Correct image encoding in MRI (manipulation of the NMR signal from the subject such that it can be used to form an image) results from the coordination and proper operation of two complex scanner subsystems:

• The gradients, which drive the encoding process; and
• RF chain, which receives the NMR signal from the subject

These subsystems must perform to specification and in synchronicity with one another. If either subsystem fails to perform within an assumed specification or falls out of sync with the other, image artifacts occur.

Let’s look at the operation and assumptions made in the gradient system and how they affect image encoding.

Assumption 1: Gradients encode data precisely following the prescribed image geometry.

MRI image formation has for the past 30 years largely relied on the Fourier Transform to convert images from the acquired ‘k-space’ to images that look like the subject. The transform assumes that the underlying k-space data is collected precisely on a grid. However, gradients do not operate precisely enough to capture data on a perfect grid. Gradient technology has improved dramatically since the first generation of MRI scanners and is much closer to this assumption. However, the assumption of encoding on a perfect grid is still often violated. Their ability to completely reproduce programmed waveforms, especially if those waveforms contain sharp trapezoids (which has been one of the standard waveform shapes in MRI for over 30 years) is a common source of issues. An example of how gradients do not accurately reproduce programmed waveforms can be seen below. On the left is a single gradient blip. The black line is the programmed waveform and yellow is the actual waveform as played out by the scanner. The right figure shows how this extends to an EPI sequence, note that the measured trajectory does not align with the programmed trajectory.

S. J. Vannesjo et al., “Gradient system characterization by impulse response measurements with a dynamic field camera: Gradient System Characterization with a Dynamic Field Camera,” Magn Reson Med, vol. 69, no. 2, pp. 583–593, Feb. 2013, doi: 10.1002/mrm.24263.

Assumption 2: Gradients are the only driver of the encoding field.

The gradients are certainly the largest driver of the encoding field, but they are not the only driver. Others include the fields generated by the interaction between gradients and other scanner hardware and patient breathing. The former has long been recognized as a source of image distortion in diffusion, where eddy currents from the diffusion encoding lobes distort the encoding field during image acquisition – leading to image stretching and skewing specific to each diffusion direction.

Diffusion encoding causes image distortion through disruption of the encoding field.

Subject breathing distorts the magnetic field as well. The total scanner field is a combination (mathematically called a convolution) of the field applied by the gradients and main magnet with the object within it (all objects distort the field, this is why shimming is needed to get the field close to homogeneous). As the subject breathes, even though the breathing may be out of the imaging field of view, the change in shape reconfigures the magnetic field slightly within the imaging FOV. When this happens during image encoding, the encoding is distorted slightly. An example of how much the field is distorted at various locations is shown below.

Y. Duerst et al., “Real-time feedback for spatiotemporal field stabilization in MR systems: Feedback for Spatiotemporal Field Stabilization,” Magn. Reson. Med., vol. 73, no. 2, pp. 884–893, Feb. 2015, doi: 10.1002/mrm.25167.

These distortions are spatially dependent – meaning the region closest to the source of the distortion is most distorted.

This can also be seen in the images, as an example, high resolution T2* weighted imaging shows shading (left) seen during normal respiration that is removed when encoding errors are accounted for.

S. J. Vannesjo et al., “Retrospective correction of physiological field fluctuations in high-field brain MRI using concurrent field monitoring,” Magnetic Resonance in Medicine, vol. 73, no. 5, pp. 1833–1843, 2015, doi: 10.1002/mrm.25303.

Because magnetic fields are spatially complex, we need to develop a way to measure and describe their value over the measurement volume in a simple format. While ideally, we would measure every single point of the field, this is not practical for imaging experiments. Hence, we need to identify a basis set (set of functions which can be combined to approximate the field) which can simplify the measurement to a smaller set. One way to represent this field is to model it as a sum of spherical harmonics. This is the same representation that the static shims use. In order to achieve a third order set of spherical harmonics, we need only 16 probes, which can easily fit into the bore at the same time as the subject, allowing for full concurrent monitoring of the field. Spherical harmonics are also convenient because they are familiar from static shimming, roughly approximate the shape of a head, and in theory each component of the set is orthogonal (contains no common information) to the others.

Spherical harmonics up to third order.

This basis set can be used to represent the magnetic field at any point in time by summing the product of each spatial basis function times a coefficient representing the strength of that basis particular basis function. The coefficients are the values measured and reported by the Skope system and are called k-coefficients. A time-course of these k-coefficients is shown below for an EPI readout.

Image top: Time course of k-coefficients in an EPI sequence; Image bottom: Magnetic field during an EPI readout (axial readout, z=0).

The figure shows the time course of the kx (blue), ky (red), and kz (beige) terms of the encoding. These can be multiplied by the corresponding basis sets and summed to give the following representation of the magnetic field, which is the encoding field for this particular readout (at z=0 axial to the bore).

Using this basis set and the corresponding measurements of the k-coefficients derived from field monitoring, image reconstruction can account for real-world gradient performance and off-grid image data acquisition – leading to images with improved geometry, higher SNR, and reduced ghosting. These measurements of the magnetic field improve imaging research and image analysis through providing more reliable, reproducible data that better reflects the underlying anatomy, without confounding information from scanner artifacts.