Abstract

Coherent spontaneous blood oxygen level–dependent (BOLD) fluctuations have been intensely investigated as a measure of functional connectivity (FC) in the primate neocortex. BOLD-FC is commonly assumed to be constrained by the underlying anatomical connectivity (AC); however, cortical area pairs with no direct AC can also have strong BOLD-FC. On the mechanism generating FC in the absence of direct AC, there are 2 possibilities: 1) FC is determined by signal flows via short connection patterns, such as serial relays and common afferents mediated by a third area; 2) FC is shaped by collective effects governed by network properties of the cortex. In this study, we conducted functional magnetic resonance imaging in anesthetized macaque monkeys and found that BOLD-FC between unconnected areas depends less on serial relays through a third area than on common afferents and, unexpectedly, common efferents, which does not match the first possibility. By utilizing a computational model for interareal BOLD-FC network, we show that the empirically detected AC-FC relationships reflect the configuration of network building blocks (motifs) in the cortical anatomical network, which supports the second possibility. Our findings indicate that FC is not determined solely by interareal short connection patterns but instead is substantially influenced by the network-level cortical architecture.

Introduction

In recent years, coherent spontaneous activity in the primate cerebral cortex measured with blood oxygen level–dependent (BOLD) functional MRI (fMRI) has been intensely investigated as a powerful technique to simultaneously assess the “functional connectivity (FC)” (Friston 1994) of region pairs in the whole brain. The widespread use of BOLD-FC both in normal subjects (Biswal et al. 1995; Fox and Raichle 2007; Vincent et al. 2007; Moeller et al. 2009; Van Dijk et al. 2010) and in patients (Wang et al. 2009; Lynall et al. 2010) has led to attempts to elucidate how BOLD-FC is shaped on the anatomical network in the brain (Bressler and Menon 2010; Honey et al. 2010). BOLD-FC is commonly assumed to be constrained by the underlying anatomical connectivity (AC), and some studies have suggested that BOLD-FC is correlated with the strength of direct anatomical connections (Honey et al. 2009). However, even without direct axonal connections between 2 cortical areas, strong BOLD-FC is often observed (Koch et al. 2002; Vincent et al. 2007; Skudlarski et al. 2008; Honey et al. 2009), suggesting important roles of indirect pathways.

The causal directions in the neuronal interactions along the anatomical pathways are essentially determined by the direction of axonal projections; nevertheless, there has been no empirical study on how the directionality of AC contributes to FC at the interareal level because of the lack of noninvasive techniques to distinguish the directionality of AC in humans. In macaque monkeys, anatomical projections across a wide range of brain areas have been investigated for decades (Felleman and Van Essen 1991), and their directionality is known.

In this study, we used fMRI in macaque monkeys (Nakahara et al. 2002, 2006; Koyama et al. 2004; Vincent et al. 2007; Ekstrom et al. 2008; Moeller et al. 2009; Logothetis et al. 2010; Scholvinck et al. 2010; Wardak et al. 2010; Matsui et al. 2011) under anesthesia to empirically examine which features of interareal AC could predict FC. The presence and directionality of interareal axonal projections were based on past tracing studies collected in the CoCoMac database (Stephan et al. 2001). In particular, we asked whether the number of short connection patterns (of length 2) is related to the presence of FC, in the absence of direct anatomical connections. We confirmed this to be true; but to our surprise, FC was higher when 2 areas sent connections to a third region than when 2 regions were serially connected through a third region. This means that FC via indirect AC does not match the inference from apparent signal flows represented by the direction of axonal projections. Furthermore, to demonstrate the role of the network structure in which these short connection patterns are embedded, we then went on to examine whether the effect of small connection patterns on FC depends on the characteristic network properties of the cortical anatomy, using realistic computational modeling of the interareal BOLD-FC network of the macaque cortex (Honey et al. 2007).

Materials and Methods

fMRI Experiments in Macaque Monkeys

We used 2 female macaque monkeys (Macaca fuscata; Monkey 1 and Monkey 2, 5–8 kg). All experimental protocols were in full compliance with the regulations of the University of Tokyo School of Medicine and with the NIH guidelines for the care and use of laboratory animals. Magnetic resonance scanning was performed using a 4.7-T MRI scanner (Biospec 47/40, Bruker, Ettlingen, Germany) with 100 mT/m actively shielded gradient coils and a transceiver saddle RF coil (Takashima, Tokyo, Japan). Anesthesia of the animals was introduced with an intramuscular injection of medetomidine/midazolam (30 μg/kg and 0.3 mg/kg, respectively) before the fMRI experiments. During the acquisition of fMRI data, anesthesia was maintained with continuous intravenous infusion of propofol (6–10 mg/kg/h) and intramuscular injections of xylazine (1 mg/kg) as needed. Oxygen saturation was kept over 95%, heart rate and blood pressure were continuously monitored, and body temperature was kept constant using hot water bags. Functional data were acquired using gradient-echo echo-planar imaging (GE-EPI; 1-shot, time repetition = 2.0 s, time echo = 18 ms, 1.5 × 1.5 mm2 in plane resolution, 64 × 80 matrix, slice thickness = 1.5 mm, gapless, 33 horizontal slices covering the whole brain). Each scanning session consisted of 26 runs of 450 volumes (15 min per run; the first 5 volumes of each run were discarded). In each monkey, 3 sessions were performed (i.e., a total of 11 570 volumes per monkey were analyzed). High-resolution T1-weighted structural images of the monkeys were also scanned by using 3D MDEFT sequence (0.5-mm isotropic) in separate sessions. The preprocessing steps for the functional data included slice timing correction, realignment, and spatial normalization to template images made from the same monkeys’ GE-EPI images with interpolation into a 1 × 1 × 1 mm3 space, which were conducted using SPM5 (http://www.fil.ion.ucl.ac.uk/spm). The template image for each monkey was constructed by undistorting an EPI volume using a field map (Zeng and Constable 2002). The preprocessed images were not spatially smoothed.

Empirical BOLD-FC between the Macaque Cortical Areas

Using the Caret software suite (Van Essen et al. 2001), flattened cortical reconstruction of each monkey was made from the high-resolution structural images of each monkey. The constructed surfaces were registered to a macaque cortical surface atlas (F99UA1, http://sumsdb.wustl.edu:/sums/directory.do?id5679531) by using 20 major sulci as anatomical landmarks. In each monkey, the registration procedure determined which of the vertices on the constructed cortical surface were included in each of the macaque cortical areas in the parcellation scheme of Felleman and Van Essen (1991).

In the preprocessed 3D functional images, the region of interest (ROI) corresponding to each cortical area was defined as the voxels that contained the coordinates corresponding to the vertices assigned to the area. If a voxel contained vertices from multiple areas, we selected the vertex that is the closest to the center of the voxel and assigned the voxel to the area of the selected vertex. We extracted the BOLD time series from the voxels inside the ROIs of 39 areas (Fig. 1B). These areas are a subset of the 47 macaque cortical areas among which BOLD-FC was simulated in a previous computational study (Honey et al. 2007) and in the present study (“macaque-type” simulation, see below). Area 35, area 36, AITv, AITd, CITv, CITd, PITv, and PITd were not included in the analyses for this study because the voxels of the EPIs assigned to these areas by the above procedure partially suffered from signal decrease due to magnetic field inhomogeneity.

Figure 1.

Functional and anatomical connectivity networks in the macaque cortex. (A) Voxelwise FC map for an exemplar seed ROI of the right FST (green) in Monkey 1. High FC is observed in area 46 that is known to have no direct connection with FST. Scale bars = 10 mm. (B) Empirical BOLD-FC matrix among macaque cortical areas. Rows and columns indicate cortical areas. (C) AC matrix (modified from Honey et al. [2007], Copyright 2007 National Academy of Sciences, U.S.A.). A white (black) square indicates the presence (absence) of a confirmed directed anatomical connection from row to column. The arrangements of the areas in rows and columns are the same as (B). (D) FC matrix in the macaque-type simulation (modified from Honey et al. [2007], Copyright 2007 National Academy of Sciences, U.S.A.; see Materials and Methods). The arrangements of the areas in rows and columns are the same as (B). The abbreviations for the areas are provided in Supplementary Table 1. AS, arcuate sulcus; IPS, intraparietal sulcus; PS, principal sulcus; STS, superior temporal sulcus.

Figure 1.

Functional and anatomical connectivity networks in the macaque cortex. (A) Voxelwise FC map for an exemplar seed ROI of the right FST (green) in Monkey 1. High FC is observed in area 46 that is known to have no direct connection with FST. Scale bars = 10 mm. (B) Empirical BOLD-FC matrix among macaque cortical areas. Rows and columns indicate cortical areas. (C) AC matrix (modified from Honey et al. [2007], Copyright 2007 National Academy of Sciences, U.S.A.). A white (black) square indicates the presence (absence) of a confirmed directed anatomical connection from row to column. The arrangements of the areas in rows and columns are the same as (B). (D) FC matrix in the macaque-type simulation (modified from Honey et al. [2007], Copyright 2007 National Academy of Sciences, U.S.A.; see Materials and Methods). The arrangements of the areas in rows and columns are the same as (B). The abbreviations for the areas are provided in Supplementary Table 1. AS, arcuate sulcus; IPS, intraparietal sulcus; PS, principal sulcus; STS, superior temporal sulcus.

We calculated the time series of the areas by averaging the BOLD time series over all voxels in each of the ROIs. The time series from each BOLD run were temporally filtered to retain frequencies in the 0.0025 < f < 0.05 Hz band (Vincent et al. 2007) (FSL, http://www.fmrib.ox.ac.uk/fsl/). Then, several sources of spurious variance were removed by regression of nuisance variables including 6 parameters obtained by realignment and the signal averaged over whole brain (Fox et al. 2005; Vincent et al. 2007; Buckner et al. 2009). Pearson correlation coefficient matrix between the 39 areas was calculated for each hemisphere from the monkeys and for each run. The BOLD-FC matrix combined across all runs and across all hemispheres by using a fixed-effects analysis (Fox et al. 2005) is shown in Figure 1B.

We also produced FC maps at the voxel level, for seed ROIs (Fig. 1A and Supplementary Fig. 1A). This contrasts with the FC matrices among the ROIs above that we used for our main analyses. For the generation of the correlation maps, the functional data were spatially smoothed in a full-width at half-maximum of 3 mm before the temporal filtering. Correlation maps were combined across runs by using a fixed-effect analysis (Fox et al. 2005).

AC Matrix between the Macaque Cortical Areas

The AC matrix among the 39 areas (Fig. 1C) is a binary matrix whose components represent the presence of interareal axonal projections (from row to column) confirmed in past tract tracing studies. This AC matrix is a subset of the matrix among the 47 areas adopted in previous studies (Honey et al. 2007; Sporns et al. 2007) (“macaque large-scale visual and sensorimotor area corticocortical connectivity” available at http://www.brain-connectivity-toolbox.net). The data were collated in the CoCoMac database (Stephan et al. 2001). In this study, we refer to this anatomical matrix between the 47 areas as “macaque-type anatomical network.”

Evaluation of the Effects of Indirect Anatomical Connection Patterns on FC

Two areas that are not directly connected with each other can have anatomical connections with a common third area. The existence of connections among these 3 areas can be associated with a variety of patterns of directed connections. The connections could be reciprocal or not, convergent or divergent on the middle area, and so on. Figure 3A shows all the possible connection patterns among 3 areas, which will be called “length2-AC” patterns (af) in the following. To examine how FC of area pairs with no direct anatomical connection is dependent on the length2-AC patterns af (Fig. 3A), we adopted the following multiple regression equation: 

[1]
yi=α+j{a,b,,f}βjnij+ϵi,
where yi is the FC of area pair i; nij is the number of length2-AC pattern j (j ∈ {a, b, …, f}, Fig. 3A) that connect area pair i; α is the constant term; ϵi is the error term. Each nij was counted based on the AC matrix in Figure 1C. The estimated values of βj (j ∈ {a, b, …, f}) are considered as the increment of FC due to length2-AC pattern j (ΔFCj). Only area pairs with no direct AC (n = 479 for the AC matrix in Fig. 1C) are included in this regression analysis. The numbers of the patterns af in the AC matrix (Fig. 1C) are 96, 141, 68, 456, 356, and 535, respectively. This model quantitatively examines the linear effect of each pattern of connections, in proportion to their number between any 2 areas, without interactions among different sorts of connections that will need more complicated models. For the empirical data, the regression was conducted for the FC matrix combined across runs within each hemisphere of each animal (Fig. 3A). The mean value of βj across hemispheres for each j was used for the calculation of match-with-empirical index (MEI; Figs 3B and 4A,B).

Simulation of BOLD-FC in the Macaque-Type and the Rewired Anatomical Networks

BOLD-FC among the macaque cortical areas was simulated (macaque-type simulation) in a computational model introduced previously (Honey et al. 2007, 2009; Alstott et al. 2009), which incorporates the empirically known cortico–cortical connections in the macaque-type anatomical network (see Supplementary Methods). This model allowed us to examine how the local AC-FC relationships observed in the macaque cortex is dependent on the global network structure by rewiring the anatomical connections in the whole cerebral cortex and simulating FC in the rewired networks. We rewired the connections of the macaque-type anatomical network to generate the 5 sets of rewired networks: random networks, modularity-matched networks, clustering-matched networks, mf2-matched networks, and mf3-matched networks (mf2 and mf3 stand for motif frequencies of size M = 2 and 3, respectively; see Supplementary Fig. 4. Motif frequency is defined as the set of the numbers of occurrences of the respective motifs within a network). The simulation of BOLD-FC was also conducted in each rewired network, by utilizing the same model as the macaque-type simulation (Supplementary Methods). The models were implemented in FORTRAN 90 and in MATLAB (Mathworks). The simulations (FORTRAN) were carried out on the HA8000 Cluster System (T2K Open Supercomputer) at the Information Technology Center, The University of Tokyo.

Results

Interareal BOLD-FC in the Absence of Direct AC

We acquired BOLD fMRI in 2 anesthetized macaque monkeys and, after standard preprocessing steps (Fox et al. 2005; Vincent et al. 2007; Nelson et al. 2010; Van Dijk et al. 2010) (Materials and Methods), extracted the time series of BOLD signals from 39 areas (Felleman and Van Essen 1991) in each hemisphere of the animals. Figure 1A shows an exemplar BOLD-FC map in which the correlation with the time series of the floor of superior temporal area (FST) in the right hemisphere is spatially mapped (Monkey 1; see Supplementary Fig. 1A for Monkey 2). Previous literatures reported that direct connections were not found between the FST and area 46 in either direction even though the connections were explicitly examined with axonal tracers (Boussaoud et al. 1990; Felleman and Van Essen 1991). However, in Figure 1A, it can be seen that FST has high FC with area 46, as well as with area frontal eye field that is known to have direct AC with area FST (Boussaoud et al. 1990; Felleman and Van Essen 1991).

We computed the FC of all the area pairs (n = 741) within each hemisphere by correlating the BOLD time series in each functional run (for details, see Materials and Methods). Figure 1B shows the FC matrix combined across all BOLD runs and across both hemispheres from both animals using a fixed-effects analysis (the FC matrices are significantly correlated between animals, P < 0.001; see Supplementary Fig. 1B).

We then examined the relationship between the FC matrix and the underlying AC network. Data on the presence and the direction of anatomical connections among the macaque cortical areas examined in the present study (Fig. 1C) is based on the CoCoMac database (Stephan et al. 2001; Honey et al. 2007), containing a compilation of tracer studies (see Materials and Methods). In the empirical FC and AC matrices (Fig. 1B,C), area pairs with direct AC (unidirectional or bidirectional) indeed have larger FC on average than those with no direct AC (P < 0.001, t-test, 2-tailed) but nonetheless considerable proportions of unconnected area pairs have FC values comparable to connected area pairs (Fig. 2A) (Koch et al. 2002; Honey et al. 2009). To verify whether the presence of indirect AC increases FC, we examined how the number of indirect AC (regardless of the axonal directions here) between an area pair affects the FC of the area pair. In area pairs with no direct AC, FC significantly increases with the total number of indirect AC mediated by just one area in-between (length2-AC) (simple linear regression, n = 479, slope = 7.3 × 10−3, P < 0.001, one-tailed; Fig. 2B, blue), similar to a previous report in humans using diffusion imaging to detect AC (Honey et al. 2009). This result indicates that adding a single length2-AC results in a positive increment of FC (ΔFC) on average. On the other hand, FC does not increase with the number of length3-AC (2 areas in-between) in area pairs with neither direct- nor length2-AC (simple linear regression, n = 74, slope = −7.9 × 10−4, P > 0.9, one-tailed). In the macaque AC matrix (Fig. 1C), there is only one area pair with neither direct-, length2-, nor length3-AC, and there is no area pair with neither direct-, length2-, length3-, nor length4-AC. These results imply that FC increases with the number of indirect AC only at length2-AC.

Figure 2.

BOLD-FC in the macaque cortex depends on indirect AC. (A) Probability distribution of empirical FC values in area pairs with no direct AC (cyan, n = 479), unidirectional AC (yellow, n = 97), and bidirectional AC (red, n = 165). All comparisons of the means of the 3 distributions are significant (P < 0.001, t-test, two-tailed), but these distributions have large overlaps. (B) The relationship between FC and the number of indirect AC with just one area in-between (length2-AC). FC significantly increases with the number of length2-AC both in the empirical data (blue) and the macaque-type simulation (green) (P < 0.001 for both blue and green, simple linear regression, n = 479 area pairs with no direct AC). Error bars = standard error of the mean.

Figure 2.

BOLD-FC in the macaque cortex depends on indirect AC. (A) Probability distribution of empirical FC values in area pairs with no direct AC (cyan, n = 479), unidirectional AC (yellow, n = 97), and bidirectional AC (red, n = 165). All comparisons of the means of the 3 distributions are significant (P < 0.001, t-test, two-tailed), but these distributions have large overlaps. (B) The relationship between FC and the number of indirect AC with just one area in-between (length2-AC). FC significantly increases with the number of length2-AC both in the empirical data (blue) and the macaque-type simulation (green) (P < 0.001 for both blue and green, simple linear regression, n = 479 area pairs with no direct AC). Error bars = standard error of the mean.

Common Efferents and Common Afferents Increase BOLD-FC but Serial Relay Does Not

The local relationship between AC and FC observed here, that is, the positive ΔFC per length2-AC, might lead to a mechanistic interpretation that ΔFC is induced by causal synaptic actions along single length2-AC. Thus, corresponding to this interpretation, we can posit a hypothesis that FC in the absence of direct AC is increased by local signal flows via a serial relay through a third area and afferents from a common area. However, the possible patterns of length2-AC classified by the axonal directions (af in Fig. 3A) also include efferents to a common area, which should not convey causal flows between the area pair. If the hypothesis is valid, ΔFC of common efferents should be smaller than that of a serial relay through a third area (two-step relay) and common afferents. To test this prediction, we investigated how the magnitude of ΔFC varies with the axonal directions of length2-AC. Note that, in order to test the hypothesis, we should compare the effect of single length2-AC on FC apart from the effect of the number of pathways rather than the overall summation of ΔFC across the cortex.

Figure 3.

FC between unconnected areas does not depend on a serial relay but rather on common afferents and common efferents. (A) Increment of FC per length2-AC varies with the direction of axonal projections. Bottom, schematic illustrations of the 6 patterns of length2-AC. Two areas (orange circles) with no direct AC are connected via an intermediate area (white circle), and arrows represent the directions of axonal projections. Increment of FC due to each length2-AC pattern (ΔFCj, j = {a, b, …, f}) is defined as each of the 6 parameter estimates in the regression analysis of equation (1) (Materials and Methods). Gray bars indicate the mean values. **P < 0.01 and *P < 0.05, Tukey test after a three-way ANOVA (see Results). The common efferents (a) and the common afferents (c) have significantly larger ΔFC than the two-step serial relay (b). (B) Scatter plots of ΔFC of the length2-AC patterns (af). Abscissa, empirical data; ordinate, macaque-type simulation. The macaque-type simulation significantly preserves the respective ΔFCj of the 6 length2-AC patterns measured in the empirical data. The z-score-transformed correlation coefficient was defined as MEI. MEI is significant at the 5% level if its value >1.64. Error bars = standard error of the mean.

Figure 3.

FC between unconnected areas does not depend on a serial relay but rather on common afferents and common efferents. (A) Increment of FC per length2-AC varies with the direction of axonal projections. Bottom, schematic illustrations of the 6 patterns of length2-AC. Two areas (orange circles) with no direct AC are connected via an intermediate area (white circle), and arrows represent the directions of axonal projections. Increment of FC due to each length2-AC pattern (ΔFCj, j = {a, b, …, f}) is defined as each of the 6 parameter estimates in the regression analysis of equation (1) (Materials and Methods). Gray bars indicate the mean values. **P < 0.01 and *P < 0.05, Tukey test after a three-way ANOVA (see Results). The common efferents (a) and the common afferents (c) have significantly larger ΔFC than the two-step serial relay (b). (B) Scatter plots of ΔFC of the length2-AC patterns (af). Abscissa, empirical data; ordinate, macaque-type simulation. The macaque-type simulation significantly preserves the respective ΔFCj of the 6 length2-AC patterns measured in the empirical data. The z-score-transformed correlation coefficient was defined as MEI. MEI is significant at the 5% level if its value >1.64. Error bars = standard error of the mean.

Information about the directionality of interareal axonal projections in the macaque monkey allows us to distinguish the 6 different patterns of length2-AC (Fig. 3A), which are not distinguishable in diffusion MRI tractography (Koch et al. 2002; Skudlarski et al. 2008; Honey et al. 2009). We conducted multiple linear regressions of FC on the numbers of the length2-AC patterns for each hemisphere of each monkey (eq. 1 in Materials and Methods; n = 479 area pairs with no direct AC, overall fit P < 0.001 in all the hemispheres). We define ΔFC of each AC pattern (ΔFCj, j = {a, b, …, f}) as each of the 6 regression coefficients (βj) in this analysis. A three-way analysis of variance (ANOVA) for the estimated ΔFCj (AC pattern × Monkey × Hemisphere) revealed a significant main effect of AC pattern (F5,5 = 19.02, P < 0.01), no significant main effects of Monkey and Hemisphere (F1,5 = 0.22 and F1,5 = 0.48, respectively, P > 0.5 for both), and no significant two-way interactions (P > 0.1 for all). Then, we compared the ΔFC of pattern a, b, and c, which represent common efferents, two-step relay, and common afferents, respectively. As mentioned above, based on the apparent causal relationships represented in the AC patterns a, b, and c, one might predict that the ΔFC of pattern a (common efferents) is smaller than that of the other 2 patterns; however, our comparison revealed that, contrary to the prediction, not only common afferents (pattern c) but also common efferents (pattern a) show significantly larger ΔFCj than a two-step relay (pattern b) (P < 0.01, Tukey test after three-way ANOVA). We confirmed that these relationships for patterns a, b, and c were generally valid throughout the macaque cortical network and did not depend on specific area pairs (see Supplementary Fig. 2). We also performed an additional analysis to regress FC on the numbers of common efferents, two-step relays, and common afferents included not only in the patterns ac but also in d, e, and f (eq. 2 in Supplementary Methods). The result showed again significantly larger regression coefficients of common efferents and afferents than that of a two-step relay (P < 0.05, Supplementary Fig. 3). Therefore, these results indicate that FC cannot be inferred solely from the apparent signal flows represented by the local AC patterns.

The Global Network Structure of Cortical Anatomy Maintains Local AC-FC Relationships

The discrepancy between the inference from local axonal directions and the observed increments of FC demands an interpretation from a viewpoint beyond the local aspects of the AC patterns. Therefore, we posited a second hypothesis that the observed local AC-FC relationships seen in ΔFC of each length2-AC pattern (Fig. 3A) are shaped by the network structure of the cortical anatomy. To examine this hypothesis, we computationally investigated how the global network structure relates to ΔFC of the length2-AC patterns. A previous computational study (Honey et al. 2007) simulated the BOLD time series of macaque cortical areas including the areas examined in the present empirical data, based on a model incorporating empirically known axonal projections (macaque-type anatomical network; see Materials and Methods). By modifying the anatomical network in this model and simulating BOLD signals in various different anatomical network structures, we can examine how the interareal BOLD-FC is affected by the entire structure of the anatomical network.

First, we examined whether the simulated BOLD-FC in the macaque-type anatomical network (macaque-type simulation) captures our empirical observations. 1) The FC matrix of the macaque-type simulation (Fig. 1D) and the empirical FC matrix (Fig. 1B) correlates significantly (r = 0.55, P < 0.001; Supplementary Fig. 1C). 2) Also in the macaque-type simulation, considerable proportions of unconnected area pairs have FC values comparable to connected area pairs, while the difference of mean FC values between area pairs with direct AC (bidirectional and unidirectional) and those with no direct AC is significant (P < 0.001, t-test, two-tailed) (Supplementary Fig. 1D). We confirmed that 3) positive ΔFC per length2-AC (simple linear regression, slope = 1.0 × 10−2, P < 0.001; Fig. 2B, green) is significant in the macaque-type simulation. Most importantly, 4) the respective ΔFCj for the 6 length2-AC patterns are also preserved (correlation coefficient r = 0.91, P < 0.01, one-tailed; Fig. 3B). The agreements of 1–4 suggest that these empirically detected AC-FC relationships are induced by the anatomical network of the macaque neocortex that is shared by the macaque-type simulation. For later use, we defined MEI as the z-score-transformed correlation coefficient of the respective ΔFCj of length2-AC patterns between the simulation and the empirical data (MEI = 2.64 for the macaque-type simulation; see Fig. 3B). MEI represents how well the simulation preserves the respective ΔFCj of the length2-AC patterns (If MEI > 1.64, it is significant at the 5% level).

Next, we performed BOLD signal simulations on randomly rewired anatomical networks. If ΔFCj of the length2-AC patterns (Fig. 3A,B) is not locally determined but is maintained by the cortical network structure, the MEIs in the random networks should have values close to or less than zero, as opposed to the MEI in the macaque-type network. We generated random anatomical networks in which the number of afferent and efferent connections of each area (degree) is matched with that in the macaque-type network (Supplementary Methods). Then, we simulated the BOLD-FC matrix and computed the MEI for each random network. No random network (n = 1000; Fig. 4A, green) had MEI significantly larger than zero (all were <1.64) (Fig. 4B), supporting the second hypothesis that the empirically measured ΔFCj of the length2-AC patterns (Fig. 3A) is maintained by the specific structure of the anatomical network in the macaque neocortex.

Figure 4.

The local AC-FC relationship is shaped by network-level properties of the cortical anatomy. (A) Probability distributions of MEI in the rewired networks (for generation of rewired networks, see Results and Supplementary Methods). Five sets of anatomical networks were constructed by rewiring the macaque-type network: random (RD, green), modularity-matched (MD, cyan), clustering-matched (CL, magenta), mf2-matched (MF2, red), and mf3-matched (MF3, blue) networks (n = 1000 for each). mf2 (mf3), motif frequencies of size M = 2 (M = 3) (Supplementary Fig. 4). The distributions are significantly different from one another in all the combinations (P < 0.001, Mann–Whitney test). Dashed line is at MEI = 1.64: The networks at the right side of this line significantly preserve (P < 0.05) the empirically measured ΔFCj of the 6 length2-AC patterns (Fig. 3A). Chain line indicates the value in the macaque-type simulation. (B) Proportion of rewired networks with significant values of MEI (>1.64). The proportions in MF3 and MF2 networks (38.5% and 26.0%, respectively) are significantly larger (P < 0.001) than in the other networks (RD, 0%; MD, 0.3%; and CL, 1.3%). Error bars = 95% confidence interval (CI). Asterisks denote significance compared with the random networks (**P < 0.001, *P < 0.05). (C, D) Probability distributions of “combined ΔFC” of length2-AC in the rewired networks. Combined ΔFC is defined as the slope in the linear regression of FC on the number of length2-AC (see Fig. 2B green for the case of the macaque-type simulation). The distributions are significantly different from one another in all the combinations (P < 0.001, Mann–Whitney test). Bars in (D) indicate medians, and error bars are 95% CI of combined ΔFC. The value in the macaque-type simulation (chain line) is exceptionally large (**P < 0.002 in RD, MD, CL, and MF2 networks) except in the MF3 network (P = 0.57).

Figure 4.

The local AC-FC relationship is shaped by network-level properties of the cortical anatomy. (A) Probability distributions of MEI in the rewired networks (for generation of rewired networks, see Results and Supplementary Methods). Five sets of anatomical networks were constructed by rewiring the macaque-type network: random (RD, green), modularity-matched (MD, cyan), clustering-matched (CL, magenta), mf2-matched (MF2, red), and mf3-matched (MF3, blue) networks (n = 1000 for each). mf2 (mf3), motif frequencies of size M = 2 (M = 3) (Supplementary Fig. 4). The distributions are significantly different from one another in all the combinations (P < 0.001, Mann–Whitney test). Dashed line is at MEI = 1.64: The networks at the right side of this line significantly preserve (P < 0.05) the empirically measured ΔFCj of the 6 length2-AC patterns (Fig. 3A). Chain line indicates the value in the macaque-type simulation. (B) Proportion of rewired networks with significant values of MEI (>1.64). The proportions in MF3 and MF2 networks (38.5% and 26.0%, respectively) are significantly larger (P < 0.001) than in the other networks (RD, 0%; MD, 0.3%; and CL, 1.3%). Error bars = 95% confidence interval (CI). Asterisks denote significance compared with the random networks (**P < 0.001, *P < 0.05). (C, D) Probability distributions of “combined ΔFC” of length2-AC in the rewired networks. Combined ΔFC is defined as the slope in the linear regression of FC on the number of length2-AC (see Fig. 2B green for the case of the macaque-type simulation). The distributions are significantly different from one another in all the combinations (P < 0.001, Mann–Whitney test). Bars in (D) indicate medians, and error bars are 95% CI of combined ΔFC. The value in the macaque-type simulation (chain line) is exceptionally large (**P < 0.002 in RD, MD, CL, and MF2 networks) except in the MF3 network (P = 0.57).

Effects of Network Properties of Cortical Anatomy on FC

We further examined whether network metrics defined in the context of graph theory (Bullmore and Sporns 2009; Rubinov and Sporns 2010) could capture the uniqueness of the macaque cortical network that is revealed in the local AC-FC relationship. As candidates for graph metrics (Supplementary Methods), we focused on the clustering coefficient, the modularity, and the motif frequencies of size M = 2 and 3 (mf2 and mf3; Supplementary Fig. 4). The clustering coefficient and the modularity are found at higher levels in the macaque network (0.58 and 0.33, respectively), compared with the random networks (0.37 and 0.12, respectively, on average; Supplementary Methods) (Hilgetag and Kaiser 2004; Sporns et al. 2007). For each metric, we constructed rewired anatomical networks (n = 1000) in which the values of the metric as well as the degrees are matched with those of the macaque-type network (Supplementary Methods). Then, for each network, the BOLD-FC matrix was simulated, and the MEI was computed. The mf2-matched (MF2) and the mf3-matched (MF3) networks have significantly larger MEIs than the other rewired networks (Fig. 4A; P < 0.001). MEI is significant (>1.64) in 38.5% and 26.0% of the MF3 and MF2 networks, respectively but only in 0%, 0.3%, and 1.3% of the random (RD), the modularity-matched (MD), and the clustering-matched (CL) networks, respectively (Fig. 4B). We also confirmed that the large values of MEI in MF3 and MF2 networks are not attributable to the effect of network-similarity to the macaque-type network as quantified here by “graph edit distance” (Trusina et al. 2005) (Supplementary Methods; see Discussion below and Supplementary Fig. 5A,B). These results suggest that the global configuration of anatomical motifs in the cortical network plays a significant role in shaping the local relationship between AC and FC that was empirically observed.

Finally, we returned to “combined ΔFC,” which is defined as the regression slope of FC on the total number of length2-AC (see Fig. 2B, green for the macaque-type simulation) to verify whether the network properties of the macaque cortex shape the apparently local AC-FC relationship (the positive ΔFC per length2-AC) that was empirically detected (Fig. 2B). MF3 networks have significantly larger values of combined ΔFC than the other rewired networks (Fig. 4C; P < 0.001). The value of combined ΔFC in the macaque-type network is exceptionally high compared with RD, MD, CL, and MF2 networks (at 99.8—99.9 percentile for all), but on the other hand, it is within the normal range in MF3 networks (at 43.1 percentile) (Fig. 4C,D). We also confirmed that this effect of mf3 cannot be attributed to network-similarity with the macaque-type network (see Discussion below and Supplementary Fig. 5C,D). These results suggest again that the basic empirical observation of the positive ΔFC of length2-AC (Fig. 2B) cannot be attributed to exclusively local origins but is substantially influenced by the global structure of AC, in particular, the network-wide configuration of 3-node motifs.

Discussion

In this study, we empirically investigated the relationship of BOLD-FC with the underlying AC network among macaque cortical areas. We demonstrated how cortical FC varies depending on the directionality of interareal anatomical pathways (Fig. 3), using available data about the presence and the directions of axonal projections in the macaque cortex. Our results indicate that the relationship between AC and FC cannot be inferred from apparent local signal flows represented by the axonal directions. Instead, interareal FC is shaped by global features of the anatomical network architecture of the cortex (Fig. 4), an inference that is supported by a comparison of computationally modeled BOLD signals obtained from the anatomical network of the macaque cortex or from various modified control networks.

We empirically found that the ΔFC of common efferents is larger than that of a serial relay through a third area (Fig. 3 and Supplementary Fig. 3). This may sound counterintuitive because, if one considers the pattern of common efferents in isolation, it is unlikely that the signals sent out from an area pair into a common area are themselves a source of coherent activity of the area pair. Thus, we can conclude that the increases in FC cannot be exclusively attributed to the signal flow inferred from the local AC patterns. On the other hand, the finding of larger ΔFC in common efferents and afferents is consistent with another intuitive notion stating that functionally related (thus, functionally connected) areas will have similar anatomical afferent and efferent connections with other cortical areas (Young 1992; Passingham et al. 2002). This notion has received support from studies in several species (Young 1993; Scannell et al. 1995), for instance, by comparing the connection profiles of visual, auditory, and somatosensory areas (Young 1993) and by comparing the electrophysiological properties and anatomical connection profiles in motor and premotor areas (Passingham et al. 2002). Our finding leads to the suggestion that patterns of common efferents in the cerebral cortex are more likely to exist between areas that are functionally related and integrate information that is passed on to common target areas.

One potential caveat regarding the observation of larger ΔFC in common efferents is that, because of a possible high correlation between the number of the common efferents (pattern a) and that of other length2-AC patterns (bf), the separation of ΔFC of common efferents from that of the other patterns (such as common afferents) might be incompletely achieved in their statistical estimation (eq. 1). However, this is unlikely to occur because the correlations between the number of common efferents (pattern a) and that of the other patterns are very low (= –0.08 to 0.08; Supplementary Table 2).

Among the network properties we focused on in this study, the configuration of motifs (in particular, of size M = 3) is revealed to be an important determinant of the AC-FC relationship (Fig. 4). The observation that the frequencies of motifs largely affect the ΔFCj of the length2-AC patterns (which are motifs of size = 3 themselves) indicates that the dynamical property of each motif are not determined by the isolated motif in itself, but it is necessary to take into account the interactions between the motifs within the entire network, at least in the cortex. Although the importance of the configuration of motifs is revealed in this study, the MEI of the macaque-type network is still at high percentiles in the 5 sets of metric-matched networks (at 99.9, 99.9, 99.9, 98.8, and 96.3 percentiles for RD, MD, CL, MF2, and MF3 networks, respectively; Fig. 4A). This suggests that other anatomical features, which should be relevant to network structures larger than short connection patterns with length2-AC (e.g., within- or between-module structures [Meunier et al. 2010]), could play a role in shaping the FC network of the macaque cortex.

Because the MF3 networks tend to be more similar to the macaque-type network than the other rewired networks as measured by edit distance (Supplementary Fig. 5A,C; Supplementary Methods), this network-similarity could account for the large values of MEI and combined ΔFC in the MF3 networks. However, this is unlikely because even after removing the effect of network-similarity, the effects of mf3 remain significantly larger (P < 0.001) than those of the other network metrics (Supplementary Fig. 5B,D).

We conclude that the functional interactions among primate cortical areas are not solely determined by signal flows in local AC patterns, but instead the cortical anatomy embodies a network-level design that enables the interaction between 2 areas to be sensitive to influences from other remote cortical areas. Our findings constitute an important step toward unraveling how the network of AC shapes and generates functional interactions among the cerebral areas that support primate cognition.

Supplementary Material

Supplementary material can be found at: http://www.cercor.oxfordjournals.org/

Funding

This work was supported by a Grant-in-Aid for Specially Promoted Research from Ministry for Education, Culture, Sports, Science and Technology (MEXT) to Y.M. (19002010), by a grant from Takeda Science Foundation to Y.M., by Japan Society for the Promotion of Science (JSPS) Research Fellowships for Young Scientists to Y.A. (1611569), T.O. (1711447), T.W. (222882), and T.M. (218747); JS McDonnell Foundation (to O.S.).

Conflict of Interest: None declared.

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