.1 s, 1 s, or 10 s, does not affect the results in this case, as the joint angles remain constant. A 1 s duration was chosen in this study to make sure we get enough time steps while minimizing computational time. Further, for static cases like this, the kinematic and kinetics results remain the same for each time step irrespective of simulation duration.  
The resulting motion file was then used as input for static optimization (SO) to solve the muscle redundancy problem, minimizing the objective function as follows:  
\[J=\sum_{m=1}^{n}(a_{m})^{3} \tag{1}\]  
Figure 3: Final resting posture for the hand-behind-the-back test using OpenSim: (**a**) posterior view and (**b**) sagittal view.  
where \(n\) is the number of muscles and \(a_{m}\) is the muscle's activation level at a discrete time step. Further, along with the motion file, reserve actuators were appended to each degree of freedom to provide any additional force required to obtain the desired kinematics of tests and to run the simulation successfully. Since this work only simulated the static postures of the CBA and HBB tests based on known kinematics or joint angles, scaling the models based on the subject-specific motion capture data was not required. However, this model has been validated against the subject-specific data in previous research [22], and their ability to represent typical upper extremity motions is well established. However, it is essential to acknowledge that this model is not validated using subject-specific data related to this study. Finally, the reserved actuators' force predictions were checked to ensure they have no forces greater than 10 Newtons. This work predicted the muscle forces for the CBA and HBB test using OpenSim v4.4 [24; 25].  
In the AnyBody Modeling SystemTM, an initial calibration was first run to calibrate the muscle parameters associated with the MuscleModel3E muscle model. Then, an inverse dynamics analysis was run to solve the muscle redundancy problem using a polynomial muscle recruitment criterion as follows [23]:  
\[G=\sum_{i=1}^{n(M)}\left(\frac{f_{i}^{(M)}}{N_{i}}\right)^{3} \tag{2}\]  
where \(G\) is an objective function, \(n^{(M)}\) is the number of muscles, \(f_{i}^{(M)}\) is the respective predicted muscle force in Newtons, and \(N_{i}\) is isometric muscle strength in Newtons. This work predicted muscle force using AnyBody Modeling SystemTM v7.1.  
Figure 4: Final resting posture for the hand-behind-the-back test using AnyBody Modeling SystemTM; (**a**) posterior view and (**b**) sagittal view.