Rajesh Nandy

Cluster analysis of fMRI data using dendrogram sharpening.

The major disadvantage of hierarchical clustering in fMRI data analysis is that an appropriate clustering threshold needs to be specified. Upon grouping data into a hierarchical tree, clusters are identified either by specifying their number or by choosing an appropriate inconsistency coefficient. Since the number of clusters present in the data is not known beforehand, even a slight variation of the inconsistency coefficient can significantly affect the results. To address these limitations, the dendrogram sharpening method, combined with a hierarchical clustering algorithm, is used in this work to identify modality regions, which are, in essence, areas of activation in the human brain during an fMRI experiment. The objective of the algorithm is to remove data from the low‐density regions in order to obtain a clearer representation of the data structure. Once cluster cores are identified, the classification algorithm is run on voxels, set aside during sharpening, attempting to reassign them to the detected groups. When applied to a paced motor paradigm, task‐related activations in the motor cortex are detected. In order to evaluate the performance of the algorithm, the obtained clusters are compared to standard activation maps where the expected hemodynamic response function is specified as a regressor. The obtained patterns of both methods have a high concordance (correlation coefficient = 0.91). Furthermore, the dependence of the clustering results on the sharpening parameters is investigated and recommendations on the appropriate choice of these variables are offered. Hum. Brain Mapping 20:201–219, 2003.

Estimation of the intrinsic dimensionality of fMRI data.

A new method based on an autoregressive noise model of order 1 is introduced to the problem of detecting the number of components in fMRI data. Unlike current information-theoretic criteria like AIC, MDL, and related PPCA, which do not incorporate autocorrelations in the noise, the new method leads to more consistent estimates of the model order, as illustrated in simulated and real fMRI resting-state data.

Novel nonparametric approach to canonical correlation analysis with applications to low CNR functional MRI data

Detection of activation in functional MRI (fMRI) is often complicated by the low contrast‐to‐noise ratio (CNR) in the data. The primary source of the difficulty is the fact that for activities that are subtle the signal can be hidden inside the inherent noise in the data. Classical univariate methods based on t‐test or F‐test are susceptible to noise, as they fail to harness systematic correlations in evoked responses within neighboring voxels. Here the power of a multivariate statistical analysis tool known as canonical correlation analysis (CCA) in fMRI studies is demonstrated where the CNR is low. As a further illustration of the power of the method, a comparative study of CCA and ordinary correlation analysis using simulated data under various noise levels is also performed. A novel nonparametric approach is introduced to calculate the P‐values from the distribution of the complicated test statistic. The circumstances under which CCA is a better performer as well as when it is not the case are discussed. As an example, this method is applied to detect hippocampal activation from memory‐related tasks. Magn Reson Med 50:354–365, 2003.

Novel ROC‐type method for testing the efficiency of multivariate statistical methods in fMRI

The receiver operating characteristic (ROC) method is a useful and popular tool for testing the efficiency of various diagnostic tests applicable to functional MRI (fMRI) data. Typically, the diagnostic tests are applied on simulated and pseudo‐human fMRI data, and the area under the ROC curve is used as a measure of the efficiency of the diagnostic test. The effectiveness of such a method depends on how well the simulated data approximate the real data. For multivariate statistical methods, however, this technique is usually inadequate, as the spatial dependence among voxels is ignored for simulated data. In this work a modified ROC method using real fMRI data with a broader scope is proposed. This method can be applied to most fMRI postprocessing techniques, including multivariate analyses such as canonical correlation analysis (CCA). Also, the relationship of the modified ROC method with the conventional ROC method is discussed in detail. Magn Reson Med 49:1152–1162, 2003.

Improving the spatial specificity of canonical correlation analysis in fMRI

The contrast‐to‐noise ratio (CNR) is often very low in fMRI data, and standard univariate methods suffer from a loss of sensitivity in the context of noise. The increased power of a multivariate statistical analysis method known as canonical correlation analysis (CCA) in fMRI studies with low CNR was established previously. However, CCA in its conventional form has weak spatial specificity. In this work we propose a new assignment scheme to rectify this problem. It is shown that the new method has improved spatial specificity as well as sensitivity compared to conventional CCA for detecting activation patterns in fMRI. Magn Reson Med 52:947–952, 2004.

A semi-parametric approach to estimate the family-wise error rate in fMRI using resting-state data

One of the most important considerations in any hypothesis based fMRI data analysis is to choose the appropriate threshold to construct the activation maps, which is usually based on p-values. However, in fMRI data, there are three factors which necessitate severe corrections in the process of estimating the p-values. First, the fMRI time series at an individual voxel has strong temporal autocorrelation which needs to be estimated to obtain the corrected parametric p-value. The second factor is the multiple comparisons problem arising from simultaneously testing tens of thousands of voxels for activation. A common way in the statistical literature to account for multiple testing is to consider the family-wise error rate (FWE) which is related to the distribution of the maximum observed value over all voxels. The third problem, which is not mentioned frequently in the context of adjusting the p-value, is the effect of inherent low frequency processes present even in resting-state data that may introduce a large number of false positives without proper adjustment. In this article, a novel and efficient semi-parametric method, using resampling of normalized spacings of order statistics, is introduced to address all the three problems mentioned above. The new method makes very few assumptions and demands minimal computational effort, unlike other existing resampling methods in fMRI. Furthermore, it will be demonstrated that the correction for temporal autocorrelation is not critical in implementing the proposed method. Results using the proposed method are compared with SPM2.

Symptomatic and functional correlates of regional brain physiology during working memory processing in patients with recent onset schizophrenia

Patients with schizophrenia show altered patterns of functional activation during working memory processing; specifically, high-performing patients appear to hyper-activate and low-performing patients appear to hypo-activate when compared with controls. It remains unclear how these individual differences in neurophysiological activation relate to the clinical presentation of the syndrome. In this functional magnetic resonance imaging (fMRI) study, the relationship is examined using partial least squares (PLS), a multivariate statistical technique that selects underlying latent variables based on the covariance between two sets of variables, in this case, clinical variables and regional fMRI activations during a verbal working memory task. The PLS analysis extracted two latent variables, and the significance of these associations was confirmed through permutation. Lower levels of activation during task performance across frontal and parietal regions of interest in the left hemisphere were found to covary with poorer role functioning and greater severity of negative and disorganized symptoms, while lower activation in right frontal and subcortical regions of interest was found to covary with better social functioning and fewer positive symptoms. These results suggest that appropriately lateralized patterns of functional activation during working memory processing are related to the severity of negative and disorganized symptoms and to the level of role and social functioning in schizophrenia.

A preliminary study of functional abnormalities in aMCI subjects during different episodic memory tasks.

Functional magnetic resonance imaging (fMRI) is an important imaging modality to understand the neurodegenerative course of mild cognitive impairment (MCI) and early Alzheimers disease (AD), because the memory dysfunction may occur before structural degeneration is obvious. In this research, we investigated the functional abnormalities of subjects with amnestic MCI (aMCI) using three episodic memory paradigms that are relevant to different memory domains in both encoding and recognition phases. Both whole-brain analysis and region-of-interest (ROI) analysis of the medial temporal lobes (MTL), which are central to the memory formation and retrieval, were used to compare the efficiency of the different memory paradigms and the functional difference between aMCI subjects and normal control subjects. We also investigated the impact of using different functional activation measurements in ROI analysis. This pilot study could facilitate the use of fMRI activations in the MTL as a marker for early detection and monitoring progression of AD.

Extending local canonical correlation analysis to handle general linear contrasts for fMRI data

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

Optimizing the performance of local canonical correlation analysis in fMRI using spatial constraints

The benefits of locally adaptive statistical methods for fMRI research have been shown in recent years, as these methods are more proficient in detecting brain activations in a noisy environment. One such method is local canonical correlation analysis (CCA), which investigates a group of neighboring voxels instead of looking at the single voxel time course. The value of a suitable test statistic is used as a measure of activation. It is customary to assign the value to the center voxel for convenience. The method without constraints is prone to artifacts, especially in a region of localized strong activation. To compensate for these deficiencies, the impact of different spatial constraints in CCA on sensitivity and specificity are investigated. The ability of constrained CCA (cCCA) to detect activation patterns in an episodic memory task has been studied. This research shows how any arbitrary contrast of interest can be analyzed by cCCA and how accurate P‐values optimized for the contrast of interest can be computed using nonparametric methods. Results indicate an increase of up to 20% in detecting activation patterns for some of the advanced cCCA methods, as measured by ROC curves derived from simulated and real fMRI data. Hum Brain Mapp, 2012.