Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Biomedical Engineering

Supervisor

Dr. Terry Peters

Abstract

A fundamental step in diagnosis of cardiovascular diseases, automated left and right ventricle (LV and RV) segmentation in cardiac magnetic resonance images (MRI) is still acknowledged to be a difficult problem. Although algorithms for LV segmentation do exist, they require either extensive training or intensive user inputs. RV segmentation in MRI has yet to be solved and is still acknowledged a completely unsolved problem because its shape is not symmetric and circular, its deformations are complex and varies extensively over the cardiac phases, and it includes papillary muscles. In this thesis, I investigate fast detection of the LV endo- and epi-cardium surfaces (3D) and contours (2D) in cardiac MRI via convex relaxation and distribution matching. A rapid 3D segmentation of the RV in cardiac MRI via distribution matching constraints on segment shape and appearance is also investigated. These algorithms only require a single subject for training and a very simple user input, which amounts to one click. The solution is sought following the optimization of functionals containing probability product kernel constraints on the distributions of intensity and geometric features. The formulations lead to challenging optimization problems, which are not directly amenable to convex-optimization techniques. For each functional, the problem is split into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Finally, an information-theoretic based artificial neural network (ANN) is proposed for normal/abnormal LV myocardium motion classification. Using the LV segmentation results, the LV cavity points is estimated via a Kalman filter and a recursive dynamic Bayesian filter. However, due to the similarities between the statistical information of normal and abnormal points, differentiating between distributions of abnormal and normal points is a challenging problem. The problem was investigated with a global measure based on the Shannon's differential entropy (SDE) and further examined with two other information-theoretic criteria, one based on Renyi entropy and the other on Fisher information. Unlike the existing information-theoretic studies, the approach addresses explicitly the overlap between the distributions of normal and abnormal cases, thereby yielding a competitive performance. I further propose an algorithm based on a supervised 3-layer ANN to differentiate between the distributions farther. The ANN is trained and tested by five different information measures of radial distance and velocity for points on endocardial boundary.

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