Analogues of Kähler geometry on Sasakian manifolds

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliographical references (p. 53-54).A Sasakian manifold S is equipped with a unit-length, Killing vector field ( which generates a one-dimensional foliation with a transverse Kihler structure. A differential form a on S is called basic with respect to the foliation if it satisfies [iota][epsilon][alpha] = [iota][epsilon]d[alpha] = 0. If a compact Sasakian manifold S is regular, i.e. a circle bundle over a compact Kähler manifold, the results of Hodge theory in the Kahler case apply to basic forms on S. Even in the absence of a Kähler base, there is a basic version of Hodge theory due to El Kacimi-Alaoui. These results are useful in trying to imitate Kähler geometry on Sasakian manifolds; however, they have limitations. In the first part of this thesis, we will develop a "transverse Hodge theory" on a broader class of forms on S. When we restrict to basic forms, this will give us a simpler proof of some of El Kacimi-Alaoui's results, including the basic dd̄-lemma. In the second part, we will apply the basic dd̄-lemma and some results from our transverse Hodge theory to conclude (in the manner of Deligne, Griffiths, and Morgan) that the real homotopy type of a compact Sasakian manifold is a formal consequence of its basic cohomology ring and basic Kähler class.by Aaron Michael Tievsky.Ph.D

Abnormal water diffusivity in corticostriatal projections in children with Tourette syndrome

The fronto-striato-thalamic circuit has been implicated in the pathomechanism of Tourette Syndrome (TS). To study white and gray matter comprehensively, we used a novel technique called Tract-Based Spatial Statistics (TBSS) combined with voxel-based analysis (VBA) of diffusion tensor MR images in children with TS as compared to typically developing controls. These automated and unbiased methods allow analysis of cerebral white matter and gray matter regions. We compared 15 right-handed children with TS (mean age: 11.6 ± 2.5 years, 12 males) to 14 age-matched right-handed healthy controls (NC; mean age: 12.29 ± 3.2 years, 6 males). Tic severity and neurobehavioral scores were correlated with FA and ADC values in regions found abnormal by these methods. For white matter, TBSS analysis showed regions of increased ADC in the corticostriatal projection pathways including left external capsule and left and right subcallosal fasciculus pathway in TS group compared to NC group. Within the TS group, ADC for the left external capsule was negatively associated with tic severity ( r = −0.586, P = 0.02). For gray matter, VBA revealed increased ADC for bilateral orbitofrontal cortex, left putamen, and left insular cortex. ADC for the right and left orbitofrontal cortex was highly correlated with internalizing problems ( r = 0.665; P = 0.009, r = 0.545; P = 0.04, respectively). Altogether, this analysis revealed focal diffusion abnormalities in the corticostriatal pathway and in gray matter structures involved in the fronto-striatal circuit in TS. These diffusion abnormalities could serve as a neuroimaging marker related to tic severity and neurobehavioral abnormalities in TS subjects. Hum Brain Mapp, 2010. © 2010 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78224/1/20970_ftp.pd

Apparent diffusion coefficient restriction in the white matter: going beyond acute brain territorial ischemia

BACKGROUND: Reduction of apparent diffusion coefficient (ADC) values in white matter is not always ischaemic in nature. METHODS: We retrospectively analysed our MRI records featuring reduced ADC values in the centrum semiovale without grey matter involvement or significant vasogenic oedema. RESULTS: Several conditions showed the aforementioned MR findings: moose-horn lesions on coronal images in X-linked Charcot-Marie-Tooth disease; small fronto-parietal lesions in Menkes disease; marked signal abnormalities in the myelinised regions in the acute neonatal form of maple syrup urine disease; strip-like involvement of the corpus callosum in glutaric aciduria type 1; persistent periventricular parieto-occipital abnormalities in phenylketonuria; diffuse signal abnormalities with necrotic evolution in global cerebral anoxia or after heroin vapour inhalation; almost completely reversible symmetric fronto-parietal lesions in methotrexate neurotoxicity; chain-like lesions in watershed ischaemia; splenium involvement that normalises in reversible splenial lesions or leads to gliosis in diffuse axonal injury. CONCLUSION: Neuroradiologists must be familiar with these features, thereby preventing misdiagnosis and inappropriate management

Clinical applications of diffusion tensor imaging

Directionally-ordered cellular structures that impede water motion, such as cell membranes and myelin, result in water mobility that is also directionally-dependent. Diffusion tensor imaging characterizes this directional nature of water motion and thereby provides structural information that cannot be obtained by standard anatomic imaging. Quantitative apparent diffusion coefficients and fractional anisotropy have emerged from being primarily research tools to methods enabling valuable clinical applications. This review describes the clinical utility of diffusion tensor imaging, including the basic principles of the technique, acquisition, data analysis, and the major clinical applications. J. Magn. Reson. Imaging 2004;19:6–18. © 2003 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/35153/1/10424_ftp.pd

Investigation of apparent diffusion coefficient and diffusion tensor anisotrophy in acute and chronic multiple sclerosis lesions.

BACKGROUND AND PURPOSE: The various stages of multiple sclerosis (MS) are characterized by de- and remyelination as well as by inflammation. Diffusion MR imaging is sensitive to tissue water motion, which might correspond to these pathologic processes. Our purpose was to demonstrate differences in apparent diffusion coefficient (ADC) and diffusion tensor anisotropy in acute and chronic MS plaques and in normal-appearing brain. METHODS: Twelve MS patients underwent conventional and full-tensor diffusion MR imaging with B = 1221 s/mm2. Derivation of trace ADC and calculation of anisotropic scalars, including eccentricity, relative anisotropy (RA), and fractional anisotropy (FA) was performed on a per-pixel basis. Regions of interest of plaques and normal structures were determined on coregistered maps. MS lesions were classified as acute, subacute, or chronic on the basis of their appearance on conventional images and in relation to clinical findings. RESULTS: Seven patients had acute plaques with a concentric arrangement of alternating high and low signal intensity on diffusion-weighted images. In nine acute lesions, plaque centers had high ADC with reduced anisotropy compared with rim, normal-appearing white matter (NAWM), and chronic lesions. The thin rim of diffusion-weighted hyperintensity surrounding the center showed variable ADC and anisotropic values, which were not statistically different from NAWM. Subacute and chronic MS lesions had intermediate ADC elevations/anisotropic reductions. Calculated FA pixel maps were superior to eccentricity or RA maps; however, quality was limited by signal-to-noise constraints. CONCLUSION: ADC and diffusion anisotropic scalars reflect biophysical changes in the underlying pathology of the demyelinating process

Wegener granulomatosis invading the cavernous sinus: a CT demonstration.

A case of localized cranial Wegener granulomatosis was imaged with high resolution computed tomography. The mass extended from the infratemporal fossa, through the basal foramina, and into the cavernous sinus, causing complete occlusion of the internal carotid artery. Computed tomography demonstrated absence of bone destruction and a normal parotid gland and nasopharynx. Although uncommon, Wegener granulomatosis should be considered in the differential diagnosis of a parapharyngeal mass with intracranial extension