BRAIN NETWORK CONNECTIVITY FROM MATCHING CORTICAL FEATURE DENSITIES

Abstract

We present a new method for constructing structural inference brain networks from functional measures of cortical features. Instead of averaging vertex-wise cortical features, we propose the use of full functions of spatial densities of measures such as thickness and use two dimensional pairwise correlations between regions to construct population networks. We show increased within group correlations for both healthy controls and toddlers with prenatal alcohol exposure compared to the existing mean-based correlation approach. Further, we also show significant differences in brain connectivity between the healthy controls and the exposed group.

1. INTRODUCTION

The idea of using pairwise structural correlations to extract and analyze brain association networks was first introduced by He and Evans et al. [1]. Since then, there have also been other analogous approaches that have used structural covariance of cortical measures for assessing both long range and short range brain connectivity [2]. Different from the functional connectivity (measured by signal co-activation) or the diffusion connectivity (measured by direct connections of white matter pathways), the structural correlational connectivity approach is based on statistical inference, and is also understood as effective or statistical network connectivity.

Similar to the correlational approach, the structural covariance approach computes pairwise associations of brain morphology measures between different brain regions and has been widely applied to brain connectivity analysis both in healthy neurodevelopment and neurological disease [3]. Of late there have been several suggestions by researchers to investigate approaches other than single parameter measures such as mean cortical thickness, volume or surface area values, and incorporate other metrics of morphological similarity including microstructural MRI features that yield multiparametric measures [3].

Our paper is a first step towards such efforts and proposes to use a functional approach that goes beyond single valued measures of features. The contributions of the paper are as follows. We use a spatial density function as a representation for cortical valued features. The idea here is to use the full function that may potentially serve as a richer descriptor of cortical regions instead of single valued estimates such as the mean. Then instead of computing correlations between means, we compute correlations between full functions to get pairwise similarity measures between regions. These correlations are thresholded within and across groups to obtain network representations and further analyzed to investigate differences between cohorts. We show results on brain connectivity differences between healthy controls and prenatally alcohol exposed toddlers from a population-based birth cohort study.

2. APPROACH

We rely on a standard brain surface parcellation to obtain cortical valued features. These features can be related to the tissue properties such as thickness or myelin content, or exclusively shape-based features such as curvedness, shape index, curvature, or gyrification, which is a measure of local folding per surface area. In this paper, we use a Freesurfer parcellation of the cortex [4].

2.1. Representation

We use the idea in Joshi et al. [5] to represent a vertex valued cortical measure such as thickness by a continuous function $f:[0,\mathcal{T}]\to ℝ$, where $[0,\mathcal{T}]$ is the interval for thickness value with $\mathcal{T}$ being the maximum thickness. This function can be defined for the entire cortex, in which case it becomes a global function, or it can be defined individually for a given choice of parcellation of regions. For a single region of interest (ROI), we represent the discrete observations of a cortical measure (thickness) by a vector (m₁, m₂, … , m_n), where n is the number of vertices for that region. Then we estimate the kernel density function $f:[0,\mathcal{T}]\to ℝ$ as

$$f(s)=\frac{1}{n}\sum _{i=1}^n{\varphi }_{\Delta }\left(s-m_i\right)=\frac{1}{n\Delta }\sum _{i=1}^n\varphi \left(\frac{s-m_i}{\Delta }\right),$$ (1)

where ϕ is a kernel and Δ is the bandwidth selection parameter. In this paper we use a normal kernel function. Then for a set of K ROIs, the set of functions {f_i, i = 1, 2, … , K} represents the feature set of cortical values for a single subject. Figure 1 shows the kernel density estimates of cortical thickness for a set of 33 ROIs.

Fig. 1.

The left panel shows a schematic of the kernel density functions of thickness from a Freesurfer cortical parcellation. The right panel shows the histograms of thickness as well as the estimated density function (in red) for 33 different ROIs.

2.2. Density Function Matching

Analogous to finding sample pairwise correlations between singleton (mean) values across ROIs, we use the two dimensional correlation of density functions to find similarity measures between pairs of ROIs. For a given ROI, for N subjects, we discretize the function f using T samples and stack the N functions into a two dimensional matrix $X\in {ℝ}^{N\times T}$. As an example, Figure 2 visualizes this matrix both as an image and a surface for the lingual and the paracentral regions. Then, the two dimensional correlation between two ROI matrices Xⁱ and X^j r_ij is defined as,

$$\frac{{\sum }_{p=1}^N{\sum }_{q=1}^T\left(X_{pq}^i-{\widehat{X}}^i\right)\left(X_{pq}^j-{\widehat{X}}^j\right)}{\sqrt{{\left({\sum }_{p=1}^N{\sum }_{q=1}^T{X}_{pq}^i-{\widehat{X}}^i\right)}^2{\left({\sum }_{p=1}^N{\sum }_{q=1}^T{X}_{pq}^j-{\widehat{X}}^j\right)}^2}},$$ (2)

where i, j = 1, … , K, ${\widehat{X}}^i={\sum }_p{\sum }_q{X}_{pq}^i$ and ${\widehat{X}}^j={\sum }_p{\sum }_q{X}_{pq}^j$. We compute the correlation r_ij between all K ROIs.

Fig. 2.

Example of stacked density functions visualized in a matrix form (left) and a surface form (right) for the lingual and the paracentral regions.

3. EXPERIMENTAL RESULTS

Finally, we present experimental results comparing both within-group population networks and between-group population network differences for the mean-correlation approach as well as the density functional approach.

3.1. Data

Our data consisted of 179 toddlers (105 M/74 F, ages from 30–39 months, mean age 34 ± 1.8 months) collected from the Drakenstein Child Health Study [6, 7]. The data consisted of 130 healthy controls and 49 toddlers with prenatal alcohol exposure. The structural scans constituted T1-weighted (T1w) multi-echo MPRAGE (voxel size (VS)=1.0mm3; TR=2530ms; TE=1.69:3.54:5.39:7.24ms; TI=1100ms; flip angle=7.0deg; acquisition time (TA)=5:21min) acquisitions. Automated processing using FreeSurfer version 6.0 [4] was performed at the Centre for High Performance Computing (CHPC, Rosebank, SA). Vertex-wise cortical thickness for all subjects were extracted. The study was approved by the respective institutional review boards (IRB) at UCLA and UCT in South Africa.

3.2. Within Group Networks

Figure 3 shows qualitative structural association networks for both mean correlations (first two columns) and density function correlations (last column) within each group. No significance test is performed. The mean correlation network is thresholded at r = 0.3 and r = 0.5 levels separately to observe the effect of the strength of correlations on the network architecture. At the r = 0.3 threshold, we visually identified a modular structure of brain networks in healthy controls. This structure is noticeably disrupted in the alcohol exposed group. Both the modular structure and the disruption visually appears to be suppressed at a threshold of r = 0.5. Owing to generally increased correlations across most ROIs, the density function network was thresholded at a much higher value (r = 0.85). We observe that the network architecture is sparser in both healthy controls and the exposed group. Instead of global disruption in the exposed group, we observed subtle differences between them at this higher threshold.

Fig. 3.

Structural association networks within a group of healthy controls and alcohol exposed toddlers for both the mean-based correlation (first two columns) and the density correlation (third column) approaches.

3.3. Between Group Networks

To assess statistical differences in brain connectivity between healthy controls and the alcohol exposed group, we performed the William’s test [8], which compares the pairwise correlations between them. Figure 4 shows significant differences in brain connectivity for the mean correlations (first column) and density function correlations (second column) between healthy controls and the alcohol exposed group after adjusting for multiple comparisons using the Bonferroni correction. The surviving edges are displayed on a cortical surface to visualize anatomical connectivity. Connectivity patterns using the density functions showed increased edges (not necessarily between the same ROIs) compared to the mean correlation network.

Fig. 4.

Differences in brain connectivity between controls and the alcohol exposed group for mean correlation network (first column) and the density functional network (second column).

4. DISCUSSION AND CONCLUSION

Differently from the methods used before, we propose a new method for extracting brain connectivity information by using high dimensional feature descriptors that represent a ROI measure such as vertex-wise thickness by a spatial density function. Differences within and between groups in brain connectivity suggest suboptimal integration of structural networks in the group of children with prenatal alcohol exposure. Since within group differences for the exposed group were particularly noticeable at weaker correlation network strengths, this may reflect a less organized network. These more sensitive approaches are particularly critical in understanding the dynamic changes during the first two years of life where rapid brain growth and development occur.

Going forward, we plan to perform alternative statistical tests for estimating both within group and between group networks. One possibility is the use of permutation testing at each node followed by multiple comparisons. Another possibility is to define a Markov random field to define conditional distributions on the nodes of the graph. In this paper, the number of controls (N = 130) was much greater than the exposed toddlers (N = 49) leading to an unbalanced sample size. This may potentially lead to the control group showing robust pairwise correlations compared to the exposed group. We plan to perform resampling tests and cross-validation by repeated random downsampling of the number of controls to match the patient group to determine if the patterns are consistent across subsets of the healthy controls. Lastly, one can also perform registration of networks to yield an optimal alignment between the underlying data as proposed by Lee at al. [9].