Target Audience

Researchers interested in non-cartesian readouts, including but not limited to readouts for diffusion MRI, and iterative image reconstruction, including information from dynamic field monitoring.

Outcome

Audience members will learn:

• the advantages and disadvantages of spiral vs EPI readouts
• how to recognise common artefacts in spiral images and where there causes
  
• how to determine true k-space trajectory
• how k-space and B0 inhomogeneity information can be included in the image reconstruction

Purpose

Echo-planar imaging (EPI) is the work horse in diffusion weighted imaging with its cartesian readout trajectory. It allows for 2D single shot imaging, that is acquiring the data necessary to get the image of a whole slice with a single excitation. This is achieved by traversing the k-space line by line from one end to the other with the centre of k-space acquired at the echo time (TE). This leads to a prolonged TE and thus reduced signal to noise ratio (SNR), since k-space lines acquired before reaching the centre need to fit in TE.
This disadvantage can be overcome by changing the readout trajectory starting in the centre of k-space and going outwards, e.g. in a spiral. This change in readout trajectory leads to a shorter TE at the cost of adding complexity to image reconstruction. For one, the image cannot be reconstructed with a simple fast Fourier transform. Additionally, field inhomogeneities and k-space trajectory need to be well known to obtain high quality images. Because of gradient imperfections (e.g. delays or eddy currents) the true and prescribed k-space trajectories can differ notably. This discrepancy increases when using strong gradients, e.g. for diffusion weighting, as they cause major field perturbations due to eddy currents. For EPI acquisitions these translate mostly to geometric distortions which can be ameliorated after the image has been reconstructed. Many of the methods developed for EPI are not applicable with spiral readouts as the field distortions mostly lead to image blurring.
In this talk, I will give a short introduction into the different methods of measuring the real k-space trajectory, before explaining the advanced signal model. I will show how to include the different sources of artefacts into the model for the reconstruction of high-quality images.

Methods

A reduction in image artefacts can be achieved by using the true k-space trajectory during the image reconstruction. This trajectory can be determined with different approaches. One of the most popular being spatio-temporal field monitoring [1], where a number of field probes (basically small NMR experiments that are placed inside the main magnet) determine the local field at different positions. By fitting a set of spatial basis functions (mostly spherical harmonics, $$$b_l(\mathbf {r})$$$ ) the field distribution can be determined at each time point and thus the k-space trajectory can be reconstructed. Another approach is the use of the gradient impulse response function (GIRF) [2], which allows us to relate the prescribed gradient shape to the one played out by the MRI. The GIRF describes how the scanner would play out a very short gradient pulse. By convolving this with the prescribed gradient shape, the actual gradient profile can be determined. Both approaches can also be used to determine higher order spatial magnetic field variations.
When only the terms up to linear field variations are considered, the image can be reconstructed with a gridding approach, which is fairly fast but does not account for many potential sources of artefacts. With the expanded signal model [3], this information can be included in the image reconstruction. This model includes the real k-space trajectory, including higher order terms, ($$$k_l(t) b_l(\mathbf{r})$$$) and field inhomogeneities ($$$\Delta B(\mathbf{r})$$$) in the MRI signal ($$$s(t)$$$) equation (not including coil sensitivities):
$$
s(t) = \int_V m(\mathbf{r}) e^{i\sum_l k_l(t) b_l(\mathbf{r})} e^{i \gamma \Delta B (\mathbf{r}) t} dV
$$
With the magnetisation $$$m(\mathbf{r})$$$ the gyromagnetic ratio $$$\gamma$$$ and the imaging volume $$$V$$$. The reconstruction, in this case, is based on an iterative approach (with conjugate gradients method). This is slower than gridding but normally yields images with less artefacts.