“…8). Details of the SRC-NLLS algorithm can be found in (25-26). Briefly, for each iteration, 20,000 random samples were generated within the specified parameter bounds.…”
Section: Methodsmentioning
confidence: 99%
“…To correspond to actual practice (24, 26, 46), the boundary conditions for the SRC-NLLS algorithm were set to 0 ≤ f s ≤ 0.6, 2 ms ≤ T 2,s ≤ 45 ms, 75 ms ≤ T 2,l ≤ 200 ms, 100 ms ≤ T 1,s ≤ 700 ms and 700 ms ≤ T 1,l ≤ 3000 ms. The same boundary conditions were used as sampling ranges for BMC.…”
Section: Methodsmentioning
confidence: 99%
“…Δω = 0 Hz), while in the experimental analyses, B 1 and Δω were calculated using the saturated double angle method (S-DAM) (35) and the DESPOT 2 -FM method (36), respectively, and used as known parameters for the calculation of the f s maps, reflecting MWF. Further, in all cases, two different bSSFP datasets were obtained with phase increments ϑ equal to 0 or π (bSSFP 0 and bSSFP π ) respectively, corresponding to the usual implementation of mcDESPOT (18-24, 26, 32). …”
Section: Theorymentioning
confidence: 99%
“…Further, we can avoid marginalization over by normalizing both the experimental and theoretical signals by their respective mean values calculated over FAs (18, 24, 26, 32): …”
Section: Theorymentioning
confidence: 99%
“…(24) showed that, even for a simple two-pool model, quantitative parameter estimation from mcDESPOT is problematic, especially at low-to-moderate SNR. This parameter instability was found to persist in spite of the use of stochastic region contraction (SRC) in combination with nonlinear least squares (SRC-NLLS) algorithm, which has been proposed as an effective procedure for extracting parameter values from mcDESPOT data (25-26). It has been found (24) that given the flatness of NLLS parameter fit energy surfaces, SRC-NLLS remains highly sensitive to local minima and requires, therefore, high SNR data for reliable estimation of MWF.…”
Myelin water fraction (MWF) mapping with magnetic resonance imaging has led to the ability to directly observe myelination and demyelination in both the developing brain and in disease. Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry and has been applied to map MWF in human brain. However, even for the simplest two-pool signal model consisting of MWF and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNR), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. In this study, we introduce three Bayesian approaches for analysis of the mcDESPOT signal model to determine MWF. Given the high dimensional nature of mcDESPOT signal model, and, thereby, the high dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of MWF parameter, the introduced Bayesian analyses use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis of in-vivo human brain datasets exhibiting a range of SNR and spatial resolution, we demonstrated the markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS.
“…8). Details of the SRC-NLLS algorithm can be found in (25-26). Briefly, for each iteration, 20,000 random samples were generated within the specified parameter bounds.…”
Section: Methodsmentioning
confidence: 99%
“…To correspond to actual practice (24, 26, 46), the boundary conditions for the SRC-NLLS algorithm were set to 0 ≤ f s ≤ 0.6, 2 ms ≤ T 2,s ≤ 45 ms, 75 ms ≤ T 2,l ≤ 200 ms, 100 ms ≤ T 1,s ≤ 700 ms and 700 ms ≤ T 1,l ≤ 3000 ms. The same boundary conditions were used as sampling ranges for BMC.…”
Section: Methodsmentioning
confidence: 99%
“…Δω = 0 Hz), while in the experimental analyses, B 1 and Δω were calculated using the saturated double angle method (S-DAM) (35) and the DESPOT 2 -FM method (36), respectively, and used as known parameters for the calculation of the f s maps, reflecting MWF. Further, in all cases, two different bSSFP datasets were obtained with phase increments ϑ equal to 0 or π (bSSFP 0 and bSSFP π ) respectively, corresponding to the usual implementation of mcDESPOT (18-24, 26, 32). …”
Section: Theorymentioning
confidence: 99%
“…Further, we can avoid marginalization over by normalizing both the experimental and theoretical signals by their respective mean values calculated over FAs (18, 24, 26, 32): …”
Section: Theorymentioning
confidence: 99%
“…(24) showed that, even for a simple two-pool model, quantitative parameter estimation from mcDESPOT is problematic, especially at low-to-moderate SNR. This parameter instability was found to persist in spite of the use of stochastic region contraction (SRC) in combination with nonlinear least squares (SRC-NLLS) algorithm, which has been proposed as an effective procedure for extracting parameter values from mcDESPOT data (25-26). It has been found (24) that given the flatness of NLLS parameter fit energy surfaces, SRC-NLLS remains highly sensitive to local minima and requires, therefore, high SNR data for reliable estimation of MWF.…”
Myelin water fraction (MWF) mapping with magnetic resonance imaging has led to the ability to directly observe myelination and demyelination in both the developing brain and in disease. Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry and has been applied to map MWF in human brain. However, even for the simplest two-pool signal model consisting of MWF and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNR), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. In this study, we introduce three Bayesian approaches for analysis of the mcDESPOT signal model to determine MWF. Given the high dimensional nature of mcDESPOT signal model, and, thereby, the high dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of MWF parameter, the introduced Bayesian analyses use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis of in-vivo human brain datasets exhibiting a range of SNR and spatial resolution, we demonstrated the markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS.
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