The quantitative evaluation of functional neuroimaging experiments: mutual information learning curves.

Learning curves are presented as an unbiased means for evaluating the performance of models for neuroimaging data analysis. The learning curve measures the predictive performance in terms of the generalization or prediction error as a function of the number of independent examples (e.g., subjects) used to determine the parameters in the model. Cross-validation resampling is used to obtain unbiased estimates of a generic multivariate Gaussian classifier, for training set sizes from 2 to 16 subjects. We apply the framework to four different activation experiments, in this case [(15)O]water data sets, although the framework is equally valid for multisubject fMRI studies. We demonstrate how the prediction error can be expressed as the mutual information between the scan and the scan label, measured in units of bits. The mutual information learning curve can be used to evaluate the impact of different methodological choices, e.g., classification label schemes, preprocessing choices. Another application for the learning curve is to examine the model performance using bias/variance considerations enabling the researcher to determine if the model performance is limited by statistical bias or variance. We furthermore present the sensitivity map as a general method for extracting activation maps from statistical models within the probabilistic framework and illustrate relationships between mutual information and pattern reproducibility as derived in the NPAIRS framework described in a companion paper.

Comparison of matched BOLD and FAIR 4.0T-fMRI with [15O]water PET brain volumes.

Valid comparisons of functional activation volumes from fMRI and PET require accurate registration, matched spatial resolution, and if possible matched noise. We coregistered 4.0T-fMRI and PET volumes, using a series of linear and nonlinear transformations applied to the PET volumes. Because of the limited number of fMRI slices that were available, PET volumes were transformed to the fMRI space. Since 4.0T-fMRI and 4.0T-MRI volumes have significant spatial distortion due to magnet inhomogeneities, high resolution 1.5T-MRI volumes were nonlinearly transformed to 4.0T-MRI volumes as part of the transformation chain. The smoothing effects of these registration transformations were measured, in order to match the spatial resolution of the coregistered fMRI and PET volumes. Spatial resolution of the transformed PET volumes in the fMRI space was degraded by up to 60% due to the transformation process. Due to both the image acquisition characteristics and the coregistration process, the transformed PET volumes had a spatial resolution that was lower than that of tMRI. Therefore, significant smoothing of fMRI volumes was necessary to match their spatial resolution with that of the transformed PET volumes. Matching the spatial resolution of the fMRI volumes to those of the transformed PET volumes was achieved by matching the shape of their point spread functions. In order to do this, Gaussian kernels were employed to smooth the fMRI volumes. We were unable to simultaneously match the resolution and noise of fMRI and PET signals in the motor cortex. Activation maps derived from transformed PET and smoothed fMRI volumes were compared. Contralateral motor cortex was active in all modalities but there were large variations in the size of the activated region and its signal to noise ratio across BOLD, FAIR, and PET images within each subject. Nevertheless, the relative CBF changes measured by FAIR were consistent with those determined by PET.

Enhancing the multivariate signal of [15O] water PET studies with a new nonlinear neuroanatomical registration algorithm.

This paper addresses the problem of neuro-anatomical registration across individuals for functional [15O] water PET activation studies. A new algorithm for three-dimensional (3-D) nonlinear structural registration (warping) of MR scans is presented. The method performs a hierarchically scaled search for a displacement field, maximizing one of several voxel similarity measures derived from the two-dimensional (2-D) histogram of matched image intensities, subject to a regularizer that ensures smoothness of the displacement field. The effect of the nonlinear structural registration is studied when it is computed on anatomical MR scans and applied to coregistered [15O] water PET scans from the same subjects: in this experiment, a study of visually guided saccadic eye movements. The performance of the nonlinear warp is evaluated using multivariate functional signal and noise measures. These measures prove to be useful for comparing different intersubject registration approaches, e.g., affine versus nonlinear. A comparison of 12-parameter affine registration versus non-linear registration demonstrates that the proposed nonlinear method increases the number of voxels retained in the cross-subject mask. We demonstrate that improved structural registration may result in an improved multivariate functional signal-to-noise ratio (SNR). Furthermore, registration of PET scans using the 12-parameter affine transformations that align the coregistered MR images does not improve registration, compared to 12-parameter affine alignment of the PET images directly.