Demonstration Code for Gradient Impulse Response Function (GIRF) Calculation and Analysis

This is the demonstration code of the abstract MR Gradient System Long-Term Stability Investigation and Protocol Optimization for Quality Control using Gradient Impulse Response Function (GIRF) by Zhe Wu, Alexander Jaffray, Johanna Vannesjo, Kamil Uludag, and Lars Kasper for the Joint Annual Meeting ISMRM-ESMRMB & ISMRT 31st Annual Meeting, which will be held in London UK, between May 7 - 12, 2022. The full information of this abstract can be found in references, and the PDF version of the published abstract can be found here.

Copyright (C) 2021-2022
Zhe "Tim" Wu
zhe.wu@rmp.uhn.ca

Brain Research in Advanced Imaging and Neuromodeling - Toronto (BRAIN-TO) Lab
Techna Institute
University Health Network

Quick Start

1. Download the demonstration data from here and extract them under the same folder. See details of the description of each file in the section Dataset for Demonstration.

2. In the main.m file, change the variables under the section "Set User Parameters". Set the variable dataPath as the path that stores all the downloaded data; set the variable gradientAxis to the gradient axis that needs to be analysed (choose from 'X', 'Y', and 'Z', case insensitive); set the variable measNum to the measurement dataset to be analysed (only applicable to script_OriginGIRFCalculation.m, see the following section Script List and the instructions inside this script for details).

3. Run the main.m file and all the demo scripts should be executed. You may change the variable gradientAxis to check the other gradient axis.

Dataset for Demonstration

The demonstration data used by the code in this repository can be found here. There are three .zip files and they should be copied to and be extracted under the same folder.

The demonstration data contains three parts:

1. Meas1.zip contains raw T2* decay signal acquired only with the positive triangle blips using phantom-based method (See Figure 1 in the abstract).

2. Meas2.zip contains raw T2* decay signal acquired with both positive and negative triangle blips using phantom-based method（See Figure 1 in the abstract). This data was acquired 8 months after the acquisition of Meas1.zip.

3. CalculatedGIRF.zip provides the author's pre-calculated GIRFs using the data without coil averaging. This data is used for all the postprocessing (e.g., SNR and stability analysis, comparison between original and optimized GIRF methods, etc.) in the published abstract with the source code provided in the same Github repository.

Please note that the raw T2* decay signal in Meas1.zip and Meas2.zip is only for the purpose of demonstrating GIRF calculations (using blips with single polarity and dual polarities) - they are NOT used in the analysis in the abstract. The reason is that we averaged across the coil dimension of raw to save data volume for demonstration purposes, which leads a reduced SNR of the calculated output gradients and GIRFs. For the analysis of GIRF (SNR, stability, etc.) we use the pre-calculated GIRFs in CalculatedGIRF.zip.

Script List

1. main.m executes all the following scripts. The users need to set the path of the downloaded data and the axis they would like to calculate or analysis. Alternatively, each following scripts can be run individually.

2. script_OriginGIRFCalculation.m demonstrates the calculation of GIRF using the original method (positive blips only).

3. script_OptimizedGIRFCalculation.m demonstrates the calculation of GIRF using the optimized method (both positive and negative blips).

4. script_GIRFStability.m analyses stability of GIRFs in 8-month gap (Figure 3 C-E).

5. script_GIRFDiffBetweenMethods.m compares the GIRF results from two calculation methods (Figure 4 top row).

6. script_SNRAnalysis.m analyses the SNR level of the GIRF results from two calculation methods (Figure 4 bottom row).

Figure List

All the figures of the abstract are in the folder figures/.

Figure 1

Figure 1 (A) Slice positions, in which only two out of three directions were indicated. (B) Reference scans were inserted between acquisition of every two blip amplitudes. (C) Measurements for long-term stability and protocol optimization studies.

Figure 2

Figure 2 Magnitude & phase for GIRF in frequency domain for both measurements for all three gradient axis. The blue curves indicate the mean of 50 repetitions, and the orange shadows in magnitude part of the frequency domain GIRF indicate the standard deviation of the noise. Gradient delays were estimated by fitting the phase ramp.

Figure 3

Figure 3 (A - B) Frequency spectrums of typical spiral and EPI readout gradients, the dashed lines show the frequency threshold of 99% of total power deposition. (C-E) Measured GIRF on Gx, Gy and Gz for two measurement in the 8-month period, together with their difference. Two frequency ranges (-3.2 – 3.2 kHz shown as green, and -14.6 – 14.6 kHz shown as orange) are chosen and the maximum relative differences in these ranges of GIRF are shown.

Figure 4

Figure 4 Top row: GIRF before and after protocol optimization and their differences. Bottom row: The SNR before and after protocol optimization. The improvements of the peak SNR and the averaged SNR are listed in each subfigure, using the ratios of SNR between two methods.

Figure 5

Figure 5 EPI and Spiral trajectories (whose frequency spectrums are shown in Figure 3A and 3B) before and after correction using GIRFs in long-term and protocol optimized studies. A and B: Zoomed-in EPI trajectories; C and D: Zoomed-in spiral trajectories. All trajectories are in unit of rad/m.

Execution Efficiency and Required Resources

The code in this repository were tested on a laptop equipped with Intel Core i7-8850H @ 2.60 GHz.

Execution time (all scripts through main.m): < 10 seconds.

Peak RAM capacities needed: < 3GB.

References

The Corresponding ISMRM 2022 Abstract to This Repository Wu, Z., Jaffray, A., Vannesjo, S.J., Uludag, K., Kasper, L., 2022. MR System Stability and Quality Control using Gradient Impulse Response Functions (GIRF). Proc. Intl. Soc. Mag. Reson. Med. 30, 0641. Link

Gradient system characterization Vannesjo, S.J., Haeberlin, M., Kasper, L., Pavan, M., Wilm, B.J., Barmet, C., Pruessmann, K.P., 2013. Gradient system characterization by impulse response measurements with a dynamic field camera. Magn Reson Med 69, 583–593. Link

Image reconstruction based on the GIRF characterization Vannesjo, S.J., Graedel, N.N., Kasper, L., Gross, S., Busch, J., Haeberlin, M., Barmet, C., Pruessmann, K.P., 2016. Image reconstruction using a gradient impulse response model for trajectory prediction. Magn Reson Med 76, 45–58. Link

GIRF-based spiral fMRI Graedel, N.N., Kasper, L., Engel, M., Nussbaum, J., Wilm, B.J., Pruessmann, K.P., Vannesjo, S.J., 2019. Feasibility of spiral fMRI based on an LTI gradient model. bioRxiv 805580. Link

GIRF-based pre-emphasis of gradient or shim channels Vannesjo, S.J., Duerst, Y., Vionnet, L., Dietrich, B.E., Pavan, M., Gross, S., Barmet, C., Pruessmann, K.P., 2017. Gradient and shim pre-emphasis by inversion of a linear time-invariant system model. Magn Reson Med 78, 1607–1622. Link