Towards automated three-dimensional tracking of nephrons through stacked histological image sets

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of Witwatersrand for the degree of Master of Science in Engineering. August, 2015The three-dimensional microarchitecture of the mammalian kidney is of keen interest in the fields of cell biology and biomedical engineering as it plays a crucial role in renal function. This study presents a novel approach to the automatic tracking of individual nephrons through three-dimensional histological image sets of mouse and rat kidneys. The image database forms part of a previous study carried out at the University of Aarhus, Denmark. The previous study involved manually tracking a few hundred nephrons through the image sets in order to explore the renal microarchitecture, the results of which forms the gold standard for this study. The purpose of the current research is to develop methods which contribute towards creating an automated, intelligent system as a standard tool for such image sets. This would reduce the excessive time and human effort previously required for the tracking task, enabling a larger sample of nephrons to be tracked. It would also be desirable, in future, to explore the renal microstructure of various species and diseased specimens. The developed algorithm is robust, able to isolate closely packed nephrons and track their convoluted paths despite a number of non-ideal conditions such as local image distortions, artefacts and connective tissue interference. The system consists of initial image pre-processing steps such as background removal, adaptive histogram equalisation and image segmentation. A feature extraction stage achieves data abstraction and information concentration by extracting shape iii descriptors, radial shape profiles and key coordinates for each nephron crosssection. A custom graph-based tracking algorithm is implemented to track the nephrons using the extracted coordinates. A rule-base and machine learning algorithms including an Artificial Neural Network and Support Vector Machine are used to evaluate the shape features and other information to validate the algorithm’s results through each of its iterations. The validation steps prove to be highly effective in rejecting incorrect tracking moves, with the rule-base having greater than 90% accuracy and the Artificial Neural Network and Support Vector Machine both producing 93% classification accuracies. Comparison of a selection of automatically and manually tracked nephrons yielded results of 95% accuracy and 98% tracking extent for the proximal convoluted tubule, proximal straight tubule and ascending thick limb of the loop of Henle. The ascending and descending thin limbs of the loop of Henle pose a challenge, having low accuracy and low tracking extent due to the low resolution, narrow diameter and high density of cross-sections in the inner medulla. Limited manual intervention is proposed as a solution to these limitations, enabling full nephron paths to be obtained with an average of 17 manual corrections per mouse nephron and 58 manual corrections per rat nephron. The developed semi-automatic system saves a considerable amount of time and effort in comparison with the manual task. Furthermore, the developed methodology forms a foundation for future development towards a fully automated tracking system for nephrons

Identical synchronization of time-continuous chaotic oscillators

Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded in the fully synchronized state lose their transverse stability, and the appearance of globally and locally riddled basins of attraction is discussed in terms of the sub-, respectively supercritical nature of the riddling bifurcations. We show how the introduction of a small parameter mismatch between the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled Rössler oscillators

Synchronization of Time-Continuous Chaotic Oscillators

Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded in the fully synchronized state lose their transverse stability, and the appearance of globally and locally riddled basins of attraction is discussed, respectively, in terms of the subcritical, supercritical nature of the riddling bifurcations. We show how the introduction of a small parameter mismatch between the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled Rössler oscillators

A theoretical and computational study of cavity formation in biological systems

In this thesis, I present my work on the emergence of self-organised structure within cellular systems, with a particular emphasis on the formation of fluid filled cavities. Self-organisation is a striking hallmark of living systems, and plays a particularly import role in developmental biology. To study such systems, I develop a novel hydrodynamic theory of cells in a background fluid of water and solutes. The solutes and water can move passively across the membrane of the cells. Furthermore, solutes can be actively transported in or out of the cell both isotropi- cally and along a polar axis. Within this theory I demonstrate the existence of two potential mechanisms for cavity formation: spinodal phase separation driven by cell-cell adhesions, and an instability driven by active pumping of solutes into defects in the polarity field. This theory is general in scope, i.e. it is a framework to describe a variety of behaviours of any system consisting of adhering cells that can polarise and actively pump fluid. I also present a study of a specific experimental system: mouse embryonic stem cell (mESC) aggregates. When grown from wild type cells, these aggregates form a spherical structure with cells polarised towards the centre. Fluid is pumped into the centre and a cavity opens. Such aggregates are the simplest example of mESC organoids that recapitulate key in vivo developmental processes in vitro. In order to quantify the growth of mESC aggregates, I develop an image segmentation and analysis pipeline. This pipeline allows me to extract meaningful, structured information from noisy 3D experimental time series data. In order to model the growth of mESC aggregates in silico, I develop a novel 2D model of polarised, deformable cells with continuous boundaries, called the Spline Model. Using the Spline Model as a prototype, I recapitulate key features of the experiments. Finally, I develop a 3D model of polarised, deformable cells. I demonstrate quantitative agreement between cell shapes produced by this model and in experiment. I study the dynamics of cell aggregates for the case where adhesion forces are coupled to apicobasal polarity, and make quantitative comparisons between these simulations and experiments. I find a positive correlation between the measured polarity of E- cadherin and predictions based on integration of extracellular matrix signalling. Furthermore, by coupling polarity to increased apical adhesion, I demonstrate the ability of extended cellular aggregates to undergo a transition to a compact state. When the coupling is removed, the transition no longer occurs. This behaviour is reminiscent of β1-KO cells, in which polarity alignment mechanisms are disrupted, that fail to form compact, organised aggregates

Mathematical modelling of immune condition dynamics : a clinical perspective

This thesis describes the use of mathematical modelling to analyse the treatment of patients with immune disorders; namely, Multiple Myeloma, a cancer of plasma cells that create excess monoclonal antibody; and kidney transplants, where the immune system produces polygonal antibodies against the implanted organ. Linear and nonlinear compartmental models play an important role in the analysis of biomedical systems; in this thesis several models are developed to describe the in vivo kinetics of the antibodies that are prevalent for the two disorders studied. These models are validated against patient data supplied by clinical collaborators. Through this validation process important information regarding the dynamic properties of the clinical treatment can be gathered. In order to treat patients with excess immune antibodies the clinical staff wish to reduce these high levels in the patient to near healthy concentrations. To achieve this they have two possible treatment modalities: either using artificial methods to clear the material, a process known as apheresis, or drug therapy to reduce the production of the antibody in question. Apheresis techniques differ in their ability to clear different immune complexes; the effectiveness of a range of apheresis techniques is categorised for several antibody types and antibody fragments. The models developed are then used to predict the patient response to alternative treatment methods, and schedules, to find optimal combinations. In addition, improved measurement techniques that may offer an improved diagnosis are suggested. Whilst the overall effect of drug therapy is known, through measuring the concentration of antibodies in the patient’s blood, the short-term relationship between drug application and reduction in antibody synthesis is still not well defined; therefore, methods to estimate the generation rate of the immune complex, without the need for invasive procedures, are also presented