2009 Bragi Sveinsson
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Correction of magnetic field distortion in EPI images
Magnetic field inhomogeneities are the most common cause of distortions in fMRI images, which make matching of data to the high-resolution structural images difficult. Various methods have been proposed to correct for this distortion. For this project, some of these methods were examined and tested on EPI data. In particular, a toolbox based on magnetic field mapping methods and developed for the SPM software environment, was tested on EPI data provided by the VISTA lab. Furthermore, the toolbox was integrated better into the mrVista software environment to make it work without installing SPM.
Background
Causes of field disturbances
The main reason for magnetic field disturbances in MRI imaging is the different magnetic susceptibility of the different materials in the brain. A material's magnetic susceptibility is the degree of magnetization of the material when an outside magnetic field is applied. In areas of the head where two materials with different susceptibilities meet, especially near cavities such as the sinuses in the frontal lobe or the ear canals in the temporal lobes where you have a junction of water and air, the magnetic field will behave in a way that looks quite erratic. The exact disturbance of the field will behave on the size and shape of the cavity and its orientation relative to the magnetic flux, and will thus change should the subject move in the scanner.
Disturbances can also arise when you have blood flow in nearby large vessels, such as around the sagittal sinus, although this effect is less of a problem.
The effect of field disturbances on EPI images
During EPI imaging, each voxel in the object being imaged emits a series of echoes that identify its position - the frequency within the echoes gives its position in the frequency encode direction, and the phase difference between consecutive echoes gives its position in the phase-encode direction.
Field disturbances at a particular point in space cause the field to be slightly different than what would be expected under normal condition at that point. Then, during read-out, its signal will have a slightly different frequency than normal (we recall that the Larmor frequency varies linearly with field strength) so when the image is constructed the corresponding voxel will be displaced in the frequency encode direction. The magnitude of this displacement depends on the magnitude of the field disturbance. Since the disturbance magnitude is usually very small compared to the gradient field, this effect in the frequency encode direction is usually negligible. However, this change in frequency also leads to a change in phase difference between consecutive echoes. This causes a displacement in the phase encoded direction as well, and since this disturbance affects the measurement through the whole read-out but the gradient is only applied for a short time, this displacement can be considerable and can not be neglected.
The effects from this can be minimized by making the read-out time shorter or applying the gradient for a longer time period, but this generally results in lower image resolution unless more advanced techniques of spatial encoding are used. That leads us to correcting for these errors using magnetic field map techniques. Other methods, such as the use of shimming coils, exist for correcting these errors as well but those methods are beyond the scope of this project.
Magnetic field mapping
A field map of the main magnetic field is created by acquiring two images of the signal phase with slightly different echo times. The difference between the phase images at each voxel is proportional to the strength of the field. If the field is completely uniform, the phase difference induced by the different echo times will be the same in all voxels and the resulting image will have a uniform magnitude. If the field is not uniform, the two images should show a difference in phase, which can be attributed to a longer time for disturbance induced phase to evolve when the echo-time is longer. So the difference between the two images will tell us how fast the signal phase changes, which gives us a frequency map through the equation
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The frequency map can then be used to generate a field map through the Larmor equation:
The field map can then, in theory, be used to resample the distorted image so that all field distortions are corrected for.
Practical problems with magnetic field mapping
Phase wrapping
One problem with the approach described above to produce the frequency map, and subsequently the field map, is that \delta \phi is periodic (with period 2 \pi) in its effect on the image, i.e. there is no way to tell whether a perceived phase difference between the two images is truly \delta \phi or \delta \phi + 2\pi. This can lead to wrong estimations of frequency shift, for example if the true phase difference is 13\pi/6 and the echo time difference is 20 ms, then the correct frequency shift would be about 58 Hz, but there would be a danger of determining the frequency shift to be \pi/6 and thus get a frequency estimate of 34 Hz.
This can be dealt with using a short enough echo-time difference for it to be highly unlikely that a phase difference larger than \pi would ever be obtained. However, this leads to most values of phase shift being very low and hardly distinguishable from noise.
Another approach is to use phase unwrapping - add/subtract a value of 2\pi whenever we see a jump in phase of more than \pi, as shown in the figure below.
\figure
However, using this method, whenever an error is made (which most often happens in regions of low signal-to-noise ratio, such as in air or bone), then the error will propagate through all subsequent voxels. Therefore, it is quite important to make every effort to prevent such errors. This is usually done either by starting the unwrapping in an area with high SNR, so any errors will likely occur late in the process and affect fewer voxels, or by dividing the brain into regions, where each region should have a small face shift, and the use the unwrapping procedure on the region boundaries. Both approaches are tested in this project.
Choice of phase-mapping sequence
In theory, it should not matter whether the method of phase mapping described above uses an EPI sequence or a non-EPI sequence. Using EPI measurements for the fieldmap gives us a fieldmap in distorted space, which then has to be inverted and should then theoretically be the same as a fieldmap based on non-EPI data. However, this is most often not the case, and the reasons are not well known. However, empirical evidence suggests that EPI-based fieldmaps give better results than the alternative. This project solely uses EPI based fieldmaps since other data was not available.
Methods
How to use the software
Once mrFieldMap has been installed, either by extracting the zip file provided at the bottom of this page on the hard drive and adding its path in Matlab or by checking out a version of the VistaSoft repository which includes mrFieldMap, the software can then be started by typing mrFieldMap at the Matlab command prompt. The following image will appear:
Normally, one would begin by clicking the "load distorted" button, which allows the user to load the distorted EPI image which needs to be corrected. By clicking the "load field map" button, the user can load the field map which is used to correct the image. The button "load structural" allows the user to load a structural image which should be undistorted. This is not a necessity, but is useful to estimate how well the unwarping algorithm is working. The fourth button, "correct image", uses the field map to unwarp the distorted image and produce a new image more similar to the field map.
The user can also specify whether the field map is EPI based, in which case the unwarping must take into account that the field map itself is distorted. Theoretically this should not be a problem but in practice, however, unwarping an image using a warped EPI based field map (by unwarping the field map first) does produce a slightly different image than unwarping it using a non-EPI based field map. The theoretical reasons for this are unclear but imperical results suggest it is generally better to use an EPI based field map.
Also, one can specify whether the data acquisition was done with positive or negative phase encoding blips - basically whether the phase increments in the phase-encoded direction are positive or negative. If the wrong value is chosen, the unwarping will be in the wrong direction and the resulting image will actually be more distorted than the original.
The user can choose to apply Jacobian modulation in the unwarping. This increases the intensity in the unwarped image of voxels which are stretched and decreases the intensity of compressed voxels.
Finally, one can enter the readout time of the EPI measurement. This is used to convert the field map, which is in units of Hz (i.e. it is in the frequency domain) to the spatial domain by simple multiplication. This is defaulted to 32 ms.
As soon as an image has been loaded using one of the three loading buttons, a second GUI pops up, displaying the loaded images:
This GUI is an altered version of the mrViewer GUI and allows the user to choose any slice along any of the three main axis. The user can also switch between any of the loaded images and the unwarped image, as well as an image showing the difference between the unwarped image and the structural image, to make the estimation of the performance of the unwarping algorithms easier.
Once the correction button in the main GUI is clicked, the unwarped image is automatically saved into the same directory as the distorted image, and two graphs appear, showing the difference between the distorted image and the structural image on the one hand, and between the unwarped image and the structural image on the other hand. The user can choose between simple mean square error or the mutual information between the images as the error metric.
Results
The program was tested on a squashed phantom image, provided with the SPM FieldMap toolbox, as well as on an EPI image of an actual brain provided by the VISTA lab.
Squashed phantom image
Unwarping of squashed phantom image
Included in the SPM FieldMap toolbox is an EPI image of a ball which has been distorted in the image acquisition to become more oval-shaped. Also included are the corresponding fieldmap and structural image. When unwarping this image, all parameters can be kept at their default values, except the phase blip value must be set to negative. The results are shown below:
As can be seen from the images, the unwarped image looks more spherical shaped like the structural image. As can be seen from the differential image, the difference between the two shapes is highest at the edges but overall the difference seems to be relatively uniform, indicating a successful unwarping.
Estimates of unwarping quality for phantom ball
Using the main mrFieldMap GUI, the mean square error between the slices of the distorted image and the structural image as well as between the unwarped image and the structural image can be examined. The same can be done for the mutual information between the images. The results are shown below:
Retinotopic models in individual subjects transformed into MNI space
Some text. Some analysis. Some figures.
Retinotopic models in group-averaged data on the MNI template brain
Some text. Some analysis. Some figures.
Retinotopic models in group-averaged data projected back into native space
Some text. Some analysis. Some figures.
Conclusions
Here is where you say what your results mean.
References - Resources and related work
- Jezzard P and Balaban RS (1995) Correction for geometric distortions in echoplanar images from B0 field variations. Magn Reson Med 34:65-73
- Andersson JLR, Hutton C, Ashburner J, Turner R, Friston K (2001) Modelling geometric deformations in EPI time series. NeuroImage 13:903-919
- Hutton C, Bork A, Josephs O, Deichmann R, Ashburner J, Turner R. (2002). Image distortion correction in fMRI: A quantitative evaluation. NeuroImage 16:217-240
- Jenkinson M. 2003. Fast, automated, N-dimensional phase-unwrapping algorithm. MRM 49:193-197
- S. Balac and G. Caloz , Mathematical modeling and numerical simulation of magnetic susceptibility artifacts in magnetic resonance imaging. Comput. Methods Biomech. Biomed. Eng. 3 (2000), pp. 335–349.
Software