Relevant bibliographies by topics / MRI mathematical analysis

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'MRI mathematical analysis'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "MRI mathematical analysis"

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Özcan, Alpay, Kenneth H. Wong, Linda Larson-Prior, Zang-Hee Cho, and Seong K. Mun. "Background and mathematical analysis of diffusion MRI methods." International Journal of Imaging Systems and Technology 22, no. 1 (February 14, 2012): 44–52. http://dx.doi.org/10.1002/ima.22001.

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BOUCHET, A., F. BENALCÁZAR PALACIOS, M. BRUN, and V. L. BALLARIN. "PERFORMANCE ANALYSIS OF FUZZY MATHEMATICAL MORPHOLOGY OPERATORS ON NOISY MRI." Latin American Applied Research - An international journal 44, no. 3 (July 31, 2014): 231–36. http://dx.doi.org/10.52292/j.laar.2014.446.

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Despite a large amount of publications on Fuzzy Mathematical Morphology, little effort was done on systematic evaluation of the performance of this technique. The goal of this work is to compare the robustness against noise of Fuzzy and non Fuzzy Morphological operators when applied to noisy images. Magnetic Resonance Images (MRI) of the brain are a kind of images containing some characteristics that make fuzzy operators an interesting choice, because of their intrinsic noise and imprecision. The robustness was evaluated as the degree in which the results of the operators are not affected by artificial noise in the images. In the analysis we compared different implementation of Fuzzy Mathematical Morphology, and observed that in most of the cases they show higher robustness against noise than the classical morphological operators.
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Yufang, Bao. "Mathematical Analysis of SMASH-Based Reconstruction Methods for Parallel MRI." International Journal of Intelligent Computing in Medical Sciences & Image Processing 4, no. 1 (January 2011): 65–76. http://dx.doi.org/10.1080/1931308x.2011.10644183.

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Noyel, Guillaume, Jesus Angulo, Dominique Jeulin, Daniel Balvay, and Charles-André Cuenod. "MULTIVARIATE MATHEMATICAL MORPHOLOGY FOR DCE-MRI IMAGE ANALYSIS IN ANGIOGENESIS STUDIES." Image Analysis & Stereology 34, no. 1 (May 30, 2014): 1. http://dx.doi.org/10.5566/ias.1109.

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We propose a new computer aided detection framework for tumours acquired on DCE-MRI (Dynamic Contrast Enhanced Magnetic Resonance Imaging) series on small animals. To perform this approach, we consider DCE-MRI series as multivariate images. A full multivariate segmentation method based on dimensionality reduction, noise filtering, supervised classification and stochastic watershed is explained and tested on several data sets. The two main key-points introduced in this paper are noise reduction preserving contours and spatio temporal segmentation by stochastic watershed. Noise reduction is performed in a special way to select factorial axes of Factor Correspondence Analysis in order to preserves contours. Then a spatio-temporal approach based on stochastic watershed is used to segment tumours. The results obtained are in accordance with the diagnosis of the medical doctors.
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KP, Dr Uma Anand, and Dr Justin Moses. "Mathematical analysis of femoral version controversies in MRI and axial oblique CT measurement." International Journal of Orthopaedics Sciences 6, no. 2 (April 1, 2020): 24–26. http://dx.doi.org/10.22271/ortho.2020.v6.i2a.2012.

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Borbély, Katalin, Miklós Emri, István Kenessey, Márton Tóth, Júlia Singer, Péter Barsi, Zsolt Vajda, et al. "PET/MRI in the Presurgical Evaluation of Patients with Epilepsy: A Concordance Analysis." Biomedicines 10, no. 5 (April 20, 2022): 949. http://dx.doi.org/10.3390/biomedicines10050949.

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The aim of our prospective study was to evaluate the clinical impact of hybrid [18F]-fluorodeoxyglucose positron emission tomography/magnetic resonance imaging ([18F]-FDG PET/MRI) on the decision workflow of epileptic patients with discordant electroclinical and MRI data. A novel mathematical model was introduced for a clinical concordance calculation supporting the classification of our patients by subgroups of clinical decisions. Fifty-nine epileptic patients with discordant clinical and diagnostic results or MRI negativity were included in this study. The diagnostic value of the PET/MRI was compared to other modalities of presurgical evaluation (e.g., electroclinical data, PET, and MRI). The results of the population-level statistical analysis of the introduced data fusion technique and concordance analysis demonstrated that this model could be the basis for the development of a more accurate clinical decision support parameter in the future. Therefore, making the establishment of “invasive” (operable and implantable) and “not eligible for any further invasive procedures” groups could be much more exact. Our results confirmed the relevance of PET/MRI with the diagnostic algorithm of presurgical evaluation. The introduction of a concordance analysis could be of high importance in clinical and surgical decision-making in the management of epileptic patients. Our study corroborated previous findings regarding the advantages of hybrid PET/MRI technology over MRI and electroclinical data.
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Truszkiewicz, Adrian, David Aebisher, Zuzanna Bober, Łukasz Ożóg, and Dorota Bartusik-Aebisher. "Radio Frequency MRI coils." European Journal of Clinical and Experimental Medicine 18, no. 1 (2020): 24–27. http://dx.doi.org/10.15584/ejcem.2020.1.5.

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Introduction. Magnetic Resonance Imaging (MRI) coils technology is a powerful improvement for clinical diagnostics. This includes opportunities for mathematical and physical research into coil design. Aim. Here we present the method applied to MRI coil array designs. Material and methods. Analysis of literature and self-research. Results. The coils that emit the radiofrequency pulses are designed similarly. As much as possible, they deliver the same strength of radiofrequency to all voxels within their imaging volume. Surface coils on the other hand are usually not embedded in cylindrical surfaces relatively close to the surface of the body. Conclusion. The presented here results relates to the art of magnetic resonance imaging (MRI) and RF coils design. It finds particular application of RF coils in conjunction with bore type MRI scanners.
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Enyagina, Irina M., Andrey N. Polyakov, Alexey A. Poyda, and Vadim L. Ushakov. "System for Automatic Processing and Analysis of MRI/fMRI Data on the Kurchatov Institute Supercomputer." EPJ Web of Conferences 226 (2020): 03006. http://dx.doi.org/10.1051/epjconf/202022603006.

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This paper presents the Computer Model of the System for Automatic Processing and Analysis of MRI/fMRI tomography data, obtained at the Kurchatov Institute Resource Center “Cognimed”. The System is based on the “Digital Lab” IT-Platform, involving the Kurchatov Institute Supercomputer Cluster HPC4, which allows speeding up the processing of data for groups (2–350 subjects) by parallelization of computations on the supercomputer nodes (1 subject – 1 node). The proposed System allows scientists to remotely use the installed on the supercomputer specialized software to process and analyze MRI/fMRI data; organizes a unified data storage; permits the work with data by web a interface. The System also enables the use of program modules developed by KI researchers which implement mathematical methods to improve data analysis results. As an example of the realization of this Computer Model, the Module “MRI FS” is presented that provides automatic processing and analysis of MRI data using the open specialized software FreeSurfer v.6.0.
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Shevchenko, Olha S., Liliia D. Todoriko, Iryna A. Ovcharenko, Olga O. Pogorelova, and Ihor O. Semianiv. "A MATHEMATICAL MODEL FOR PREDICTING THE OUTCOME OF TREATMENT OF MULTIDRUD-RESISTANT TUBERCULOSIS." Wiadomości Lekarskie 74, no. 7 (2021): 1649–54. http://dx.doi.org/10.36740/wlek202107117.

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The aim: Predicting the effectiveness of treatment for MRI of the lungs by developing a mathematical model to predict treatment outcomes. Materials and methods: 84 patients with MRI of the lungs: group 1 (n = 56) – with signs of effective TB treatment at the end of the intensive phase; group 2 (n = 28) – patients with signs of ineffective treatment. We used the multivariate discriminant analysis method using the statistical environment STATISTICA 13. Results: During the discriminant analysis, the parameters of the clinical blood analysis (monocytes, stab leukocytes, erythrocytes) were selected, which were associated with high (r> 0.5) statistically significant correlations with the levels of MMP-9, TIMP-1, oxyproline and its fractions and aldosterone in the formation of the prognosis. The mathematical model allows, in the form of comparing the results of solving two linear equations and comparing their results, to predict the outcome of treatment: “1” effective treatment, “2” – ineffective treatment. Early prediction of treatment effectiveness is promising, as it allows the use of the developed mathematical model as an additional criterion for the selection of patients for whom surgical treatment is recommended, in order to increase the effectiveness of treatment. Conclusions: An additional criterion for predicting ineffective MRI treatment, along with the criteria provided for by WHO recommendations, is a mathematical model that takes into account probably strong correlation (r = 0.5, p <0.05) between the factors of connective tissue destruction, collagen destruction, aldosterone , and indicators of a clinical blood test (between levels of OBZ and monocytes (r = 0.82, p = 0.00001), OB and monocytes (r = 0.92, p = 0.000001) OB and stab leukocytes (r = – 0.87, p = 0.0003) OBZ and stab leukocytes (r = – 0.53, p = 0.017), aldosterone and ESR.
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Bonizzoni, Francesca, Davide Pradovera, and Michele Ruggeri. "Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots." Mathematics in Engineering 5, no. 4 (2023): 1–38. http://dx.doi.org/10.3934/mine.2023074.

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<abstract><p>We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least-squares or an interpolatory approach, yielding a function-valued version of the the standard rational interpolation method ($ \mathcal{V} $-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the real axis), the spatially adaptive $ \mathcal{V} $-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the $ \mathcal{V} $-SRI method seems to be the best-performing one.</p></abstract>
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Dissertations / Theses on the topic "MRI mathematical analysis"

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Lam, Hoi Ieng Helen. "Mathematical tools for ventricular analysis using cardiac MRI." Thesis, University of Auckland, 2012. http://hdl.handle.net/2292/12974.

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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.
Whole document restricted until Mar. 2014, but available by request, use the feedback form to request access.
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González, Ballester Miguel Ángel. "Morphometric analysis of brain structures in MRI." Thesis, University of Oxford, 1999. http://ora.ox.ac.uk/objects/uuid:9b70d5d7-5a38-454c-b545-696b726092b8.

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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.
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Li, Fang. "An Analysis of the Linked-pulse in Steady-state Free Precession in MRI." PDXScholar, 1994. https://pdxscholar.library.pdx.edu/open_access_etds/4769.

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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.
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Groves, Adrian R. "Bayesian learning methods for modelling functional MRI." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:fe46e696-a1a6-4a9d-9dfe-861b05b1ed33.

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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.
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Zepp, Jonathan Nicolas [Verfasser], and Norbert [Akademischer Betreuer] Graf. "An innovative mathematical analysis of routine MRI scans in patients with glioblastoma using DoctorEye / Jonathan Nicolas Zepp. Betreuer: Norbert Graf." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2015. http://d-nb.info/1068503025/34.

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Daniels, Charlotte Jane. "Mathematical approaches for the clinical translation of hyperpolarised 13C imaging in oncology." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/275339.

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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.
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Bishop, Courtney Alexandra. "Development and application of image analysis techniques to study structural and metabolic neurodegeneration in the human hippocampus using MRI and PET." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:2549bad2-432f-4d0e-8878-be9cce6ae0d2.

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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.
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Mehndiratta, Amit. "Quantitative measurements of cerebral hemodynamics using magnetic resonance imaging." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:b9dfb1a4-f297-47b9-a95f-b60750065008.

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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.
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Doel, Thomas MacArthur Winter. "Developing clinical measures of lung function in COPD patients using medical imaging and computational modelling." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:34bbf6fd-ea01-42a2-8e99-d1e4a3c765b7.

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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.
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NARDELLO, Francesca. "Human locomotion: centre of mass and symmetry." Doctoral thesis, Università degli Studi di Verona, 2010. http://hdl.handle.net/11562/341818.

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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.
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Books on the topic "MRI mathematical analysis"

1

S̆imunić, Dina. Thermal and stimutalting effects of time-varying magnetic fields during MRI. Aachen: Shaker, 1995.

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Colloque en l'honneur de Laurent Schwartz (1983 Ecole polytechnique). Colloque en l'honneur de Laurent Schwartz: Ecole polytechnique, 30 mai-3 juin 1983. Paris: Société mathématique de France, 1985.

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France) Colloque Inter-IREM (11th 1996 Reims. Analyse & démarche analytique: Les neveux de Descartes : actes du XIème Colloque inter-IREM d'épistémologie et d'histoire des mathématiques, Reims, 10 et 11 mai 1996. Reims: IREM de Reims, 1998.

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Géometrie Symplectique et Mécanique: Colloque international La Grande Motte, France, 23-28 Mai, 1988. Berlin: Springer-Verlag, 1990.

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pétrole, Institut français du, and Laboratoire central des ponts et chaussées., eds. Numerical methods in offshore piling: 3rd international conference, Nantes, May 21-22 1986 = Méthodes numériques de calcul des pieux pour les ouvrages en mer : 3e colloque international, Nantes, 21-22 Mai 1986. Paris: Technip, 1986.

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C, Albert, and Colloque International du Séminaire Sud-Rhodanien de Géométrie, (5th : 1988 : La Grand Motte), eds. Géométrie symplectique et mécanique: Colloque international, La Grand Motte, 23-28 mai, 1988. Berlin: Springer, 1990.

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1944-, Albert C., ed. Géometrie symplectique et mécanique: Colloque international, la Grande Motte, France, 23-28 Mai, 1988. Berlin: Springer-Verlag, 1989.

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author, Lupu Mihaela, and Briguet André author, eds. NMR probeheads for biophysical and biomedical experiments: Theoretical principles & practical guidelines. London: Imperial College Press, 2015.

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Mihaela, Lupu, and Briguet André, eds. NMR probeheads for biophysical and biomedical experiments: Theoretical principles & practical guidelines. London: Imperial College Press, 2006.

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MEI Structured Mathematics: Numerical Analysis (MEI Structured Mathematics). Hodder & Stoughton Educational Division, 2000.

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Book chapters on the topic "MRI mathematical analysis"

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Liu, Jia, Fang Chen, Xianyu Wang, and Hongen Liao. "An Edge Enhanced SRGAN for MRI Super Resolution in Slice-Selection Direction." In Multimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy, 12–20. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33226-6_2.

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Fick, Rutger H. J., Marco Pizzolato, Demian Wassermann, and Rachid Deriche. "Diffusion MRI Anisotropy: Modeling, Analysis and Interpretation." In Mathematics and Visualization, 203–28. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61358-1_9.

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Wang, Jiaming, Qing Wang, Jun Du, Jianshu Zhang, Bin Wang, and Bo Ren. "MRD: A Memory Relation Decoder for Online Handwritten Mathematical Expression Recognition." In Document Analysis and Recognition – ICDAR 2021, 39–54. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86334-0_3.

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Wilkins, Bryce, Namgyun Lee, Vidya Rajagopalan, Meng Law, and Natasha Leporé. "Effect of Data Acquisition and Analysis Method on Fiber Orientation Estimation in Diffusion MRI." In Mathematics and Visualization, 13–24. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02475-2_2.

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Forte, B., and R. Mininni. "Maximum Expected Information (MEI) Discretization Method for Spatial Data Analysis." In Proceedings of the Fourth European Conference on Mathematics in Industry, 283. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-009-0703-4_33.

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Aetesam, Hazique, Suman Kumar Maji, and Jerome Boulanger. "Image Enhancement Under Gaussian Impulse Noise for Satellite and Medical Applications." In Advances in Computational Intelligence and Robotics, 309–42. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-8892-5.ch020.

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Remote sensing technologies such as hyperspectral imaging (HSI) and medical imaging techniques such as magnetic resonance imaging (MRI) form the pillars of human advancement. However, external factors like noise pose limitations on the accurate functioning of these imaging systems. Image enhancement techniques like denoising therefore form a crucial part in the proper functioning of these technologies. Noise in HSI and MRI are primarily a mixture of Gaussian and impulse noise. Image denoising techniques designed to handle mixed Gaussian-impulse (G-I) noise are thus an area of core research under the field of image restoration and enhancement. Therefore, this chapter discusses the mathematical preliminaries of G-I noise followed by an elaborate literature survey that covers the evolution of image denoising techniques for G-I noise from filtering-based to learning-based. An experimental analysis section is also provided that illustrates the performance of several denoising approaches under HSI and MRI, followed by a conclusion.
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Saha, Manas, Mrinal Kanti Naskar, and B. N. Chatterji. "Wavelet and Curvelet Transforms for Biomedical Image Processing." In Handbook of Research on Information Security in Biomedical Signal Processing, 95–129. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-5152-2.ch006.

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This chapter introduces two mathematical transforms—wavelet and curvelet—in the field of biomedical imaging. Presenting the theoretical background with relevant properties, the applications of the two transforms are presented. The biomedical applications include heart sound analysis, electrocardiography (ECG) characterization, positron emission tomography (PET) image analysis, medical image compression, mammogram enhancement, magnetic resonance imaging (MRI) and computer tomography (CT) image denoising, diabetic retinopathy detection. The applications emphasize the development of algorithms to diagnose human diseases, thereby rendering fast and reliable support to the medical personnel. The transforms—one classical (wavelet) and another contemporary (curvelet)—are selected to focus the difference in architecture, limitation, evolution, and application of individual transform. Two joint applications are addressed to compare their performance. This survey is also supplemented by a case study: mammogram denoising using wavelet and curvelet transforms with the underlying algorithms.
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Suh, Jennifer M., and Melissa A. Gallagher. "Preservice Teachers Decomposing Ambitious Mathematics Teaching." In Research Anthology on Facilitating New Educational Practices Through Communities of Learning, 788–99. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7294-8.ch039.

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We examined preservice teachers' experiences during a clinically embedded mathematics methods course, specifically examining the impact of video-based professional learning structures using the Mathematical Quality of Instruction (MQI; Learning Mathematics for Teaching, 2014) instruments on their collaborative planning and collective observations. Preservice teachers co-taught the summer PDS Math Lab within a Professional Learning Community with structured observations with video analysis that entailed: a) Collaborative planning; b) Structured Observations targeting instructional analysis focused on ambitious teaching practices; c) Use of the MQI that focused on the richness of mathematics. The authors detail the specific affordances of the structured observation with video analysis in a math methods course in a teacher preparation program and how the clinically embedded coursework supported preservice teachers' decomposition of ambitious teaching and bridge practitioner and academic knowledge.
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"Introductory Tensor Analysis." In Essential Mathematics for NMR and MRI Spectroscopists, 177–96. The Royal Society of Chemistry, 2016. http://dx.doi.org/10.1039/bk9781782627975-00177.

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In order to construct a completely general Hamiltonian it is necessary to use tensors. The starting point here is dyadic algebra that is introduced and then used to calculate the gradient of a vector. Rotational transformation of dyads is developed and the parallel between the results and that of vectors is drawn and is used to introduce a more formal definition of tensors. Scalars, vectors and tensors are grouped into 0th-, 1st- and 2nd-rank tensors to show their similarities and differences. The detailed algebra of tensors is given including isotropic, symmetric, antisymmetric and irreducible tensors.
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"The Product Operator Formalism." In Essential Mathematics for NMR and MRI Spectroscopists, 561–97. The Royal Society of Chemistry, 2016. http://dx.doi.org/10.1039/bk9781782627975-00561.

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Density matrix calculations are very powerful but also very time-consuming and error-prone when done by hand. The product operator formalism provides a compact way of doing “back-of-the-envelope” density matrix operations. In order to contrast the density operator method with the product operator method and to make clear the genesis of the product operator formalism a short discussion of a density matrix calculation is performed. The Cartesian product operator method is then presented and the rules for its use are developed. Multiple quantum coherence is defined and its genesis and evolution in time are explored. Helpful visualisations of product operator evolutions are presented as rotation diagrams. Several NMR pulse sequences are analysed and a visual operator-tree approach to analysis is presented. Single-transition product operators are discussed in preparation for the treatment of coherence transfer and relaxation.
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Conference papers on the topic "MRI mathematical analysis"

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Waks, E., J. L. Prince, and A. S. Douglas. "Cardiac motion simulator for tagged MRI." In Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis. IEEE, 1996. http://dx.doi.org/10.1109/mmbia.1996.534070.

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Soltanian-Zadeh, H., J. P. Windham, and D. J. Peck. "Optimal linear transformation for MRI feature extraction." In Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis. IEEE, 1996. http://dx.doi.org/10.1109/mmbia.1996.534058.

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Cheng-Yi Liu, Juan Eugenio Iglesias, and Zhuowen Tu. "Pictorial multi-atlas segmentation of brain MRI." In 2012 IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA). IEEE, 2012. http://dx.doi.org/10.1109/mmbia.2012.6164743.

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Maddah, Mahnaz, Lilla Zollei, W. Eric L. Grimson, Carl-Fredrik Westin, and William M. Wells. "A Mathematical Framework for incorporating anatomical knowledge in DT-MRI analysis." In 2008 IEEE International Symposium on Biomedical Imaging: From Macro to Nano (ISBI '08). IEEE, 2008. http://dx.doi.org/10.1109/isbi.2008.4540943.

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Rusinek, Roza. "Evaluation of renal function with contrast MRI: mathematical modeling and error analysis." In Medical Imaging '99, edited by Kenneth M. Hanson. SPIE, 1999. http://dx.doi.org/10.1117/12.348555.

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Radeva, P., A. Amini, Jiantao Huang, and E. Marti. "Deformable B-solids and implicit snakes for localization and tracking of SPAMM MRI-data." In Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis. IEEE, 1996. http://dx.doi.org/10.1109/mmbia.1996.534071.

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Zepp, Jonathan, Norbert Graf, Holger Stenzhorn, Wolfgang Reith, Ioannis Karatzanis, Georgios C. Manikis, Vangelis Sakkalis, Konstantinos Marias, and Georgios Stamatakos. "An innovative mathematical analysis of routine MRI scans in patients with glioblastoma using DoctorEye." In 2012 IEEE 12th International Conference on Bioinformatics & Bioengineering (BIBE). IEEE, 2012. http://dx.doi.org/10.1109/bibe.2012.6399773.

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FU, ZHUO-JIA, JUN-PU LI, and QIANG XI. "FAST SINGULAR BOUNDARY METHOD: MATHEMATICAL BACKGROUND AND APPLICATION IN WAVE PROPAGATION ANALYSIS." In BEM/MRM 42 2019. Southampton UK: WIT Press, Southampton UK, 2019. http://dx.doi.org/10.2495/be420161.

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Staniszewski, Michał. "Image quality parameters in application of compressed sensing for MRI data." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043760.

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Sahay, Chittaranjan, Suhash Ghosh, and Hari Kiran Kammila. "Analysis of Ultrasonic Machining Using Monte Carlo Simulation." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63240.

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Proper selection of manufacturing conditions is one of the most important aspects in Ultrasonic Machining process, as these conditions determine the Material Removal Rate (MRR). In this work, two very popular mathematical models proposed by Miller and Shaw have been investigated using Monte Carlo simulation based Crystal Ball analysis tool. Effects of abrasive particle size, particle concentration, amplitude of tool vibration, tool radius and depth of hole on MRR have been analyzed for both models. Miller’s model indicates a strong positive relationship between abrasive grain size, concentration and MRR. Contrary to the literature search on experimental data, Shaw’s mathematical model indicates a negative relationship between MRR and grain size, and a very weak relationship between MRR and concentration. No definite relationship could be established between either tool radius and MRR or amplitude and MRR. A negative relationship between depth of hole and MRR was obtained for Shaw’s model.
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