![[SPM]](/spm/images/SPM_Central.gif)
Created by members of the Wellcome Department of Imaging Neuroscience
Even after realignment there is considerable variance in fMRI time series that covary with, and is most probably caused by, subject movements. It is also the case that this variance is typically large compared to experimentally induced variance. Anyone interested can include the estimated movement parameters as covariates in the design matrix, and take a look at an F-contrast encompassing those columns. It can be quite dramatic. The result is loss of sensitivity, and if movements are correlated to tas specificity. I.e. we may mistake movement induced variance for true activations. Because the movement induced variance is often very large compared to "true" activations false positives may ensue even from a relatively modest correlation between task and movement.
The problem is well known, and several solutions have been suggested. A quite pragmatic (and conservative) solution is to include the estimated movement parameters (and possibly squared) as covariates in the design matrix. Since we typically have loads of degrees of freedom in fMRI we can usually afford this. The problem occurs when movements are correlated with the task, since the strategy above will discard "good" and "bad" variance alike.
The "covariate" strategy described above was predicated on a model where variance was assumed to be caused by "spin history" effects, but will work pretty much equally good/bad regardless of what the true underlying cause is.
Others have assumed that the residual variance is caused mainly by errors caused by the interpolation kernel in the resampling step of the realignment. One has tried to solve this through higher order resampling (huge Sinc kernels, or k-space resampling).
The "adjustment for sampling errors" in SPM is also predicated on the assumption. The idea there is that the use of a finite size interpolation kernel (e.g. 9x9x9) will cause resampling errors, but that it should be possible to calculate a range for how large these errors can be. Hence let us say a given voxel have the quantity a of variance correlated with movement, and the calculations show that interpolation errors may cause at the most the quantity b of variance in this particular voxel. Then no m re than b variance will be removed. This would potentially allow for the removal of as much variance that can possibly be explained by movement, while preserving experimentally induced variance. However, if movement related variance isn't caused mainly by interpolation errors this method will not remove all artefactual movement related variance.
The "Unwarp99" toolbox is based on a different hypothesis regarding the residual variance. EPI images are not particularly faithful reproductions of the object, and in particular there are severe geometric distortions in regions where there is an air-tissue interface (e.g. orbitofronal cortex and the anterior medial temporal lobes). In these areas in particular the observed image is a severely warped version of reality, much like a funny mirror at a fair ground. When one moves in front of such a mirror nes image will distort in different ways and ones head may change from very elongated to seriously flattened. If we were to take digital snapshots of the reflection at these different positions it is rather obvious that realignment will not suffice to bring them into a common space.
The situation is similar with EPI images, and an image collected for a given subject position will not be identical to that collected at another. Hence, even after a "successful" realignment there will be residual variance caused by the object having different shape at different time points. We call this effect susceptibility-by-movement interaction. The "Unwarp99" toolbox is predicated on the assumption that the susceptibility-by-movement interaction is responsible for a sizeable part of residual movem nt related variance.
Assume that we know how the deformations change when the subject changes position (i.e. we know the derivatives of the deformations with respect to subject position). That means that for a given time series and a given set of subject movements we should be able to predict the "shape changes" in the object and the ensuing variance in the time series. It also means that, in principle, we should be able to formulate the inverse problem, i.e. given the observed variance (after realignment) and known (esti ated) movements we should be able to estimate how deformations change with subject movement.
We have made an attempt at formulating such an inverse model, and at solving for the "derivative fields". A deformation field can be thought of as little vectors at each position in space showing how that particular location has been deflected. A "derivative field" is then the rate of change of those vectors with respect to subject movement. Given these "derivative fields" we should be able to remove the variance caused by the susceptibility-by-movement interaction. Since the underlying model is so re tricted we would also expect experimentally induced variance to be preserved. Our experiments have also shown this to be true. Indeed one particular experiment even indicated that in some cases the method will reintroduce experimental variance that had been obliterated by movement related variance.
In theory it should be possible to estimate also the "static" deformation field, yielding an unwarped (to some true geometry) version of the time series. In practice that doesn't really seem to work, hence the method deals only with residual movement related variance induced by the susceptibility-by-movement interaction.
The method requires no additional measurements. Given an EPI time-series and a set of movement parameters (obtained from SPM realign) it will estimate the derivative fields and remove the associated variance from the time series. Upon installation the toolbox is reached from the "Toolboxes" menu, and a additional help page will describe its practical use.
It should be noted that this is a method intended to correct data afflicted by a particular problem. If there is little movement in your data to begin with this method will do you no good. If on the other hand there is appreciable movement in your data (>1mm or >1deg) it will remove some of that unwanted variance. If, in addition, movements are task related it will do so without removing all your "true" activations.
The method attempts to minimise total (across the image volume) variance in the data set. It should be realised that while (for small movements) a rather limited portion of the total variance is removed, the susceptibility-by-movement interaction effects are quite localised to "problem" areas. Hence, for a subset of voxels in e.g. frontal-medial and orbitofronal cortices and parts of the temporal lobes the reduction can be quite dramatic (>90%).
It should also be noted that the susceptibility-by-movement interaction causes differential deformations AND differential signal drop-out. At present the toolbox deals only with variance caused by the first component. This is the subject of ongoing work.
Friston KJ, Williams SR, Howard R, Frackowiak RSJ and Turner R (1995) Movement-related effect in fMRI time-series. Magn Reson Med. 35:346-355
Jezzard P and Balaban RS (1995) Correction for geometric distortions in echoplanar images from B0 field variations. Magn Reson Med 34:65-73
Wu DH, Lewin JS and Duerk JL (1997) Inadequacy of motion correction algorithms in functional MRI: Role of susceptibility-induced artefacts.J Magn Reson Imag 7:365-370
The software was developed while JLRA was supported by STINT (Stiftelsen for internationalisering av högre utbildning och forskning.)
This software has been tested by the authors on data collected on two different make MR scanners. Undoubtedly there are numerous bugs that will surface when more people start using it. We are grateful for bug reports, and other input, and the more we receive the faster bugs will be weeded out.