1. How can Riemannian partial least squares (R-PLS) model enhance functional connectivity analysis?
Riemannian partial least squares (R-PLS) model enhances functional connectivity analysis by accounting for the intricate relationships enforced by the positive definite criteria. It extends the standard PLS model to allow Riemannian manifold response and predictor data, providing a more comprehensive understanding of functional connectivity. The R-PLS model predicts from functional connectivity data while considering the non-linear geometry of symmetric positive definite matrices. This approach enables researchers to explore the relationships between fMRI data and various factors such as behavioral data, experimental designs, or seed region activation. By incorporating the Riemannian geometry, R-PLS offers new insights into functional connectivity, allowing for a more accurate interpretation of high-dimensional functional connectivity data. The proposed tangent non-linear iterative partial least squares (tNIPALS) algorithm aids in fitting the R-PLS model, determining the optimal number of latent variables through cross-validation. Additionally, significant functional connections identified by R-PLS can be determined using permutation tests on the variable importance in the projection (VIP) statistic, enhancing the interpretability of the results. Overall, R-PLS provides a powerful tool for investigating functional connectomes and understanding the impact of neurological diseases on brain function.
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2. How did R-PLS compare to Euclidean PLS?
R-PLS outperformed Euclidean PLS in all metrics except specificity in group prediction. It showed better performance when compared with Euclidean PLS using raw and Fisher-transformed correlations. Both methods produced similar results for every metric, but R-PLS was more effective in predicting age and subject group. The permutation test of the VIP statistic found significant functional connections between ROIs as being predictive of age and subject group. R-PLS also aided interpretability by reducing the 39 ROIs of the MSDL atlas into 17 resting state networks associated with the atlas 20.
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3. What is the most parsimonious latent variable in ABIDE?
The most parsimonious latent variable in ABIDE is K = 3, as found through ten-fold cross validation. This value is within one standard error of the minimum RMSE, compared to K = 6. The R-PLS method outperformed Euclidean PLS in terms of R-squared value and other metrics, except for specificity in group classification. The permutation test of the VIP statistic with 200 permutations identified 208 significant functional connections between ROIs, predicting age, subject group, sex, and eye status. The AAL atlas was used to aid interpretability, associating 116 ROIs with seven resting-state networks and an eighth cerebellum network. Age was associated with increased and decreased functional connectivity within resting-state networks. Subjects with ASD showed increased within-network connectivity, except for the limbic network and thalamus. Closed eyes resulted in decreased within-network connectivity, except for the default mode network and limbic network. The ABIDE dataset consists of preprocessed fMRI images from 16 international imaging sites, with 539 individuals diagnosed with ASD and 573 neurotypical controls. The data were collected using a 3 Tesla Allegra MRI, preprocessed using the NIAK pipeline, and subjected to motion realignment, non-uniformity correction, motion scrubbing, nuisance regression, band-pass filtering, and global signal regression. The AAL atlas was used to extract time series from 116 ROIs, aiding interpretability and identifying significant functional connections between ROIs and predictors such as age, subject group, sex, and eye status.
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4. How does R-PLS model identify functional connections?
The R-PLS model identifies functional connections by analyzing the relationships between subject phenotype data and functional connectivity. It has identified connections associated to age, ASD, schizophrenia, sex, and eye status, which are well represented in the literature. The model has identified the reduction of within-network connectivity with age in both the COBRE and ABIDE datasets, with exceptions in specific networks. It has also identified decreased connectivity with the default mode network and the cerebellum in subjects with ASD. The model has highlighted the role of the basal ganglia in schizophrenic patients and the connectivity patterns involving the default mode network. The use of the VIP statistic to identify significant connections in functional connectivity has been demonstrated, although it has limitations in considering Riemannian geometry and multivariate outcome variables. Overall, the R-PLS model provides insights into the functional connectome and its relation to subject phenotype data, and it can be applied to other imaging modalities and multimodal imaging studies.
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