Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Monitoring mesenchymal stem cell cultures using image processing and pattern recognition techniques

Stem cells have attracted tremendous interest in recent times due to their promise in providing innovative new treatments for a great range of currently debilitating diseases. This is due to their potential ability to regenerate and repair damaged tissue, and hence restore lost body function, in a manner beyond the body's usual healing process. Bone marrow-derived mesenchymal stem cells or bone marrow stromal cells are one type of adult stem cells that are of particular interest. Since they are derived from a living human adult donor, they do not have the ethical issues associated with the use of human embryonic stem cells. They are also able to be taken from a patient or other donors with relative ease and then grown readily in the laboratory for clinical application. Despite the attractive properties of bone marrow stromal cells, there is presently no quick and easy way to determine the quality of a sample of such cells. Presently, a sample must be grown for weeks and subject to various time-consuming assays, under the direction of an expert cell biologist, to determine whether it will be useful. Hence there is a great need for innovative new ways to assess the quality of cell cultures for research and potential clinical application. The research presented in this thesis investigates the use of computerised image processing and pattern recognition techniques to provide a quicker and simpler method for the quality assessment of bone marrow stromal cell cultures. In particular, aim of this work is to find out whether it is possible, through the use of image processing and pattern recognition techniques, to predict the growth potential of a culture of human bone marrow stromal cells at early stages, before it is readily apparent to a human observer. With the above aim in mind, a computerised system was developed to classify the quality of bone marrow stromal cell cultures based on phase contrast microscopy images. Our system was trained and tested on mixed images of both healthy and unhealthy bone marrow stromal cell samples taken from three different patients. This system, when presented with 44 previously unseen bone marrow stromal cell culture images, outperformed human experts in the ability to correctly classify healthy and unhealthy cultures. The system correctly classified the health status of an image 88% of the time compared to an average of 72% of the time for human experts. Extensive training and testing of the system on a set of 139 normal sized images and 567 smaller image tiles showed an average performance of 86% and 85% correct classifications, respectively. The contributions of this thesis include demonstrating the applicability and potential of computerised image processing and pattern recognition techniques to the task of quality assessment of bone marrow stromal cell cultures. As part of this system, an image normalisation method has been suggested and a new segmentation algorithm has been developed for locating cell regions of irregularly shaped cells in phase contrast images. Importantly, we have validated the efficacy of both the normalisation and segmentation method, by demonstrating that both methods quantitatively improve the classification performance of subsequent pattern recognition algorithms, in discriminating between cell cultures of differing health status. We have shown that the quality of a cell culture of bone marrow stromal cells may be assessed without the need to either segment individual cells or to use time-lapse imaging. Finally, we have proposed a set of features, that when extracted from the cell regions of segmented input images, can be used to train current state of the art pattern recognition systems to predict the quality of bone marrow stromal cell cultures earlier and more consistently than human experts.

Pattern recognition using invariants defined from higher order spectra : 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Metabolite profiling and pathway analysis of acute hepatitis rats by UPLC-ESI MS combined with pattern recognition methods

BACKGROUND & AIMS Metabolomics is comprehensive analysis of low-molecular-weight endogenous metabolites in a biological sample. It could enable mapping of perturbations of early biochemical changes in diseases and hence provide an opportunity to develop predictive biomarkers that could provide valuable insights into the mechanisms of diseases. The aim of this study was to elucidate the changes in endogenous metabolites and to phenotype the metabolic profiling of d-galactosamine (GalN)-inducing acute hepatitis in rats by UPLC-ESI MS. METHODS The systemic biochemical actions of GalN administration (ip, 400 mg/kg) have been investigated in male wistar rats using conventional clinical chemistry, liver histopathology and metabolomic analysis of UPLC- ESI MS of urine. The urine was collected predose (-24 to 0 h) and 0-24, 24-48, 48-72, 72-96 h post-dose. Mass spectrometry of the urine was analysed visually and via conjunction with multivariate data analysis. RESULTS Results demonstrated that there was a time-dependent biochemical effect of GalN dosed on the levels of a range of low-molecular-weight metabolites in urine, which was correlated with developing phase of the GalN-inducing acute hepatitis. Urinary excretion of beta-hydroxybutanoic acid and citric acid was decreased following GalN dosing, whereas that of glycocholic acid, indole-3-acetic acid, sphinganine, n-acetyl-l-phenylalanine, cholic acid and creatinine excretion was increased, which suggests that several key metabolic pathways such as energy metabolism, lipid metabolism and amino acid metabolism were perturbed by GalN. CONCLUSION This metabolomic investigation demonstrates that this robust non-invasive tool offers insight into the metabolic states of diseases.

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Mathematical models of bubble evolution in a Hele-Shaw Cell

This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined. In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.

Bearing Fault Diagnostics Using the Spectral Pattern Recognition

In the field of diagnostics of rolling element bearings, the development of sophisticated techniques, such as Spectral Kurtosis and 2nd Order Cyclostationarity, extended the capability of expert users to identify not only the presence, but also the location of the damage in the bearing. Most of the signal-analysis methods, as the ones previously mentioned, result in a spectrum-like diagram that presents line frequencies or peaks in the neighbourhood of some theoretical characteristic frequencies, in case of damage. These frequencies depend only on damage position, bearing geometry and rotational speed. The major improvement in this field would be the development of algorithms with high degree of automation. This paper aims at this important objective, by discussing for the first time how these peaks can draw away from the theoretical expected frequencies as a function of different working conditions, i.e. speed, torque and lubrication. After providing a brief description of the peak-patterns associated with each type of damage, this paper shows the typical magnitudes of the deviations from the theoretical expected frequencies. The last part of the study presents some remarks about increasing the reliability of the automatic algorithm. The research is based on experimental data obtained by using artificially damaged bearings installed in a gearbox.

Pattern-based topic models for information filtering

Topic modelling, such as Latent Dirichlet Allocation (LDA), was proposed to generate statistical models to represent multiple topics in a collection of documents, which has been widely utilized in the fields of machine learning and information retrieval, etc. But its effectiveness in information filtering is rarely known. Patterns are always thought to be more representative than single terms for representing documents. In this paper, a novel information filtering model, Pattern-based Topic Model(PBTM) , is proposed to represent the text documents not only using the topic distributions at general level but also using semantic pattern representations at detailed specific level, both of which contribute to the accurate document representation and document relevance ranking. Extensive experiments are conducted to evaluate the effectiveness of PBTM by using the TREC data collection Reuters Corpus Volume 1. The results show that the proposed model achieves outstanding performance.

A comparison of mathematical models for phase separation in high-rate LiFePO4 cathodes

We construct a two-scale mathematical model for modern, high-rate LiFePO4cathodes. We attempt to validate against experimental data using two forms of the phase-field model developed recently to represent the concentration of Li+ in nano-sized LiFePO4crystals. We also compare this with the shrinking-core based model we developed previously. Validating against high-rate experimental data, in which electronic and electrolytic resistances have been reduced is an excellent test of the validity of the crystal-scale model used to represent the phase-change that may occur in LiFePO4material. We obtain poor fits with the shrinking-core based model, even with fitting based on “effective” parameter values. Surprisingly, using the more sophisticated phase-field models on the crystal-scale results in poorer fits, though a significant parameter regime could not be investigated due to numerical difficulties. Separate to the fits obtained, using phase-field based models embedded in a two-scale cathodic model results in “many-particle” effects consistent with those reported recently.

Mathematical Models of Tumor-Immune System Dynamics

"This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences."--Publisher website

Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.