【Q&A in MRI】5.1.6 Filling k-space k 空间填充

一切权利归原作者所有。

原著：Allen D. Elster, MD

译注：蒋强盛

The data to fill k-space is taken directly from the MR signal. Because gradients have been applied for phase and frequency encoding, the MR signal is already in a Fourier-like format suitable for filling the k-space matrix.

填充 k 空间的数据直接来源于 MR 信号。由于 MR 信号包含了相位编码与频率编码，那么 MR 信号就已经是一个类傅立叶的格式，适合填充 k 空间矩阵。

In a prior Q&A we explained how the MR signal is detected in quadrature. Each digitized data point of the MR signal can be represented as a complex number, with real and imaginary components. Alternatively, each data point can be defined as having a magnitude and phase, computed by simple trigonometric relations. 

Representation of the MR signal in terms of real and imaginary components.

%%%%%%%%%%%%%%%

【译者注1】

The data to fill k-space is taken directly from the MR signal but can be acquired in any order. The dominant method for filling k-space over the last 30 years has been the line-by-line Cartesian method. Today spiral and radially oriented trajectories are becoming more popular. 

填充 k 空间的数据直接来源于 MR 信号，但它可以以任意的顺序进行采集填充。在过去的 30 年里，k 空间的填充方式主要是一条线一条线填充的笛卡尔方式。现在，螺旋和辐射状 k 空间填充方式越来越流行。

In the Cartesian method each digitized echo completely fills a line of k-space. The echo signal is recorded in quadrature, so each k-space point contains real and imaginary components. The k-space values on the left side of each row are obtained early in the evolution of the echo, while those on the right side are obtained later. The center of the echo (and hence largest values) occur near the middle of each row of k-space.

Cartesian (line-by-line) filling of k-space.

In 2DFT imaging, each row in k-space corresponds to the echo data obtained from a single application of the phase-encoding gradient.  By convention, rows near the center of the k-space grid are defined to correspond to low-order phase-encode steps, whereas those rows near the top and bottom correspond to higher-order phase-encodings.  Since echo amplitudes are larger at the low-order phase-encode steps (there is less gradient-induced dephasing), the values of k-space will be greater near the center of the grid. 

在二维傅立叶变换成像中，k 空间每一行的值对应于某一相位编码梯度编码的回波数据。按照惯例，k 空间网格中心附近的数据行对应于低阶相位编码步长；然而靠近 k 空间网格顶部与底部的数据行对应于高阶相位编码步长。由于低阶相位编码步长的回波幅度更大（更少的梯度导致的散相），因此填充 k 空间网格中心数据的值更大。

%%%%%%%%%%%%%%%

【译者注2】

作者这里描述的真的是太细致了，将 k 空间数据的填充结合每次的相位编码与回波信号的形成并采集填充 k 空间数据解释的很完美。

那么频率编码与相位编码又是如何包含空间频率信息的呢？我们后期将不断地进行解读，欢迎关注 CTMR技术园 并一起探索！