Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work

Neural Deformable Cone Beam CT

In oral and maxillofacial cone beam computed tomography (CBCT), patient motion is frequently observed and, if not accounted for, can severely affect the usability of the acquired images. We propose a highly flexible, data driven motion correction and reconstruction method which combines neural inverse rendering in a CBCT setting with a neural deformation field. We jointly optimize a lightweight coordinate based representation of the 3D volume together with a deformation network. This allows our method to generate high quality results while accurately representing occurring patient movements, such as head movements, separate jaw movements or swallowing. We evaluate our method in synthetic and clinical scenarios and are able to produce artefact-free reconstructions even in the presence of severe motion. While our approach is primarily developed for maxillofacial applications, we do not restrict the deformation field to certain kinds of motion. We demonstrate its flexibility by applying it to other scenarios, such as 4D lung scans or industrial tomography settings, achieving state-of-the art results within minutes with only minimal adjustments

Technologies for Biomechanically-Informed Image Guidance of Laparoscopic Liver Surgery

Laparoscopic surgery for liver resection has a number medical advantages over open surgery, but also comes with inherent technical challenges. The surgeon only has a very limited field of view through the imaging modalities routinely employed intra-operatively, laparoscopic video and ultrasound, and the pneumoperitoneum required to create the operating space and gaining access to the organ can significantly deform and displace the liver from its pre-operative configuration. This can make relating what is visible intra-operatively to the pre-operative plan and inferring the location of sub-surface anatomy a very challenging task. Image guidance systems can help overcome these challenges by updating the pre-operative plan to the situation in theatre and visualising it in relation to the position of surgical instruments. In this thesis, I present a series of contributions to a biomechanically-informed image-guidance system made during my PhD. The most recent one is work on a pipeline for the estimation of the post-insufflation configuration of the liver by means of an algorithm that uses a database of segmented training images of patient abdomens where the post-insufflation configuration of the liver is known. The pipeline comprises an algorithm for inter and intra-subject registration of liver meshes by means of non-rigid spectral point-correspondence finding. My other contributions are more fundamental and less application specific, and are all contained and made available to the public in the NiftySim open-source finite element modelling package. Two of my contributions to NiftySim are of particular interest with regards to image guidance of laparoscopic liver surgery: 1) a novel general purpose contact modelling algorithm that can be used to simulate contact interactions between, e.g., the liver and surrounding anatomy; 2) membrane and shell elements that can be used to, e.g., simulate the Glisson capsule that has been shown to significantly influence the organ’s measured stiffness

Advancements and Breakthroughs in Ultrasound Imaging

Ultrasonic imaging is a powerful diagnostic tool available to medical practitioners, engineers and researchers today. Due to the relative safety, and the non-invasive nature, ultrasonic imaging has become one of the most rapidly advancing technologies. These rapid advances are directly related to the parallel advancements in electronics, computing, and transducer technology together with sophisticated signal processing techniques. This book focuses on state of the art developments in ultrasonic imaging applications and underlying technologies presented by leading practitioners and researchers from many parts of the world

Improved 3D MR Image Acquisition and Processing in Congenital Heart Disease

Congenital heart disease (CHD) is the most common type of birth defect, affecting about 1% of the population. MRI is an essential tool in the assessment of CHD, including diagnosis, intervention planning and follow-up. Three-dimensional MRI can provide particularly rich visualization and information. However, it is often complicated by long scan times, cardiorespiratory motion, injection of contrast agents, and complex and time-consuming postprocessing. This thesis comprises four pieces of work that attempt to respond to some of these challenges. The first piece of work aims to enable fast acquisition of 3D time-resolved cardiac imaging during free breathing. Rapid imaging was achieved using an efficient spiral sequence and a sparse parallel imaging reconstruction. The feasibility of this approach was demonstrated on a population of 10 patients with CHD, and areas of improvement were identified. The second piece of work is an integrated software tool designed to simplify and accelerate the development of machine learning (ML) applications in MRI research. It also exploits the strengths of recently developed ML libraries for efficient MR image reconstruction and processing. The third piece of work aims to reduce contrast dose in contrast-enhanced MR angiography (MRA). This would reduce risks and costs associated with contrast agents. A deep learning-based contrast enhancement technique was developed and shown to improve image quality in real low-dose MRA in a population of 40 children and adults with CHD. The fourth and final piece of work aims to simplify the creation of computational models for hemodynamic assessment of the great arteries. A deep learning technique for 3D segmentation of the aorta and the pulmonary arteries was developed and shown to enable accurate calculation of clinically relevant biomarkers in a population of 10 patients with CHD

Multidimensional Data Processing for Optical Coherence Tomography Imaging

Optical Coherence Tomography (OCT) is a medical imaging technique which distinguishes itself by acquiring microscopic resolution images in-vivo at millimeter scale fields of view. The resulting in images are not only high-resolution, but often multi-dimensional to capture 3-D biological structures or temporal processes. The nature of multi-dimensional data presents a unique set of challenges to the OCT user that include acquiring, storing, and handling very large datasets, visualizing and understanding the data, and processing and analyzing the data. In this dissertation, three of these challenges are explored in depth: sub-resolution temporal analysis, 3-D modeling of fiber structures, and compressed sensing of large, multi-dimensional datasets. Exploration of these problems is followed by proposed solutions and demonstrations which rely on tools from multiple research areas including digital image filtering, image de-noising, and sparse representation theory. Combining approaches from these fields, advanced solutions were developed to produce new and groundbreaking results. High-resolution video data showing cilia motion in unprecedented detail and scale was produced. An image processing method was used to create the first 3-D fiber model of uterine tissue from OCT images. Finally, a compressed sensing approach was developed which we show to guarantee high accuracy image recovery of more complicated, clinically relevant, samples than had been previously demonstrated. The culmination of these methods represents a step forward in OCT image analysis, showing that these cutting edge tools can also be applied to OCT data and in the future be employed in a clinical setting

4-D Tomographic Inference: Application to SPECT and MR-driven PET

Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference