Bayesian analysis of transverse signal decay with application to human brain

Spencer

2016

NeuroImage

Self Cite

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.

Section: Discussionsupporting

confidence: 93%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Spencer

2016

NeuroImage

Self Cite

“…For mcDESPOT, the bSSFP signals were generated for FAs of θ ° = {2, 6, 14, 22, 30, 38, 46, 54, 62, 70} and TR bSSFP = 6.5 ms, while the SPGR signals were generated for FAs of θ ° = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} and TR SPGR = 6.5 ms. For CPMG, signals were generated for 32 echoes with TE increasing linearly from 8 to 256 ms. All simulations used input parameters T 2, s = 15 ms, T 2, l = 90 ms, T 1, s = 450 ms, and T 1, l = 1400 ms; these are based on reported values from human brain imaging (1–4,7,8,16,17,24). All numerical calculations were performed using routines developed inhouse with MATLAB (MathWorks, Natick, Massachusetts, USA).…”

Section: Methodsmentioning

confidence: 99%

Analysis of mcDESPOT‐ and CPMG‐derived parameter estimates for two‐component nonexchanging systems

Magnetic Resonance in Med

Reiter

Çelik

et al. 2015

Self Cite

Purpose To compare the reliability and stability of the multicomponent-driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) and Carl-Purcell-Meiboom-Gill (CPMG) approaches to parameter estimation. Methods The stability and reliability of mcDESPOT and CPMG-derived parameter estimates were compared through examination of energy surfaces, evaluation of model sloppiness, and Monte Carlo simulations. Comparisons were performed on an equal time basis and assuming a two-component system. Parameter estimation bias, reflecting accuracy, and dispersion, reflecting precision, were derived for a range of signal-to-noise ratios (SNRs) and relaxation parameters. Results The energy surfaces for parameters incorporated into the mcDESPOT signal model exhibit flatness, a complex structure of local minima, and instability to noise to a much greater extent than the corresponding surfaces for CPMG. Although both mcDESPOT and CPMG performed well at high SNR, the CPMG approach yielded parameter estimates of considerably greater accuracy and precision at lower SNR. Conclusion mcDESPOT and CPMG both permit high-quality parameter estimates under SNR that are clinically achievable under many circumstances, depending upon available hardware and resolution and acquisition time constraints. At moderate to high SNR, the mcDESPOT approach incorporating two-step phase increments can yield accurate parameter estimates while providing values for longitudinal relaxation times that are not available through CPMG. However, at low SNR, the CPMG approach is more stable and provides superior parameter estimates.

“…In particular, analyses of factors that result in signal deviation from the ideal SPGR and bSSFP models are needed. These factors include diffusion [20, 21], magnetization transfer [22], signal modeling [23], magnetization spoiling [24, 25], magic angle effects [26], internal gradients [27, 28] and noise distribution [29, 30]. Nevertheless, the present work stands to indicate the feasibility of high quality in-vivo HR mapping of PgWF in articular cartilage of the human knee joint in an acceptable clinical acquisition time through use of BMC-mcDESPOT.…”

Section: Discussionmentioning

confidence: 99%

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

Magnetic Resonance Imaging

Reiter

Sexton

et al. 2017

Self Cite

Purpose we applied a recently introduced method to achieve clinically-feasible in-vivo mapping of the proteoglycan water fraction (PgWF) of human knee cartilage with improved spatial resolution and stability as compared to existing methods. Material and Methods Multicomponent driven equilibrium single-pulse observation of T1 and T2 (mcDESPOT) datasets were acquired from the knees of two healthy young subjects and one older subject with previous knee injury. Each dataset was processed using Bayesian Monte Carlo (BMC) analysis incorporating a two-component tissue model. We assessed the performance and reproducibility of BMC and of the conventional analysis of stochastic region contraction (SRC) in the estimation of PgWF. Stability of the BMC analysis of PgWF was tested in two independent high-resolution (HR) datasets from each of the two young subjects. Results Unlike SRC, the BMC-derived maps from the two HR datasets were essentially identical. Furthermore, SRC maps showed substantial random variation in estimated PgWF, and mean values that differed from those obtained using BMC. In addition, PgWF maps derived from conventional low-resolution (LR) datasets exhibited partial volume and magnetic susceptibility effects. These artifacts were absent in HR PgWF images. Finally, our analysis showed regional variation in PgWF estimates, and substantially higher values in the younger subjects as compared to the older subject. Conclusions BMC-mcDESPOT permits HR in-vivo mapping of PgWF in human knee cartilage in a clinically-feasible acquisition time. HR mapping reduces the impact of partial volume and magnetic susceptibility artifacts compared to LR mapping. Finally, BMC-mcDESPOT demonstrated excellent reproducibility in the determination of PgWF.