Jensen Jens H
Center for Biomedical Imaging, Medical University of South Carolina, Charleston, SC, USA; Department of Radiology and Radiological Science, Medical University of South Carolina, Charleston, SC, USA.
Magn Reson Imaging. 2015 Nov;33(9):1182-1186. doi: 10.1016/j.mri.2015.07.001. Epub 2015 Jul 26.
A fundamental theoretical result for diffusion MRI is the formula by Stejskal showing that the diffusion NMR signal is proportional to the Fourier transform of the diffusion displacement probability density function. Here this result is extended to multiple-pulsed diffusion MRI (MP-dMRI) by using a higher dimensional q-space formalism to express the diffusion-weighted signal for a sequence with N diffusion wave vectors in terms of a Fourier transform of a diffusion displacement probability density function in a 3N-dimensional space. As an illustration of the application of this extended version of Stejskal's formula, it is used to analyze the cumulant expansion of the signal magnitude for MP-dMRI.
扩散磁共振成像的一个基本理论结果是斯泰伊卡尔给出的公式，该公式表明扩散核磁共振信号与扩散位移概率密度函数的傅里叶变换成正比。在此，通过使用更高维的q空间形式体系，将这一结果扩展到多脉冲扩散磁共振成像（MP-dMRI），以便根据3N维空间中扩散位移概率密度函数的傅里叶变换来表示具有N个扩散波矢的序列的扩散加权信号。作为斯泰伊卡尔公式这一扩展版本应用的一个示例，它被用于分析MP-dMRI信号幅度的累积量展开。
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