Improved determination of the myelin water fraction in human brain using magnetic resonance imaging through Bayesian analysis of mcDESPOT

Abstract

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.

Clinical high-resolution mapping of the proteoglycan-bound water fraction in articular cartilage of the human knee joint

“…Our work is based on the use of the BMC-mcDESPOT protocol previously described for HR mapping of MWF in the brain, in which data collected according to the mcDESPOT protocol is analyzed using Bayesian methods and a corrected signal model [14, 17]. We note that while the basic methodology for BMC-mcDESPOT has been presented previously [12, 14], there are significant challenges involved in applying this approach to cartilage, with its much shorter T 2 values, higher noise due to HR imaging and strong susceptibility effects as compared to brain. Our work builds on previously published use of mcDESPOT for PgWF determination in human cartilage at substantially lower spatial resolution [4, 5].…”

“…A set of full simulations indicating the improved performance of BMC- as compared to SRC-mcDESPOT was presented in Refs. [11, 12, 14] for a wide range of tissue parameters and SNRs, including input values encompassing typical and plausible parameters for cartilage analysis. Thus, while precision may be evaluated from the reproducibility of our human cartilage results, accuracy can be determined by the results of these simulation analyses performed with known input parameters.…”

“…To account for the off-resonance effects seen with the bSSFP images, off-resonance maps were generated according to the DESPOT 2 -FM method [16], and combined with the SPGR and bSSFP datasets to generate PgWF maps [4, 5, 12, 15]. Analysis was performed explicitly accounting for nonzero TE, as incorporated into the TE-corrected-mcDESPOT (TEC-mcDESPOT) signal model [11, 17], using an underlying two-component non-exchanging model [11, 12]. Manual segmentation was performed to delineate the cartilage regions over which PgWF maps were generated.…”

“…Wide limits for the initial parameter bounds were used to avoid an over-constrained parameter space [12, 15]. These limits were 0 ≤ f s ≤ 0.5, 1 ms ≤ T 2,s ≤ 50 ms, 30 ms ≤ T 2,1 ≤ 200 ms, 100 ms ≤ T 1,s ≤ 2000 ms and 100 ms ≤ T 1,l ≤ 3000 ms. For each of these datasets, representative PgWF maps were compared, and the mean and standard deviation (SD) of PgWF values were calculated over all cartilage regions of several slices.…”

“…In a recent studies [12, 14], it has been shown that both accuracy and precision in quantitative parameter estimates from mcDESPOT were greatly enhanced through use of a new Bayesian Monte Carlo (BMC) analysis as compared to estimates obtained using stochastic region contraction (SRC), a nonlinear least squares-based algorithm conventionally used for parameter estimation from mcDESPOT data [4, 5, 11, 12, 15]. Our principal aim in this study is to demonstrate the potential of the BMC analysis of mcDESPOT data (BMC-mcDESPOT) to provide HR maps of PgWF in human knee cartilage.…”