## 2 Materials and Methods
### Description of Model Studies  
This work uses an appropriate prepared model available in the AnyBody Managed Model Repository (AMMR) repository of the AnyBody environment (AnyBody Modeling System 5.2.0, AnyBody Technology A/S, Niels Jernes Vej 10, DK-9220 Aalborg \(\mathcal{O}\), Denmark). To conduct the model studies, 33 personalized models were prepared based on the FreePostureMove environment available in the AMMR repository. The FreePostureMove model is characterized by 69 rigid bodies, approximately 1000 muscle actions, a simple muscle model (AnyMuscleModel), and the ScalingLengthMassFat linear scaling method, which is based on the input body mass and height values [21; 22]. The optimization criterion used is the minimization of the sum of the cubes of the ratios of muscle forces to their maximum values. The form of the optimization problem was identified using the following dependences:  
* Objective function: \[minG\Big{(}f^{(M)}\Big{)}\] \[G\Big{(}f^{(M)}\Big{)}=\sum_{i=1}^{m}\Big{(}\frac{\dot{f}_{i}^{(M)}}{N _{i}}\Big{)}^{3},i=1,\dots,n^{M}\]* Limiting conditions: \[Cf=d\] \[0\leq f_{i}^{(M)}\leq N_{i},i\in 1,\ldots,n^{(M)}\] where the following apply: \[f^{M}\] --muscular force; \[N_{i}\] --maximum muscle forces; \[n^{M}\] --number of muscles; C--matrix of arms of muscular strength action and reactions in relation to a given joint; \[f\] --matrix of muscular forces and reactions present in the system; \[d\] --resultant moments of external forces determined in relation to a given joint. FreePostureMove is a dynamic model controlled by angles that can be implemented in the MannequinInterpolation.any file. The MannequinInterpolation.any file is a crucial part of the AnyBody Modeling System and is specifically used for dynamic models where joint angles need to be controlled over time [22]. The FreePosture model was validated using in vivo force data by [PERSON] et al. and [PERSON] et al. [23; 24]. For each case studied, the model was scaled by inputting the body height and mass of the individual. The dynamic simulation using the FreePostureMove model lasted 8 s and was conducted at a frequency of 20 Hz. The input data for the model over time included \[\bullet\] pelvic tilt in the sagittal plane, \[G\Big{(}f^{(M)}\Big{)}=\sum_{i=1}^{m}\Big{(}\frac{\dot{f}_{i}^{(M)}}{N _{i}}\Big{)}^{3},i=1,\dots,n^{M}\]0 rotational moments of the left and right limbs, \[G\Big{(}f^{(M)}\Big{)}=\sum_{i=1}^{m}\Big{(}\frac{\dot{f}_{i}^{(M)}}{N _{i}}\Big{)}^{3},i=1,\dots,n^{M}\]1 load on the inner forefoot of the left and right limbs, \[G\Big{(}f^{(M)}\Big{)}=\sum_{i=1}^{m}\Big{(}\frac{\dot{f}_{i}^{(M)}}{N _{i}}\Big{)}^{3},i=1,\dots,n^{M}\]2 load on the outer forefoot of the left and right limbs, \[G\Big{(}f^{(M)}\Big{)}=\sum_{i=1}^{m}\Big{(}\frac{\dot{f}_{i}^{(M)}}{N _{i}}\Big{)}^{3},i=1,\dots,n^{M}\]3 load on the hindfoot of the left and right limbs. The kinematics of the lower limbs were excluded due to the recorded values being smaller than the measurement error of the device. This was attributed to the characteristics of the movement. Twelve muscles were analyzed due to their functional importance in generating external hip rotation torque and in stabilizing the pelvis and knee during upright posture. The examined muscles included the knee joint stabilizers--_Sartorius_ and _Tensor fasciae latate_--and the primary and secondary lower limb rotators: _Iliopsoas_, _Gluteus minimus_, _Gluteus medius_, _Gluteus maximus_, _Piriformis_, _Quadratus femoris_, _Obturator intermus_, _Obturator externus_, _Gemellus inferior_, and _Gemellus superior_. As reported by [PERSON] et al. (2013), the gluteal muscles--particularly _Gluteus medius_ and _minimus_--along with the deep external rotators, play a crucial role in maintaining pelvic control and lower limb alignment during stance and locomotion [25]. In addition, the _Iliopsoas_, although primarily a hip flexor, has been shown to contribute to lumbopelvic stability and to assist in hip external rotation in postural contexts [26].