Reasoning with Uncertainty in Deep Learning for Safer Medical Image Computing

Deep learning is now ubiquitous in the research field of medical image computing. As such technologies progress towards clinical translation, the question of safety becomes critical. Once deployed, machine learning systems unavoidably face situations where the correct decision or prediction is ambiguous. However, the current methods disproportionately rely on deterministic algorithms, lacking a mechanism to represent and manipulate uncertainty. In safety-critical applications such as medical imaging, reasoning under uncertainty is crucial for developing a reliable decision making system. Probabilistic machine learning provides a natural framework to quantify the degree of uncertainty over different variables of interest, be it the prediction, the model parameters and structures, or the underlying data (images and labels). Probability distributions are used to represent all the uncertain unobserved quantities in a model and how they relate to the data, and probability theory is used as a language to compute and manipulate these distributions. In this thesis, we explore probabilistic modelling as a framework to integrate uncertainty information into deep learning models, and demonstrate its utility in various high-dimensional medical imaging applications. In the process, we make several fundamental enhancements to current methods. We categorise our contributions into three groups according to the types of uncertainties being modelled: (i) predictive; (ii) structural and (iii) human uncertainty. Firstly, we discuss the importance of quantifying predictive uncertainty and understanding its sources for developing a risk-averse and transparent medical image enhancement application. We demonstrate how a measure of predictive uncertainty can be used as a proxy for the predictive accuracy in the absence of ground-truths. Furthermore, assuming the structure of the model is flexible enough for the task, we introduce a way to decompose the predictive uncertainty into its orthogonal sources i.e. aleatoric and parameter uncertainty. We show the potential utility of such decoupling in providing a quantitative “explanations” into the model performance. Secondly, we introduce our recent attempts at learning model structures directly from data. One work proposes a method based on variational inference to learn a posterior distribution over connectivity structures within a neural network architecture for multi-task learning, and share some preliminary results in the MR-only radiotherapy planning application. Another work explores how the training algorithm of decision trees could be extended to grow the architecture of a neural network to adapt to the given availability of data and the complexity of the task. Lastly, we develop methods to model the “measurement noise” (e.g., biases and skill levels) of human annotators, and integrate this information into the learning process of the neural network classifier. In particular, we show that explicitly modelling the uncertainty involved in the annotation process not only leads to an improvement in robustness to label noise, but also yields useful insights into the patterns of errors that characterise individual experts

Quantitative Magnetic Resonance Imaging of Tissue Microvasculature and Microstructure in Selected Clinical Applications

This thesis is based on four papers and aims to establish perfusion and diffusion measurements with magnetic resonance imaging (MRI) in selected clinical applications. While structural imaging provides invaluable geometric and anatomical information, new disease relevant information can be obtained from measures of physiological processes inferred from advanced modelling. This study is motivated by clinical questions pertaining to diagnosis and treatment effects in particular patient groups where inflammatory processes are involved in the disease. Paper 1 investigates acquisition parameters in dynamic contrast enhanced (DCE)-MRI of the temporomandibular joint (TMJ) with possible involvement of juvenile idiopathic arthritis. High level elastic motion correction should be applied to DCE data from the TMJ, and the DCE data should be acquired with a sample rate of at least 4 s. Paper 2 investigates choices of arterial input functions (AIFs) in dynamic susceptibility contrast (DSC)-MRI in brain metastases. AIF shapes differed across patients. Relative cerebral blood volume estimates differentiated better between perfusion in white matter and grey matter when scan-specific AIFs were used than when patient-specific AIFs and population-based AIFs were used. Paper 3 investigates DSC-MRI perfusion parameters in relation to outcome after stereotactic radiosurgery (SRS) in brain metastases. Low perfusion prior to SRS may be related to unfavourable outcome. Paper 4 applies free water (FW) corrected diffusion MRI to characterise glioma. Fractional anisotropy maps of the tumour region were significantly impacted by FW correction. The estimated FW maps may also contribute to a better description of the tumour. Although there are challenges related to post-processing of MRI data, it was shown that the advanced MRI methods applied can add to a more accurate description of the TMJ and of brain lesions.Doktorgradsavhandlin

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails