k-Space tutorial: an MRI educational tool for a better understanding of k-space

Abstract

A main difference between Magnetic Resonance (MR) imaging and other medical imaging modalities is the control over the data acquisition and how it can be managed to finally show the adequate reconstructed image. With some basic programming adjustments, the user can modify the spatial resolution, field of view (FOV), image contrast, acquisition velocity, artifacts and so many other parameters that will contribute to form the final image. The main character and agent of all this control is called k-space, which represents the matrix where the MR data will be stored previously to a Fourier transformation to obtain the desired image.This work introduces 'k-Space tutorial', a MATLAB-based educational environment to learn how the image and the k-space are related, and how the image can be affected through k-space modifications. This MR imaging educational environment has learning facilities on the basic acceleration strategies that can be encountered in almost all MR scanners: scan percentage, rectangular FOV and partial Fourier imaging. It also permits one to apply low- and high-pass filtering to the k-space, and to observe how the contrast or the details are selected in the reconstructed image. It also allows one to modify the signal-to-noise ratio of the acquisition and create some artifacts on the image as a simulated movement of the patient - with variable intensity level - and some electromagnetic spikes on k-space occurring during data acquisition.

Keywords: Magnetic resonance imaging; artifacts; k-space; tutorial.

Figure 1

Main window of the k-Space tutorial. At the upper part of the window we can see the k-Space (a) and its associated image (b) to which all the desired operations will be applied. After having applied the desired operations (c-h), it is also possible to save the resulting image and its k-Space

Figure 2

k-Space (left) and its associated image (right). (a) Original k-Space and its associated image. (b) Low pass filtering on the original k-Space. The resulting image only shows the contrast of the image. The information of the high spatial frequencies, that contains the details and contours of the objects, have disappeared. (c) High pass filtering, where only the high spatial frequencies have been selected in the k-Space, providing only information about the details and edges of the objects in the image domain.

Figure 3

Rectangular field of view at 50%. The spacing between phase-encodings (vertical direction) in the k-space produces a reduction of the FOV in the image in the same proportion and in the same direction (it does not affect the FOV size in the other direction).

Figure 4

Scan percentage at 30%. Only 30% of the central data of k-space has been acquired, resulting in a reduction of the spatial resolution in the image as well as in an increase of the SNR in the image.

Figure 5

Half (partial) Fourier imaging in the phase-encoding direction (vertical direction), reducing the number of phase-encoding steps necessary to reconstruct the image, and thus reducing the scan time. The non-acquired phase-encodings are filled with complex conjugate data of the other half plane. In the example shown in this figure, 20 additional phase-encodings have been acquired in the center of k-space for phase-coherence.

Figure 6

k-Space and its reconstructed image where the SNR has been adjusted to 4.04 dB.

Figure 7

Motion-related artifact, due to a severe movement of the patient, simulated using the presented k-Space tutorial.

Figure 8

Bad data points in k-space result in band artifacts on the MR image. The location of the bad data points, and their distance from the center of k-space, determine the angulation of the bands and the distance between them. The intensity of the spike determines the severity of the artifact. The displacement of the spike of noise from the center of k-space determines the spacing between the stripes and the angulation of the stripes with respect to the readout direction. The displayed images show the resulting images from two different k-spaces where a spike has been simulated using the 'k-Space tutorial'. The stripes shown in the image on the left are closer to those shown in the image on the right, indicating that the spike has occured further to the centre of its corresponding k-space (higher spatial frequency) than that of the image on the right. Following the angulation of the bands of the images, it can be known that the spike of the associated k-space of the image on the left has occured in the upper-left or in the lower-right quadrant of the k-space while the spike of the associated k-space of the image on the right has occured in the upper-right or in the lower-left quadrant of its corresponding k-space.