**4. Discussion**

Our objective was to test for correlations between scapular morphology and glenoid retroversion, both in patients with normal scapulae but also in those with primary glenohumeral OA. Two specific acromion landmarks were used and represented by their coordinates in the 3D scapular coordinate system. In normal (non-osteoarthritic) glenohumeral joints, we observed that the posterior extension of the acromion was strongly correlated with the GRA. This anatomical acromion measure was represented by the APA, a novel angular measure of the scapula. By comparison with the primary glenohumeral OA population, we found a critical APA value, which needs to be further investigated and might eventually be used as a predictive anatomical parameter or risk factor for posterior glenoid wear in osteoarthritic shoulders.

The two acromion landmarks used in this study characterized the acromion as a linear segment. Using the six coordinates of these two landmarks in the local scapular coordinate system, we tested all possible simple and multiple morphological associations between the defined acromion segmen<sup>t</sup> and GRA. These two scapular landmarks were carefully selected to be unaffected by osteoarthritic wear or osteophytes [18,19]. Bearing this in mind, the glenoid center was deliberately avoided, as its location can be modified by glenoid wear. The same logic was applied for the APA by selecting the inferior edge of the scapula (AI) as the third landmark. Although glenoid version is classically defined as negative when oriented posteriorly, we decided to use a positive value for the sake of simplicity. Hence, we used the term retroversion to avoid any confusion, and a positive correlation between the APA and GRA was reported here.

Our statistical analysis revealed that two of these six coordinates (AAx and ACx) were mainly associated with the GRA. These coordinates were therefore subsequently used to define angles that could be conveniently measured in daily clinical practice on sagittaloblique reformats derived from preoperative shoulder CT scans. As highlighted by our results, these angles appeared to be reliable and easy-to-use alternatives to characterizing the acromion morphology. A previous analysis of the inter- and intra-observer variability in the positioning of scapular landmarks showed moderate to excellent reliability, with intraclass correlation coefficients ranging from 0.67 to 0.99 [19]. As expected, the correlation between the APA and GRA in normal scapulae was strong. The APA and AAx indeed had a strong linearly correlated since AAx is proportional to the trigonometric tangent function of the APA, which is highly linear between 0 and 20 degrees. This correlation was further enhanced after normalization of the AAx coordinate by the scapula height (R<sup>2</sup> = 0.999 and 0.830, with and without normalization by the scapula height, respectively). For normal scapulae, the more posterior the acromion extension, the wider the GRA. This was reported by the posterior extension of the AA (AAx), and by the APA. According to our regression analysis, one degree in APA related to two additional degrees in the GRA.

When secondarily looking at osteoarthritic scapulae, the correlation between AAx and the APA was still significant but weaker than in normal scapulae (R<sup>2</sup> = 0.482, *p* < 0.0001 vs. R<sup>2</sup> = 0.197, *p* < 0.0001, respectively). This meant that the correlation observed in normal scapulae seemed to be disrupted in primary glenohumeral OA patients. Our hypothesis is that this might have been related to posterior glenoid wear. Previous research identified scapulae with increased glenoid retroversion or posterior glenoid wear as a risk factor for implant failure in total shoulder arthroplasty [20,21]. In addition, posterior glenoid bone loss is known to progress over a 5- to 15-year timeframe in up to 55% of patients [22]. Our research might therefore be critical for helping council patients by defining a critical APA value related to posterior glenoid wear. We first identified a critical GRA with a ROC curve analysis. Then, by using the Youden index, we determined the optimal APA cut-off value that could distinguish between scapulae above and below this critical GRA threshold.

Glenoid retroversion also correlated with ACx, but ACx strongly correlated with AAx (see correlation matrix in Supplementary Material), meaning that the relative AP acromion length (distance between AA and AC) had a low variability. Glenoid retroversion also negatively correlated with the lateral extension of the AA (AAz), which further partly correlated with the posterior extension (Table 1). These correlations between the two acromion landmark coordinates were also present between the four tested acromion angles, and explain why they do not all appear in the multiple correlations obtained with the stepwise multiple linear regression analysis.

It appears likely that the strong correlation observed between the acromion and glenoid in normal scapulae was determined by the end of growth [23]. While several hypotheses regarding posterior glenoid wear were raised (e.g., premorbid glenoid retroversion [24], muscular imbalance [25], and lower humeral retroversion [26]), its pathophysiology remains unknown. We might reasonably assume that the acromion affected the glenoid through the action of muscles, but this remains purely conjectural. This link might also be more deeply anchored in human evolution [27].

Normalized values of the two important acromion landmarks that are the AA and AC joint have not been previously reported. However, a wide range of acromion angles have recently been described with increasing interest in characterizing the acromion morphology. The APA presents similarities with the "posterior glenoid coverage" proposed by Beeler et al. as both are based on AAx and the medio-lateral scapular plane [7,8]. However, Beeler et al. used the glenoid center as the middle point, while we used the AI instead not only because it is not affected by glenohumeral osteoarthritis, unlike the glenoid center, but also and primarily to better correlate the APA with the posterior extension of the acromion (AAx). These two angles are thus very different, and we verified that the "posterior glenoid coverage" was not correlated with the GRA in our series of normal scapulae.

The ALA corresponded to the distance between AA and AC in the sagittal (*xy*) plane, measured as an angle using AI as the third landmark. Again, it is similar to the "overall glenoid coverage" proposed by Beeler et al. [7,8], but uses AI instead of the glenoid center as the middle point, to better correlate with the AA–AC segmen<sup>t</sup> (R<sup>2</sup> = 0.908 vs. R<sup>2</sup> = 0.093, respectively). In our series of normal scapulae, these two angles were only weakly correlated (R<sup>2</sup> = 0.127), and the variability range of ALA was five times lower.

The ATA corresponds approximately to the previously defined acromion tilt [28], or 90 degrees minus the posterior acromion slope [9], or the sagittal tilt [7,8]. The ATA was 25.2 ± 8.2 (range, 5.2–46.9) degrees in our normal scapulae vs. 23.4 ± 8.7 (range, 4.5–42.5) degrees in osteoarthritic scapulae, which corresponds closely to the values in the articles referenced above.

The AXA corresponds approximately to the previously defined axial tilt angle [7,8]. The AXA was 26.1 ± 8.9 (range, 4.2–52.1) degrees in our normal scapulae vs. 29.1 ± 9.9 (range, 2.5–52.1) in osteoarthritic scapulae, which also matches the previous works mentioned above.

The main strength of the present study was the use of the 3D coordinates of two relevant acromion landmarks in a dedicated local scapular coordinate system generated from points not affected by glenoid wear that is secondary to glenohumeral osteoarthritis. This setup permitted multiple linear regression testing to identify the most significant determinants of glenoid retroversion, which was also comprehensively analyzed in 3D. A step further was taken by defining acromion angles that normalize measures to patients' height, thereby obviating the need for subsequent data processing.

The major limitation of our method was the manual identification of the two acromion landmarks, the effect of which was minimized by the good reliability in the positioning of scapular landmarks by a single experienced human observer [19]. This could be improved by using sophisticated fully automatic landmark detection methods [29]. However, even with such automated methods, the AC might still be affected by osteoarthritis, conversely to all other anatomical landmarks used to characterize the acromion morphology, the angles, and the local (i.e., scapular) coordinate system. Nevertheless, the AC is not related to the APA or the scapular coordinate system, and its variability caused by OA is supposedly weak since we found no significant difference when comparing the normal and osteoarthritic datasets. Second, patient characteristics differed between normal and osteoarthritic scapulae, as per the study design and primary objective (association between 3D acromion shape and glenoid retroversion), and considering that trauma is more common in males and shoulder OA in females. However, our aim was to assess potential morphological associations separately, first in normal and then osteoarthritic scapulae. We verified that the same correlations held true in males and females, with variations within the 95% CIs. Regarding aging, we further checked that this demographic parameter did not affect the critical APA value reported here. Finally, although trauma patients with normal scapulae and patients with glenohumeral OA were not scanned with the same CT protocols, the differences in the reconstructed geometric volumes were small (with slightly smaller voxels for OA than trauma patients) and had no impact on the positioning of scapular landmarks.
