The most important finding of this study is that the bundles of the AC ligament have an unequal load-sharing behavior in both the elevation of the shoulder in the coronal plane and the horizontal adduction. During the dynamic evaluation, we consistently found a pattern of higher von Mises stress values in the clavicular footprint of the AIB, between 2:00 to 2:30. On the contrary, the SPB showed a lower stress, and its maximum values were consistently located on the clavicular side, between 9:00 and 10:00, according to the clockface model of the right shoulder described previously . Maier et al.  reported the pattern of AC ligament injury in acute ACJ lesions. They found that more than 70% of the injuries were associated with detachment of the ligament in the clavicular area. The outcome in the present study suggests that the AIB plays a significant role compared to the SPB by controlling the clavicular strut function in the ACJ kinematics, according to the levels of energy that it bears in the motions tested.
Our simulations were based on the normal AC ligament's anatomy and the articular kinematics' descriptions. Recently, Nakazawa et al.  have detailed the morphology of the AC ligament. SPB is a well-defined capsular thickening consistently found in all specimens with a 30° oblique orientation. The attachments of this bundle originate from the superior, posterior, and inferior aspects of the clavicle. The insertion on the superior acromion in all specimens marks the oblique orientation of this structure.
In contrast, AIB was a thinner structure classified into three types according to the variations of its footprint sites and dimensions . Based on the prevalence reported, we reconstructed type 2. In addition, Nolte et al.  determined the footprint width of the AC joint capsule and ligaments. The widest insertional footprint (6.6 mm) was measured in the posterosuperior quadrant of the clavicular (limits between 8:00 and 12:00 in a clockface model) and the acromial sides, corresponding to the PSB.
Morphological descriptions suggest that the SPB plays a crucial role in the ACJ function. Several published studies have determined the function of different areas of the AC ligament [9-11, 32, 33]. Kurata et al. demonstrated that the SPB, in conjunction with the CC ligaments, plays an important role in supporting the superior translation of the ACJ compared to the AIB. After sequential sectioning of the AC ligament and uniaxial loading tests, the superior displacement increased >50% after SPB sectioning .
In contrast, Dyrna et al.  demonstrated that the anterior segment of the ACJ capsule provides the highest stability. Conversely, they evaluated the biomechanical response under rotational loading and posterior translation rather than vertical displacement. In these experiments, the amplitude of the joint motion increased significantly after the dissection of this structure. Furthermore, 91% of native posterior translation stability was restored after ACJ anterior bracing reconstruction in a cadaver model that evaluated horizontal stability .
Similarly, Morikawa et al.  evaluated the specific regional contributions (anterior, superior, and posterior segments) of the superior half of ACLC. They evaluated posterior translation and rotational stability after sequential sectioning of the ACLC. The authors found a significant increase in resistance to posterior translation after suturing the anterior third of the AC ligament (P = 0.025). Furthermore, the resistance torque increased significantly only after suturing the anterior and posterior regions, unlike any other combination of regions (P < 0.001). These results are comparable to the highest stress distribution that we observed.
However, other biomechanical experiments have not restored the joint condition before injury [34, 35, 39]. According to these studies, a closer approximation of normal kinematics was obtained only after reconstructing the entire ACLC and not by reconstructing other specific regions of the AC ligament [33,34,35,39]. Nevertheless, those results do not rigorously apply to the actual postoperative state since they did not reproduce the physiological ACJ motion. Consequently, comparing these outcomes with our data should be done with caution due to the different experimental conditions.
In the present study, we identified the individual function of the AC ligament during shoulder motion, and we located areas that yielded significantly more stability. These findings might be used as a guide to improve the location of fixation points in reconstruction techniques. Due to the complex 3D motion in the shoulder girdle, ligament function may not be adequately assessed by uniaxial translational or rotational loads in a fixed model , as is the case in almost all previous studies [34,35,39].
On the contrary, we aimed to simulate the 3D motion of the normal shoulder girdle to evaluate the kinematics and mechanical behaviors of the ligaments under physiological conditions. During shoulder motion, ST motion is generated by a mechanical coupling at the SC joint and ACJ rather than isolated uniaxial rotations or angular displacements [36-38,40], which rarely occurs in real-life . Accordingly, the coupling theory is crucial to developing biomechanical models to explain functional and movement patterns . Thus, to better evaluate the function of the AC ligament and create a more realistic model, we aimed to simulate the ST, the SC, and ACJ kinematics [14, 28, 41].
Several studies have investigated the 3D shoulder girdle kinematics by various methods [36-38-40]. Oki et al.  evaluated shoulder girdle kinematics using electromagnetic tracking devices in cadaver models. The scapula rotated internally and then externally, tilted posteriorly, and rotated upward (6°, 10°, 37°, respectively); meanwhile, the clavicle rotated posteriorly and upward, and retracted posteriorly (17°,16°,18° respectively) when the humerus is elevated in the coronal plane On the contrary, they showed that the scapula rotates internally compared to the clavicle in horizontal adduction, and the upward rotation is significantly lower than in elevation . Those coupling angular rotations are challenging to be replicated in conventional experiments [14, 28, 41].
According to our results, the virtual AC ligament is exposed to an unequal strain during shoulder elevation and horizontal adduction due to the pattern of deformations demonstrated. During coronal plane elevation, the AIB showed its highest enlengthen (27%) at the 2:00 position. Furthermore, the highest levels of AIB were seen from 90 ° of shoulder elevation, which corresponded to a significantly higher stress concentration at 2:00. Sahara et al. , after an in-vivo ACJ kinematics analysis, described a directional change of the clavicular translation as the shoulder elevation surpasses 90° of abduction. The authors suggested that the dominant muscular traction force of the superior trapezius causes a posterior clavicular displacement from 90° of shoulder abduction. Consequently, our results suggest a primary role for the AIB in constraining posterior displacement of the clavicle during abduction.
At the 3:00 and 4:00 clock positions, the virtual AIB was exposed to significantly higher strain during horizontal adduction than at shoulder elevation. However, the higher level of stress at the 2:00 position that the AIB bears throughout horizontal adduction suggests its ability to prevent AC dissociation compared to the other positions of the bundle. It is important to note that the AIB did not demonstrate nearly isometric distance in any position studied.
During coronal plane elevation, the reference nodes on the SPB moved away at 10:00, 11:00, and 12:00 positions (31, 18, 24% respectively), especially after 90° of coronal elevation. In contrast, the nodes of the SPB at 8:00 and 9:00 were approached from 60° of shoulder elevation. Therefore, as long as the highest stress distribution in the AIB during this motion occurred at the 9:00 position, we hypothesized that the approach between the footprints does not necessarily reflect slack in the ligament. On the contrary, the AC rotational motion during shoulder elevation could create a torsional force on the SPB that creates significant stress to the fibers but does not increase the distance between the center of the footprint. This assumption is supported because the ACJ rotates significantly during shoulder abduction. Previous studies reported between 15 to 35° of normal rotation of the ACJ [42- 44]. The current study found 20° ACJ relative rotation during coronal plane shoulder elevation [see Additional file 4].
In addition, the displacement of the AIB was mainly on the Y-and Z- axes during coronal elevation. Thus, according to the direction of the reference nodes, the AIB controls the articular stability against the posterosuperior translation of the ACJ. On the contrary, during horizontal adduction, the overall displacement of the AIB was primarily in the superior and lateral directions (Fig. 10). Likewise, the SPB demonstrated a similar path of displacement on the Y-and Z- axes along shoulder elevation. However, a lower magnitude in displacement and a lower peak von Mises stress distribution suggest a secondary stabilizer role in the physiologic kinematics of this motion.
In contrast, the primarily SPB displacement occurred on the Z-axis during horizontal adduction. An anterior direction of the displacement of the SPB indicates that this bundle may constraint the ACJ against anterior loadings. Furthermore, the SPB seems to play a complementary role in restricting the superior translation. To our knowledge, there is not a single study that assesses the stress distribution, deformation, and displacement of the AC ligament in a dynamic or even rigid model. In this context, little is known about the stress patterns of the AC ligament to establish straight comparisons.
This study has several limitations. First, FEA has intrinsic restrictions, such as simplified boundary conditions and material properties, which can affect the numerical simulation results. Although our dynamic model allowed five DOF for the scapula, three DOF for the clavicle, and only restrained the translation of the sternal surface of the clavicle, boundary conditions constructed on muscle loadings might be even more realistic. However, we believe that the results would not differ significantly because SC rotation was fully allowed in our models; thus, the function of the clavicular strut between the scapula and the sternum is preserved. In addition, we assumed that the ligaments were hyperelastic and incompressible materials, although they are viscoelastic and compressible.
For this reason, rather than using only absolute values as a reference, we compared stress distribution patterns. Therefore, we also reconstructed the CC ligaments to incorporate their stabilizing effect into the model. Consequently, the numerical stress values measured in the AC ligament were closer to reality. Nonetheless, there is no indication that incompressibility influences experimental outcomes [45, 46].
Second, we assumed that the footprints would not be 100 percent accurate compared to a patient-specific model. Consequently, they were reproduced as precisely as possible, using data from anatomical descriptions and a reference of marginal bone ridges. Third, the simulated shoulder movements did not fully replicate the theoretical range of motion. Thus, we cannot accurately predict ligament behavior beyond 120° of shoulder elevation and 100° of horizontal adduction. However, the ligament stress pattern did not follow a trend that appeared to modify the body of the conclusions if we were able to extend the range of motion.
Fourth, we only reconstructed a type 2 AIB. In other smaller-size ligament variations, the magnitude of the stress distribution could be affected; nevertheless, in those circumstances, the component of the ACLC located in the anteroinferior aspect of the ACJ could bear the stress loading correspondingly, as occurred in our model. In addition, many authors have reported that the anterior region of the ACLC has a significant role in joint stability, although their experimental settings were different [34, 39]. Therefore, it is unlikely to obtain different results if the anterior capsule is preserved. Finally, we have not considered the joint constraint effect of fascia in our model, and its impact on stability is still uncertain.
Contrary to our hypothesis, the AIB has shown a primary role in maintaining the stability of the ACJ during shoulder coronal plane elevation and horizontal adduction. The peak von Mises stress was greater in the AIB throughout the shoulder motion. According to the clock model, the maximum stresses were supported in the 2:00 and 3:00 locations of the bundle. A secondary role was consistently observed in the SPB, notably at the 9:00 and 10:00 positions.