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Minimally invasive fetal interventions, such as those used for therapy of twin-to- twin transfusion syndrome (TTTS), require accurate image guidance to optimise patient outcomes. Photoacoustic imaging can provide molecular contrast based on the optical absorption of the haemoglobin, and in this dissertation, it was proposed as a novel technique to image the human placental vasculature. Normal term and in utero TTTS treated placentas were imaged post-partum using two novel photoacoustic imaging systems. With PA imaging, vasculature was resolved to a depth of approximately 7 mm from the chorionic placental surface; the photocoagulated tissue provided a negative contrast and the ablation depth of the scar was visualised. Complementary imaging of the placental vasculature in a microscopic size scale was performed with a handheld incident dark field illumination video microscope in fresh and formalin-fixed term placentas. Real time visualisation of the villus tree down to the terminal villi level was achieved without any contrast injection or extensive tissue preparation. Additionally, the novel application of photoacoustic imaging to guide minimally invasive fetal interventions motivated the development of tissue-mimicking placental phantoms for bench-top system validation and for clinical training. Ideally, phantoms for this modality comprise materials with optical and acoustic properties that can be precisely and independently controlled, which are stable over time, and which are non-toxic and low-cost. Gel wax was proposed as a novel tissue-mimicking material (TMM) that satisfies these criteria, and that it can be used to represent various soft tissues and fabricate heterogeneous phantoms with structures based on patient-specific anatomy. This dissertation sets the stage for the development of miniaturised photoacoustic imaging probes for intraoperative guidance, and new methods of understanding the placental vascular anatomy in health and disease. Gel wax has strong potential to become a next generation TMM for evaluation, and standardisation of imaging systems, and for clinical training.

Despite recent advances in acquisition techniques and reconstruction algorithms, magnetic resonance imaging (MRI) remains challenging in the presence of motion. To mitigate this, ultra-fast two-dimensional (2D) MRI sequences are often used in clinical practice to acquire thick, low-resolution (LR) 2D slices to reduce in-plane motion. The resulting stacks of thick 2D slices typically provide high-quality visualizations when viewed in the in-plane direction. However, the low spatial resolution in the through-plane direction in combination with motion commonly occurring between individual slice acquisitions gives rise to stacks with overall limited geometric integrity. In further consequence, an accurate and reliable diagnosis may be compromised when using such motion-corrupted, thick-slice MRI data. This thesis presents methods to volumetrically reconstruct geometrically consistent, high-resolution (HR) three-dimensional (3D) images from motion-corrupted, possibly sparse, low-resolution 2D MR slices. It focuses on volumetric reconstructions techniques using inverse problem formulations applicable to a broad field of clinical applications in which associated motion patterns are inherently different, but the use of thick-slice MR data is current clinical practice. In particular, volumetric reconstruction frameworks are developed based on slice-to-volume registration with inter-slice transformation regularization and robust, complete-outlier rejection for the reconstruction step that can either avoid or efficiently deal with potential slice-misregistrations. Additionally, this thesis describes efficient Forward-Backward Splitting schemes for image registration for any combination of differentiable (not necessarily convex) similarity measure and convex (not necessarily smooth) regularization with a tractable proximal operator. Experiments are performed on fetal and upper abdominal MRI, and on historical, printed brain MR films associated with a uniquely long-term study dating back to the 1980s. The results demonstrate the broad applicability of the presented frameworks to achieve robust reconstructions with the potential to improve disease diagnosis and patient management in clinical practice.

In this thesis we present a range of computational tools for medical imaging purposes within two main research projects. The first one is a methodological project oriented towards the improvement of the performance of a numerical computation utilised in diffeomorphic image registration. The second research project is a pre-clinical study aimed at the investigation of the effects of antenatal corticosteroids in a preterm rabbit animal model. In the first part we addressed the problem of integrating stationary velocity fields. This mathematical challenge had originated with early studies in fluid dynamics and had been subsequently mathematically formalised in the Lie group theory. Given a tangent velocity field defined in the tridimensional space as in input, the goal is to compute the position of the particles to which the velocity field is applied. This computation, also called numerical Lie exponential, is a fundamental component of several medical image registration algorithm based on diffeomorphisms, i.e. bijective differentiable maps with differentiable inverse. It is as well a widely utilised tool in computational anatomy to quantify the differences between two anatomical shapes measuring the parameters of the transformation that belongs to a metric vector space. The resulting new class of algorithms introduced in this thesis was created combining the known scaling and squaring algorithm with a class of numerical integrators aimed to solve systems of ordinary differential equations called exponential integrators. The introduced scaling and squaring based approximated exponential integrator algorithm have improved the computational time and accuracy respect to the state- of-the-art methods. The second part of the research is a pre-clinical trial carried forward in collab- oration with the Department of Development and Regeneration, Woman and Child Cluster at the KU Leuven University. The clinical research question is related to the understanding of the possible negative effects of administering antenatal cor- ticosteroids for preterm birth. To tackle this problem we designed and started a pre-clinical study using a New Zealand perinatal rabbit model. In this part of the research I was involved in the research team to provide the tools to automatise the data analysis and to eliminate the time consuming and non reproducible manual segmentation step. The main result of this collaboration is the creation of the first multi-modal multi-atlas for the newborn rabbit brain. This is embedded in a segmentation propagation and label fusion algorithm at the core of the proposed open-sourced automatic pipeline, having as input the native scanner format and as output the main MRI readouts, such as volume, fractional anisotropy and mean diffusivity.

Placenta segmentation from fetal Magnetic Resonance (MR) images is important for fetal surgical planning. However, accurate segmentation results are difficult to achieve for automatic methods, due to sparse acquisition, inter-slice motion, and the widely varying position and shape of the placenta among pregnant women. Interactive methods have been widely used to get more accurate and robust results. A good interactive segmentation method should achieve high accuracy, minimize user interactions with low variability among users, and be computationally fast. Exploiting recent advances in machine learning, I explore a family of new interactive methods for placenta segmentation from fetal MR images. I investigate the combination of user interactions with learning from a single image or a large set of images. For learning from a single image, I propose novel Online Random Forests to efficiently leverage user interactions for the segmentation of 2D and 3D fetal MR images. I also investigate co-segmentation of multiple volumes of the same patient with 4D Graph Cuts. For learning from a large set of images, I first propose a deep learning-based framework that combines user interactions with Convolutional Neural Networks (CNN) based on geodesic distance transforms to achieve accurate segmentation and good interactivity. I then propose image-specific fine-tuning to make CNNs adaptive to different individual images and able to segment previously unseen objects. Experimental results show that the proposed algorithms outperform traditional interactive segmentation methods in terms of accuracy and interactivity. Therefore, they might be suitable for segmentation of the placenta in planning systems for fetal and maternal surgery, and for rapid characterization of the placenta by MR images. I also demonstrate that they can be applied to the segmentation of other organs from 2D and 3D images.