Thèses sur le sujet « MRI mathematical analysis »

Non-invasive imaging techniques are now being used routinely for the analysis of cardiac function. The objective of this thesis was to develop mathematical modelling tools for the semi-automatic quantification of cardiac structure and function from magnetic resonance imaging (MRI). Two main problem areas were considered. Firstly, tools were developed to investigate the changes in cardiac function and myofibre structure during the progression of myocardial infarction, and the effect of using angiotensin-converting enzyme inhibitor (ACEI) as a treatment of myocardial infarction. Ex vivo diffusion tensor MRI (DTMRI) could then be compared with in vivo myocardial strain from MRI tissue tagging. These tools were applied to data from four healthy male Sprague Dawley rats, and eight with myocardial infarction induced by ligating the left anterior descending artery. Half of the infarcted rats were treated by ACEI. The results showed that myocyte structure as well as function were altered in myocardial infarction, altering the correlations between structure and function. A positive correlation between strain and fractional isotropy in the control group became negative in the infarct group and did not change with ACEI. Strain was positively correlated with the proportion of left-handed myofibres in the control group. This relationship was not significant in the infarct group but returned in the ACEI group. The results from these preliminary studies indicate that treatment with ACEI helps to restore normal myocardial structure-function relationships. Secondly, a modelling tool was developed for the efficient evaluation of right and left ventricular function in standard cine MRI imaging examinations. The biventricular modelling tool used a human biventricular deformable model, which was developed based on a porcine model, for customisation to cardiac MRI data. The customisation used an interactive guide point modelling technique which was modified to include a `predictor' step using a host mesh fitting algorithm, thereby obtaining a significant decrease in solution time. The tool was applied to cine MRI data of seventeen patients with various types of congenital heart disease. The results were compared against with those obtained from a current gold standard technique. The comparison showed generally good agreement between the two methods, in terms of both the reproducibility of global cardiac function measurements and the reproducibility between analysts. In conclusion, the tools developed in this thesis enabled novel examinations of cardiac structure and function in animal models and humans with cardiac disease.
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Medical computer vision is a novel research discipline based on the application of computer vision methods to data sets acquired via medical imaging techniques. This work focuses on magnetic resonance imaging (MRI) data sets, particularly in studies of schizophrenia and multiple sclerosis. Research on these diseases is challenged by the lack of appropriate morphometric tools to accurately quantify lesion growth, assess the effectiveness of a drug treatment, or investigate anatomical information believed to be evidence of schizophrenia. Thus, most hypotheses involving these conditions remain unproven. This thesis contributes towards the development of such morphometric techniques. A framework combining several tools is established, allowing for compensation of bias fields, boundary detection by modelling partial volume effects (PVE), and a combined statistical and geometrical segmentation method. Most importantly, it also allows for the computation of confidence bounds in the location of the object being segmented by bounding PVE voxels. Bounds obtained in such fashion encompass a significant percentage of the volume of the object (typically 20-60%). A statistical model of the intensities contained in PVE voxels is used to provide insight into the contents of PVE voxels and further narrow confidence bounds. This not only permits a reduction by an order of magnitude in the width of the confidence intervals, but also establishes a statistical mechanism to obtain probability distributions on shape descriptors (e.g. volume), instead of just a raw magnitude or a set of confidence bounds. A challenging clinical study is performed using these tools: to investigate differences in asymmetry of the temporal horns in schizophrenia. This study is of high clinical relevance. The results show that our tools are sufficiently accurate for studies of this kind, thus providing clinicians, for the first time, with the means to corroborate unproven hypotheses or reliably assess patient evolution.

The steady-state free precession (SSFP) is one type of the fast scanning technique in MRI. So far most of its analysis are concentrated on the gradient echo SSFP (GR SSFP), very few paper~discuss the spin echo (SSFP (SE SSFP), and they are usually based on the simplified the hard pulse assumption. The advantage of the SE SSFP is that it can refocus the dephasing caused by the magnetic field inhomogeniety, which is the disadvantage of the GR SSFP. Also the hard pulse model can provide very limited information. The purpose of this paper is to establish the soft pulse model for both GR SSFP and SE SSFP. By using the spinor method to describe the interaction between the RF pulse, magnetic field, and the spin's magnetization, we create the steady state equations of the GR SSFP and SE SSFP, and give their analytical solutions. Because the SE SSFP's mathematical model is very complicated, we introduce a new concept, the linked-pulse, to simplify the problem, and provide the valuable results. Based on both traditional hard pulse model and our soft pulse model, we did a series of simulations, and compared both results. First of all, the soft pulse model can provide the slice profile and gradient effects, which is impossible for the hard pulse model. Second, in both models, the signal intensities are all depended on the Tl/T2 ratio, which is the characterization of the SSFP image. Third, we also observed how the pulse shape and the flip angles affect the slice profile and the signal intensity. In conclusion, the soft pulse model can give more information than hard pulse model can, such as slice profile and gradient effects, etc., provide more aspects for analyzing the SSFP image.

Bayesian learning methods are the basis of many powerful analysis techniques in neuroimaging, permitting probabilistic inference on hierarchical, generative models of data. This thesis primarily develops Bayesian analysis techniques for magnetic resonance imaging (MRI), which is a noninvasive neuroimaging tool for probing function, perfusion, and structure in the human brain. The first part of this work fits nonlinear biophysical models to multimodal functional MRI data within a variational Bayes framework. Simultaneously-acquired multimodal data contains mixtures of different signals and therefore may have common noise sources, and a method for automatically modelling this correlation is developed. A Gaussian process prior is also used to allow spatial regularization while simultaneously applying informative priors on model parameters, restricting biophysically-interpretable parameters to reasonable values. The second part introduces a novel data fusion framework for multivariate data analysis which finds a joint decomposition of data across several modalities using a shared loading matrix. Each modality has its own generative model, including separate spatial maps, noise models and sparsity priors. This flexible approach can perform supervised learning by using target variables as a modality. By inferring the data decomposition and multivariate decoding simultaneously, the decoding targets indirectly influence the component shapes and help to preserve useful components. The same framework is used for unsupervised learning by placing independent component analysis (ICA) priors on the spatial maps. Linked ICA is a novel approach developed to jointly decompose multimodal data, and is applied to combined structural and diffusion images across groups of subjects. This allows some of the benefits of tensor ICA and spatially-concatenated ICA to be combined, and allows model comparison between different configurations. This joint decomposition framework is particularly flexible because of its separate generative models for each modality and could potentially improve modelling of functional MRI, magnetoencephalography, and other functional neuroimaging modalities.

Dissolution dynamic nuclear polarisation is an emerging clinical technique which enables the metabolism of hyperpolarised 13C-labelled molecules to be dynamically and non- invasively imaged in tissue. The first molecule to gain clinical approval is [1-13C]pyruvate, the conversion of which to [1-13C]lactate has been shown to detect early treatment re- sponse in cancers and correlate with tumour grade. As the technique has recently been translated into humans, accurate and reliable quantitative methods are required in order to detect, analyse and compare regions of altered metabolism in patients. Furthermore, there is a requirement to understand the biological processes which govern lactate pro- duction in tumours in order to draw reliable conclusions from this data. This work begins with a comprehensive analysis of the quantitative methods which have previously been applied to hyperpolarised 13C data and compares these to some novel approaches. The most appropriate kinetic model to apply to hyperpolarised data is determined and some simple, robust quantitative metrics are identified which are suitable for clinical use. A means of automatically segmenting 5D hyperpolarised imaging data using a fuzzy Markov random field approach is presented in order to reliably identify regions of abnormal metabolic activity. The utility of the algorithm is demonstrated on both in silico and animal data. To gain insight into the processes driving lactate metabolism, a mathematical model is developed which is capable of simulating tumour growth and treatment response under a range of metabolic and tissue conditions, focusing on the interaction between tumour and stroma. Finally, hyperpolarised 13C-pyruvate imaging data from the first human subjects to be imaged in Cambridge is analysed. The ability to detect and quantify lactate production in patients is demonstrated through application of the methods derived in earlier chapters. The mathematical approaches presented in this work have the potential to inform both the analysis and interpretation of clinical hyperpolarised 13C imaging data and to aid in the clinical translation of this technique.

Despite the association between hippocampal atrophy and a vast array of highly debilitating neurological diseases, such as Alzheimer’s disease and frontotemporal lobar degeneration, tools to accurately and robustly quantify the degeneration of this structure still largely elude us. In this thesis, we firstly evaluate previously-developed hippocampal segmentation methods (FMRIB’s Integrated Registration and Segmentation Tool (FIRST), Freesurfer (FS), and three versions of a Classifier Fusion (CF) technique) on two clinical MR datasets, to gain a better understanding of the modes of success and failure of these techniques, and to use this acquired knowledge for subsequent method improvement (e.g., FIRSTv3). Secondly, a fully automated, novel hippocampal segmentation method is developed, termed Fast Marching for Automated Segmentation of the Hippocampus (FMASH). This combined region-growing and atlas-based approach uses a 3D Sethian Fast Marching (FM) technique to propagate a hippocampal region from an automatically-defined seed point in the MR image. Region growth is dictated by both subject-specific intensity features and a probabilistic shape prior (or atlas). Following method development, FMASH is thoroughly validated on an independent clinical dataset from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), with an investigation of the dependency of such atlas-based approaches on their prior information. In response to our findings, we subsequently present a novel label-warping approach to effectively account for the detrimental effects of using cross-dataset priors in atlas-based segmentation. Finally, a clinical application of MR hippocampal segmentation is presented, with a combined MR-PET analysis of wholefield and subfield hippocampal changes in Alzheimer’s disease and frontotemporal lobar degeneration. This thesis therefore contributes both novel computational tools and valuable knowledge for further neurological investigations in both the academic and the clinical field.

Cerebral ischemia is a vascular disorder that is characterized by the reduction of blood supply to the brain, resulting in impaired metabolism and finally death of brain cells. Cerebral ischemia is a major clinical problem associated with global morbidity and mortality rates of about 30%. Clinical management of cerebral ischemia relies heavily on perfusion analysis using dynamic susceptibility contrast MRI (DSC-MRI). DSC-MRI analysis is performed using mathematical models that simulate the underlying vascular physiology of brain. Cerebral perfusion is calculated using perfusion imaging and is used as a marker of tissue health status; low perfusion being an indicator of impaired tissue metabolism. In addition to measurement of cerebral perfusion, it is possible to quantify the blood flow variation within the capillary network referred to as cerebral microvascular hemodynamics. It has been hypothesized that microvascular hemodynamics are closely associated with tissue oxygenation and that hemodynamics might undergo a considerable amount of variation to maintain normal tissue metabolism under conditions of ischemic stress. However with DSC-MRI perfusion imaging, quantification of cerebral hemodynamics still remains a big challenge. Singular Value Decomposition (SVD) is currently a standard methodology for estimation of cerebral perfusion with DSC-MRI in both research and clinical settings. It is a robust technique for quantification of cerebral perfusion, however, the quantification of hemodynamic information cannot be achieved with SVD methods because of the non-physiological behaviour of SVD in microvascular hemodynamic estimation. SVD is sensitive to the noise in the MR signal which appears in the calculated microvascular hemodynamics, thus making it difficult to interpret for pathophysiological significance. Other methods, including model-based approaches or methods based on likelihood estimation, stochastic modeling and Gaussian processes, have been proposed. However, none of these have become established as a means to study tissue hemodynamics in perfusion imaging. Possibly because of the associated constrains in these methodologies that limited their sensitivity to hemodynamic variation in vivo. The objective of the research presented in this thesis is to develop and to evaluate a method to perform a quantitative estimation of cerebral hemodynamics using DSC-MRI. A new Control Point Interpolation (CPI) method has been developed to perform a non-parametric analysis for DSC-MRI. The CPI method was found to be more accurate in estimation of cerebral perfusion than the alternative methods. Capillary hemodynamics were calculated by estimating the transit time distribution of the tissue capillary network using the CPI method. The variations in transit time distribution showed quantitative differences between normal tissue and tissue under ischemic stress. The method has been corrected for the effects of macrovascular bolus dispersion and tested over a larger clinical cohort of patients with atherosclerosis. CPI method is thus a promising method for quantifying cerebral hemodynamics using perfusion imaging. CPI method is an attempt to evaluate the use of quantitative hemodynamic information in diagnostic and prognostic monitoring of patients with ischemia and vascular diseases.

Chronic obstructive pulmonary disease (COPD) describes a range of lung conditions including emphysema, chronic bronchitis and small airways disease. While COPD is a major cause of death and debilitating illness, current clinical assessment methods are inadequate: they are a poor predictor of patient outcome and insensitive to mild disease. A new imaging technology, hyperpolarised xenon MRI, offers the hope of improved diagnostic techniques, based on regional measurements using functional imaging. There is a need for quantitative analysis techniques to assist in the interpretation of these images. The aim of this work is to develop these techniques as part of a clinical trial into hyperpolarised xenon MRI. In this thesis we develop a fully automated pipeline for deriving regional measurements of lung function, making use of the multiple imaging modalities available from the trial. The core of our pipeline is a novel method for automatically segmenting the pulmonary lobes from CT data. This method combines a Hessian-based filter for detecting pulmonary fissures with anatomical cues from segmented lungs, airways and pulmonary vessels. The pipeline also includes methods for segmenting the lungs from CT and MRI data, and the airways from CT data. We apply this lobar map to the xenon MRI data using a multi-modal image registration technique based on automatically segmented lung boundaries, using proton MRI as an intermediate stage. We demonstrate our pipeline by deriving lobar measurements of ventilated volumes and diffusion from hyperpolarised xenon MRI data. In future work, we will use the trial data to further validate the pipeline and investigate the potential of xenon MRI in the clinical assessment of COPD. We also demonstrate how our work can be extended to build personalised computational models of the lung, which can be used to gain insights into the mechanisms of lung disease.

In ambito di ricerca (clinica e sportiva), la necessità di sviluppare un approccio ‘multilaterale’ (qualitativo e quantitativo) che caratterizzi matematicamente la traiettoria tri-dimensionale di una variabile fisica assolutamente importante ma spesso dimenticata, quale il centro di massa corporeo (CMC) (ovvero, il punto immaginario assimilabile al corpo umano in cui si suppone che tutte le masse corporee stiano concentrate), diviene oggi sempre più impellente e quanto mai urgente. Pertanto l’obiettivo di questo dottorato, perseguito tramite un differente utilizzo delle classiche metodologie biomeccaniche, è rappresentare le grandezze cinematiche che descrivono il movimento dei segmenti corporei e del suddetto CMC nel tempo e nello spazio. Per conseguire questo traguardo si sono pensati e realizzati due diversi progetti. Con il primo progetto si sono previsti: a) lo sviluppo di un metodo matematico quantitativo (Serie di Fourier) per descrivere e rappresentare graficamente la traiettoria tri-dimensionale del CMC durante la locomozione su treadmill (la cosiddetta Impronta Digitale Locomotoria, specifica per soggetto/popolazione); b) la caratterizzazione della simmetria nella traiettoria del CMC (il cosiddetto Indice di Simmetria); infine, c) la costituzione di un database di valori normali (coefficienti di equazioni) in un insieme piuttosto esteso di condizioni, al variare di sesso (maschi versus femmine), età (dai 6 ai 65 anni), tipologia di locomozione (marcia versus corsa), velocità e pendenza (piano, salita e discesa). Questo database iniziale rappresenta il parametro principale di riferimento per la locomozione sana. Attraverso questo studio è stato ampiamente dimostrato che la locomozione umana risulta genericamente asimmetrica. Nello specifico: 1) tra maschi e femmine non si sono riscontrate differenze significative; 2) indipendentemente da età e pendenza, le velocità più basse, meno naturali e comuni, sono caratterizzate da pattern di Impronte Digitali Locomotorie più variabili. Viceversa, un aumento di velocità è accoppiato con un progressivo e continuo innalzamento del CMC; 3) l’asimmetria destra e sinistra del passo è molto probabilmente correlata sia con l’anatomia (lunghezza della gamba) che con la predominanza dell’arto; in linea con l’ipotesi iniziale, 4) mediamente, la corsa è più asimmetrica della marcia; infine, 5) i bambini e gli anziani presentano maggiori asimmetrie (marcia e corsa): questo è dovuto alla progressiva maturazione del ciclo del cammino (nei bambini) ed alle caratteristiche muscolari e scheletriche dell’apparato locomotore (negli anziani). Pertanto, attraverso una caratterizzazione matematica della traiettoria tri-dimensionale del CMC, si è potuto: a) quantificare il suo spostamento nel tempo e nello spazio; b) individuare l’Impronta Digitale Locomotoria specifica di sesso, età, tipologia di locomozione, velocità e pendenza. Questo importante traguardo permetterà, in un immediato futuro, la comparazione con la situazione di normalità di condizioni di locomozione compromessa o impedita (ad esempio, bambini con paralisi cerebrale infantile, obesi e amputati). Infine, la stima della principali variabili biomeccaniche è risultata fondamentale sia nel descrivere la meccanica di marcia e corsa che nel caratterizzarne la corrispondente impronta locomotoria. Le nostre misure di tali variabili (semplici e complesse), ottenute con metodo discreto (ciclo per ciclo), con l’impiego di una funzione matematica continua (Serie di Fourier) e con l’applicazione di un’equazione predittiva (misura indiretta), soddisfano completamente ed addirittura ampliano la letteratura già esistente. Nel secondo progetto, partendo da uno studio sulla performance dei cavalli, si è cercato di verificare se esiste una correlazione tra simmetrie corporee (statiche e dinamiche) ed economia nella corsa anche in corridori umani variamente allenati (classificati in tre gruppi sulla base del loro miglior tempo nella maratona). Inoltre: a) si sono sviluppati metodi di analisi bi- e tri-dimensionale delle Risonanze Magnetiche per Immagini (regione pelvica ed arti inferiori), impiegate come riferimento per le simmetrie statiche; b) attraverso sia l’Impronta Digitale Locomotoria che l’Indice di Simmetria si sono caratterizzate le simmetrie dinamiche; infine c) l’economia della corsa è stata espressa attraverso il suo reciproco, ovvero il costo metabolico. L’analisi sia bi- che tri-dimensionale delle immagini ha evidenziato differenze davvero esigue in base al livello di allenamento. Positivamente ed indipendentemente dai corridori, si è dimostrato che ad una maggiore simmetria nella regione del ginocchio corrisponde una maggiore simmetria nella regione della caviglia. Inoltre l’analisi delle simmetrie dinamiche ha permesso di osservare che: 1) il CMC si solleva leggermente in funzione della velocità; 2) le asimmetrie destre e sinistre del passo sono principalmente marcate lungo la direzione di movimento e, contemporaneamente, ridotte lungo la direzione verticale. Esse sono strettamente dipendenti dall’anatomia e dall’arto dominante; 3) diversamente da quanto ci si aspettava, sono state comunque evidenziate solamente poche differenze tra i corridori. Negativamente, l’economia della corsa non mostra differenze significative tra i gruppi testati. Perciò, diversamente dall’ipotesi iniziale, non è stata evidenziata l’esistenza di alcuna relazione tra le simmetrie corporee e l’economia della corsa, quanto piuttosto solo la presenza di una discreta variabilità in simmetria statica e dinamica. Infine, l’analisi di bioenergetica (treadmill versus pista) e biomeccanica (variabili semplici/complesse e variabilità spazio/temporale del CMC) della corsa ha evidenziato la presenza solamente di poche differenze dovute al livello di allenamento dei soggetti studiati.
In both research laboratory and sport/clinical settings, it becomes very important to develop a ‘multilateral approach’ (qualitative and quantitative) to fully describe the individual behaviour of the centre of mass of the human body (BCOM) (i.e. the imaginary specific point at which the body behaves as if its masses were concentrated) over time and space. Consequently, the aim of this doctorate is to describe kinematic variables of the BCOM in varying locomotion conditions. This purpose, focusing on the BCOM as the investigation object fulfilling such a need, has been achieved through a different use of classic biomechanical procedures. In effect, two different studies were carried out. The first project sought: a) to develop a mathematical method (Fourier Series) which could describe and graphically represent each individual (subject or population) gait signature (i.e. Digital Locomotory Signature, a global index of the BCOM dynamics) during locomotion on a treadmill; b) to assess the symmetry (i.e. Symmetry Index) in each movement direction, along the BCOM trajectory, between the two stride phases; finally, c) to build up an initial comprehensive database of ‘healthy values’ (equation coefficients) in a set of different conditions considering gender (males versus females), age (from 6 to 65 years), gait (walking versus running), speed and gradient (level, uphill and downhill). Although only slight gender differences were found, human ‘healthy’ gait is rather asymmetrical. To be precise: 1) the lowest speeds have the most peculiar signature independently of age and gradient: indeed, these speeds are not so completely natural and common. However, if speed increases, the BCOM raises in such a way that its corresponding 3D contour becomes more regular; 2) right and left sides of the stride are quite asymmetrical (i.e. in the forward direction). Globally, this asymmetry is probably related both to anatomy (i.e. leg length) and which hand you use (i.e. right-handedness); 3) on average, the symmetry pattern is slightly lower in running gaits; and as expected, 4) young children and elderly adults are the most asymmetrical subjects, independently of testing conditions: while, during the early stages of life, this global asymmetry could be ascribed to the process of gait development, old age asymmetries are probably due to structural wearing down of the musculoskeletal system. Importantly, the mathematical methodology used here, by analysing even subtle changes in the 3D BCOM trajectory: a) characterizes its displacements over both time and space; b) quantitatively describes the individual gait signature; and c) represents the basis for the evaluation of gait anomaly/pathology (e.g. children with cerebral palsy, obese people and amputees). Finally, knowing the main biomechanical variables becomes fundamental both to fully describe the mechanics of walking and running and to extract and characterize the individual gait signature. In effect, our measurements (discrete method versus continuous mathematical function, and direct versus indirect measurement) of both simple and complex variables wholly confirm, complete and amplify previous literature data. Similarly to what previously demonstrated in horse performances, the second project tried: a) to verify both static anatomical and kinematic functional symmetries as important and relevant indicators of running economy (i.e. the reciprocal of metabolic cost) in humans featuring different running levels (i.e. occasional, skilled and top runners categorized primarily upon their best marathon time); b) to develop imaging based bi- and three-dimensional methods to analyse static symmetries recorded by Magnetic Resonance Imaging (lower limbs and pelvic area); c) to describe the kinematic symmetries defining both the Digital Locomotory Signature and the Symmetry Index; finally, d) to investigate running economy as a performance determinant. In effect, both the 2D/3D analysis of static symmetries highlight very few differences among runners; however, a strong relationship between ankle and knee areas has been underlined in all runners. Furthermore, independently of training ability: as expected, 1) the BCOM raises and lifts slightly as a function of running speed; 2) right and left steps are mostly asymmetrical in the forward direction and symmetrical in the vertical direction (i.e. combined action of gravity and ground reaction force); 3) differently to what was expected, slight differences have been found among runners. On the whole, the asymmetry is probably related both to anatomy and handedness. Other than that, no running economy differences were found. In conclusion, while a relationship between symmetries and running economy has not been found, significant results have however been underlined in each trial (static and dynamic symmetries). Finally, the deep investigation of both bioenergetics (treadmill versus over-ground) and biomechanics (simple/complex variables and spatial/temporal variability of the BCOM) of running has highlights only little (significant) differences among groups.

This thesis addresses the problem of producing three-dimensional constrained Delaunay triangulated meshes from the sequential two dimensional MRI medical image slices. The approach is to generate the volumetric meshes of the scanned organs as a result of a several low-level tasks: image segmentation, connected component extraction, isosurfacing, image smoothing, mesh decimation and constrained Delaunay tetrahedralization. The proposed methodology produces a portable application that can be easily adapted and extended by researchers to tackle this problem. The application requires very minimal user intervention and can be used either independently or as a pre-processor to an adaptive mesh refinement system.
Finite element analysis of the MRI medical data depends heavily on the quality of the mesh representation of the scanned organs. This thesis presents experimental test results that illustrate how the different operations done during the process can affect the quality of the final mesh.

This paper considers some numerical schemes for the approximate solution of conservation laws and various wavelet methods are reviewed. This is followed by the construction of wavelet spaces based on a polynomial framework for the approximate solution of conservation laws. Construction of a representation of the approximate solution in terms of an entropy satisfying Multiresolution Analysis (MRA) is defined. Finally, a proof of convergence of the approximate solution of conservation laws using the characterization provided by the basis functions in the MRA will be given.

In ischaemic stroke a disruption of cerebral blood flow leads to impaired metabolism and the formation of an ischaemic penumbra in which tissue at risk of infarction is sought for clinical intervention. In stroke trials, therapeutic intervention has largely been based on perfusion-weighted measures, but these have not been shown to be good predictors of tissue outcome. The aim of this thesis was to develop analysis techniques for magnetic resonance imaging (MRI) of chemical exchange saturation transfer (CEST) in order to quantify metabolic signals associated with tissue fate in patients with acute ischaemic stroke. This included addressing robustness for clinical application, and developing quantitative tools that allow exploration of the in-vivo complexity. Tissue-level analyses were performed on a dataset of 12 patients who had been admitted to the John Radcliffe Hospital in Oxford with acute ischaemic stroke and recruited into a clinical imaging study. Further characterisation of signals was performed on stroke models and tissue phantoms. A comparative study of CEST analysis techniques established a model-based approach, Bloch-McConnell model analysis, as the most robust for measuring pH-weighted signals in a clinical setting. Repeatability was improved by isolating non-CEST effects which attenuate signals of interest. The Bloch-McConnell model was developed further to explore whether more biologically-precise quantification of CEST effects was both possible and necessary. The additional model complexity, whilst more reflective of tissue biology, diminished contrast that distinguishes tissue fate, implying the biology is more complex than pH alone. The same model complexity could be used reveal signal patterns associated with tissue outcome that were otherwise obscured by competing CEST processes when observed through simpler models. Improved quantification techniques were demonstrated which were sufficiently robust to be used on clinical data, but also provided insight into the different biological processes at work in ischaemic tissue in the early stages of the disease. The complex array of competing processes in pathological tissue has underscored a need for analysis tools adequate for investigating these effects in the context of human imaging. The trends herein identified at the tissue level support the use of quantitative CEST MRI analysis as a clinical metabolic imaging tool in the investigation of ischaemic stroke.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Tannenbaum, Allen; Committee Member: Barnes, Christopher F.; Committee Member: Niethammer, Marc; Committee Member: Shamma, Jeff; Committee Member: Vela, Patricio.

HIV/Aids Relative Survival and Mean Residual Life Analysis BY XINJIAN ZHANG Under the Direction of Gengsheng (Jeff) Qin and Ruiguang (Rick) Song ABSTRACT Generalized linear models with Poisson error were applied to investigate HIV/AIDS relative survival. Relative excess risk for death within 3 years after HIV/AIDS diagnosis was significantly higher for non-Hispanic blacks, American Indians and Hispanics compared with Whites. Excess hazard for death was also higher in men injection drug users compared with men who have sex with men (MSM). The relative excess hazard of old HIV/AIDS patients is significantly higher compared with younger patients. When CD4 increased, the relative excess hazard decreased; while with the increase of HIV viral load, the relative excess hazard decreased. This is the first study to use national wide data to examine the significance of HIV viral load as a determinant risk factor of disease progression after HIV infection; The mean residual lie needs to be further analyzed. INDEX WORDS: Human Immunodeficiency Virus (HIV), Acquired Immunodeficiency Syndrome (AIDS), Survival, Mean residual life (MRL).

This thesis deals with the analysis of brain function in Magnetic Resonance Imaging (MRI) using two sequences: BOLD functional MRI (fMRI) and Arterial Spin Labelling (ASL). In this context, group statistical analyses are of great importance in order to understand the general mechanisms underlying a pathology, but there is also an increasing interest towards patient-specific analyses that draw conclusions at the patient level. Both group and patient-specific analyses are studied in this thesis. We first introduce a group analysis in BOLD fMRI for the study of specific language impairment, a pathology that was very little investigated in neuroimaging. We outline atypical patterns of functional activity and lateralisation in language regions. Then, we move forward to patient-specific analysis. We propose the use of robust estimators to compute cerebral blood flow maps in ASL. Then, we analyse the validity of the assumptions underlying standard statistical analyses in the context of ASL. Finally, we propose a new locally multivariate statistical method based on an a contrario approach and apply it to the detection of atypical patterns of perfusion in ASL and to activation detection in BOLD functional MRI.

Thesis (PhD)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: Multi-resolution analysis (MRA) has become a very popular eld of mathematical study in the past two decades, being not only an area rich in applications but one that remains lled with open problems. Building on the foundation of re nability of functions, MRA seeks to lter through levels of ever-increasing detail components in data sets { a concept enticing to an age where development of digital equipment (to name but one example) needs to capture more and more information and then store this information in di erent levels of detail. Except for designing digital objects such as animation movies, one of the most recent popular research areas in which MRA is applied, is inpainting, where \lost" data (in example, a photograph) is repaired by using boundary values of the data set and \smudging" these values into the empty entries. Two main branches of application in MRA are subdivision and wavelet analysis. The former uses re nable functions to develop algorithms with which digital curves are created from a nite set of initial points as input, the resulting curves (or drawings) of which possess certain levels of smoothness (or, mathematically speaking, continuous derivatives). Wavelets on the other hand, yield lters with which certain levels of detail components (or noise) can be edited out of a data set. One of the greatest advantages when using wavelets, is that the detail data is never lost, and the user can re-insert it to the original data set by merely applying the wavelet algorithm in reverse. This opens up a wonderful application for wavelets, namely that an existent data set can be edited by inserting detail components into it that were never there, by also using such a wavelet algorithm. In the recent book by Chui and De Villiers (see [2]), algorithms for both subdivision and wavelet applications were developed without using Fourier analysis as foundation, as have been done by researchers in earlier years and which have left such algorithms unaccessible to end users such as computer programmers. The fundamental result of Chapter 9 on wavelets of [2] was that feasibility of wavelet decomposition is equivalent to the solvability of a certain set of identities consisting of Laurent polynomials, referred to as Bezout identities, and it was shown how such a system of identities can be solved in a systematic way. The work in [2] was done in the univariate case only, and it will be the purpose of this thesis to develop similar results in the bivariate case, where such a generalization is entirely non-trivial. After introducing MRA in Chapter 1, as well as discussing the re nability of functions and introducing box splines as prototype examples of functions that are re nable in the bivariate setting, our fundamental result will also be that wavelet decomposition is equivalent to solving a set of Bezout identities; this will be shown rigorously in Chapter 2. In Chapter 3, we give a set of Laurent polynomials of shortest possible length satisfying the system of Bezout identities in Chapter 2, for the particular case of the Courant hat function, which will have been introduced as a linear box spline in Chapter 1. In Chapter 4, we investigate an application of our result in Chapter 3 to bivariate interpolatory subdivision. With the view to establish a general class of wavelets corresponding to the Courant hat function, we proceed in the subsequent Chapters 5 { 8 to develop a general theory for solving the Bezout identities of Chapter 2 separately, before suggesting strategies for reconciling these solution classes in order to be a simultaneous solution of the system.
AFRIKAAANSE OPSOMMING: Multi-resolusie analise (MRA) het in die afgelope twee dekades toenemende gewildheid geniet as 'n veld in wiskundige wetenskappe. Nie net is dit 'n area wat ryklik toepaslik is nie, maar dit bevat ook steeds vele oop vraagstukke. MRA bou op die grondleggings van verfynbare funksies en poog om deur vlakke van data-komponente te sorteer, of te lter, 'n konsep wat aanloklik is in 'n era waar die ontwikkeling van digitale toestelle (om maar 'n enkele voorbeeld te noem) sodanig moet wees dat meer en meer inligting vasgel^e en gestoor moet word. Behalwe vir die ontwerp van digitale voorwerpe, soos animasie- lms, word MRA ook toegepas in 'n mees vername navorsingsgebied genaamd inverwing, waar \verlore" data (soos byvoorbeeld in 'n foto) herwin word deur data te neem uit aangrensende gebiede en dit dan oor die le e data-dele te \smeer." Twee hooftakke in toepassing van MRA is subdivisie en gol e-analise. Die eerste gebruik verfynbare funksies om algoritmes te ontwikkel waarmee digitale krommes ontwerp kan word vanuit 'n eindige aantal aanvanklike gegewe punte. Die verkrygde krommes (of sketse) kan voldoen aan verlangde vlakke van gladheid (of verlangde grade van kontinue afgeleides, wiskundig gesproke). Gol es word op hul beurt gebruik om lters te bou waarmee gewensde dataof geraas-komponente verwyder kan word uit datastelle. Een van die grootste voordeel van die gebruik van gol es bo ander soortgelyke instrumente om data lters mee te bou, is dat die geraas-komponente wat uitgetrek word nooit verlore gaan nie, sodat die proses omkeerbaar is deurdat die gebruiker die sodanige geraas-komponente in die groter datastel kan terugbou deur die gol e-algoritme in trurat toe te pas. Hierdie eienskap van gol fies open 'n wonderlike toepassingsmoontlikheid daarvoor, naamlik dat 'n bestaande datastel verander kan word deur data-komponente daartoe te voeg wat nooit daarin was nie, deur so 'n gol e-algoritme te gebruik. In die onlangse boek deur Chui and De Villiers (sien [2]) is algoritmes ontwikkel vir die toepassing van subdivisie sowel as gol es, sonder om staat te maak op die grondlegging van Fourier-analise, soos wat die gebruik was in vroe ere navorsing en waardeur algoritmes wat ontwikkel is minder e ektief was vir eindgebruikers. Die fundamentele resultaat oor gol es in Hoofstuk 9 in [2], verduidelik hoe suksesvolle gol e-ontbinding ekwivalent is aan die oplosbaarheid van 'n sekere versameling van identiteite bestaande uit Laurent-polinome, bekend as Bezout-identiteite, en dit is bewys hoedat sodanige stelsels van identiteite opgelos kan word in 'n sistematiese proses. Die werk in [2] is gedoen in die eenveranderlike geval, en dit is die doelwit van hierdie tesis om soortgelyke resultate te ontwikkel in die tweeveranderlike geval, waar sodanige veralgemening absoluut nie-triviaal is. Nadat 'n inleiding tot MRA in Hoofstuk 1 aangebied word, terwyl die verfynbaarheid van funksies, met boks-latfunksies as prototipes van verfynbare funksies in die tweeveranderlike geval, bespreek word, word ons fundamentele resultaat gegee en bewys in Hoofstuk 2, naamlik dat gol e-ontbinding in die tweeveranderlike geval ook ekwivalent is aan die oplos van 'n sekere stelsel van Bezout-identiteite. In Hoofstuk 3 word 'n versameling van Laurent-polinome van korste moontlike lengte gegee as illustrasie van 'n oplossing van 'n sodanige stelsel van Bezout-identiteite in Hoofstuk 2, vir die besondere geval van die Courant hoedfunksie, wat in Hoofstuk 1 gede nieer word. In Hoofstuk 4 ondersoek ons 'n toepassing van die resultaat in Hoofstuk 3 tot tweeveranderlike interpolerende subdivisie. Met die oog op die ontwikkeling van 'n algemene klas van gol es verwant aan die Courant hoedfunksie, brei ons vervolglik in Hoofstukke 5 { 8 'n algemene teorie uit om die oplossing van die stelsel van Bezout-identiteite te ondersoek, elke identiteit apart, waarna ons moontlike strategie e voorstel vir die versoening van hierdie klasse van gelyktydige oplossings van die Bezout stelsel.

L'analyse des structures curvilignes en 3 dimensions est un problème difficile en analyse d'images. En effet, ces structures sont fines, facilement corrompues par le bruit et présentent une géométrie complexe. Depuis plusieurs années, de nombreuses méthodes spécialement dédiées au traitement d'images contenant des structures curvilignes ont vu le jour. Ces méthodes concernent diverses applications en science des matériaux, télédétection ou encore en imagerie médicale. Malgré cela, l'analyse des structures curvilignes demeure une tâche complexe.Dans cette présentation nous parlerons de la caractérisation des structures curvilignes pour l'analyse d'images. Nous présenterons en premier lieu une nouvelle méthode appelée RORPO, à partir de laquelle deux caractéristiques peuvent être calculées. La première est une caractéristique d'intensité, qui préserve l'intensité des structures curvilignes tout en réduisant celle des autres structures. La deuxième est une caractéristique de direction, qui fournit en chaque point d'une image, la direction d'une structure curviligne potentielle.RORPO, contrairement à la plupart des méthodes de la littérature, est une méthode non locale, non linéaire et mieux adaptées à l'anisotropie intrinsèque des structures curvilignes. Cette méthode repose sur une notion récente de Morphologie Mathématique: les opérateurs par chemins.RORPO peut directement servir au filtrage d'images contenant des structures curvilignes, afin de spécifiquement les préserver, mais aussi de réduire le bruit. Mais les deux caractéristiques de RORPO peuvent aussi être utilisées comme information a priori sur les structure curvilignes, afin d'être intégrées dans une méthode plus complexe d'analyse d'image.Dans un deuxième temps, nous présenterons ainsi un terme de régularisation destiné à la segmentation variationnelle, utilisant les deux caractéristiques de RORPO.L'information apportée par ces deux caractéristiques permet de régulariser les structures curvilignes seulement dans la direction de leur axe principal. De cette manière, ces structures sont mieux préservées, et certaines structures curvilignes déconnectées par le bruit peuvent aussi être reconnectées.Des résultats en 2D et 3D de ces méthodes seront enfin présentées sur des images de vaisseaux sanguins provenant de diverses modalités
The analysis of curvilinear structures in 3D images is a complex and challenging task. Curvilinear structures are thin, easily corrupted by noise and present a complex geometry. Despite the numerous applications in material sciences, remote sensing and medical imaging and the large number of dedicated methods developed the last few years, the detection of such structures remains a difficult problem.In this thesis, we work on the characterization of curvilinear structures. We first propose a new framework called RORPO, to characterize such structures through two features: an intensity feature which preserves the intensity of curvilinear structures while decreasing the intensity of other structures, and a directional feature providing at each point, the direction of the curvilinear structure.RORPO, unlike classic other state of the art methods, is non-local and non-linear, which are desirable properties adapted to the intrinsic anisotropy of curvilinear structures. RORPO is based on recent advances in mathematical morphology: the path operators.We provide a full description of the structural and algorithmic details of RORPO, and we also conduct a quantitative comparative study of our features with three popular curvilinear structure analysis filters: the Frangi Vesselness, the Optimally Oriented Flux, and the Hybrid Diffusion with Continuous Switch.Besides the straightforward filtering application, both RORPO features are designed to be used as prior information to characterize curvilinear structures. We propose a regularization term for variational segmentation which embed these features. Classic regularization terms are not adapted to curvilinear structures and usually lead to the loss of most of the low-contrasted ones. We propose to only regularize curvilinear structures along their main axis thanks to both RORPO features. This directional regularization better preserves curvilinear structures but also reconnect parts of these structures which may have been disconnected by noise.We present results of the segmentation of retinal images with the Chan et al. model either with the classic total variation or our directional regularization term. This confirm that our regularization term is better suited for images with curvilinear structures

The rise in digital technology has also rose the use of digital images. The digital imagesrequire much storage space. The compression techniques are used to compress the dataso that it takes up less storage space. In this regard wavelets play important role. Inthis thesis, we studied the Haar wavelet system, which is a complete orthonormal systemin L2(R): This system consists of the functions j the father wavelet, and y the motherwavelet. The Haar wavelet transformation is an example of multiresolution analysis. Ourpurpose is to use the Haar wavelet basis to compress an image data. The method ofaveraging and differencing is used to construct the Haar wavelet basis. We have shownthat averaging and differencing method is an application of Haar wavelet transform. Afterdiscussing the compression by using Haar wavelet transform we used another method tocompress that is based on singular value decomposition. We used mathematical softwareMATLAB to compress the image data by using Haar wavelet transformation, and singularvalue decomposition.

L'objectif global de ce travail est d'étudier une modélisation multi-échelle et de développer une méthode adaptée pour la simulation numérique du processus d'érosion à l'échelle du bassin versant. Après avoir passé en revue les différents modèles existants, nous dérivons une solution analytique non triviale pour le système couplé modélisant le transport de sédiments par charriage. Ensuite, nous étudions l'hyperbolicité de ce système avec diverses lois de sédimentation proposées dans la littérature. Concernant le schéma numérique, nous présentons le domaine de validité de la méthode de splitting, pour les équations modélisant l'écoulement et celle décrivant l'évolution du fond. Pour la modélisation du transport en suspension à l'échelle de la parcelle, nous présentons un système d'équations couplant les mécanismes d'infiltration, de ruissellement et le transport de plusieurs classes de sédiments. L'implémentation et des tests de validation d'un schéma d'ordre élevé et de volumes finis bien équilibré sont également présentés. Ensuite, nous discutons sur l'application et la calibration du modèle avec des données expérimentales sur dix parcelles 1m2 au Niger. Dans le but d'aboutir la simulation à l'échelle du bassin versant, nous développons une modélisation multi échelle dans laquelle nous intégrons le taux d'inondation dans les équations d'évolution afin de prendre en compte l'effet à petite échelle de la microtopographie. Au niveau numérique, nous étudions deux schémas bien équilibrés : le schéma de Roe basé sur un chemin conservatif, et le schéma avec reconstruction hydrostatique généralisée. Enfin, nous présentons une première application du modèle avec les données expérimentales du bassin versant de Ganspoel qui nécessite la parallélisation du code.

Cette thèse traite de la modélisation et de l'approximation numérique des écoulements liquide-gaz compressibles. La difficulté essentielle réside dans la modélisation et l'approximation de l'interface liquide-gaz. Schématiquement, deux types de méthodes permettent l'étude de la dynamique de l'interface : l'approche eulérienne, aussi dite de capture de front ("front capturing method") et l'approche lagrangienne, de suivi de front ("front tracking method"). Nos travaux sont plutôt basés sur la méthode de capture de front. Le modèle bifluide est constitué d'un système de lois de conservation du premier ordre traduisant le bilan de masse, de quantité de mouvement et d'énergie du système physique. Ce système doit être fermé par une loi de pression du mélange gaz-liquide pour que sa résolution soit possible. Cette loi de comportement doit être choisie soigneusement, puisqu'elle conditionne les bonnes propriétés du système comme l'hyperbolicité ou l'existence d'une entropie de Lax. Les méthodes d'approximation doivent permettre de traduire au niveau discret ces propriétés. Les schémas conservatifs classiques de type Godunov peuvent être appliqués au modèle bifluide. Ils conduisent cependant à des imprécisions qui les rendent inutilisables en pratique. Enfin, l'existence de solutions discontinues rend difficile la construction de schémas d'ordre élevé. La structure complexe des solutions nécessite alors des maillages très fins pour une précision acceptable. Il est donc indispensable de proposer des algorithmes performants pour les calculateurs parallèles les plus récents. Au cours de cette thèse, nous allons aborder partiellement chacune de ces problématiques : construction d'une "bonne" loi de pression, construction de schémas numériques adaptés, programmation sur calculateur massivement multicoeur.

Indiana University-Purdue University Indianapolis (IUPUI)
In this study, a novel model for manipulating cancer blood cells based on multi-stage micro channels under varied low field concepts is proposed. Steering Device approach was followed to manipulate the cancer cells based on their various differential potentials across their membranes. The proposed approach considers the size and the surface potential as well as the iso electronic structure of the cells. These research objectives emphasize the separation of the cells in the blood stream, and differentiates various blood cells and tumors for further analysis within the microfluidic channels. The dimensions of the channel sets the required electric field for manipulating the cancer cells within the channels using low electrode voltage function. The outcomes of this research may introduce a new diagnostic approach of finding the minimum residual disease (MRD) scans, early detection and analysis scans. This thesis provides a mathematical model, detailing the theory of the cell sorting device, manipulating the blood cancer cells and design of the device structure are also detailed, leading to the optimum research parameters and process. A Computer Aided Design (CAD) was used to model the multi-cell sorting lab-on-chip device, details of hardware and software were used in the simulation of the device various stages. Reverse engineering to configure the potentials for sorting mechanism needs is discussed. The thesis work also presents a comparative study of this sorting mechanism and the other commercially available devices. The practical model of the proposed research is laid out for future consideration.