Fine Adjustment of Gradient Scaling for MR

Topics covered in this article:

• Introduction
• Identifying Gradient Distortion
• Procedure for Mitigating Gradient Bias
• Modified Procedure to Isolate Gradient Distortions

Introduction

A primary feature of the Magphan RT® phantom is the ability to analyze spatial distortion over a large scan field via the phantom's large number of precisely-positioned fiducial spheres.  Data from distortion measurements can be used to fine tune an MR platform's gradient calibration to an accuracy that can exceed normal scaling specifications of a typical system.  

The method involves removing as much gradient distortion as possible by adjusting the machine's gradient scaling coefficients. It is an adjustment that can be made relatively easily with the help of a service engineer from the manufacturer and can make a non-negligible improvement on the distortion.  Procedures involved with this process are detailed below.

The initial procedure assumes that scaling distortion is dominated by the MR platform's gradient system, rather than the static magnetic field.  An additional procedure is described that does not use this assumption.

Identifying Gradient Distortion

The figure below shows the 3x3 distortion plot generated by the software analysis, which conveys the spatial pattern of the geometric distortion across the entire scan. In each graph, each circle corresponds to a fiducial marker within the phantom. The vertical axis of each plot shows the location of the fiducial within the scanner, along one of three axes: L/R (left/right), A/P (anterior/posterior), and H/F (head/foot). The horizontal axis shows the measured distortion of each fiducial (relative to its known position) along one of the three dimensions. If an ideal scanner with zero distortion existed, the circles in each plot would lie on a vertical line at a horizontal value of zero, representing every sphere location along the given dimension, and the lack of any distortion. 

Positive/negative sign conventions are those defined by the DICOM standard with Left, Posterior and Superior (Head) assigned as positive. These correspond to patient coordinates, which typically default to HFS (Head-First-Supine), with the patient on their back moving head-first into the scanner. Thus, in the usual HFS patient positioning, the L/R axis corresponds to what MR manufacturers would typically call the ‘x’ axis (horizontal transverse), the A/P coordinate would correspond to the ‘y’ axis (vertical), and the H/F direction would correspond to the ‘z’ axis (along the bore of the scanner). 

Of particular interest in distortion plot sets are the three graphs along the diagonal from top-left to bottom-right. These distortion plots often show a slight linear bias away from vertical, as is evident in the set above. On those three graphs, this linear bias represents a small offset in the scaling factor for the gradient axis. A scanner can be well within specification but still show scaling offset; due to the 100:1 ratio in vertical and horizontal graph scales, even a 1% scaling offset (which is a typical specification limit for a manufacturer’s gradient calibration) appears as a strong bias in these graphs.

This scaling offset can be mitigated by adjusting the gradient scaling parameters on the scanner. This document outlines a procedure for using this data to make that adjustment with the help of a service engineer from the manufacturer. It is not recommended to perform this procedure without following up with the normal gradient scaling tests done by the manufacturer to ensure that the scanner still operates within the specifications as measured by the manufacturer’s procedures. 

Procedure for Gradient Bias Mitigation

1. Acquire a 3D set of images, ensuring that the patient positioning is set to ‘HFS’ (Head-First Supine) in the acquisition. This is the usual default setting on MR scanners. The phantom should be positioned as close to isocenter in all three directions as is practical.
2. Run the analysis software to produce the 3x3 distortion plot.  To add this test result to your schedule, see the instructional article here.
3. On each of the three diagonal plots, estimate the bias for each axis by drawing, either by eye or with a graphical tool of your choice, a line that reflects the bias, as in the example below. In this example, the bias line intercepts the 100 mm position on the vertical axis at approximately -0.4 mm. Thus the scaling adjustment needed to reverse this bias is +0.4%. Because the intercept is at -0.4 instead of positive 0.4, the images are distorted with a ‘shrinking’ distortion, and so the gradient calibration needs to make the images look larger by a positive factor of 0.4% to undo the effect.

   

4. Once the percent adjustment needed is calculated, ask the manufacturer’s service engineer to adjust the gradient scaling calibration accordingly.
5. Once the adjustment is made, acquire another image set of the phantom and run the analysis software to get a new 3x3 plot. The linear bias should be largely removed. Note: If the bias correction is applied with the wrong sign, the linear bias will approximately double rather than being removed, and the adjustment needs to be made in the opposite direction.
6. If the results of the new 3x3 plots are satisfactory, the service engineer should then perform the usual gradient scaling calibration measurement, without any adjustment, to ensure that the gradient scaling is within the manufacturer’s specifications according to their own procedures.

An example of what a 3x3 plot would look like with the linear bias removed is shown below.

Modified Procedure to Isolate Gradient Distortions

The procedure described above assumes that most of the scaling distortion comes from the gradient system. This is likely a sufficiently accurate assumption, but it is not empirically necessary to make. An augmented procedure can be performed to eliminate this assumption.

The augmented procedure uses the fact that distortion in a phase encode direction does not depend upon the constant background magnetic field - it can only be due to the gradient system. Thus, in the augmented procedure, multiple acquisitions are taken, and only those directions corresponding to a phase encode direction are used to measure the scaling offset. 

In a 2-D pulse sequence, there is one phase encode direction, which is selected on the scanner interface while prescribing the sequence. Thus, three separate acquisitions would need to be taken, with the phase encode direction placed along a different dimension for each of the three sequences.

As an example, if the original sequence is an axial scan with the phase encode in the L/R direction, then the second scan could be an axial scan with phase encode in the A/P direction. The third scan could be either sagittal or coronal, with phase encode in the Superior/Inferior (H/F) direction. In the first scan, the top-left graph would be used to measure the scaling along the x-axis, the second scan would be used to measure scaling in the y-direction using the central graph, and the third scan would be used to measure scaling in the S/I direction using the lower right graph in the 3x3 plot.

In a 3-D type sequence, there are two phase encode directions, so only two acquisitions would need to be taken. So, for example, the phase and frequency encode directions could be swapped on the second acquisition. 

As an example for a 3-D sequence, if the original scan is an axial scan with phase encoding in the A/P direction, the middle and lower graphs would both be phase encode directions corresponding to the y- and z-axes, respectively. A second scan could also be an axial scan with phase encoding moved to the L/R direction, and the upper left graph would be used to measure the scaling in the x-direction.