Applications of Statistical Shape Modelling in Orthopaedics
Creators: Palizi, Mehrdad
Publisher: name: University of Alberta Library
Year: 2023

<p>Statistical Shape Models (SSMs) describe the shape variation in a family of similar objects in a computational format. An example of a shape family is the periphery of a specific bone for different individuals. SSMs have diverse applications in computer vision and medicine. In orthopaedics, SSMs are used to study the morphology of bones, automate image segmentation, and restore the healthy shape of injured bones. To build an SSM, an invertible mapping should be identified between the objects, referred to as correspondence. Point-set registration methods are used to establish correspondence between the objects which are represented by a dense set of points. This doctoral thesis explores a range of applications of statistical shape modelling in orthopaedics.<br>
Firstly, this research implements hypoelastic constitutive equations into the finite element software Abaqus. Abaqus is a computational platform that could be used for the biomechanical simulation of anatomical structures with various types of nonlinearity; the software allows the user to implement advanced constitutive models through the user-material subroutine. However, the implementation of a constitutive model into Abaqus is not straightforward, and the constitutive model should be expressed in a special hypoelastic form. This thesis provides such reformulation for several hypoelastic models and describes the algorithms behind many variables in the UMAT subroutine.<br>
Second, the thesis employs SSMs to study the geometry of the pelvic bone, focusing on variation within individuals, asymmetry, and sexual dimorphism (sex-based differences). Using computational methods in shape analysis and statistical tests, the significant patterns of variation, as well as the areas of significant variation, are identified on the pelvic bone. Anatomical measurements and interpretation are then provided. Previous studies have been solely focused on a single type of variation on the pelvic bone or studied men and women collectively. However, the pelvic bone shows noticeable differences between men and women and its variation within a population arises from the differences in the shape, size, position, and orientation of its components. This research provides a sex-specific assessment of pelvic geometry at multiple levels of variation, including the shape of the hemipelvis, the shape-size of the hemipelvis, and the shape-size of the left-right hemipelvis in the pelvic structure. In addition, the thesis characterizes and evaluates the ability of SSMs to simulate training samples as well as predict unseen samples, for two bones, the hemipelvis, and talus.<br>
Lastly, the thesis addresses a limitation of a probabilistic point-set registration method; the Coherent Point Drift (CPD) is a probabilistic registration method that matches complex objects such as anatomical structures. However, the method might struggle to match the intricate local features of the objects. To address this limitation, this thesis investigates the effect of geometry-aware sampling on the performance of the CPD method in matching objects with local features. In geometry-aware sampling, a higher density of points is sampled on local features, which could improve the perception of point sets in the registration process. To investigate the effectiveness of the approach, a set of two- and three-dimensional synthetic experiments, as well as a set of examples of aligning femur cartilages are performed.</p>