Participants were recruited as part of a larger study (Psychological, social and biological determinants of ill health (pSoBid). Details of the design of pSoBid have been described elsewhere (Velupillai et al., 2008; Deans et al., 2009; Knox et al., 2012; McGuinness et al., 2012; McLean et al., 2012). Selection of participants was based on the Scottish Index of Multiple Deprivation 2004 (SIMD), which ranks small areas on the basis of multiple deprivation indicators across six domains, namely: income; employment; health; education, skills, and training; geographic access and telecommunications; and housing. Sampling was stratified to achieve an approximately equal distribution of the 666 participants across males and females and age groups (35–44, 45–54, and 55–64 years) within the most (bottom 5% of SIMD score) and LD areas (top 20% of SIMD score). Participants could opt-in for the neuroimaging component of the study. This paper presents the analysis from 42 male individuals who were randomly selected. This included 21 people from the most deprived regions and 21 from the least deprived regions, who were age matched.

All MR imaging were performed using GE Medical systems, 3T Signa Excite HD system (Milwaukee, USA) using an eight channel phased array (receive only) head coil. An axial 3D T1-weighted IR-FSPGR was acquired with TR = 6.8 ms; TE = 1.5 ms, Inversion Preparation time = 500 ms; Flip angle = 12°; FOV = 26 cm; Phase FOV = 70%; matrix: 320 × 320; 160 slices; Bandwidth 31.25 kHz; Slab thickness = 1 mm. The acquisition time for this scan was 8 min 54 s.

Statistical comparisons of global data and surface maps were generated by computing a general linear model (GLM) of the effect of neighborhood deprivation (independent variable) on thickness (dependent variable) at each vertex in the cortical mantle, using the Query, Design, Estimate, Contrast (QDEC) interface of FreeSurfer. Age was used as nuisance covariate in the model. QDEC is a single-binary application included in the FreeSurfer distribution that is used to perform group averaging and inference on the cortical morphometric data produced by the FreeSurfer processing stream. (http://surfer.nmr.mgh.harvard.edu/fswiki/Qdec). Maps were created using statistical thresholds of p = 0.05 and were smoothed to a full width half maximum (FWHM) level of 20 mm. Since this analysis involved performing a GLM analysis at 160000 vertices, these maps were corrected for multiple comparisons by means of a cluster-wise procedure using the Monte Carlo Null-Z simulation method adapted for cortical surface analysis and incorporated into the QDEC processing stream. For these analyses, a total of 10,000 iterations of simulation were performed for each comparison, using a threshold of p = 0.05.

Network construction was based on parcellations of cortical thickness as described by He et al. (2007). We defined an anatomical connection (edge) as statistical associations in cortical thickness between cortical parcellations based on the Desikan Killiany atlas included in the FreeSurfer pipeline (nodes). The statistical similarity in cortical thickness between 2 regions was measured by computing the Pearson's correlation coefficient across subjects to create an interregional correlation matrix (N × N, where N is the number of brain regions based on Desikan cortical parcellation atlas, here N = 68). In order to keep the analysis as close as possible to previous reports, prior to the correlation analysis, a linear regression was performed at every region to remove the effects of age, and mean overall cortical thickness; the residuals of this regression were then substituted for the raw cortical thickness values (He et al., 2007; Chen et al., 2008). In order to be consistent with the cortical thickness group difference analysis presented above, the complex network analyses were repeated without mean overall cortical thickness in the model, but the results of our analysis did not differ significantly (results not shown). A separate matrix was produced for the MD (21 subjects) and the LD (21 subjects). As a first step, all negative correlations were discarded. As the correlation analysis was performed for all 68 × 68/2 = 1431 pairs of regions, we performed a multiple comparisons correction to test the significance of these correlations.

We applied the false discovery rate (FDR) procedure separately to each matrix in order to correct the multiple comparisons at a q value of 0.2 (this was chosen as at 0.05, both matrices were very sparse). (Genovese et al., 2002) Using this threshold, we constructed a symmetric connection matrix (Figures 5, 6), whose element was 1 if the cortical thickness correlation between 2 regions was statistically significant and 0 otherwise. This binarized connection matrix captures the underlying anatomical connection patterns of the human brain common to the population sample under study. We repeated all the analyses on matrices derived from the fine grained parcellation schemes described above, in order to validate our findings using multiple parcellation schemes.

All the modularity metrics were calculated on the above two adjacency matrices separately and compared to corresponding random networks. Modularity is an intuitional concept and there are variations in the mathematical definitions, where each has its own advantages and disadvantages. One common property among the various ways of defining modularity, however, is accounting for the agreed intuition about modularity, i.e., a module is a subset of nodes in a graph, whose connections among the elements within the subset are much denser than the ones to nodes outside the subset. Newman suggested the following modularity measure,Q: Q=maxs ∈ S14msTBs, where s is a column vector and element of the set S, S is the set of all column vectors whose dimension are equal to the number of nodes in the graph, n, and each component of the vector is either −1 or +1, (·)^T is the transpose. B is equal to A − kk^T /(2m), A is the adjacency matrix, whose dimension is n × n, and the i-th column (or row) and j-th row (or column) element is 1 (or 0) if i-th and j-th nodes are connected by an edge (or if there is no edge), k is a column vector whose element is the number of edges connected for each node, i.e., the degree of node, and m is the total number of edges. Roughly speaking, B quantifies the difference between the number of edges found in a subset of the given network structure, i.e., A, and the expected average from the random graphs, whose nodes degree is the same as the one of the given graph, i.e., kk^T /(2m). Hence, positive Q values imply that there are more edges found than the expected and it is, therefore, a module.

By obtaining s that maximizes the modularity, Q, the nodes are divided into two groups, i.e., modules, depending on the corresponding values in the maximizing vector, s. The maximization problem, however, is the integer quadratic programming problem, which is NP-hard. It is even computationally very difficult to obtain the true solution, which gives the global maximum value of Q. Note that Q is always less than or equal to 1. If the condition for s is relaxed so that it can take any real numbers, then the problem becomes finding maximum eigenvalue and the corresponding eigenvector of the matrix, B. This can be solved efficiently using the power-iteration, i.e., choosing an arbitrary initial vector, s₀, and recursively updating the vector using s_k+1 = Bs_k until it converges. Then, s maximizing Q is calculated simply by taking the sign of converged s_k. To increase the chance of finding the global solution, these procedures are repeated a number of times with a different random initial vector, s₀. If the calculated maximum value, Q, is positive (or negative), then the graph is divided (or declared indivisible).

Once the graph is divided into two modules, then each module is inspected whether it can be further divided by solving the following the maximization problem: ΔQ=maxr ∈ Sg14mrTBgr, where r is an element of the set s^g, s^g is the set of n_g-dimension column vectors whose element is either +1 or −1, n_g is the number of nodes in the module, which is found in the previous step, B^g is equal to B^ij − diag[k^g], B^ij is a matrix constructed by a part of B, where the rows and columns belong to the module, k^g is the degree of each nodes only concerning B^g, and diag [·] is the diagonal matrix, where the diagonal terms are given by the vector in the argument and the other elements are zero. Again, if ΔQ >0(or ΔQ ≤ 0), then the module is divided into two smaller modules (or declared indivisible). The above procedures are repeated on every module recursively until all modules are declared indivisible. By definition, the divisibility of a module is determined based on whether the modularity measure is positive or not. Very often, it is, hard to justify whether some subgroups of a graph are modules if the modularity contribution, i.e., Q or ΔQ, is very close to zero. As the mathematically possible maximum value is 1, the modular structure is much clearer if the modularity is closer to 1. Hence, the number of modules is calculated for various Q-threshold, which decides when modules are declared as indivisible.

A network, in general, is not a simple collection of modules but a combination of complicated overlapped modular structures, i.e., it demonstrates a hierarchical modular architecture. The overlapped modular structures are hard to decipher into elementary modules that pertain to the whole network. There are several methods to unravel the overlapping modular structure. In order to use a consistent measure with the modular calculation, an extended modularity (Q_e) is defined as follows: Qe=maxse ∈ Se14mseTBse, where s_e is an element of the set, S_e, and the set S_e is the collection of vector, s_e, whose dimension is again, n, i.e., the number of nodes, and its element is either -1, +1, or 0. Compare to the vector s in S, s_e has one more degree of freedom in possible values (Zhao et al., 2011). The nodes corresponding to zero are called gray nodes, which are included in multiple modules at the same time or are not included in any module. ΔQ_e is defined in the similar manner. Gray node is a similar concept to that of connector hub and hierarchical or overlapping modular structure. While connector hubs are defined as nodes with greater than average degree of the network and distributed between both local and long range connections, gray nodes are defined as nodes that are shared by modules. It is an index of overlapping modular architecture of the network. Previous literature has described such overlapping architecture based on a prior definition of modularity by Newman and Girvan (Newman and Girvan, 2004; Nicosia et al., 2009; Lazar et al., 2010; Wang et al., 2012). On the other hand, “gray nodes” are a unified way to define the structure in the more recent modularity definition by Newman (Newman, 2006). This provides an advantage that we measure modular architecture, and the overlapping architecture using a consistent measure without requiring significant changes in the algorithm (Newman, 2006).

All calculations presented in this paper are based on Monte-Carlo simulations performed 1000 times. The distributions of all calculations are confirmed to be similar to Gaussian distributions (data not shown). Hence, there is no danger that the analyses based on the mean and the variance may give any false interpretations of the true distribution of the data. All graphs were compared to random graphs (with the same number of nodes and degree distribution as the corresponding brain networks).

Initial analysis of cortical thickness across groups showed that those from the most deprived population had significant cortical thinning pertaining to bilateral perisylvian cortices. (Figure 3).

We conducted all analyses on binarised matrices derived from interregional correlations of cortical thickness. Initial examination of number of isolated modules showed that for a given correlation threshold, the least deprived group had greater number of isolated groups compared to the deprived group (Figure 4). The raw networks and FDR filtered networks are shown in Figures 5, 6. The distribution of the groups' correlation coefficients is shown in Figure 7. A direct comparison of the networks derived from the above populations, was not possible, as for a given correlation threshold, the sparsity (density) of the two networks were significantly different (Figure 8). In addition, the FDR procedure thresholded the two networks significantly differently. This method of thresholding resulted in different number of edges—k—(sparsity) in the networks of the two groups because of differences in their inter-regional cortical thickness correlations. We therefore compared the network structure derived from the groups to their corresponding random networks. The results of this analysis are shown in Figures 9, 10.

Socio-economic status (SES) refers to a multidimensional construct that is usually measured using a number of economic (e.g., income) and non-economic (e.g., education) indicators (Hackman et al., 2010). SES can be measured at an individual/household or at a neighborhood level. Regardless of the level of measurement (individual/neighborhood), SES has been associated with significant health disparities (Diez Roux and Mair, 2010). Most of the studies previously mentioned have examined the association between individual level SES and brain morphology. But individual level explanations for poor health do not capture significant social and structural determinants of ill health (Diez Roux and Mair, 2010). It is well-established that social circumstances have direct biological consequences, as well as impact on health behaviors (see Diez Roux and Mair for a detailed review on neighborhood deprivation). However, relatively small number of studies have explored the contributions of individual level SES indicators with neighborhood level indicators to health inequalities. Neighborhood level deprivation has been associated with poor health outcomes due to inequalities in resource distribution. These neighborhoods have physical (e.g., access to food) and social (e.g., violence) attributes that are contributors to health outcomes. However, individual and neighborhood deprivation are likely to interact significantly. For example, Stafford and Marmot found that living in a deprived neighborhood has the most adverse impacts on poorer individuals possibly because they are more dependent on collective resources of the neighborhood (Stafford and Marmot, 2003). In our study, individual level SES covaried significantly with neighborhood level SES. (For details of this analysis see Table A1 in Appendix) Due to the nature of the sampling technique, people from the most deprived neighborhoods also had poorer individual SES. This is partly because neighborhood deprivation scores (SIMD) are derived from data pertaining to individuals in the area. Since our groups differed inherently in their individual SES, it was deemed inappropriate to co-vary for the effects of individual SES (Miller and Chapman, 2001). Our relatively small sample size was also not sufficiently powered to examine if individual SES contributed significant variance over and above that explained by neighborhood SES or vice versa. The extreme group sampling technique prevented us from examining any dose-response effect of either individual or neighborhood level deprivation in our sample.

Zalesky et al. have previously shown that network topology vary considerably as a function of the spatial scale of the atlas used (Zalesky et al., 2010). Previous reports that have examined cortical thickness covariance network structure in clinical and non-clinical populations have used the same parcellation scheme (Desikan-Killiany atlas) used in our study (Raj et al., 2010; Hanggi et al., 2011; Romero-Garcia et al., 2012; Yang et al., 2012). Of note, Romero-Garcia et al. in order to examine the effect of network resolution on topological properties, compared the Desikan-Killiany atlas based parcellation with finer parcellation schemes of up to 1494 parcellations (Romero-Garcia et al., 2012). Interestingly they found that highly grained cortical scales showed enhanced local connectivity (clustering coefficient), and local efficiency, but increased path length and decreased global efficiency. Our findings resonate that of Romero-Garcia et al., in that, at different parcellation schemes, the network topologies differed (Romero-Garcia et al., 2012). For fine-grained parcellation schemes that did not follow sulcogyral boundaries, the LD brain network, and MD brain network were similar. At a modularity threshold of around 0.3, both network structural properties looked similar to their random counterparts (suggesting a decrease in global properties at more fine grained schemes) (Figures 1A,B).

Anatomically, since cortical thickness is a continuous measure, regions that lie close to each other will show very similar cortical thickness and hence high correlation. Here, a fine parcellation schemes, may uncover local connection (or a forking-U fiber connection), while a coarse may not (see Figure 1 in Zalesky et al) (Zalesky et al., 2010). In addition, regions close to each other are likely to be anatomically connected by the tangential neurons and dendrites. It is possible that in our case, the group differences disappeared when geometrically close connections were exposed at the finer parcellation schemes. In addition, at finer parcellation, where the number of parcels far exceed the number of subjects in the study, the study may have been significantly underpowered to show significant differences between groups (Zalesky et al., 2010).

It is also possible that network structure derived from relatively coarse parcellations are more representative of large scale cortical networks, while the networks derived from the fine-grained parcellations also include the meso/microscale connections representing regional/local connections. Whatever the case, it is clear that the granularity of chosen parcellations may affect the results of the network analysis. Our data suggest that when exploring connectivity, choosing the right granularity that is best suited to answer the question of interest is vital. However, clear cut guidelines pertaining to this are absent. One suggestion is that in order to answer clinical questions, anatomically relevant atlases like AAL or the sulcogyral parcellations (FreeSurfer) as used in our study may be more relevant. Interestingly for a finer (than Desikan atlas) parcellation that follows the sulcogyral boundaries (the Destreaux atlas—149 parcellations), the difference between the brain and random networks in the most deprived group disappear at around a modularity threshold of around 0.2 (Figure 11A).

Although we found significant differences between the networks and their corresponding random graphs, we did not perform a direct comparison of the network structure between the two groups, as the thresholds imposed by the FDR correction led to matrices that were significantly different in their sparsity (density). Thresholding a matrix is a problem when comparing networks that have different sparsity for a given correlation coefficient (Van Wijk et al., 2010). While the reason for the sparsity difference between the groups is not known, revealing topological differences gives deeper insights into the difference in networks than just revealing the sparsity difference. One recommended way to solve this problem is by fixing the sparsity (density) of a matrix, and comparing the networks at the same fixed sparsity threshold (Hanggi et al., 2011). This approach will, however, increase the false negative or false positive correlations at a given threshold. For instance, in our case, at more than 90% of correlation thresholds, the LD network was more sparse (less edges—k) than the MD. i.e., for a given correlation threshold, the networks from both the groups were different in their size (the number of edges). The difference in modularity between groups may therefore be k dependent. This difference in correlation threshold may have arisen from anatomical difference in the bilateral perisylvian cortical thickness we found between groups. While these morphological differences could have led to a reduction in correlation between regions that are actually connected, this could also have led to an increase in the number of spurious correlations (false positive), between regions that are not biologically connected, thereby contributing to noise within the network. Therefore, introducing false edges by fixing the sparsity was not thought to be meaningful.

While the biological meaning of structural covariance is not clear, structural covariance networks have been found to be genetically heritable, associated with cognitive function, recapitulate functional networks, and change over the life span. See Alexander-Bloch et al. (2013) for a detailed recent review of this literature (Alexander-Bloch et al., 2013). Cortical volume is a construct that is derived from two distinct properties of the cortical sheet: cortical thickness and surface area and have distinct cellular and genetic basis. Rakic's (2007, 2009) radial unit hypothesis proposes that symmetrical cell division within the neural stem cell pool in the ventricular zone causes an exponential increase in the number of radial columns—that result in surface area (SA) expansion. This is independent of asymmetrical cell division in the founder cells that is responsible for a linear increase in the number of neurons within a radial column, contributing to cortical thickness (CT) (Rakic, 2007). Complex network analysis using graph theory using cortical structural covariance networks derived from CT and cortical SA shows different structural properties, suggesting that they contribute to different properties within cortical networks (Sanabria-Diaz et al., 2010). Cortical gray matter volume is almost entirely driven by differences in the cortical SA rather than CT. (Im et al., 2006) Secondly, recent large scale studies have shown that these two parameters—CT and SA—have independent genetic basis (Panizzon et al., 2009). Thirdly, life course trajectories of these cortical parameters seem to be different. While gyrification—a ratio of total SA to pial SA remains fairly stable post childhood through to early adulthood, CT changes dynamically through this period (Rathbone et al., 2011; Raznahan et al., 2011; Salinas et al., 2012). However, more recent studies suggest that the relation between age and cortical parameters in adulthood, are complex (Hogstrom et al., 2012). CT in addition appears to be highly susceptible to various environmental influences over the life course such as smoking, alcohol dependence, and marijuana use while SA appears to be influenced by various unique developmental factors (Kuhn et al., 2010; Lopez-Larson et al., 2011; Momenan et al., 2012). This highlights the importance of studying volume and thickness independently in morphometric studies (Winkler et al., 2010). Surface area appears to be influenced by various unique developmental factors and is less susceptible to age-related differences in later life (ref). These and other findings suggest that while cortical surface areas increase significantly prenatally and remain fairly stable post childhood, cortical thickness changes dynamically across the lifespan (Raznahan et al., 2011; Salinas et al., 2012; Shaw et al., 2012). We restricted our analysis to cortical thickness as we were examining the association between what an environmental variable (deprivation) and a cortical parameter (cortical thickness) that has previously shown to be influenced by environmental factors. Further analysis using other parameters may reveal differences in structural properties that are contributed by factors that may be influenced early in life.

While the positive features of this study include a well-characterized community based cohort, there are limitations to be acknowledged: the cross-sectional design limits our ability to attribute causation and there is some selection bias in that the participants opted in. We did not include any sub-cortical regions particularly those that are relevant to physiological stress response. Smaller sample size meant that there was a potential for type 2 error, especially with regards the fine grain parcellations. We excluded female subjects in order to reduce variance in cortical morphology pertaining to gender. Further work would involve replication of the study in a larger population, including younger population, targeting critical periods of brain growth. Finally, future work to develop a clearer biological framework of a more comprehensive investigation of metabolic and inflammatory markers may be more informative.

In summary, people from the MD population show less modular and overlapping modular architecture of the brain networks derived from cortical morphology compared to their corresponding random graphs at a coarse sulcogyral parcellation scheme. At fine grained parcellation scheme that did not follow sulcogyral boundaries, this difference disappeared. While the difference in network structure at the coarse level may be the result of anatomical differences at a large scale level, the exact etiopathogenesis and the consequence of this difference is not clear. Taken together we propose that brain networks associated with MD group may be less efficient in information and signal processing at a large scale level. Future studies should look at longitudinal functional and effective connectivity studies using MRI and EEG/MEG to explore the effect of socioeconomic status on development.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.