Fretting wear and fatigue in taper junctions of modular orthopaedic implants

Multi-component, or modular, implants have a number of advantages over monoblock implants, but also a number of disadvantages related to micromotion and fretting at the taper interface. Depending on the fretting regime, either fatigue or wear damage may occur, resulting in greatly reduced fatigue lives and the production of metallic wear debris. Current revision rates of hip implants with replaceable necks are double those with fixed necks. To improve the understanding of taper performance and identify factors that can reduce wear and fatigue damage, 3-D finite element modelling of a taper connection representing the neck-stem junction of a dual modular hip prosthesis was performed. This included evaluations of short- and long-term taper strength, wear simulations and fatigue life predictions. Wear simulations included material removal due to wear. Fatigue damage calculations were performed using the critical plane Smith-Watson-Topper and Fatemi-Socie parameters together with an isotropic, linear damage accumulation model. To facilitate fatigue calculations, a unique method of tracking a consistent set of material points was presented. Taper geometry, assembly force and the magnitude of the cyclic load were all found to affect taper performance. Increasing the assembly load reduced micromotion, but reductions in wear were offset by an increase in contact pressure. Increased loads resulted in significant increases in fatigue damage. Clinically relevant wear rates were predicted, suggesting that wear volumes produced by neck-stem tapers are similar to rates of head-neck and bearing surfaces of large head metal-on-metal total hips. Fatigue crack initiation sites were predicted to be within the taper junction, located at the edges of the wear patches in regions of partial slip. Due to the evolution of the contact and sub-surface stress/strains, the inclusion of material removal was found to be critical in the prediction of both crack initiation site and fatigue damage

Geometry, evolution and scaling of fault relay zones in 3D using detailed observations from outcrops and 3D seismic data

A new surface attribute was developed during the course of the thesis, which enables fault-related deformation – specifically, the apparent dip of mapped horizons measured in a direction perpendicular to the average strike of a fault array (here termed “fault-normal rotation”, or “FNR”) – to be quantitatively analysed around imaged faults. The new utility can be applied to any 3D surface and was used to analyse centimetre-scale to kilometre-scale fault-arrays, interpreted from laser scan point clouds, digital elevation models, and 3D seismic datasets. In all studied examples, faults are surrounded by volumes of fault-related deformation that have variable widths, and which can consist of faults, fractures and continuous bed rotations (i.e. monoclines). The vertical component of displacement calculated from the areas of fault-related deformation on each horizon act to “fill-in” apparently missing displacements observed in fault throw profiles at fault overlaps. This result shows that complex 3D patterns of fault-related strain commonly develop during the geometrically coherent growth of a single fault-array. However, if the component of continuous deformation was not added to the throw profile, the fault-array could have been misinterpreted as a series of isolated fault segments with coincidental overlaps. The FNR attribute allows the detailed, quantitative analysis of fault linkage geometries. It is shown that overlapping fault tip lines in relay zones can link simultaneously at multiple points, which results in a segmented branch line. Fault linkage in relay zones is shown to control the amount of rotation accommodated by relay ramps on individual horizons, with open relay ramps having accommodated by larger rotations than breached relay ramps in the same relay zone. Displacements are therefore communicated between horizons in order to maintain strain compatibility within the relay zone. This result is used to predict fault linkage in the subsurface, along slip-aligned branch lines, from the along-strike displacement distributions at the earth’s surface. Relay zone aspect ratios (AR; overlap/separation) are documented to follow power-law scaling relationships over nine orders of magnitude with a mean AR of 4.2. Approximately one order of magnitude scatter in both separation and overlap exists at all scales. Up to half of this scatter can be attributed to the spread of measurements recorded from individual relay zones, which relates to the evolution of relay zone geometries as the displacements on the bounding faults increase. Mean relay AR is primarily controlled by the interactions between the stress field, of a nearby fault, and overlapping fault tips, rather than by the host rock lithology. At the Kilve and Lamberton study areas, mean ARs are 8.60 and 8.64 respectively, which are much higher than the global mean, 4.2. Scale-dependent factors, such as mechanical layering and heterogeneities at the fault tips are present at these locations, which modify how faults interact and produce relatively large overlap lengths for a given separation distance. Despite the modification to standard fault interaction models, these high AR relay zones are all geometrically coherent

Combinatorial Solutions for Shape Optimization in Computer Vision

This thesis aims at solving so-called shape optimization problems, i.e. problems where the shape of some real-world entity is sought, by applying combinatorial algorithms. I present several advances in this field, all of them based on energy minimization. The addressed problems will become more intricate in the course of the thesis, starting from problems that are solved globally, then turning to problems where so far no global solutions are known. The first two chapters treat segmentation problems where the considered grouping criterion is directly derived from the image data. That is, the respective data terms do not involve any parameters to estimate. These problems will be solved globally. The first of these chapters treats the problem of unsupervised image segmentation where apart from the image there is no other user input. Here I will focus on a contour-based method and show how to integrate curvature regularity into a ratio-based optimization framework. The arising optimization problem is reduced to optimizing over the cycles in a product graph. This problem can be solved globally in polynomial, effectively linear time. As a consequence, the method does not depend on initialization and translational invariance is achieved. This is joint work with Daniel Cremers and Simon Masnou. I will then proceed to the integration of shape knowledge into the framework, while keeping translational invariance. This problem is again reduced to cycle-finding in a product graph. Being based on the alignment of shape points, the method actually uses a more sophisticated shape measure than most local approaches and still provides global optima. It readily extends to tracking problems and allows to solve some of them in real-time. I will present an extension to highly deformable shape models which can be included in the global optimization framework. This method simultaneously allows to decompose a shape into a set of deformable parts, based only on the input images. This is joint work with Daniel Cremers. In the second part segmentation is combined with so-called correspondence problems, i.e. the underlying grouping criterion is now based on correspondences that have to be inferred simultaneously. That is, in addition to inferring the shapes of objects, one now also tries to put into correspondence the points in several images. The arising problems become more intricate and are no longer optimized globally. This part is divided into two chapters. The first chapter treats the topic of real-time motion segmentation where objects are identified based on the observations that the respective points in the video will move coherently. Rather than pre-estimating motion, a single energy functional is minimized via alternating optimization. The main novelty lies in the real-time capability, which is achieved by exploiting a fast combinatorial segmentation algorithm. The results are furthermore improved by employing a probabilistic data term. This is joint work with Daniel Cremers. The final chapter presents a method for high resolution motion layer decomposition and was developed in combination with Daniel Cremers and Thomas Pock. Layer decomposition methods support the notion of a scene model, which allows to model occlusion and enforce temporal consistency. The contributions are twofold: from a practical point of view the proposed method allows to recover fine-detailed layer images by minimizing a single energy. This is achieved by integrating a super-resolution method into the layer decomposition framework. From a theoretical viewpoint the proposed method introduces layer-based regularity terms as well as a graph cut-based scheme to solve for the layer domains. The latter is combined with powerful continuous convex optimization techniques into an alternating minimization scheme. Lastly I want to mention that a significant part of this thesis is devoted to the recent trend of exploiting parallel architectures, in particular graphics cards: many combinatorial algorithms are easily parallelized. In Chapter 3 we will see a case where the standard algorithm is hard to parallelize, but easy for the respective problem instances

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus