Analysis of MRI for Knee Osteoarthritis using Machine Learning

Approximately 8.5 million people in the UK (13.5% of the population) have osteoarthritis (OA) in one or both knees, with more than 6 million people in the UK suffering with painful osteoarthritis of the knee. In addition, an ageing population implies that an estimated 17 million people (twice as many as in 2012) are likely to be living with OA by 2030. Despite this, there exists no disease modifying drugs for OA and structural OA in MRI is poorly characterised. This motivates research to develop biomarkers and tools to aid osteoarthritis diagnosis from MRI of the knee. Previously many solutions for learning biomarkers have relied upon hand-crafted features to characterise and diagnose osteoarthritis from MRI. The methods proposed in this thesis are scalable and use machine learning to characterise large populations of the OAI dataset, with one experiment applying an algorithm to over 10,000 images. Studies of this size enable subtle characteristics of the dataset to be learnt and model many variations within a population. We present data-driven algorithms to learn features to predict OA from the appearance of the articular cartilage. An unsupervised manifold learning algorithm is used to compute a low dimensional representation of knee MR data which we propose as an imaging marker of OA. Previous metrics introduced for OA diagnosis are loosely based on the research communities intuition of the structural causes of OA progression, including morphological measures of the articular cartilage such as the thickness and volume. We demonstrate that there is a strong correlation between traditional morphological measures of the articular cartilage and the biomarkers identified using the manifold learning algorithm that we propose (R 2 = 0.75). The algorithm is extended to create biomarkers for different regions and sequences. A combination of these markers is proposed to yield a diagnostic imaging biomarker with superior performance. The diagnostic biomarkers presented are shown to improve upon hand-crafted morphological measure of disease status presented in the literature, a linear discriminant analysis (LDA) classification for early stage diagnosis of knee osteoarthritis results with an AUC of 0.9. From the biomarker discovery experiments we identified that intensity based affine registration of knee MRIs is not sufficiently robust for large scale image analysis, approximately 5% of these registrations fail. We have developed fast algorithms to compute robust affine transformations of knee MRI, which enables accurate pairwise registrations in large datasets. We model the population of images as a non-linear manifold, a registration is defined by the shortest geodesic path over the manifold representation. We identify sources of error in our manifold representation and propose fast mitigation strategies by checking for consistency across the manifold and by utilising multiple paths. These mitigation strategies are shown to improve registration accuracy and can be computed in less than 2 seconds with current architecture.Open Acces

Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results