Özarslan Evren, Westin Carl-Fredrik, Mareci Thomas H
Department of Physics, Bođaziçi University, Bebek, Ýstanbul, Turkey; Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Concepts Magn Reson Part A Bridg Educ Res. 2015 Jul;44(4):203-213. doi: 10.1002/cmr.a.21354. Epub 2015 Dec 21.
The influence of Gaussian diffusion on the magnetic resonance signal is determined by the apparent diffusion coefficient (ADC) and tensor (ADT) of the diffusing fluid as well as the gradient waveform applied to sensitize the signal to diffusion. Estimations of ADC and ADT from diffusion-weighted acquisitions necessitate computations of, respectively, the -value and -matrix associated with the employed pulse sequence. We establish the relationship between these quantities and the gradient waveform by expressing the problem as a path integral and explicitly evaluating it. Further, we show that these important quantities can be conveniently computed for any gradient waveform using a simple algorithm that requires a few lines of code. With this representation, our technique complements the multiple correlation function (MCF) method commonly used to compute the effects of restricted diffusion, and provides a consistent and convenient framework for studies that aim to infer the microstructural features of the specimen.
高斯扩散对磁共振信号的影响由扩散流体的表观扩散系数(ADC)和张量(ADT)以及用于使信号对扩散敏感的梯度波形决定。从扩散加权采集中估计ADC和ADT分别需要计算与所采用脉冲序列相关的-值和-矩阵。我们通过将问题表示为路径积分并明确求值来建立这些量与梯度波形之间的关系。此外,我们表明使用一个只需几行代码的简单算法就可以方便地为任何梯度波形计算这些重要量。通过这种表示,我们的技术补充了常用于计算受限扩散效应的多重相关函数(MCF)方法,并为旨在推断样本微观结构特征的研究提供了一个一致且方便的框架。