Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Investigation of multisensory processing and structural brain differences in Autism Spectrum Disorder

This thesis is an investigation of structural brain abnormalities, as well as multisensory and unisensory processing deficits in autistic traits and Autism Spectrum Disorder (ASD). To achieve this, structural and functional magnetic resonance imaging (fMRI) and psychophysical techniques were employed. ASD is a neurodevelopmental condition which is characterised by the social communication and interaction deficits, as well as repetitive patterns of behaviour, interests and activities. These traits are thought to be present in a typical population. The Autism Spectrum Quotient questionnaire (AQ) was developed to assess the prevalence of autistic traits in the general population. Von dem Hagen et al. (2011) revealed a link between AQ with white matter (WM) and grey matter (GM) volume (using voxel-based-morphometry). However, their findings revealed no difference in GM in areas associated with social cognition. Cortical thickness (CT) measurements are known to be a more direct measure of cortical morphology than GM volume. Therefore, Chapter 2 investigated the relationship between AQ scores and CT in the same sample of participants. This study showed that AQ scores correlated with CT in the left temporo-occipital junction, left posterior cingulate, right precentral gyrus and bilateral precentral sulcus, in a typical population. These areas were previously associated with structural and functional differences in ASD. Thus the findings suggest, to some extent, autistic traits are reflected in brain structure - in the general population. The ability to integrate auditory and visual information is crucial to everyday life, and results are mixed regarding how ASD influences audiovisual integration. To investigate this question, Chapter 3 examined the Temporal Integration Window (TIW), which indicates how precisely sight and sound need to be temporally aligned so that a unitary audiovisual event can be perceived. 26 adult males with ASD and 26 age and IQ-matched typically developed males were presented with flash-beep (BF), point-light drummer, and face-voice (FV) displays with varying degrees of asynchrony and asked to make Synchrony Judgements (SJ) and Temporal Order Judgements (TOJ). Analysis of the data included fitting Gaussian functions as well as using an Independent Channels Model (ICM) to fit the data (Garcia-Perez & Alcala-Quintana, 2012). Gaussian curve fitting for SJs showed that the ASD group had a wider TIW, but for TOJ no group effect was found. The ICM supported these results and model parameters indicated that the wider TIW for SJs in the ASD group was not due to sensory processing at the unisensory level, but rather due to decreased temporal resolution at a decisional level of combining sensory information. Furthermore, when performing TOJ, the ICM revealed a smaller Point of Subjective Simultaneity (PSS; closer to physical synchrony) in the ASD group than in the TD group. Finding that audiovisual temporal processing is different in ASD encouraged us to investigate the neural correlates of multisensory as well as unisensory processing using functional magnetic resonance imaging fMRI. Therefore, Chapter 4 investigated audiovisual, auditory and visual processing in ASD of simple BF displays and complex, social FV displays. During a block design experiment, we measured the BOLD signal when 13 adults with ASD and 13 typically developed (TD) age-sex- and IQ- matched adults were presented with audiovisual, audio and visual information of BF and FV displays. Our analyses revealed that processing of audiovisual as well as unisensory auditory and visual stimulus conditions in both the BF and FV displays was associated with reduced activation in ASD. Audiovisual, auditory and visual conditions of FV stimuli revealed reduced activation in ASD in regions of the frontal cortex, while BF stimuli revealed reduced activation the lingual gyri. The inferior parietal gyrus revealed an interaction between stimulus sensory condition of BF stimuli and group. Conjunction analyses revealed smaller regions of the superior temporal cortex (STC) in ASD to be audiovisual sensitive. Against our predictions, the STC did not reveal any activation differences, per se, between the two groups. However, a superior frontal area was shown to be sensitive to audiovisual face-voice stimuli in the TD group, but not in the ASD group. Overall this study indicated differences in brain activity for audiovisual, auditory and visual processing of social and non-social stimuli in individuals with ASD compared to TD individuals. These results contrast previous behavioural findings, suggesting different audiovisual integration, yet intact auditory and visual processing in ASD. Our behavioural findings revealed audiovisual temporal processing deficits in ASD during SJ tasks, therefore we investigated the neural correlates of SJ in ASD and TD controls. Similar to Chapter 4, we used fMRI in Chapter 5 to investigate audiovisual temporal processing in ASD in the same participants as recruited in Chapter 4. BOLD signals were measured while the ASD and TD participants were asked to make SJ on audiovisual displays of different levels of asynchrony: the participants’ PSS, audio leading visual information (audio first), visual leading audio information (visual first). Whereas no effect of group was found with BF displays, increased putamen activation was observed in ASD participants compared to TD participants when making SJs on FV displays. Investigating SJ on audiovisual displays in the bilateral superior temporal gyrus (STG), an area involved in audiovisual integration (see Chapter 4), we found no group differences or interaction between group and levels of audiovisual asynchrony. The investigation of different levels of asynchrony revealed a complex pattern of results indicating a network of areas more involved in processing PSS than audio first and visual first, as well as areas responding differently to audio first compared to video first. These activation differences between audio first and video first in different brain areas are constant with the view that audio leading and visual leading stimuli are processed differently.

Nuclear Magnetic Resonance Spectroscopic and Computational Investigations of Chloroperoxidase Catalyzed Regio- and Enantio-Selective Transformations

Chloroperoxidase (CPO) is the most versatile heme-containing enzyme that catalyzes a broad spectrum of reactions. The remarkable feature of this enzyme is the high regio- and enantio-selectivity exhibited in CPO-catalyzed oxidation reactions. The aim of this dissertation is to elucidate the structural basis for regio- and enantio-selective transformations and investigate the application of CPO in biodegradation of synthetic dyes. To unravel the mechanism of CPO-catalyzed regioselective oxidation of indole, the dissertation explored the structure of CPO-indole complex using paramagnetic relaxation and molecular modeling. The distances between the protons of indole and the heme iron revealed that the pyrrole ring of indole is oriented toward the heme with its 2-H pointing directly at the heme iron. This provides the first experimental and theoretical explanation for the "unexpected" regioselectivity of CPO-catalyzed indole oxidation. Furthermore, the residues including Leu 70, Phe 103, Ile 179, Val 182, Glu 183, and Phe 186 were found essential to the substrate binding to CPO. These results will serve as a lighthouse in guiding the design of CPO mutants with tailor-made activities for biotechnological applications. To understand the origin of the enantioselectivity of CPO-catalyzed oxidation reactions, the interactions of CPO with substrates such as 2-(methylthio)thiophene were investigated by nuclear magnetic resonance spectroscopy (NMR) and computational techniques. In particular, the enantioselectivity is partly explained by the binding orientation of substrates. In third facet of this dissertation, a green and efficient system for degradation of synthetic dyes was developed. Several commercial dyes such as orange G were tested in the CPO-H2O2-Cl- system, where degradation of these dyes was found very efficient. The presence of halide ions and acidic pH were found necessary to the decomposition of dyes. Significantly, the results revealed that this degradation of azo dyes involves a ferric hypochlorite intermediate of CPO (Fe-OCl), compound X.

Correlations between cardiac magnetic resonance and histologic findings in Anderson Fabry disease

ABSTRACT Background Cardiac magnetic resonance (CMR) has been shown as promising diagnostic tool in Anderson-Fabry disease (AFD) cardiomyopathy due to its ability to detect fat deposits through lower native T1 values. However no histological validation has been provided to date. Objectives To correlate CMR and histologic findings in different cardiac stages of AFD focusing on T1 mapping. Methods Fifteen AFD patients (49 years [IQR 39-63], 60% females) undergoing CMR (cines, native T1 and T2 mapping, LGE and post-contrast T1 imaging) and endomyocardial biopsy (EMB, n=11) or septal myectomy (n=4), were retrospectively evaluated. Tissue specimens were analyzed with light/electron microscopy and vacuolization amount calculated as percentages of vacuolated myocytes and vacuolated myocyte area (%VMA) through a quantitative histomorphometric color-based analysis. Results In patients without increased indexed left ventricular mass (LVMi) at CMR (67%), T1 fell as %VMA increased (r= -0.883; p<0.001), whereas no clear relationship was evident once increased LVMi occurred (r= -0.501; p=0.389). At least 45% of vacuolized myocytes and 10% of VMA were needed for low T1 to occur. %VMA positively correlate with maximal wall thickness (MWT, r=0.860, p<0.0001) and LVMi (r= 0.762; p<0.001). Increased MWT and LVMi were present with at least 45% and 80% of vacuolated myocytes, respectively, and 18% and 22% of VMA. Conclusions This study demonstrated an inverse correlation between native T1 and the vacuolization amount in patients without increased LVMi at CMR, providing a histological validation of low native T1 in AFD. Importantly, a significant vacuolization burden was needed before low T1 and left ventricle hypertrophy occurred.

Emergent Antiferromagnetism Out Of The Hidden-order" State In Uru2si2: High Magnetic Field Nuclear Magnetic Resonance To 40 T."

Very high field (29)Si-NMR measurements using a fully (29)Si-enriched URu(2)Si(2) single crystal were carried out in order to microscopically investigate the hidden order (HO) state and adjacent magnetic phases in the high field limit. At the lowest measured temperature of 0.4 K, a clear anomaly reflecting a Fermi surface instability near 22 T inside the HO state is detected by the (29)Si shift, (29)K(c). Moreover, a strong enhancement of (29)K(c) develops near a critical field H(c) ≃ 35.6 T, and the ^{29}Si-NMR signal disappears suddenly at H(c), indicating the total suppression of the HO state. Nevertheless, a weak and shifted (29)Si-NMR signal reappears for fields higher than H(c) at 4.2 K, providing evidence for a magnetic structure within the magnetic phase caused by the Ising-type anisotropy of the uranium ordered moments.

Infratentorial Gray Matter Atrophy And Excess In Primary Craniocervical Dystonia.

Primary craniocervical dystonia (CCD) is generally attributed to functional abnormalities in the cortico-striato-pallido-thalamocortical loops, but cerebellar pathways have also been implicated in neuroimaging studies. Hence, our purpose was to perform a volumetric evaluation of the infratentorial structures in CCD. We compared 35 DYT1/DYT6 negative patients with CCD and 35 healthy controls. Cerebellar volume was evaluated using manual volumetry (DISPLAY software) and infratentorial volume by voxel based morphometry of gray matter (GM) segments derived from T1 weighted 3 T MRI using the SUIT tool (SPM8/Dartel). We used t-tests to compare infratentorial volumes between groups. Cerebellar volume was (1.14 ± 0.17) × 10(2) cm(3) for controls and (1.13 ± 0.14) × 10(2) cm(3) for patients; p = 0.74. VBM demonstrated GM increase in the left I-IV cerebellar lobules and GM decrease in the left lobules VI and Crus I and in the right lobules VI, Crus I and VIIIb. In a secondary analysis, VBM demonstrated GM increase also in the brainstem, mostly in the pons. While gray matter increase is observed in the anterior lobe of the cerebellum and in the brainstem, the atrophy is concentrated in the posterior lobe of the cerebellum, demonstrating a differential pattern of infratentorial involvement in CCD. This study shows subtle structural abnormalities of the cerebellum and brainstem in primary CCD.

Are Human Peripheral Nerves Sensitive To X-ray Imaging?

Diagnostic imaging techniques play an important role in assessing the exact location, cause, and extent of a nerve lesion, thus allowing clinicians to diagnose and manage more effectively a variety of pathological conditions, such as entrapment syndromes, traumatic injuries, and space-occupying lesions. Ultrasound and nuclear magnetic resonance imaging are becoming useful methods for this purpose, but they still lack spatial resolution. In this regard, recent phase contrast x-ray imaging experiments of peripheral nerve allowed the visualization of each nerve fiber surrounded by its myelin sheath as clearly as optical microscopy. In the present study, we attempted to produce high-resolution x-ray phase contrast images of a human sciatic nerve by using synchrotron radiation propagation-based imaging. The images showed high contrast and high spatial resolution, allowing clear identification of each fascicle structure and surrounding connective tissue. The outstanding result is the detection of such structures by phase contrast x-ray tomography of a thick human sciatic nerve section. This may further enable the identification of diverse pathological patterns, such as Wallerian degeneration, hypertrophic neuropathy, inflammatory infiltration, leprosy neuropathy and amyloid deposits. To the best of our knowledge, this is the first successful phase contrast x-ray imaging experiment of a human peripheral nerve sample. Our long-term goal is to develop peripheral nerve imaging methods that could supersede biopsy procedures.

Cerebral Cortex Involvement In Machado-joseph Disease.

Machado-Joseph disease (MJD/SCA3) is the most frequent spinocerebellar ataxia, characterized by brainstem, basal ganglia and cerebellar damage. Few magnetic resonance imaging based studies have investigated damage in the cerebral cortex. The objective was to determine whether patients with MJD/SCA3 have cerebral cortex atrophy, to identify regions more susceptible to damage and to look for the clinical and neuropsychological correlates of such lesions. Forty-nine patients with MJD/SCA3 (mean age 47.7 ± 13.0 years, 27 men) and 49 matched healthy controls were enrolled. All subjects underwent magnetic resonance imaging scans in a 3 T device, and three-dimensional T1 images were used for volumetric analyses. Measurement of cortical thickness and volume was performed using the FreeSurfer software. Groups were compared using ancova with age, gender and estimated intracranial volume as covariates, and a general linear model was used to assess correlations between atrophy and clinical variables. Mean CAG expansion, Scale for Assessment and Rating of Ataxia (SARA) score and age at onset were 72.1 ± 4.2, 14.7 ± 7.3 and 37.5 ± 12.5 years, respectively. The main findings were (i) bilateral paracentral cortex atrophy, as well as the caudal middle frontal gyrus, superior and transverse temporal gyri, and lateral occipital cortex in the left hemisphere and supramarginal gyrus in the right hemisphere; (ii) volumetric reduction of basal ganglia and hippocampi; (iii) a significant correlation between SARA and brainstem and precentral gyrus atrophy. Furthermore, some of the affected cortical regions showed significant correlations with neuropsychological data. Patients with MJD/SCA3 have widespread cortical and subcortical atrophy. These structural findings correlate with clinical manifestations of the disease, which support the concept that cognitive/motor impairment and cerebral damage are related in disease.

Scaphoid Fracture Nonunion: Correlation Of Radiographic Imaging, Proximal Fragment Histologic Viability Evaluation, And Estimation Of Viability At Surgery: Diagnosis Of Scaphoid Pseudarthrosis.

The purpose of this study was to correlate the pre-operative imaging, vascularity of the proximal pole, and histology of the proximal pole bone of established scaphoid fracture non-union. This was a prospective non-controlled experimental study. Patients were evaluated pre-operatively for necrosis of the proximal scaphoid fragment by radiography, computed tomography (CT) and magnetic resonance imaging (MRI). Vascular status of the proximal scaphoid was determined intra-operatively, demonstrating the presence or absence of puncate bone bleeding. Samples were harvested from the proximal scaphoid fragment and sent for pathological examination. We determined the association between the imaging and intra-operative examination and histological findings. We evaluated 19 male patients diagnosed with scaphoid nonunion. CT evaluation showed no correlation to scaphoid proximal fragment necrosis. MRI showed marked low signal intensity on T1-weighted images that confirmed the histological diagnosis of necrosis in the proximal scaphoid fragment in all patients. Intra-operative assessment showed that 90% of bones had absence of intra-operative puncate bone bleeding, which was confirmed necrosis by microscopic examination. In scaphoid nonunion MRI images with marked low signal intensity on T1-weighted images and the absence of intra-operative puncate bone bleeding are strong indicatives of osteonecrosis of the proximal fragment.

ECG scar quantification correlates with cardiac magnetic resonance scar size and prognostic factors in Chagas' disease

Objective To test the hypothesis that 12-lead ECG QRS scoring quantifies myocardial scar and correlates with disease severity in Chagas' heart disease. Design Patients underwent 12-lead ECG for QRS scoring and cardiac magnetic resonance with late gadolinium enhancement (CMR-LGE) to assess myocardial scar. Setting University of Sao Paulo Medical School, Sao Paulo, Brazil. Patients 44 Seropositive patients with Chagas' disease without a history of myocardial infarction and at low risk for coronary artery disease. Main outcome measures Correlation between QRS score, CMR-LGE scar size and left ventricular ejection fraction. Relation between QRS score, heart failure (HF) class and history of ventricular tachycardia (VT). Results QRS score correlated directly with CMR-LGE scar size (R=0.69, p<0.0001) and inversely with left ventricular ejection fraction (R=-0.54, p=0.0002), which remained significant in the subgroup with conduction defects. Patients with class II or III HF had significantly higher QRS scores than those with class I HF (5.1 +/- 3.4 vs 2.1 +/- 3.1 QRS points (p=0.002)) and patients with a history of VT had significantly higher QRS scores than those without a history of VT (5.3 +/- 3.2% vs 2.6 +/- 3.4 QRS points (p=0.02)). A QRS score >= 2 points had particularly good sensitivity and specificity (95% and 83%, respectively) for prediction of large CMR-LGE, and a QRS score >= 7 points had particularly high specificity (92% and 89%, respectively) for predicting significant left ventricular dysfunction and history of VT. Conclusions The wide availability of 12-lead ECG makes it an attractive screening tool and may enhance clinical risk stratification of patients at risk for more severe, symptomatic Chagas' heart disease.

Striatal volume abnormalities in treatment-naive patients diagnosed with pediatric major depressive disorder

Objective: The striatum, including the putamen and caudate, plays an important role in executive and emotional processing and may be involved in the pathophysiology of mood disorders. Few studies have examined structural abnormalities of the striatum in pediatric major depressive disorder (MDD) patients. We report striatal volume abnormalities in medication-naive pediatric MDD compared to healthy comparison subjects. Method: Twenty seven medication-naive pediatric Diagnostic and Statistical Manual of Mental Disorders, 4(th) edition (DSM-IV) MDD and 26 healthy comparison subjects underwent volumetric magnetic resonance imaging (MRI). The putamen and caudate volumes were traced manually by a blinded rater, and the patient and control groups were compared using analysis of covariance adjusting for age, sex, intelligence quotient, and total brain volumes. Results: MDD patients had significantly smaller right striatum (6.0% smaller) and right caudate volumes (7.4% smaller) compared to the healthy subjects. Left caudate volumes were inversely correlated with severity of depression in MDD subjects. Age was inversely correlated with left and right putamen volumes in MDD patients but not in the healthy subjects. Conclusions: These findings provide fresh evidence for abnormalities in the striatum of medication-naive pediatric MDD patients and suggest the possible involvement of the striatum in the pathophysiology of MDD.

Stimuli-responsive magnetic particles for biomedical applications

In recent years, magnetic nanoparticles have been studied due to their potential applications as magnetic carriers in biomedical area. These materials have been increasingly exploited as efficient delivery vectors, leading to opportunities of use as magnetic resonance imaging (MRI) agents, mediators of hyperthermia cancer treatment and in targeted therapies. Much attention has been also focused on ""smart"" polymers, which are able to respond to environmental changes, such as changes in the temperature and pH. In this context, this article reviews the state-of-the art in stimuli-responsive magnetic systems for biomedical applications. The paper describes different types of stimuli-sensitive systems, mainly temperature- and pH sensitive polymers, the combination of this characteristic with magnetic properties and, finally, it gives an account of their preparation methods. The article also discusses the main in vivo biomedical applications of such materials. A survey of the recent literature on various stimuli-responsive magnetic gels in biomedical applications is also included. (C) 2010 Elsevier B.V. All rights reserved.

Frequency Domain Connectivity Identification: An Application of Partial Directed Coherence in fMRI

Functional magnetic resonance imaging (fMRI) has become an important tool in Neuroscience due to its noninvasive and high spatial resolution properties compared to other methods like PET or EEG. Characterization of the neural connectivity has been the aim of several cognitive researches, as the interactions among cortical areas lie at the heart of many brain dysfunctions and mental disorders. Several methods like correlation analysis, structural equation modeling, and dynamic causal models have been proposed to quantify connectivity strength. An important concept related to connectivity modeling is Granger causality, which is one of the most popular definitions for the measure of directional dependence between time series. In this article, we propose the application of the partial directed coherence (PDC) for the connectivity analysis of multisubject fMRI data using multivariate bootstrap. PDC is a frequency domain counterpart of Granger causality and has become a very prominent tool in EEG studies. The achieved frequency decomposition of connectivity is useful in separating interactions from neural modules from those originating in scanner noise, breath, and heart beating. Real fMRI dataset of six subjects executing a language processing protocol was used for the analysis of connectivity. Hum Brain Mapp 30:452-461, 2009. (C) 2007 Wiley-Liss, Inc.

NMR imaging of fluid pathways during drainage of softwood in a pressure membrane chamber

An experiment was implemented to study fluid flow in a pressure media. This procedure successfully combines nuclear magnetic resonance imaging with a pressure membrane chamber in order to visualize the non-wetting and wetting fluid flows with controlled boundary conditions. A specially designed pressure membrane chamber, made of non-magnetic materials and able to withstand 4 MPa, was designed and built for this purpose. These two techniques were applied to the drainage of Douglas fir sapwood. In the study of the longitudinal flow, narrow drainage fingers are formed in the latewood zones. They follow the longitudinal direction of wood and spread throughout the sample length. These fingers then enlarge in the cross-section plane and coalesce until drainage reaches the whole latewood part. At the end of the experiments, when the drainage of liquid water in latewood is completed, just a few sites of percolation appear in earlywood zones. This difference is a result of the wood anatomical structure, where pits, the apertures that allow the sap to flow between wood cells, are more easily aspirated in earlywood than in latewood. (C) 2007 Elsevier Ltd. All rights reserved.

Quantitative Determination of Dimethylaminoethanol in Cosmetic Formulations by Nuclear Magnetic Resonance Spectroscopy

A nuclear magnetic resonance (NMR) spectroscopic method was validated for the quantitative determination of dimethylaminoethanol (DMAE) in cosmetic formulations. The linearity in the range from 0.5000 to 1.5000 g (DMAE salt/mass maleic acid) presents a correlation coefficient > 0.99 for all DMAE salts. The repeatability (intraday), expressed as relative standard deviation, ranged from 1.08 to 1.44% for samples and 1.31 to 1.88% for raw materials. The detection limit and quantitation limit were 0.0017 and 0.0051 g for DMAE, 0.0018 and 0.0054 g for DMAE bitartrate, and 0.0023 and 0.0071 g for DMAE acetamidobenzoate, respectively. The proposed method is simple, precise, and accurate and can be used in the quality control of raw materials and cosmetic gels containing these compounds as active substances.