Recently, a number of magnetic resonance imaging protocols have been reported that seek to exploit the effect of dissolved oxygen (O2, paramagnetic) on the longitudinal 1H relaxation of tissue water, thus providing image contrast related to tissue oxygen content. However, tissue water relaxation is dependent on a number of mechanisms and this raises the issue of how best to model the relaxation data. This problem, the model selection problem, occurs in many branches of science and is optimally addressed by Bayesian probability theory. High signal-to-noise, densely sampled, longitudinal 1H relaxation data were acquired from rat brain in vivo and from a cross-linked bovine serum albumin (xBSA) phantom, a sample that recapitulates the relaxation characteristics of tissue water in vivo. Bayesian-based model selection was applied to a cohort of five competing relaxation models: (1) monoexponential, (2) stretched-exponential, (3) biexponential, (4) Gaussian (normal) R1-distribution, and (5) gamma R1-distribution. Bayesian joint analysis of multiple replicate datasets revealed that water relaxation of both the xBSA phantom and in vivo rat brain was best described by a biexponential model, while xBSA relaxation datasets truncated to remove evidence of the fast relaxation component were best modeled as a stretched exponential. In all cases, estimated model parameters were compared to the commonly used monoexponential model. Reducing the sampling density of the relaxation data and adding Gaussian-distributed noise served to simulate cases in which the data are acquisition-time or signal-to-noise restricted, respectively. As expected, reducing either the number of data points or the signal-to-noise increases the uncertainty in estimated parameters and, ultimately, reduces support for more complex relaxation models.

中文翻译：

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NMR 数据的贝叶斯建模：使用组织水松弛模拟物（交联牛血清白蛋白）量化体内和体外的纵向松弛


最近，已报道了许多磁共振成像协议，这些协议试图利用溶解氧（O2，顺磁性）对组织水纵向 1H 弛豫的影响，从而提供与组织氧含量相关的图像对比度。然而，组织水弛豫取决于多种机制，这就提出了如何最好地对弛豫数据进行建模的问题。这个问题，即模型选择问题，出现在许多科学分支中，并且可以通过贝叶斯概率论得到最佳解决。高信噪比、密集采样、纵向 1H 松弛数据是从体内大鼠大脑和交联牛血清白蛋白 (xBSA) 模型中获取的，该模型重现了体内组织水的松弛特性。基于贝叶斯的模型选择应用于五个竞争松弛模型的队列：(1) 单指数、(2) 拉伸指数、(3) 双指数、(4) 高斯（正态）R1 分布和 (5) 伽玛 R1 -分配。对多个重复数据集的贝叶斯联合分析表明，xBSA 模型和体内大鼠大脑的水弛豫最好通过双指数模型来描述，而截断以消除快速弛豫成分证据的 xBSA 弛豫数据集最好建模为拉伸指数。在所有情况下，估计的模型参数都与常用的单指数模型进行了比较。降低弛豫数据的采样密度和添加高斯分布噪声分别用于模拟数据采集时间或信噪比受限的情况。 正如预期的那样，减少数据点的数量或信噪比会增加估计参数的不确定性，并最终减少对更复杂的松弛模型的支持。