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, Each voxel in the synthetic phantom is composed of 50 (= n base ) T 2 curves in proportion of the true water fraction values as shown in Fig. A.2. Instead of using the pure exponentials, we account for the stimulated echoes, 2012.

, The B 1 scale factor for generating the EPG curve is chosen from the true B 1 map shown in Fig. A.2. The T 2 curve for a voxel from each section for different B 1 values are shown in Fig. A.3. The simulations are performed for six levels of additive Gaussian noise. The SNR values evaluated are {50, 75, 100, 200, 500, 1000}. The SNR is stated with respect to the signal value at first echo. The T 2 curves were generated for two specifications: (i) echo spacing = 9

M. .. Relapsing, 21 2.3 Definition of active and inactive MS lesions in terms of demyelination, 1995.

, True values of the variables used for generating the decay curve using the multi-compartment T 2 relaxometry model. The units for the Gaussian PDF mean (µ) and standard deviation (?) are in ms, p.43

. , The water fractions for short T 2 , medium T 2 and high T 2 compartments for the three sections are shown here. The mean (µ) and standard deviation (?) of the water fraction maps are computed over for each section over the regions indicated in Fig

. , This table show the mean (µ) and standard deviation (?) of short T 2 , medium T 2 and high T 2 compartments for the 14 T 2 spheres in the NIST phantom. The label index can be checked from Fig. 5.12. The T 2 values shown in this table are obtained by performing a mono T 2 analysis of the data

. , 15 for short, medium and high-T 2 water fraction estimates. For each compartment the mean bias of the difference in the estimates (m d ), the 95% confidence interval (CI) around m d and the limits of agreement (LoA) are shown, This table summarizes the statistics of the Bland-Altman (BA) plots shown in Fig. 5

, This table summarizes the regression statistics of the plots shown in Fig. 5.15 for short, medium and high-T 2 water fraction estimates respectively. The regression statistics are obtained by comparing all the voxels in the 15 ROIs of four healthy controls, p.61

. , The T 2 values of the spheres of the NIST phantom (refer Fig. 6.7) are shown here. The values are obtained by performing a mono T 2 estimation from the T 2 relaxometry data. The label values correspond to the annotations in Fig

. Statistics-of-the-bland-altman, BA) plots shown in Fig. 6.9 for short, medium and high-T 2 water fraction estimates respectively. For each compartment the mean bias of the difference in the estimates (m d ), the 95% confidence interval (CI) around m d and the limits of agreement (LoA) are shown

. , The regression statistics are obtained by comparing all the voxels in the 15 ROIs of four healthy controls, Regression statistics of the plots shown in Fig. 6.9 for short, medium and high-T 2 water fraction estimates

, Water fraction values for the short, medium and high T 2 compartments for the different sections of the phantom shown in Fig, p.93

L. ?. , The common language (CL) effect size are reported for the measurements which were significantly different for E+, vol.104

A. , The water fraction values for the short, medium and high T 2 compartments for the different sections of the phantom shown in Fig. A.1 are provided here

. , When a bulk of these are considered, the net magnetization tends to be zero. (b) In the presence of an external field (B 0 ), the spinning nuclei precesses around the external field at a frequency ? 0 (Larmor frequency), absence of an external field, spinning nuclei are randomly oriented

, (a) The bulk magnetization precesses around both B 0 and B 1. (b) Observation from the rotating frame allows us to describe the transverse plane magnetization with much more ease, 2005.

. , The RF signal while observing from the (left) laboratory and (right) rotation frame. When observation is made from the rotation frame, the B 1 applied along the transverse plane is constant (unlike oscillating when observed from laboratory frame)

, The spin echo method has been shown here. The signal at echo time (2? ) is T 2 weighted, 2014.

. , On application of the refocusing pulse (at t = ? ) the phases of the isochromats are flipped

. , The multiple echo spin echo method has been shown here. The signal at multiple echo times by applying successive refocusing pulses, Image courtesy, 2014.

. , (Left) Electron microscope image of myelinated CNS tissue. The myelin sheath surrounds the axons. (Right) T 2 distributions of the myelin and intra/extracellular water are shown here, general, using pure exponential leads to higher T 2 estimations, 2016.

. , b) The resolution capability is shown for a given separation and SNR level. The plot is color coded with respect to the resolution values. It can be seen that greater separation is required for full resolution as the SNR drops, The resolution (R) and separation (S) between the T 2 pools are shown here as defined by, 2001.

, The normal nerve fiber and a demyelinated one are illustrated here. Demyelination marks the onset of MS in patients, p.18

. .. , This disrupts the capability of nerve fibers to normally transmit messages. Demyelination also exposes the axons to damage from extracellular bodies, p.20

, MS Phenotype for Relapsing Disease, p.21, 2014.

]. .. , MS Phenotype for Progressive MS, p.22, 2014.

. , to the duration of Phase 1 (mean time from multiple sclerosis clinical onset to DSS 3) in the 718 multiple sclerosis patients who had reached both DSS 3 & DSS 6. Image courtesy: [Leray, Image courtesy, 2010.

. , The objective is to obtain robust and reliable short T 2 , medium T 2 and high T 2 water fraction maps from a T 2 relaxometry MRI data, The idea of the multi-compartment T 2 relaxometry model is illustrated here

. , Distributions T 2 de la myéline et des tissus intra/extra cellulaires. Image extraite de, 2016.

. , L'objectif est d'obtenir de manière robuste les fractions de trois compartiments T 2 : court, moyen et long T 2 , et ce à partir d'images cliniques de relaxométrie, Idée générale des modèles multi-compartiment T 2 de relaxométrie

. , Cost function values as a function of PDF mean and weights evaluated separately for the three compartments are shown for varying levels of SNR

, Cost function values as a function of weights of two compartments evaluated separately are shown for varying levels of SNR, p.46

. , True values of the flip angle error (FAE) percentage, short T 2 , medium T 2 and high T 2 water fraction for the synthetic phantom are shown here

, List of Figures 143

, The first echo for all SNR levels of the synthetic phantom are shown here. The synthetic phantom data is generated with following specification: echo spacing = 9.0ms, number of echoes = 32, p.49

. , The T 2 relaxometry MRI of the phantom used for in-vivo phantom experiment I is shown here. The three sections are annotated in this figure

N. The and . Phantom, Phannie

. , This figure shows the 15 regions which were marked on the healthy controls over which the repeatability was studied

. , 8 rMSE values for estimated water fraction (left) and FAE (right) are shown here. Both axes are in log scale

;. .. Short, Left to right) The phantom with the annotated sections. Region of interest over which statistics of the estimated water fraction values are analyzed for the 14 T 2 spheres. FAE percentage maps estimated using the model, vol.54

. , The values for the estimated water fraction value for three compartments are plotted with respect to the T 2 value of the spheres. The three sections shown in the graph pertain to regions where water fractions for one compartment is dominant

. , 7) are compared in the form of Bland-Altman (BA) plots and scatter here. The BA plots compare the ROI mean values whereas the scatter plot compares values at each the voxel in ROIs. The BA plot and scatter plot statistics are summarized in Table 5.4 and 5.5 respectively, The test retest values for the estimated water fraction of three compartments in the ROIs (shown in Fig. 5

. , Water fraction maps estimated for the short T 2 , medium T 2 and high T 2 compartments for a healthy control

. , Water fraction maps estimated for the short T 2 , medium T 2 and high T 2 compartments for a MS patient

. , Evolution of the water fraction values of the short T 2 , medium T 2 and high T 2 compartments over a period of 24 months for two lesions in a MS patient

, The evolution of water fractions for the three compartments are compared for lesions and NAWM regions in MS patients, p.62

. , VARPRO cost function values for two voxels in the dense white matter region are shown here

, VARPRO cost function plots for voxels in other white matter regions, p.70

. , The VARPRO cost functions for a voxel in a free water region of the brain tissue

N. The and . Phantom, Phannie

. , This figure shows the 15 regions which were marked on the healthy controls over which the repeatability was studied

. , Left to right) First echo of the T 2 relaxometry data is shown with label annotations. The estimated water fractions maps for short T 2 , medium T 2 and high T 2 compartments are shown here, The plots show distribution of the estimated values over 1000 iterations for each SNR of the synthetic data, p.77

. , The red region in the graph denotes the T 2 values where the estimated short T 2 water fraction is greater than or equal to all other weights. In a similar manner, the green and blue regions correspond to the estimated medium T 2 and high T 2 water fraction being greater than the others respectively, The water fraction values estimated is plotted against the T 2 values of each sphere of the NIST phantom containing mono T 2 solution

. , The repeatability of the water fraction estimation in four healthy controls are compared over 15 ROIs (refer Fig. 6.5) using Bland-Altman plot (where ROI means are compared) and voxel-wise regression plot. The repeatability results for short T 2 , medium T 2 and high T 2 water fraction estimations are shown in Fig. 6.9a, 6.9b and 6.9c. The Bland-Altman and regression plot statistics for the plots shown here are summarized in Table 6

, The estimated water fraction maps for five axial slices of a healthy control are shown here. The acquired data had following specifications: echo spacing = 9ms, 32 echoes, repetition time = 3720ms, voxel resolution = 1.3mm×1.33mm×4.0mm, matrix size = 192×192, p.81

, The estimated water fraction maps and medium T 2 gamma PDF mean are shown here for a patient with MS lesions, p.82

A. , The T 2 decay curves for all a voxel from each section with the different B 1 values are shown here. The sections mentioned in the figure are the same as those annotated in Fig. A.1. The water fraction values for the sections are provided in Table A

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