In this paper we have described a method for performing SPM group analysis with image data as an independent variable using the BPM software package. It is a massively-univariate approach that utilizes the general linear model for statistical estimation and RFT or FDR for statistical inference. Although the BPM package is designed to take imaging data as covariates, it can also accept scalar dependent measures into the design matrix. The use of the SPM inference and visualization tools will make this tool immediately useful and familiar to a large portion of the neuroimaging community. At this time, the BPM package is not compatible with the SnPM package (SnPM Authors, the University of Michigan; Ann Arbor, MI, USA) for non-parametric analysis, although an extension to non-parametric methodologies is feasible. The computational demand for performing a BPM analysis is highly dependent on the size of the search region, the number of subjects, and the number of imaging covariates incorporated into the model. For the ANCOVA example provided here, using a single imaging covariate, computational demand is similar to a standard SPM analysis with a single column regressor. For larger analyses that incorporate multiple imaging regressors, performance increases can be achieved by implementing distributed grid computing with slice-wise or voxel-wise parcellation schemes.
Most fMRI analysis packages allow users to collapse an entire image data set or region of interest (ROI) into a single value (i.e. taking a mean value) and enter this value into a linear regression model. Although such analyses can be useful in controlling for image-based variables, results obtained from a BPM analysis and an ROI-based analysis are importantly distinct. The region-specific nature of the BPM analysis ensures that imaging metrics from one brain area (e.g. temporal lobe) are not meaninglessly regressed against data from another entirely disparate region of the brain (e.g. frontal lobe). BPM is also fundamentally different from a conjunction analysis (Friston, et al. 1999
; Pell, et al. 2004
). A conjunction analysis is used to determine common areas of activation in different data sets, but cannot be used to perform voxel-wise regression analysis between modalities.
The example provided here demonstrates some uses of this technique for the analysis of neuroimaging data. In the ANCOVA, group differences in functional activity were evaluated while controlling for gray matter volume. The analysis revealed that activity in the left temporooccipital area was explained by the differences in gray matter density in the same area. Moreover, the negative correlation between the fMRI signal and GM volume was demonstrated by the correlation analysis. Based on these findings, one can conclude that the reduced GM and increased BOLD activation are associated. Without a tool like BPM, such a multi-modal quantitative assessment would not have been possible.
An important addition to the BPM toolbox is the inclusion of a cluster-level inference using a homologous correlation field, rather than a t-transformation of correlation coefficients. At each voxel, the t-transformation of a correlation coefficient follows a t-distribution, but a t-transformed correlation image is not a t-field in a strict sense, defined as a Gaussian image divided by a chi-square image (Cao and Worsley 1999
). In this case, the random field results for a homologous correlation field (Cao and Worsley 1999
) are more appropriate, since a correlation field is modeled directly as a product of two sets of Gaussian images divided by the geometric mean of their variances. This cluster correction used here to perform the BPM correlation analysis was able to identify an area of negative correlation that could not otherwise have been detected using a t-transformation of a correlation image (data not presented). The use of the homologous correlation field is particularly relevant to the BPM method because multiple image sets are correlated rather than correlating a single variable with one image set, as is done with conventional analysis software.
The BPM analysis presented in this manuscript demonstrates one of the most obvious uses of this software. It is frequent that imaging scientists wish to control for differences in cerebral cortical volume when comparing functional datasets. For example, positron emission tomography studies frequently perform volume corrections to account for brain atrophy in studies of aging (Meltzer, et al. 2000
). However, the BPM tool has many potential uses that may not be quite so obvious. Although it would not be possible to address all potential uses of this tool, we would like to highlight a few that may be of particular interest.
One potential use would be to employ the correlation function to evaluate reproducibility data. In such a study a new imaging modality or method could be used to collect images in 2 different sessions and/or on 2 different days. A correlation analysis could be used to determine the reproducibility of any 2 datasets. One could even include 4 image sets from each subject in what is termed a Gage Repeatability and Reproducibility analysis (Automotive Industry Task Force (AIAG) 1994
). Such an analysis would allow one to determine the regional variation in repeatability or reproducibility (e.g., reproducibility may be diminished in susceptibility prone areas for EPI-based methods). The use of BPM to analyze reproducibility data would eliminate the need for ROI based measures reducing bias and expanding conclusions that could be drawn.
A second possible use would be to analyze longitudinal imaging studies, regardless of the imaging modality, with multiple different BPM functions, depending on the hypothesis being evaluated. The correlation tool could be used to determine if timepoint 1 is significantly predictive of timepoint 2. The ANCOVA tool could be used to control for time-dependent changes in one variable while comparing another variable. The multiple regression could be used to identify the relationship between time-dependent changes in several imaging modalities. Most longitudinal clinical studies employ multiple variable regressions for the analysis of multiple scalar variables and it would be very useful to do the same with multiple imaging variables.
A third potential use would be to control for scanner variability in multi-site clinical imaging studies using either an ANCOVA or a multiple variable regression. Following each subject scan session a study-specific phantom could be imaged. The phantom would have to be appropriately designed to allow normalization to MNI space, and it would be included as a variable of no interest. Such an analysis would not only account for variability within a single site but would also capture between-site variability. Although it may seem somewhat onerous to scan a phantom after each participant, this could considerably improve multi-site imaging studies (and is currently being done for the ADNI - Alzheimer’s Disease Neuroimaging Initiative, www.adni-info.org
). The use of BPM to analyze such data would allow for spatial variability to be captured in the analysis. This was not meant to be an exhaustive list of potential uses of BPM, as multimodality regressions of any imaging data that can brought into a common stereotaxic space can be performed. The potential uses are not restricted to MRI but also include other modalities such as magnetoencephalography data, transcranial magnetic stimulation data, electro-encephalography data, and optical imaging.
Although BPM provides a new insight into neuroimaging studies, there are some challenges we need to address. For multi-modal imaging data it is important to have accurate co-registration between image data sets. For the example provided here, we used the tools within the SPM package for coregistering the structural MRI with the functional MRI. Similar tools are available within SPM for coregistering non-MRI data (ie, PET, SPECT) with MRI using modality-specific normalization procedures, or multi-modality mutual information algorithms. Additionally, the voxel specific nature of the BPM design matrix raises some issues that are distinct from more conventional SPM type analyses. Specifically, the estimability of the desired contrast can be problematic. Since the design matrix varies from voxel to voxel, it is theoretically possible to have a non-estimable contrast in a subset of voxels. While we have not yet encountered this situation with simulations or our in-vivo testing, this issue will need to be dealt with. One approach would be to generate a voxel-wise map of estimability for a given contrast and make it available to the user. Another approach would be to omit voxels that are not estimable.