Bayesian framework for robust seed‐based correlation analysis
Authors: Bell Charreau S. , Mohd Khairi Nazirah , Ding Zhaohua , Wilkes Don Mitchell 
Published: April 2019

Purpose

One popular method of assessing brain functional connectivity (FC) is through seed‐based correlation (SCA) analysis. One drawback of this method is when the seed location is varied slightly, the FC can vary dramatically. We propose a method superior to SCA, robust to variations in seed location, which confers a probabilistic interpretation.

Methods

We introduce a probabilistic method which generates a cloud of highly connected voxels to determine a stable set of voxels connected to the seed location (SC‐SCA). This cloud can generate a correlation map or a probabilistic map. The method is applied to the default mode network (DMN) based on a posterior cingulate cortex (PCC) seed, and the auditory network (AN) as validation on a smaller network. A Bayesian interpretation is demonstrated through performing a maximum a posteriori (MAP) estimation on the DMN. The advantages of the method are tested by performing stability analyses on its influential parameters. The method is extended to region‐based SC‐SCA, and then comparisons are made based on seed‐based vs region‐based versions of the methods SC‐SCA vs traditional SCA. The statistical significance between the methods is assessed via a bootstrap method using the difference in medians of the standard deviation of the voxels for 16 subjects.

Results

The proposed method, SC‐SCA, is able to identify a set of regions — the DMN — that are known to be associated with and have high correlation with the PCC, and the method is also extensible to smaller networks as shown by its performance on the AN. Based on the certainty of the a priori distribution for MAP analysis, the method is able to identify regions with high probability of belonging to the DMN. The stability analyses demonstrated that substantial deviations from the initial seed locations in the sagittal, posterior transverse, and axial directions by ±10 mm do not cause substantial variation in the correlation network produced.

Qualitative inspection of the average correlation maps garnered from the four methods showed that SC‐SCA shows a larger amount of detail in FC connectivity as compared to SCA. Seed‐based methods show higher detail and contrast in the maps in comparison with region‐based methods. Quantitatively, the statistical tests between seed‐based vs region‐based and SC‐SCA vs SCA revealed that there is no significant difference between the following methods: region‐based SCA or region‐based SC‐SCA, and seed‐based SC‐SCA or region‐based SC‐SCA. However, there are statistically significant differences and advantages conferred between the following methods: seed‐based SC‐SCA over seed‐based SCA, region‐based SC‐SCA over seed‐based SCA, region‐based SCA over seed‐based SCA, and region‐based SCA over seed‐based SC‐SCA. Finally, seed‐based SC‐SCA outperforms sphere‐based SCA.

Conclusions

The proposed method offers several advantages over traditional SCA: robust single‐seed FC estimation, novel Bayesian estimation capabilities, enhanced detail of brain structures, robustness to initial seed location, and enhanced consistency in the correlation maps generated. Region‐based SC‐SCA is equivalent or superior to all investigated methods, where seed‐based SCA is inferior to all methods. The method confers improved single‐seed SCA with the additional benefit of Bayesian estimation.