Multicompartment quantification of tissue in vitro and in vivo with magnetic resonance imaging and spectroscopy

多组分驱动的T1和T2平衡单脉冲观测(McDESPOT)被认为是一种快速的多组分弛豫测量方法。然而，即使对于由髓鞘相关水和非髓鞘相关水组成的最简单的两池信号模型，用于获得MWF估计的参数空间的维度仍然很高。这使得参数估计变得困难，特别是在中低信噪比(SNR)时，这是由于局部极小的存在以及用于使用传统的基于非线性最小二乘(NLLS)的参数确定的拟合剩余能量表面的平坦性 算法。我们引入了贝叶斯方法来分析mcDESPOT信号模型，以稳定分析。鉴于mcDESPOT信号模型的高维特性，并且因此对于推导MWF的后验概率分布所需的干扰参数的高维边际化，这里介绍的贝叶斯分析使用不同的方法来降低参数空间的维度。第一种方法使用按平均信号幅度进行归一化，并假设噪声 可以准确地从图像的无信号区域进行估计。第二种方法同样使用平均幅度归一化，但通过边际化将噪声作为未知变量进行了全面处理。第三种方法不使用幅度归一化，并且结合了对噪声和信号幅度的边际化。通过大量的蒙特卡罗数值模拟和分析，我们表明，与NLLS的随机区域收缩(SRC)实现相比，使用这些贝叶斯方法估计MWF的准确度和精确度都有显著提高。这些方法是通用的，并已被应用于在活体内定位人类膝关节中的蛋白多糖含量。

Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry. However, even for the simplest two-pool signal model consisting of myelin-associated 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 (SNRs), 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. We have introduced Bayesian approaches for analysis of the mcDESPOT signal model to stabilize the analysis. Given the high-dimensional nature of the mcDESPOT signal model, and, therefore the high-dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of the MWF, the Bayesian analyses introduced here 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, we demonstrated 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. These methods are general and have been applied to mapping proteoglycan content in the human knee in vivo.