We analyzed the properties of the logarithm of the Rician distribution leading to a full characterization of the probability law of the errors in the linearized diffusion tensor model. An almost complete lack of bias, a simple relation between the variance and the signal-to-noise ratio in the original complex data, and a close approximation to normality facilitated estimation of the tensor components by an iterative weighted least squares algorithm. The theory of the linear model has also been used to derive the distribution of mean diffusivity, to develop an informative statistical test for relative lack of fit of the ellipsoidal (or spherical) model compared to an unrestricted linear model in which no specific shape is assumed for the diffusion process, and to estimate the signal-to-noise ratios in the original data. The false discovery rate (FDR) has been used to control thresholds for statistical significance in the context of multiple comparisons at voxel level. The methods are illustrated by application to three diffusion tensor imaging (DTI) datasets of clinical interest: a healthy volunteer, a patient with acute brain injury, and a patient with hydrocephalus. Interestingly, some salient features, such as a region normally comprising the basal ganglia and internal capsule, and areas of edema in patients with brain injury and hydrocephalus, had patterns of error largely independent from their mean diffusivities. These observations were made in brain regions with sufficiently large signal-to-noise ratios (>2) to justify the assumptions of the log Rician probability model. The combination of diffusivity and its error may provide added value in diagnostic DTI of acute pathologic expansion of the extracellular fluid compartment in brain parenchymal tissue.
The mean cerebral blood flow (CBF) has generally been demonstrated to be lower in normal pressure hydrocephalus (NPH) than in normal controls. We investigated the distribution of the regional peri- and paraventricular white matter CBF (WM CBF) in NPH at baseline and during a controlled rise in intracranial pressure (ICP). Twelve patients with idiopathic NPH (mean age 69 years) underwent a CSF infusion study. CBF was measured by H2(15)O PET at baseline and then during the steady-state plateau of raised ICP. The PET images were co-registered and resliced to 3D structural T1-weighted MRIs. Ten healthy normal volunteers served as control subjects for baseline CBF determination only. Profiles of the regional distribution of the baseline WM CBF and of the percentage change in WM CBF as a function of distance from the ventricles were plotted. The global mean baseline CBF in patients (28.4 +/- 5.2 ml/100 ml/min) was lower than in the control subjects (33 +/- 5.4 ml/100 ml/min) (P < 0.005). In patients, the profile of the regional WM CBF at baseline showed an increase with distance from the ventricles (P < 0.0001), with a maximal reduction adjacent to the ventricles and progressive normalization with distance, whereas in controls no relationship was apparent (P = 0.0748). In 10 patients, the rise in ICP during the infusion produced a fall in cerebral perfusion pressure (CPP) and a significant decrease of the global mean CBF from 27.6 +/- 3.1 to 24.5 +/- 2.9 ml/100 ml/min (P < 0.0001). The profile of the percentage changes in regional WM CBF in patients showed a U-shaped relationship with distance from the ventricles (P = 0.0007), with a maximal decrease skewed on the side of the lateral ventricles at around a mean distance of 9 mm. The WM CBF is reduced in NPH, with an abnormal gradient from the lateral ventricles towards the subcortical WM. An excessive decrease in CBF is brought about by reductions in CPP and appears to be maximal in the paraventricular watershed region. These results are discussed in the light of previous hypotheses concerning the aetiology of periventricular CBF reduction in NPH.
Summary:Regional cerebral blood flow (CBF) was studied with O 15-water positron emission tomography and anatomic region-of-interest analysis on coregistered magnetic resonance in patients with idiopathic (n ס 12) and secondary (n ס 5) normal pressure hydrocephalus (NPH). Mean CBF was compared with values obtained from healthy volunteers (n ס 12) and with clinical parameters. Mean CBF was significantly decreased in the cerebrum and cerebellum of patients with NPH.The regional analysis demonstrated that CBF was reduced in the basal ganglia and the thalamus but not in white matter regions. The results suggest that the role of the basal ganglia and thalamus in NPH may be more prominent than currently appreciated. The implications for theories regarding the pathogenesis of NPH are discussed.
Background and Purpose-The increase in fractional anisotropy (FA) in acute stroke has yet to be explained. Using an engineering methodology known as pq diagrams, we sought to explain the increase in FA by describing changes in the total magnitude of the diffusion tensor (L) as well as the isotropic (p) and anisotropic (q) components. Methods-Diffusion tensor imaging was performed in 10 patients with stroke Ͻ27 hours old. The diffusion tensor was decomposed into the p and q components and plotted to describe the diffusion trajectories. FA was also calculated and compared. Results-There was significant and consistent reduction in p, q, and L (p: mean, Ϫ50.0%; range, Ϫ36.6% to Ϫ64.5%; q: mean, Ϫ50.8%; range, Ϫ30.8% to Ϫ72.8%; L: mean, Ϫ50.3%; range, Ϫ37.0% to Ϫ65.1%). There were inconsistent changes in FA (mean, Ϫ0.5%; range, Ϫ44.9% to ϩ45.0%). Five patients had elevated FA due to proportionately higher loss of L than q. Conclusions-Changes in FA only occur when there is a change in the ratio of q/L. Acute elevation of FA occurred in the context of a larger reduction in L than q. The elevation in FA occurs in the context of a reduction in the anisotropic tensor and therefore is a consequence of ratio-metric measurement. This appears to clarify the reported increase in FA in terms of alterations in the shape of the apparent diffusion tensor. pq diagrams appear to offer improved resolution of acute diffusion changes in ischemia.
BackgroundThe pathogenesis of normal pressure hydrocephalus (NPH) remains unclear which limits both early diagnosis and prognostication. The responsiveness to intervention of differing, complex and concurrent injury patterns on imaging have not been well-characterized. We used diffusion tensor imaging (DTI) to explore the topography and reversibility of white matter injury in NPH pre- and early after shunting.MethodsTwenty-five participants (sixteen NPH patients and nine healthy controls) underwent DTI, pre-operatively and at two weeks post-intervention in patients. We interrogated 40 datasets to generate a full panel of DTI measures and corroborated findings with plots of isotropy (p) vs. anisotropy (q).ResultsConcurrent examination of DTI measures revealed distinct profiles for NPH patients vs. controls. PQ plots demonstrated that patterns of injury occupied discrete white matter districts. DTI profiles for different white matter tracts showed changes consistent with i) predominant transependymal diffusion with stretch/ compression, ii) oedema with or without stretch/ compression and iii) predominant stretch/ compression. Findings were specific to individual tracts and dependent upon their proximity to the ventricles. At two weeks post-intervention, there was a 6·7% drop in axial diffusivity (p = 0·022) in the posterior limb of the internal capsule, compatible with improvement in stretch/ compression, that preceded any discernible changes in clinical outcome. On PQ plots, the trajectories of the posterior limb of the internal capsule and inferior longitudinal fasciculus suggested attempted ‘round trips’. i.e. return to normality.ConclusionDTI profiling with p:q correlation may offer a non-invasive biomarker of the characteristics of potentially reversible white matter injury.
The inherent invasiveness of malignant cells is a major determinant of the poor prognosis of cerebral gliomas. Diffusion tensor MRI (DTI) can identify white matter abnormalities in gliomas that are not seen on conventional imaging. By breaking down DTI into its isotropic (p) and anisotropic (q) components, we can determine tissue diffusion "signatures". In this study we have characterised these abnormalities in peritumoural white matter tracts. Thirty-five patients with cerebral gliomas and seven normal volunteers were imaged with DTI and T2-weighted sequences at 3 T. Displaced, infiltrated and disrupted white matter tracts were identified using fractional anisotropy (FA) maps and directionally encoded colour maps and characterised using tissue signatures. The diffusion tissue signatures were normal in ROIs where the white matter was displaced. Infiltrated white matter was characterised by an increase in the isotropic component of the tensor (p) and a less marked reduction of the anisotropic component (q). In disrupted white matter tracts, there was a marked reduction in q and increase in p. The direction of water diffusion was grossly abnormal in these cases. Diffusion tissue signatures may be a useful method of assessing occult white matter infiltration.
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