Reverse Total shoulder arthroplasty (RTSA) is an effective treatment and a surgical alternative approach to conventional total shoulder arthroplasty for patients with severe rotator cuff tears and glenoid erosion. To help optimize RTSA design, it is necessary to gain insight into the geometry of glenoid erosions and consider their unique morphology across the entire bone. One of the most powerful tools to systematically quantify and visualize the variation of bone geometry throughout a population is Statistical Shape Modeling (SSM);​ this method can assess the variation in the full shape of a bone, rather than of discrete anatomical features, which is very useful in identifying abnormalities, planning surgeries, and improving implant designs. Recently, many scapula SSMs have been presented in the literature;​ however, each has been created using normal and healthy bones. Therefore, creation of a scapula SSM derived exclusively from patients exhibiting complex glenoid bone erosions is critical and significantly challenging.

In addition, several studies have quantified scapular bone properties in patients with complex glenoid erosion. However, because of their discrete nature these analyses cannot be used as the basis for Finite Element Modeling (FEM). Thus, a need exists to systematically quantify the variation of bone properties in a glenoid erosion patient population using a method that captures variation across the entire bone. This can be achieved using Statistical Intensity Modeling (SIM), which can then generate scapula FEMs with realistic bone properties for evaluation of orthopaedic implants. Using an SIM enables researchers to generate models with bone properties that represent a specific, known portion of the population variation, which makes the findings more generalizable. Accordingly, the main purpose of this research is to develop an SSM and SIM to mathematically quantifying the variation of bone geometries in a systematic manner for the complex geometry of scapulae with severe glenoid erosion and to determine the main modes of variation in bone property distribution, which could be used for future FEM studies, respectively.

To draw meaningful statistical conclusions from the dataset, we need to compare and relate corresponding parts of the scapula. To achieve this correspondence, 3D triangulated mesh models of 61 scapulae were created from pre-operative CT scans from patients who were treated with RTSA and then a Non-Rigid (NR) registration method was used to morph one Atlas point cloud to the shapes of all other bones. However, the more complex the shape, the more difficult it is to maintain good correspondence. To overcome this challenge, we have adapted and optimized a NR-Iterative Closest Point (ICP) method and applied that on 61 eroded scapulae which results in each bone shape having identical mesh structure (i.e., same number and anatomical location of points).

To assess the quality of our proposed algorithm, the resulting correspondence error was evaluated by comparing the positions of ground truth points and the corresponding point locations produced by the algorithm. The average correspondence error of all anatomical landmarks across the two observers was 2.74 mm with inter and intra-observer reliability of ±0.31 and ±0.06 mm. Moreover, the Root-Mean-Square (RMS) and Hausdorff errors of geometric registration between the original and the deformed models were calculated 0.25±0.04 mm and 0.76±0.14 mm, respectively.

After registration, Principal Component Analysis (PCA) is applied to the deformed models as a group to describe independent modes of variation in the dataset. The robustness of the SSM is also evaluated using three standard metrics:​ compactness, generality, and specificity. Regarding compactness, the first 9 principal modes of variations accounted for 95% variability, while the model’s generality error and the calculated specificity over 10,000 instances were found to be 2.6 mm and 2.99 mm, respectively.

The SIM results showed that the first mode of variation accounts for overall changes in intensity across the entire bone, while the second mode represented localized changes in the glenoid vault bone quality. The third mode showed changes in intensity at the posterior and inferior glenoid rim associated with posteroinferior glenoid rim erosion which suggests avoiding fixation in this region and preferentially placing screws in the anterosuperior region of the glenoid to improve implant fixation.