Structural covariability hubs in old age

Abstract

Studies have shown that inter-individual differences in grey matter, as measured by voxel-based morphometry, are coordinated between voxels. This has been done by studying covariance maps based on a limited number of seed regions. Here, we used GPU-based (Graphics Processing Unit) accelerated computing to calculate, for the first time, the aggregated map of the total structural topographical organisation in the brain on voxel level in a large sample of 960 healthy individuals in the age range 68-83 years. This map describes for each voxel the number of significant correlations with all other grey matter voxels in the brain. Voxels that correlate significantly with many other voxels are called hubs. A majority of these hubs were found in the basal ganglia, the thalamus, the brainstem, and the cerebellum; subcortical regions that have been preserved through vertebrate evolution, interact with large portions of the neocortex and play fundamental roles for the control of a wide range of behaviours. No significant difference in the level of covariability could be found with increasing age or between men and women in these hubs.

Graphical Abstract

1. Introduction

The human brain’s morphology shows large variations across individuals, even when controlling for global brain size (Kennedy et al., 1998). By using voxel-based morphometry (VBM), a technique that allows investigating structural tissue concentration differences in the brain (Good et al., 2001), it has been demonstrated that the morphology across healthy adults is largely governed by covariation in grey matter density among different regions. This topographical principle was shown in 12 different regions by Mechelli et al. (2005), where grey matter densities were used as regressors in the analysis, demonstrating that the inter-individual difference in grey matter for a given voxel is coordinated with other voxels. In old age, it has further been shown that the brain goes through gross morphological changes over time (Sigurdsson et al., 2012).

While some studies have used a limited number of “seed” voxels to gain insight into the topographical organisation of structural covariance patterns (Mechelli et al., 2005; Li et al., 2013), other studies have used graph theory to characterise organisational properties on a large-scale (Alexander-Bloch et al., 2013). The seed voxel approach is a powerful tool to answer specific questions about specific regions, where a number of voxels are selected as seeds and then correlated against all other voxels in the brain, thereby obtaining a correlation map of the whole brain for each seed. However, a severe limitation of this approach is that the results are only obtained for a limited number of seed voxels, thus precluding a complete analysis of the topographical organisation of the whole brain. This limitation is surmounted by the graph theory approach, where all correlations between a set of regions are calculated to get a large-scale characterisation of the brain. The different regions are known as “nodes” in the graph and the significant connections between regions are known as “edges”. The number of edges for a given node is called the degree centrality, which is calculated as the sum of significant correlations for that node (Rubinov and Sporns, 2010). Nodes with a high degree centrality have many significant correlations with other nodes and are known as hubs. If the number of nodes is reduced to the order of ~ 100, the computational burden is decreased and it becomes possible to apply different graph theory measures (Evans, 2013). Degree centrality can then be further divided into provincial hubs and connector hubs, where provincial hubs have a high within-network connectivity and connector hubs have a high between-network connectivity (Bullmore and Sporns, 2009).

The graph theory approach is often used on a regional level rather than voxel level, which means the results are highly dependent on which atlas that is used and do not reveal the degree centrality on a more granular level. However, graph theory based estimations of degree centrality can also be performed on a voxel level, which then results in a degree centrality map of the whole brain. Each voxel is then a node in the graph. In functional MRI (fMRI), this is known as “Global Brain Connectivity” (GBC) (Buckner et al., 2009; Cole et al., 2010), and a common tool for this kind of analysis is AFNI’s 3dTcorrMap¹. With this approach, degree centrality maps are calculated for each individual using either an arbitrary threshold or no threshold at all in which case all positive correlations for a given voxel are added together to calculate a weighted GBC. The weighted approach is more sensitive to weaker correlations whereas the threshold approach rewards hubs with stronger correlation, thereby filtering out weaker connections. This method has also been used to calculate voxel-wise correlations across different wavelet scales on individual grey matter maps (Wang et al., 2018). Since the number of nodes is very large, the method becomes computationally expensive. For this reason, it cannot separate degree centrality into provincial hubs and connector hubs (Cole et al., 2015). This computational burden is aggravated when applied on structural data where the correlations are calculated across individuals. The number of voxels is then larger compared to fMRI and permutation analysis is required to obtain a significant threshold across individuals.

In this study, we aimed at answering two fundamental questions about the topographical organisation of inter-individual covariance in grey matter brain structure at old age that have hitherto remained unexplored, presumably in large part due to the computational challenges involved. First, we investigated to what degree the inter-individual differences in grey matter are coordinated over many voxels and if this differs between regions. This was done by obtaining the degree centrality at voxel level using the GBC method on structural data (structural GBC). The correlation threshold approach was used in order to reward stronger hubs and filter out weaker correlations. Secondly, we investigated if the obtained degree centrality at voxel level changes with age or differs between men and women. To answer these questions, we have used the GPU (Graphics Processing Unit) to accelerate the permutation calculations needed to obtain a significant correlation threshold across an ageing cohort of 960 non-demented individuals (68 to 83 years) and calculated, for the first time, a complete aggregated structural correlation map of the whole brain at voxel level (a degree centrality map), which for each voxel reveals the level of covariability with other voxels. We call this a “covariability map”. Given that the brain goes through gross morphological changes during the ageing process and that these are greater in men than women (Sigurdsson et al., 2012), our a-priori hypothesis was that the covariability map would differ between sexes and change with increasing age.

2. Methods

2.1. Study sample

The AGES-Reykjavik study cohort consists of 5764 participants, where 4811 underwent brain MRI (Harris et al., 2007). All MRI brain scans were processed through a global tissue pipeline, where 4614 scans passed quality control (1934 men, 2680 women, mean age 76 ± 6 years) (Sigurdsson et al., 2012). From this pool, 30 men and 30 women without dementia or larger infarcts were randomly selected for each year of age between 68 and 83 years, giving a total of 960 individuals.

2.2. Data acquisition

The MRI images were acquired on a General Electrics 1.5-Tesla Signa Twinspeed EXCITE System (Waukesha, WI) with a multi-channel phased array head cap coil. The following image parameters were used: T1-weighted (TE, 8 ms; TR, 21 ms; FA 30; FOV, 240 mm; matrix, 256×256) with 1.5 mm slice thickness and 0.94 × 0.94 mm in-plane pixel size, proton density (PD)/T2-weighted fast spin echo (FSE) sequence (TE1, 22 ms; T2, 90 ms; TR, 3220 ms; echo training length, 8, FA, 90; FOV, 220 mm; matrix 256×256), and fluid attenuated inversion recovery (FLAIR) sequence (TE, 100 ms; TR, 8000 ms; inversion time, 2000 ms, FA, 90; FOV, 220 mm; matrix, 256×256). Proton density (PD)/T2-weighted and FLAIR were acquired with 3 mm slice thickness and 0.86 mm × 0.86 mm in-plane pixel size. The processing of the covariability maps were done in OpenCL on an AMD 7970 GPU, GHz edition. The host computer was a Supermicro with 32 CPU cores running at 2.6 GHz with Linux Ubuntu as operating system. This computer was also used for the VBM pre-processing.

2.3. Tissue segmentation

The MR images were first processed through a global tissue pipeline, separating the brains into cerebrospinal fluid, grey matter, white matter, and white matter hyperintensities. This pipeline has been described in detail elsewhere (Sigurdsson et al., 2012). In brief, the T1-weighted, T2/PD-weighted and FLAIR images were first corrected for non-uniformity using the N3 algorithm (Sled et al., 1998), and then spatially normalised to the MNI-ICBM152 1 mm isotropic template (Mazziotta et al., 2001) with a 9-parameter affine transformation (Collins et al., 1994), where they were linearly intensity-normalised before used as input to a trained artificial neural network tissue classifier. The grey matter masks from the classifier were obtained for further processing.

2.4. Voxel-based morphometry pre-processing

Before the grey matter masks could be used for correlation analysis, they needed to be pre-processed using parts of FSL-VBM (Douaud et al., 2007), which is an optimised VBM protocol (Good et al., 2001) carried out with FSL tools (Smith et al., 2004). First, the grey matter masks were non-linearly registered to the MNI-ICBM152 2 mm isotropic template and the resulting images were flipped and averaged to create a symmetric, study-specific grey matter template. This template was then used as a target to warp all grey matter images to the template. The images were then corrected (“modulated”) for local expansion or contraction due to the non-linear transformation. Finally, the corrected grey matter images were smoothed with an isotropic Gaussian kernel with a sigma of 3 mm, which were used to calculate the covariability maps and to run a voxelwise General Linear Model (GLM). A grey matter template along with a grey matter mask was created in the process, with a total of 207110 voxels within the mask. These voxels were used as seed voxels in the calculation of the covariability maps.

2.5. Calculating covariability maps

The covariability maps were obtained by calculating the number of significant correlations for each grey matter seed voxel in the brain across 960 subjects, given a significant correlation threshold T. Since different thresholds will give different levels of degree centrality, it is common to explore a range of plausible thresholds (Bullmore and Sporns, 2009). In this study, two threshold T_0.05 and T_0.001 were chosen corresponding to p = 0.05 and p = 0.001.

A seed voxel map shows, for a given voxel that we call the “seed”, which other voxels that this voxel significantly correlates with. These voxels are thus either set to 0 or 1, depending on whether they correlate significantly or not. Let us define the seed voxel map for seed voxel s as S_s(x) for a given coordinate x in the map. This map is then calculated as

$$S_s\left(x\right)=\{\begin{array}{cc}1& \text{if}\rho (s,x)\ge T\\ 0& \text{if}\rho (s,x)<T\end{array}$$ (1)

where ρ(s, x) is the Pearson correlation and T is the significant correlation threshold common for all seeds. The correlation is calculated as

$$\rho (s,x)=\frac{\sum _{i=1}^n(s_i-\overline{s})(x_i-\overline{x})}{\sqrt{\sum _{i=1}^n{(s_i-\overline{s})}^2\sum _{i=1}^n{(x_i-\overline{x})}^2}}$$ (2)

where i ϵ 1, 2, …, 960 is the subject index and n = 960 is the total number of subjects. The seed voxel map S_s(x) is thus a binary brain map of all significant correlations given seed voxel s. The covariability map D(x) is then calculated as a sum over all seed voxel maps, given as

$$D(x)=\sum _{s=1}^N{S}_s(x)$$ (3)

where N = 207110 is the total number of seed voxels. This map has the property that the value of a particular voxel denotes how many other voxels it correlates significantly with. This is the covariability level of the voxel, also known as degree centrality in graph theory.

2.6. Calculating the significant thresholds

The significant threshold level T needs to be calculated for a given p-value before the covariability map can be calculated. This can be done by estimating the null distribution of H₀ (no true correlation), which is the distribution of max-values in ρ(s, x) across all voxels x for each seed voxel s as the 960 values in s are permuted, from which T can be obtained for a given p-value. A total of 5000 permutations were done. Let us denote permutation i of the values in a given seed voxel s as σ_i(s), where i ∈ 1,2, …, 5000 and the number of elements in s is 960. For a given permutation i, the permutation order is the same for all seed voxels S. The max-value for each permutation is then given as

$$\underset{s,x}{\arg \max }\rho \text{(}{\sigma }_i(s),x):=\{s,x|\forall S,X\text{:}\rho \text{(}{\sigma }_{\text{i}}(S),X)\le \rho \text{(}{\sigma }_{\text{i}}(s),x)\}$$ (4)

where S is the set of all seed voxels, X is the set of all voxels that each seed correlate with, and {s, x} are the two voxels having the highest correlation. Each permutation thus calculates a 207110 × 207110 correlation matrix using the permuted seeds and then gives the max value of each permuted matrix. This requires calculating a total of 5000 permuted matrices. The empirically adjusted p-value is calculated as

$$p=\frac{N_{GE}+1}{N+1}$$ (5)

where N_GE is the number of permutations with a max-value greater or equal to the threshold T_p and N = 5000 is the total number of permutations. From this, the following formula was derived to calculate the number of permutations that are allowed to have a max-value greater than or equal to the threshold T_p:

$$N_{GE}=\lfloor p(N+1)-1\rfloor$$ (6)

We get N_GE = 249 for p = 0.05 and N_GE = 4 for p = 0.001, from which the thresholds T_0.05 and T_0.001 were obtained.

2.7. Testing group covariability differences

To test the age and sex differences of the covariability level, the data was divided into four groups. First, men and women were divided into two groups with 480 subjects each, then each sex group was further divided into a younger (age ≤ 75) and an older group (age ≥ 76) with 240 subjects in each group. Let us denote the groups as M_Y for younger men, M_O for older men, W_Y for younger women, and W_O for older women. All combinations of comparing the absolute difference between two groups were tested, giving a total of six different comparisons. For a given group comparison, e.g. M_O vs W_O, the null distribution of H₀ (no difference between the two groups) was estimated by calculating the absolute max difference of the covariability maps between two randomised groups, using equations 1–3 to calculate the map for each group and then calculating the absolute difference. For each permutation, two new groups were created by randomly selecting 240 subjects for each group from the original two groups. Let us denote the covariability map for each permuted group as A_i and B_i, where i is the permutation number. The max-difference value for each permutation i is then given as

$$\underset{x}{\arg \max }|A_i\text{(}x)-B_i\text{(}x)|\text{:=}\{x|\forall X\text{:|}{A}_i\text{(}X)-B_i\text{(}X)|\le |A_i\text{(}x)-B_i\text{(}x)|\}$$ (7)

where x is the voxel with the absolute max difference for each permutation. When calculating the covariability map for each group, a threshold T must be chosen. Notably, since the statistical significance testing concerns group differences in maps, the threshold level chosen within groups is arbitrary. Nevertheless, choosing a low within group non-significant threshold would give too many false correlations, resulting in too much noise in the group maps. Here, both significant threshold levels T_0.05 and T_0.001 were independently tested for the group comparisons.

For the significance test of the absolute difference, a p < 0.05 was chosen for each test. Since the calculations were computationally expensive and took weeks to run for each test, a stop strategy had to be used if it was unlikely that a significant p-value would be obtained with more permutations. This can be achieved by using the confidence interval of p, which is calculated using the margin of error since the p-value estimation is a binomial proportion (Li et al., 2009). The confidence interval for p can be calculated given N number of permutations using the following formula:

$$p\pm Z\sqrt{\frac{p(1-p)}{N}}$$ (8)

We denote the lower part of this confidence interval as p_L, with Z = 3.291 for a 99.9% confidence interval. If the confidence interval, for a given N, does not reach below p_L = 0.05 it is highly unlikely that p will drop below 0.05 even if more permutations are computed. This fact was used to either stop the calculations if p_L > 0.05 or continue to run till N = 5000. From equation 8, we can calculate what p must be to continue to run the Monte Carlo simulation:

$$p\le \frac{z^2/N+2p_L+\sqrt{{\left(z^2/N+2p_L\right)}^2-4p_L^2(z^2/N+1)}}{2(z^2/N+1)}$$ (9)

This formula was implemented as a conditional statement that terminated the permutations if the relation was not fulfilled. For instance, if N = 100, z = 3.291 and p_L = 0.05, the calculations will stop if p > 0.1751. As N increases, p must decrease and get closer to 0.05 for the process to continue to run. Equation 6 was used to obtain, for a given p, the number of permutations N_GE that are allowed to have a max-value greater or equal to the absolute difference of the two groups that were tested, e.g. the absolute difference between M_O and W_O. Since N must not be too small to calculate the margin of error, the stop strategy was only employed on N > 100, i.e. a minimum of 100 permutations were ran before testing the relation in equation 9.

Age and sex differences in covariability level were also tested by using a GLM with FSL’s randomise (Winkler et al., 2014). The 960 subjects were divided into 32 groups according to year of age (68-83) and sex, giving 30 subjects for each group. The covariability map was then calculated for each group, giving 32 different covariability maps. The previously calculated thresholds T_0.05 and T_0.001 were chosen to calculate the maps and run the tests at two threshold levels. The mean, age, second order demeaned age, and sex were used as independent variables and the voxel value (covariability level) was used as dependent variable, giving a design matrix with 32 rows and 4 columns.

2.8. VBM GLM

A standard VBM GLM analysis was done using the modulated grey matter maps to test if there is any difference in grey matter density between men and women or with increasing age, resulting in a design matrix with 960 rows and 3 columns.

2.9. Mapping the AGES atlas to the results

In order to present the covariability levels by region, the regional grey matter specific AGES atlas and corresponding grey matter probability template were used. This open access atlas consists of 35 grey matter regions and was constructed from old individuals, making it suitable for geriatric studies (Forsberg et al., 2017). Since the optimised VBM pipeline created a study specific non-linear grey matter template, the AGES regional grey matter atlas first needed to be warped to the VBM study template. This was done by first non-linearly register the AGES grey matter template to the VBM grey matter template using FSL FNIRT. The deformation field obtained was then used to warp the AGES regional grey matter atlas to VBM template space, from which the percentiles of the covariability in each region could be calculated to create boxplots.

2.10. GPU implementation using OpenCL

The GPU of the AMD 7970 graphics card was used to accelerate the calculations of the covariability maps and the software was developed in C and OpenCL. The OpenCL language is a framework for a range of different parallel computing devices such as multicore CPUs (central processing units), GPUs (graphics processing units) and FPGAs (field-programmable gate arrays). We have made this software open source².

3. Results

3.1. Covariability hubs

The result of the Monte Carlo simulation for estimating the distribution of the null hypothesis H₀ using equation 4, from which the significant threshold levels T_0.05 and T_0.001 were obtained, is shown in Figure 1. The figure demonstrates that H₀ was not normally distributed but rather had a skewness in the right side tail, which is common for random complex networks (Bullmore and Sporns, 2009). The two thresholds were found to be T_0.05 = 0.441 and T_0.001 = 0.550. Each threshold was used to calculate the covariability map for the 960 subjects, where each voxel’s covariability level was normalised to the total number of voxels in order to reflect the number of significant correlations in percentage, by calculating x_norm = 100x/207110 for each covariability level x. The 5% voxels with the highest covariability were regarded as hub voxels. For each map, the covariability level among these hub voxels was at minimum L_0.05 = 2.04% and L_0.001 = 0.94%, corresponding to 4227 and 1940 correlated voxels respectively, which were regarded as hub thresholds. Figure 2 shows two boxplots of the covariability level for all voxels within each grey matter region in the AGES atlas, sorted by the median value of each region. The left boxplot represents the T_0.05 map and the right boxplot represents the T_0.001 map. The vertical lines depict the 5% hub thresholds level.

Figure 1:

Histogram of the null hypothesis distribution of max correlation across 5000 permuted matrices calculated using equation 4.

Figure 2:

Boxplots of the covariability level for all voxels within each grey matter (GM) region. The left boxplot depicts the covariability levels for the T_0.05 map and the right boxplot depicts the covariability level for the T_0.001 map. The vertical lines represent the L_0.05 = 2.04% and L_0.001 = 0.94% hubs threshold, where voxels above these lines are considered to be hub voxels. The common hub regions are the thalamus, the basal ganglia (the putamen, the globus pallidus, the nucleus accumbens, the caudate nucleus), the cerebellum, and the brainstem. For the T_0.05 map, the amygdala and the insula were also considered to be hubs.

Generally, subcortical regions had higher covariability than cortical regions. Common hub voxels for both maps were detected in the thalamus, the basal ganglia (the putamen, the globus pallidus, the nucleus accumens, and the caudate nucleus), the cerebellum, and the brainstem. These are thus considered the main hub regions. For T_0.05, the insula and the amygdala were also considered to be hubs, albeit with a lower covariability than most other hub regions. Figure 3 shows the comparison of the two covariability maps for the hub voxels. Red voxels depict hubs that were unique for the T_0.05 map (2714 voxels) and blue voxels depict hubs that were unique for the T_0.001 map (2715 voxels). Yellow voxels depict the common hub voxels in both maps (7642 voxels), which were found in the thalamus, the basal ganglia, the cerebellum and the brainstem. The T_0.05 map further extended into the insula and the amygdala, while the T_0.001 map extended to cover a larger region in the cerebellum.

Figure 3:

The covariability maps across all 960 subject, showing the 5% voxels with the highest covariability that were considered to be hub voxels. The red voxels depict hubs unique for the T_0.05 map (2714 voxels). The blue voxels depict hubs unique for the T_0.001 map (2715 voxels). The yellow voxels depict common hubs in both maps (7642 voxels). The common hub voxels were found in the thalamus, the basal ganglia, the cerebellum and the midbrain part of brainstem. A few red hub voxels extended to the insula and the amygdala and a blue voxels extended to a larger region in the cerebellum. Radiological view.

3.2. Group covariability differences

The covariability maps at threshold T_0.001 for the subgroups Younger Men, Younger Women, Older Men, Older Women, are shown in Figure 4. The maps show only voxels having at least L_0.001 = 0.94% covariability with other grey matter voxels. The results were very similar for the different groups, highlighting the same regions in the brain. When comparing the different groups using Monte Carlo simulation for both the T_0.05 and T_0.001 thresholds independently, no significant differences between any of the groups could be found even though these p-values were not corrected for multiple group testing. Table 1 shows the p-value for each test and the number of permutations required to establish non-significance. The greatest difference was for the T_0.001 threshold between older men and older women, with a p = 0.0635 (uncorrected). At α = 0.05, a Bonferroni correction of multiple testings requires p < 0.0083 for significant difference at each threshold and p < 0.0042 for both thresholds.

Figure 4:

T_0.001 covariability maps for each subgroup, showing voxels from L_0.001 = 0.94% to 4% level of covariability with other grey matter voxels. Younger individuals are between 68 and 75 years. Older individuals are between 76 and 83 years. No significant difference could be found between the maps. Radiological view.

Table 1:

Differences between groups and the number of permutations needed to establish non-significance for the two thresholds T_0.05 and T_0.001. Younger individuals are between 68 to 75 years and older individuals are between 76 and 83 years. The difference between older women and older men for threshold T_0.001 required 3541 permutations before giving up.

Comparison	p-value	p-value threshold	Permutations
1. T0.05: Older women vs younger women	0.0993	0.0983	412
2. T0.05 Older women vs younger men	0.7525	0.1751	100
3. T0.05 Older women vs older men	0.2079	0.1751	100
4. T0.05 Younger women vs younger men	0.5248	0.1751	100
5. T0.05 Younger women vs older men	0.9406	0.1751	100
6. T0.05 Older men vs younger men	0.3762	0.1751	100
1. T0.001 Older women vs younger women	0.1980	0.1751	100
2. T0.001 Older women vs younger men	0.7426	0.1751	100
3. T0.001 Older women vs older men	0.0635	0.0635	3541
4. T0.001 Younger women vs younger men	0.6832	0.1751	100
5. T0.001 Younger women vs older men	0.6337	0.1751	100
6. T0.001 Older men vs younger men	0.1683	0.1678	109

Figure 5 shows the covariability maps for all subgroups that were used in the GLM analysis at threshold T_0.001. Although the threshold level gives rise to false positives in each group of 30 subjects, the covariability pattern from the whole group of 960 subjects appeared for the whole age range between 68 and 83 and for both men and women (see Figure 3). None of the six contrasts gave a significant result for any of the two thresholds that were independently analysed using GLM statistics (see Table 2).

Figure 5:

T_0.001 covariability maps for each age and sex, showing voxels from L_0.001 = 0.94% to 4% level of covariability with other grey matter voxels. No significant change could be found with increasing age or between men and women. Radiological view.

Table 2:

GLM covariability regression showing for each contrast and threshold the lowest p-value obtained. No significance difference was found.

Contrast	p-value for T0.05	p-value for T0.001
1. Increased with age	0.1582	0.1988
2. Decreased with age	0.3496	0.2838
3. Increased with demeaned age2	0.7084	0.6626
4. Decreased with demeaned age2	0.5026	0.4889
5. Men > women	0.3884	0.4922
6. Women > men	0.7132	0.6016

3.3. VBM results

The results from the VBM GLM analysis of grey matter density are shown in Figure 6 and Table 3. A large proportion of the brain decreased with increasing age. Also, men had less grey matter throughout the brain compared to women. A few voxels increased with increasing age and had significantly more grey matter in men than women, but these were likely to be dirty-appearing white matter given their location adjacent to the ventricles (Beggs et al., 2015).

Figure 6:

VBM grey matter in right hemisphere. From left to right: Grey matter decreasing with age, grey matter increasing with age, men having more grey matter than women, women having more grey matter than men, p < 0.01.

Table 3:

Significant VBM grey matter results (p<0.01).

Contrast	Number of voxels	Percentage of total grey matter
Decreasing with increasing age	132386	63.9%
Increasing with increasing age	5200	2.5%
Men > Women	2595	1.3%
Men < Women	137437	66.4%

3.4. Processing time and performance

Calculating the covariabity map one time for all 207110 voxels across 960 individuals took about 355 seconds using the GPU. The total time to calculate all 5000 permutations took about three weeks. In comparison, when calculating the covariability map using AFNI’s 3dTcorrMap (assuming threshold T is known), it took 27965 seconds using the OpenMP version, where 15 CPU cores were found to be optimal. Running the analysis 5000 times would would thus take approximately 4 years if 3dTcorrMap would allow to permute the seeds.

4. Discussion

4.1. Covariability hubs

The present study represents the first analysis of the aggregated structural correlation in the whole brain at voxel level in a large sample of healthy elderly individuals. The resulting map showed large differences in covariability between voxels and indicated the existence of central hub regions with a high level of covarability.

These main hubs were found in subcortical regions, with a strikingly similar pattern in the left and the right hemisphere. In the present sample of elderly healthy adults, these hubs consistently appeared across the age range and between sex (Figure 5). Although a small age effect cannot be excluded, we did not get a significant difference in the covariability maps across age and between sex, in spite of the fact that we replicated other well-known sex and age effects of grey matter anatomy from VBM. The VBM based analysis showed that women had more relative grey matter than men (after removing global brain size) and that grey matter to a large extent decreased significantly with increasing age in the studied age range, which is in line with other studie. (Luders et al., 2009; Matsuda, 2013).

The thalamus, the basal ganglia, the cerebellum, and a small part of the brainstem were all identified as main hub regions with a covariability in the top 5% of all voxels in both the T_0.05 and the T_0.001 covariability maps, while the amygdala and the insula were only identified in the T_0.05 (Figure 2). The highest level of covariability was found in the thalamus. The thalamus works as a relay system between a wide set of subcortical and cortical areas, and is involved in a broad range of functions including sensorimotor processing, emotion, arousal and cognition (Shim et al., 2008). A second group of hub regions was found within the basal ganglia; subcortical structures that are also highly interconnected with broad areas of the cerebral cortex and involved in many different aspects of human behaviour, from motor control to cognitive, affective and somatosensory processes (Arsalidou et al., 2012). Hub regions were found within the major nuclei of the basal ganglia, including the putamen, the globus pallidus, the caudate nucleus and the nucleus accumbens. A third subcortical structure with a high level of covariability was the cerebellum. This region is extensively connected with the cortex and plays an important role in motor control and learning, where it contributes to coordination, precision and accurate timing (Fine et al., 2002; Ullman, 2004). The dorsal part of the brainstem (midbrain) was also found to have a high level of covariability. Midbrain and brainstem nuclei have extensive and widespread projections to the cortex, contributing profoundly to cognitive processes and adaptive behaviour (Koot et al., 2012; Br et al., 2016). The amygdala and the insula appeared as hubs in the T_0.05 map. The amygdala has been identified as a hub in three large-scale brain networks that support social interactions (Bickart et al., 2014), and the anterior insula has been found to work as an integral hub for switching between the default mode network and the central executive network (Menon and Uddin, 2010). Generally speaking, the main covariability hubs are thus subcortical regions that are broadly implicated in a wide range of behaviours, and that interacts with widespread regions of the neocortex.

4.2. Relation to previous studies

How do these results compare to other studies using other methodologies and modalities? Notably, several studies of within-person connectivity using either functional or structural (diffusion imaging) measures have identified similar sets of hub regions, with extensive connectivity with other parts of the brain. One functional MRI study of resting state activity using weighted GBC found that the amygdala, the thalamus, the globus pallidus, the putamen, the caudate nucleus, the cerebellum, and the midbrain were among the regions with the top 5% most connected voxels (Cole et al., 2010). The same set of regions were identified as structural covariability hubs in the present study. Further studies show that the basal ganglia and the thalamus are highly interconnected network hubs, which are part of a core circuit to support large-scale integration of functionally diverse signals (Bell and Shine, 2016). Voxel-wise analysis suggests that the basal ganglia, the thalamus and the salience network are critical brain structures for the modulation of the communication between the default mode network and the task positive networks (Di and Biswal, 2014). Midbrain/brainstem nuclei have also been shown to have a connections with both the default mode network and the task positive networks (Br et al., 2016). Finally, structural analysis of white matter connectivity using diffusion tensor imaging (DTI) has identified the thalamus, the putamen and the globus pallidus to be among the top 5% most connected regions in the brain (Crossley et al., 2014).

In the present study, we did not observe significant age-related changes in covariability at old age. This is consistent with a number of other studies. One study employed a graph theory approach on regional grey matter volumes where the participants were divided into a young, middle and old aged group. They found differences in local efficiency between the young group and the middle group but not between the middle group and the old group (Wu et al., 2011). Another study found the structural covariance patterns to change for younger and middle aged participants, while being relatively stable for older participants (Li et al., 2013). A third study extended these results, demonstrating that the integrity of structural covariance patterns declined with increasing age up to the age of approximately 70 years where it plateaued (DuPre and Spreng, 2017).

The picture from studies of between-person correlations in cortical thickness is somewhat different. In general, such studies have found structural covariance hubs in heteromodal or unimodal association cortices (He et al., 2007), and that hub regions are predominantly intermodular connectors in parietal, temporal, and frontal heteromodal association cortex (Chen et al., 2008). In line with this, Achard and coworkers found hubs in multimodal association cortices in a functional connectivity study (Achard et al., 2006). One study using cortical thickness also showed both linear age effects and sex-related differences for a broader age-range (Gong et al., 2009). What may underlie this discrepancy? First, it should be noted that the subcortical regions showing up as main hubs in the present study will not even be included in studies of cortical thickness. Another important methodological difference is that the mentioned studies were all atlas-based. The benefit of the atlas approach is that it facilitates analysis based on graph theoretical measurements by reducing the number of nodes in the graph (Evans, 2013), which also gives more power to the statistics. The benefit of voxel-wise analysis is however that a finer granularity reveals the range of voxel covariability within each brain region as seen in the boxplots in Figure 2. For instance, even though most voxels in the brainstem had very low covariability, some voxels in midbrain could still be considered as hubs (see Figure 3). It should be noted that VBM does not give a perfect correspondence at voxel level across individuals, meaning these correlations could be the result of differences in placement of structures at a voxel level. However, as discussed by Mechelli et al. (2005), this would still reflect structural covariance across individuals, induced both by differences in grey matter density and differences in placement of grey matter across individuals.

In conclusion, it seems that methodological differences, i.e. of how hubs are measured, the choice between atlas or voxel-wise approach, the age range of the participants, and the choice of modality play important roles in studies of covariability. In structural covariance studies, where correlations are measured across individuals, the result shows how voxels covary between individuals. The emerging covariance patterns could have several underlying mechanisms. One possibility is that structural covariance reflect patterns of functional interaction, i.e. regions that are commonly coactivated during performance also tend to be structurally correlated across individuals (Seeley et al., 2009). This is supported by the fact that the hubs found in the present study also have been identified as hubs in studies analysing within-person functional and structural connectivity, and by the general observation that these subcortical regions are extensively connected with large areas of the cortex. However, another mechanism underlying structural covariability could be common genetic influences on structural variation in different brain regions. Genetic factors could increase covariability e.g. by infuencing morphogenetic processes during development or ageing related changes in distributed sets of brain regions (Evans, 2013). Obviously, such genetic and environmental mechanisms are not mutually exlusive and it appears likely that the patterns of covariability we observe here are ultimately the result of an interplay between both environmental factors and genetical liability.

4.3. Regional grey matter density and behaviour

Many neuroimaging studies have demonstrated that, across task and domains, regional grey matter density is associated with individual differences in performance and competence. Differences in regional grey matter anatomy between specialists and non-experts have been demonstrated e.g. for auditory and premotor areas in musicians (Bermudez et al., 2008), posterior hippocampus in taxi drivers (Maguire et al., 2000; Woollett and Maguire, 2011), olfactory cortex in perfumers (Delon-Martin et al., 2013), and for brain regions involved in motor control and spatial navigation in professional car drivers (Bernardi et al., 2014). Furthermore, many of these studies have also reported inter-individual correlations between measures of training or performance, on the one hand, and regional grey matter anatomy, on the other hand (Ullén et al., 2016). These examples show that performance, experience and behaviour may be attributed to structural brain differences. Studies also indicate that behaviour and performance are linked to the amount of allocated neural circuitry (Mechelli et al., 2004), and that covariance in grey matter across individuals may be linked to differences in behaviour (Mechelli et al., 2005). Consequently, it could be that hub regions with a high number of significant correlations (high covariability) have a significant impact on variability in performance and behaviour in a population.

A final observation is that the hub regions identified in the present study are also evolutionary old brain areas that are implied in a broad range of functions. Regions with such properties have typically evolved through a process known as exaptation, where the ancestral core has been co-opted and reused for new functions (Anderson, 2007). For instance, it has been shown that all parts of the mammalian basal ganglia are also present in the lamprey brain but with simpler circuitry, suggesting that the basal ganglia evolved over 560 million years through exaptation to allow a broader range of behaviours and traits in the mammalian brain by changing the input and output connections of these regions (Stephenson-Jones et al., 2011). The basal ganglia has also been identified to have a large volume variation explained by genetic variation (Bryant et al., 2013). Therefore, it appears plausible that this exaptation process has contributed to extensive structural and functional connections between the subcortical regions and the rest of the brain, resulting in high covariability of these hub regions.

4.4. Limitations & conclusions

First of all, the present study is a study of structural correlations between individuals. Even if other studies demonstrate that the regions identified as hubs in the present study are also connected, structurally and functionally, with many other brain regions, the present results as such do not provide information about within-brain connectivity. Another limitation is that we focused entirely on degree centrality as outcome measure, mainly since the GBC method is computationally expensive and therefore cannot separate degree centrality into provincial and connector hubs. We opted to study elderly individuals in the age range 68 to 83, since this is an age range with drastic changes in brain morphometry (Sigurdsson et al., 2012). We did not find age effects or sex differences on covariability for these hubs. These findings can of course not be generalised beyond healthy elderly individuals.