Development of a Statistical Shape Model of the Human Pelvis Using Deformetrica and Principal Component Analysis

In the field of computational biomechanics and hip prosthesis design, the study and understanding of pelvic morphological variability provide an advantage for designing patient-specific implants and supporting custom-made production. Moreover, in the case of oncological patients with bone metastases, the pelvis may present defects and missing parts, complicating preoperative planning. A complete and standardized mathematical description of the variability of the pelvic bone is still lacking, resulting in gaps in the knowledge of local and global shape variations. To address this issue and enable the reconstruction of missing geometries in the pelvis, a powerful tool is represented by Statistical Shape Models (SSMs), which mathematically describe the main features of shape variation. Essentially, an SSM consists of a mean shape, called the template, and deformation modes that capture the most significant shape variations. For this purpose, a database of 352 3D pelvis models, consisting of both hemipelves and derived from segmentations of clinical images of patients without defects or bone pathologies, was initially created. These models were then divided into two datasets based on sex: the male dataset (134 models) and the female dataset (218 models). Subsequently, a realignment algorithm was developed in MATLAB, which was fundamental in constructing an SSM. Rigid rotations and translations were applied based on the identification of three anatomical landmarks (right ASIS, left ASIS, and the pubic symphysis (PS)). A statistical fitting algorithm was then used to identify the centroid and the two acetabular centers for each model, bringing the centroid to the origin of the reference system and aligning the two acetabular centers along the y-coordinate of the reference system. To reduce computational size and complexity, the number of points in each model was downsampled by a factor of 1/15. The open-source software Deformetrica, based on the Large Diffeomorphic Metric Mapping (LDDMM) framework, was then used to compute diffeomorphic transformations, starting from the 3D pelvis meshes. The analyses were carried out separately for the two datasets, extracting a mean model, known as the template, and the patient-specific moment vectors, used to deform the template to achieve patient-specific reconstructions. Two sensitivity analyses were conducted on the male dataset: the first to tune the optimization parameters, and the second to select the best kernel width combination to obtain accurate reconstructions. Two separate final simulations were then performed on each dataset. Principal Component Analysis (PCA) was finally performed to reduce the dimensionality of the deformation modes, resulting in the SSMs of the human pelvis for both sexes. The final reconstruction models, obtained after the two sensitivity analyses, showed an average Euclidean distance error below 1.24 mm, with a Chamfer Distance under 3.75 mm and a Hausdorff Distance below 6.33 mm. Subsequently, the PCA revealed that, in the male dataset, 58 modes were required to explain 90% of the variance, while the first 10 modes accounted for 57% of the total variance. In conclusion, this work enabled the identification of the main morphometric components of the entire pelvis, highlighting its anatomical complexity and the high variability, even among subjects of the same sex.