Examining brain maturation during adolescence using graph Laplacian learning based Fourier transform

BACKGROUND

Longitudinal neuroimaging studies have demonstrated that adolescence is a crucial developmental period of continued brain growth and change. Motivated by both achievements in graph signal processing and recent evidence that some brain areas act as hubs connecting functionally specialized systems, we propose an approach to detect these regions from a spectral analysis perspective. In particular, as the human brain undergoes substantial development throughout adolescence, we evaluate functional network difference among age groups from functional magnetic resonance imaging (fMRI) measurements.

NEW METHODS

We treated these measurements as graph signals defined on the parcellated functional brain regions and proposed a graph Laplacian learning based Fourier transform (GLFT) to transform the original graph signals into the frequency domain. Eigen-analysis was conducted afterwards to study the behaviors of the corresponding brain regions, which enabled the characterization of brain maturation.

RESULT

We first evaluated our method on the synthetic data and then applied it to resting state and task fMRI data from the Philadelphia Neurodevelopmental Cohort (PNC) dataset, comprised of normally developing adolescents from 8 to 22 years of age. The method provided an accuracy of 94.9% in distinguishing different adolescent stages and we detected 13 hubs from resting state fMRI and 16 hubs from task fMRI related to brain maturation.

COMPARISON WITH EXISTING METHODS

The proposed GLFT demonstrated its superiority over conventional graph Fourier transform and alternative graph Fourier transform with high predictive power.

CONCLUSION

The method provides a powerful approach for extracting brain connectivity patterns and identifying hub regions.

A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has been proposed to analyze multiple correlated phenotypes. It has been empirically observed that the first PC, which summarizes the largest amount of variance, can be less powerful than higher order PCs and other commonly used methods in detecting genetic association signals. In this paper, we investigate the properties of PCA-based multiple phenotype analysis from a geometric perspective by introducing a novel concept called principal angle. A particular PC is powerful if its principal angle is 0° and is powerless if its principal angle is 90°. Without prior knowledge about the true principal angle, each PC can be powerless. We propose linear, non-linear and data-adaptive omnibus tests by combining PCs. We demonstrate that the Wald test is a special quadratic PC-based test. We show that the omnibus PC test is robust and powerful in a wide range of scenarios. We study the properties of the proposed methods using power analysis and eigen-analysis. The subtle differences and close connections between these combined PC methods are illustrated graphically in terms of their rejection boundaries. Our proposed tests have convex acceptance regions and hence are admissible. The p-values for the proposed tests can be efficiently calculated analytically and the proposed tests have been implemented in a publicly available R package MPAT. We conduct simulation studies in both low and high dimensional settings with various signal vectors and correlation structures. We apply the proposed tests to the joint analysis of metabolic syndrome related phenotypes with data sets collected from four international consortia to demonstrate the effectiveness of the proposed combined PC testing procedures.