S.C. Strother

Support vector machines for temporal classification of block design fMRI data

This paper treats support vector machine (SVM) classification applied to block design fMRI, extending our previous work with linear discriminant analysis [LaConte, S., Anderson, J., Muley, S., Ashe, J., Frutiger, S., Rehm, K., Hansen, L.K., Yacoub, E., Hu, X., Rottenberg, D., Strother S., 2003a. The evaluation of preprocessing choices in single-subject BOLD fMRI using NPAIRS performance metrics. NeuroImage 18, 10-27; Strother, S.C., Anderson, J., Hansen, L.K., Kjems, U., Kustra, R., Siditis, J., Frutiger, S., Muley, S., LaConte, S., Rottenberg, D. 2002. The quantitative evaluation of functional neuroimaging experiments: the NPAIRS data analysis framework. NeuroImage 15, 747-771]. We compare SVM to canonical variates analysis (CVA) by examining the relative sensitivity of each method to ten combinations of preprocessing choices consisting of spatial smoothing, temporal detrending, and motion correction. Important to the discussion are the issues of classification performance, model interpretation, and validation in the context of fMRI. As the SVM has many unique properties, we examine the interpretation of support vector models with respect to neuroimaging data. We propose four methods for extracting activation maps from SVM models, and we examine one of these in detail. For both CVA and SVM, we have classified individual time samples of whole brain data, with TRs of roughly 4 s, thirty slices, and nearly 30,000 brain voxels, with no averaging of scans or prior feature selection.

A regional covariance approach to the analysis of functional patterns in positron emission tomographic data.

This article provides a complete description of the subprofile scaling model (SSM) approach to the analysis of positron emission tomography (PET) data. The goals and assumptions underlying the development of SSM are outlined, and its strengths and weaknesses are discussed. It is demonstrated that all obtainable information about regional ratios can, in theory, be derived from the SSM regional covariance patterns. A general constraint on the ability to effectively remove global variation while identifying region-specific information about PET data sets is outlined and discussed within the SSM framework. Finally, an extension of the SSM technique to the generation of disease-specific covariance patterns is demonstrated for paraneoplastic cerebellar degeneration, the acquired immune deficiency syndrome dementia complex, and Parkinsons disease, and the importance of multidimensional descriptions of disease, such as may be obtained from PET data using SSM, is emphasized.

Optimizing the fMRI data-processing pipeline using prediction and reproducibility performance metrics: I. A preliminary group analysis.

We argue that published results demonstrate that new insights into human brain function may be obscured by poor and/or limited choices in the data-processing pipeline, and review the work on performance metrics for optimizing pipelines: prediction, reproducibility, and related empirical Receiver Operating Characteristic (ROC) curve metrics. Using the NPAIRS split-half resampling framework for estimating prediction/reproducibility metrics (Strother et al., 2002), we illustrate its use by testing the relative importance of selected pipeline components (interpolation, in-plane spatial smoothing, temporal detrending, and between-subject alignment) in a group analysis of BOLD-fMRI scans from 16 subjects performing a block-design, parametric-static-force task. Large-scale brain networks were detected using a multivariate linear discriminant analysis (canonical variates analysis, CVA) that was tuned to fit the data. We found that tuning the CVA model and spatial smoothing were the most important processing parameters. Temporal detrending was essential to remove low-frequency, reproducing time trends; the number of cosine basis functions for detrending was optimized by assuming that separate epochs of baseline scans have constant, equal means, and this assumption was assessed with prediction metrics. Higher-order polynomial warps compared to affine alignment had only a minor impact on the performance metrics. We found that both prediction and reproducibility metrics were required for optimizing the pipeline and give somewhat different results. Moreover, the parameter settings of components in the pipeline interact so that the current practice of reporting the optimization of components tested in relative isolation is unlikely to lead to fully optimized processing pipelines.

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.

Principal Component Analysis and the Scaled Subprofile Model Compared to Intersubject Averaging and Statistical Parametric Mapping: I. “Functional Connectivity” of the Human Motor System Studied with [15O]Water PET

Using [15O]water PET and a previously well studied motor activation task, repetitive finger-to-thumb opposition, we compared the spatial activation patterns produced by (1) global normalization and intersubject averaging of paired-image subtractions, (2) the mean differences of ANCOVA-adjusted voxels in Statistical Parametric Mapping, (3) ANCOVA-adjusted voxels followed by principal component analysis (PCA), (4) ANCOVA-adjustment of mean image volumes (mean over subjects at each time point) followed by F-masking and PCA, and (5) PCA with Scaled Subprofile Model pre- and postprocessing. All data analysis techniques identified large positive focal activations in the contralateral sensorimotor cortex and ipsilateral cerebellar cortex, with varying levels of activation in other parts of the motor system, e.g., supplementary motor area, thalamus, putamen; techniques 1–4 also produced extensive negative areas. The activation signal of interest constitutes a very small fraction of the total nonrandom signal in the original dataset, and the exact choice of data preprocessing steps together with a particular analysis procedure have a significant impact on the identification and relative levels of activated regions. The challenge for the future is to identify those preprocessing algorithms and data analysis models that reproducibly optimize the identification and quantification of higher-order sensorimotor and cognitive responses.

The convergence of object dependent resolution in maximum likelihood based tomographic image reconstruction

Study of the maximum likelihood by EM algorithm (ML) with a reconstruction kernel equal to the intrinsic detector resolution and sieve regularization has demonstrated that any image improvements over filtered backprojection (FBP) are a function of image resolution. Comparing different reconstruction algorithms potentially requires measuring and matching the image resolution. Since there are no standard methods for describing the resolution of images from a nonlinear algorithm such as ML, we have defined measures of effective local Gaussian resolution (ELGR) and effective global Gaussian resolution (EGGR) and examined their behaviour in FBP images and in ML images using two different measurement techniques. For FBP these two resolution measures are equal and exhibit the standard convolution behaviour of linear systems. For ML, the FWHM of the ELGR monotonically increased with decreasing Gaussian object size due to slower convergence rates for smaller objects. For the simple simulated phantom used, this resolution dependence is independent of object position. With increasing object size, number of iterations and sieve size the object size dependence of the ELGR decreased. The FWHM of the EGGR converged after approximately 200 iterations, masking the fact that the ELGR for small objects was far from convergence. When FBP is compared to a nonlinear algorithm such as ML, it is recommended that at least the EGGR be matched; for ML this requires more than the number of iterations (e.g., < 100) that are typically run to minimize the mean square error or to satisfy a feasibility or similar stopping criterion. For many tasks, matching the EGGR of ML to FBP images may be insufficient and >> 200 iterations may be needed, particularly for small objects in the ML image because their ELGR has not yet converged.

Abnormal Functional Connectivity in Posttraumatic Stress Disorder

This study investigated the efficacy of a combined multivariate/resampling procedure for the analysis of PET activation studies. The covariance-based multivariate analysis was used to investigate distributed brain systems in posttraumatic stress disorder (PTSD) patients and matched controls during performance of a working memory task. The results were compared to univariate results obtained in an earlier study. We also examined whether the PTSD patients demonstrated a breakdown in functional connectivity that may be associated with working memory difficulties often experienced by these patients. A resampling procedure was used specifically to test the reliability of measured between-group effects, to avoid mistaken inference on the basis of random intersubject differences. Significant and reproducible differences in network connectivity were obtained for the two groups. The functional connectivity pattern of the patient group was characterized by relatively more activation in the bilateral inferior parietal lobes and the left precentral gyrus than the control group, and less activation in the inferior medial frontal lobe, bilateral middle frontal gyri and right inferior temporal gyrus. The resampling procedure provided direct evidence that working memory updating was abnormal in PTSD patients relative to matched controls. This work focuses on the need to identify extended brain networks (in addition to regionally specific changes) for the full characterization of brain responses in neuroimaging experiments. Our multivariate analysis explicitly measures the reliability of the patterns of functional connectivity we obtain and demonstrates the potential of such analyses for the study of brain network dysfunction in psychopathology.

Are Brain Functions Really Additive

Although Positron Emission Tomography (PET) and functional magnetic resonance imaging (fMRI) studies commonly subtract data obtained during two or more experimental conditions to decompose a complex task, there have been few opportunities to evaluate this approach directly. In the present study, PET was used to study three motor speech tasks selected such that two were constituent components of the third, making possible a direct examination of decomposition by subtraction. In Experiment 1, a group of 13 right-handed normal volunteers participated in three activation studies: syllable repetition; phonation; and repetitive lip closure. A scanning session was devoted to a single task, repeated four times. In Experiment 2, six of the original subjects performed the same three activation studies during a single scanning session. Whether tasks were studied in separate scanning sessions or combined within a single session, the results of decomposition by compound subtraction differed significantly from the results obtained when individual tasks were compared to a simple baseline condition. These data failed to demonstrate task additivity, a necessary property if decomposition by subtraction is to provide an accurate characterization of the brain activity accompanying complex behavior.

Commentary and Opinion: I. Principal Component Analysis, Variance Partitioning, and “Functional Connectivity”:

We briefly review the need for careful study of “variance partitioning” and “optimal model selection” in functional positron emission tomography (PET) data analysis, emphasizing the use of principal component analysis (PCA) and the importance of data analytic techniques that allow for heterogeneous spatial covariance structures. Using an [15O]water dataset, we demonstrate that—even after data processing—the intrasubject signal component of primary interest in baseline activation studies constitutes a very small fraction of the intersubject variance. This small intrasubject variance component is subtly but significantly changed by using analysis of covariance instead of scaled subprofile model processing before applying PCA. Finally, we argue that the concept of “functional connectivity” should be interpreted very generally until the relative roles of inter- and intrasubject variability in both disease and normal PET datasets are better understood.

Evaluating subject specific preprocessing choices in multisubject fMRI data sets using data-driven performance metrics

This study investigated the possible benefit of subject specific optimization of preprocessing strategies in functional magnetic resonance imaging (fMRI) experiments. The optimization was performed using the data-driven performance metrics developed recently [Neuroimage 15 (2002), 747]. We applied numerous preprocessing strategies and a multivariate statistical analysis to each of the 20 subjects in our two example fMRI data sets. We found that the optimal preprocessing strategy varied, in general, from subject to subject. For example, in one data set, optimum smoothing levels varied from 16 mm (4 subjects), 10 mm (5 subjects), to no smoothing at all (1 subject). This strongly suggests that group-specific preprocessing schemes may not give optimum results. For both studies, optimizing the preprocessing for each subject resulted in an increased number of suprathresholded voxels in within-subject analyses. Furthermore, we demonstrated that we were able to aggregate the optimized data with a random effects group analysis, resulting in improved sensitivity in one study and the detection of interesting, previously undetected results in the other.