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

多组分驱动平衡单脉冲观测T_1和T_2（mcDESPOT）是一种快速的多组分弛豫测量方法。然而，即使对于由髓磷脂相关和非髓磷脂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数仍然很高。这使得参数估计困难，特别是在低到中等信噪比（SNR）下，这是由于局部最小值的存在以及用于使用常规的基于非线性最小二乘（NLLS）的参数确定的拟合残余能量表面的平坦性。 算法 我们已经介绍了贝叶斯方法的mcDESPOT信号模型的分析，以稳定的分析。鉴于mcDESPOT信号模型的高维性质，因此需要对多余参数进行高维边缘化以推导MWF的后验概率分布，此处介绍的贝叶斯分析使用不同的方法来降低参数空间的维数。第一种方法使用通过平均信号幅度的归一化，并且假设噪声 可以从图像的无信号区域精确地估计。第二种方法同样使用平均幅度归一化，但通过边缘化将噪声作为未知变量进行全面处理。第三种方法不使用幅度归一化，并且结合了噪声和信号幅度的边缘化。通过大量的Monte Carlo数值模拟和分析，我们证明了显着提高的准确性和精度估计MWF使用这些贝叶斯方法相比，随机区域收缩（SRC）实施NLLS。 这些方法是通用的，并已被应用于映射在人体膝关节在体内的蛋白多糖含量。

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.