## Abstract

The intrinsic white matter connections of the frontal cortex are highly complex, and the organization of these connections is not fully understood. Quantitative graph-theoretical methods, which are not solely reliant on human observation and interpretation, can be powerful tools for describing the organizing network principles of frontal cortex. Here, we examined the network structure of frontal cortical subregions by applying graph-theoretical community detection analyses to a graph of frontal cortex compiled from over 400+ macaque white-matter tracing studies. We find evidence that the lateral frontal cortex can be partitioned into distinct modules roughly organized along the dorsoventral and rostrocaudal axis.

## INTRODUCTION

The frontal lobes implement cognitive control operations fundamental to flexible, goal-driven behavior (D'Esposito & Postle, 2015; Miller & Cohen, 2001). This brain region is composed of at least 19 cytoarchitectonically unique subregions (Petrides & Pandya, 1994), and for more than three decades a major aim of neuroscience has been to characterize the functional organization of these subregions.

Distinctions in cyto-myeloarchitecture as well as patterns of white matter connectivity between frontal cortical subregions likely form the basis of its functional specialization. Thus, a powerful method for understanding functional specialization is to examine detailed neuroanatomical descriptions of cyto-myeloarchitecture and white-matter tract tracings of the frontal cortex (Averbeck & Seo, 2008; Barbas & Zikopoulos, 2007; Petrides, 2005; Passingham, Stephan, & Kötter, 2002; Semendeferi, Armstrong, Schleicher, Zilles, & Van Hoesen, 2001). The rhesus macaque brain serves as an excellent model system for this pursuit because, unlike the human brain, invasive methods can be used to directly measure fiber tracts and there is a large corpus of studies that have mapped the connections and cytoarchitectonic divisions of the macaque brain (Bakker, Wachtler, & Diesmann, 2012; Kötter, 2004). Indeed, for more than 20 years, neuroanatomical studies in the macaque have provided critical insights into the anatomical or structural principles that underlie frontal cortical function.

One of the most influential ideas regarding the frontal cortex stemming from the neuroanatomical literature is that of its dual-axis organization and evolution. According to this view, originally proposed in a landmark cytoarchitectonic study by Barbas and Pandya (1989), frontal subregions can be thought of as being structurally and functionally divisible along both the rostrocaudal and dorsoventral axis. Barbas and Pandya (1989) provided evidence for this view in their observation that gradual architectonic changes across the rostrocaudal axis occurred in parallel across basoventral frontal areas as well as across mediodorsal frontal areas. Additional support for this view came from tract tracing studies focusing on the extrinsic or long-distance white matter pathways showing that dorsolateral versus ventrolateral and rostral versus caudal frontal regions maintain different patterns of connections with posterior sensory and motor regions (Yeterian, Pandya, Tomaiuolo, & Petrides, 2012; Petrides & Pandya, 2002; Petrides & Pandya, 1999; Barbas & Pandya, 1989; Cavada & Goldman-Rakic, 1989; Seltzer & Pandya, 1989; Ungerleider, Gaffan, & Pelak, 1989).

In addition to studying the long-distance pathways of the frontal cortex, neuroanatomical studies focusing on the organization of the intrinsic wiring of frontal cortex can be informative regarding its function. Throughout the primate neuroanatomy literature, there are many studies examining the interconnections between frontal regions. Yet, it has remained a challenge to extract clear principles from these individual studies. One reason for this difficulty is that the wiring diagram of frontal cortex is enormously complex, and it is difficult for even highly trained neuroanatomists to recognize and interpret these highly complex patterns of connections. That is, observer-dependent interpretations of complex neuroanatomical data have limitations. Another reason is a pragmatic one; it is often not feasible in a single neuroanatomical study to inject every region of the frontal cortex with both retrograde and anterograde tracers (but advances are being made; see Markov et al., 2014). Thus, to study the intrinsic connections from all or most frontal regions, neuroanatomists must combine results from multiple studies, which is a major challenge given that different parcellation and naming schemes are often used across studies.

Over the past 15 years, tools such as CoCoMac (Collations of Connectivity in the Macaque) database (Bakker et al., 2012; Kötter, 2004) have been developed, which house a large corpus of macaque connectivity data in an annotated form and coordinate-free registration algorithms that can operate on the annotated CoCoMac data (Bakker et al., 2012; Bezgin, Wanke, Krumnack, & Kötter, 2008; Kötter, 2004), that allow tracer results from multiple parcellation schemes to be combined. At the same time, the growing field of “connectomics” has introduced quantitative, observer-independent methods using graph theory for studying the large-scale organization of complex brain networks (Bullmore & Sporns, 2009). Combining these resources has enormous potential to advance scientific knowledge about the intrinsic organization of the frontal cortex by offering replicable, quantitative, and unbiased methods for testing an established anatomical theory and exploring new connectional patterns. For example, studies by Passingham et al. (2002) and Averbeck and Seo (2008) using CoCoMac data, along with multidimensional scaling and hierarchical clustering techniques, have shown that frontal subregions by virtue of their complex intrinsic and extrinsic connections each have a unique “connectional fingerprint,” which likely reflects functional specificity. Moreover, these studies demonstrate that there is a topological organization of frontal subregions' long-distance connections that roughly maps on to the dual-axis model (Barbas & Pandya, 1989). In essence, these previous studies have provided quantitative and observer-independent validation for the qualitative observations made by skilled neuroanatomists.

Here, our aim was to examine the intrinsic connections of macaque frontal cortex using observer-independent quantitative methods to test to the hypothesis that frontal cortical subregions can be divided into distinct networks along its rostrocaudal and dorsoventral axis. Given evidence for dual-axis frontal topology in the extrinsic wiring of frontal cortex, our aim here was to utilize sensitive graph-theory methods to examine whether a dual-axis organization is also reflected in the local white matter connections among frontal subregions. We applied a graph-theoretical community detection algorithm (Newman & Girvan, 2004) to a graph of macaque frontal cortex derived from the results of 400+ studies in the CoCoMac database (Modha & Singh, 2010; Stephan et al., 2001). Community detection algorithms subdivide or partition a network into smaller “modules” so as to maximize within-module connections and minimize between-module connections. This analysis capitalizes on the assumption that the brain maintains efficient and robust communication via connections that are clustered among regions with similar functions yet tend to be relatively sparse among regions with disparate functions (Sporns & Zwi, 2004). We use the term “modularity” and “modules” to refer to the quantitative value of network separability and the resulting network partition, respectively. We do not assume that regions within a module have the same specific function but rather that, based on their interconnectedness, regions within a module are more functionally related than regions in other modules and form a processing subnetwork.

## METHODS

### Data Set

The data set used for this study was drawn from the CoCoMac database (Stephan et al., 2001) and was published previously by Modha and Singh (2010). CoCoMac houses results from over 400 original neuroanatomical reports (spanning 100 years of research) and supplies more than 200 different mapping schemes and 30,000 anatomical connections. The database was designed to help provide logical solutions for the “parcellation problem” (Felleman & Van Essen, 1991)—the challenges associated with comparing results across different brain parcellations without the use of a common coordinate frame. CoCoMac does this by storing tracer and mapping information in a logical/relational form rather than a spatial form. Specialized coordinate-free registration algorithms have been developed to work with CoCoMac data to construct large-scale topological macro-connection matrices (i.e., “graphs”) of the macaque brain that incorporate tracer results from across different parcellation schemes (Blumenfeld, Bliss, Perez, & D'Esposito, 2014; Bakker et al., 2012; Bezgin, Vakorin, van Opstal, McIntosh, & Bakker, 2012; Stephan & Kötter, 1998). In such network graphs or connectivity matrices, brain regions are represented as nodes and white matter tract connections between nodes are represented as edges (Bullmore & Sporns, 2009). The connectivity matrix used for this study, published previously (Modha & Singh, 2010), is a macaque brain graph containing 383 unique cortical and subcortical nodes and 6,602 directed edges. Briefly, Modha and Singh (2010) constructed this matrix by first extracting all the brain regions listed in the CoCoMac database with unique sets of anatomical connections and mapping relationships. This comprehensive set of unique regions, along with all anatomical connections, was then combined into a single directed graph.

This data set has several strengths for our purpose: It is large (many nodes and edges), comprehensive (drawn from the entire CoCoMac corpus), unbiased (fully data-driven construction), and robust. However, two limitations of this data set are noteworthy. First, this graph has a hierarchical structure in that a region and its connections are represented at multiple spatial scales. For example, the original graph contained a single node for frontal cortex as well as a node for pFC and nodes for many subregions of pFC (e.g., Area 47/12). Thus, the connections of one subregion (i.e., Area 47/12) populate not only Node area 47/12's connections but also those of the prefrontal node as well as those of the frontal node. To address this limitation, we removed redundant higher-level nodes from the graph (i.e., the frontal and prefrontal nodes). The second limitation is that this network allows for spatially overlapping brain regions (e.g., 6Va, M2-FL) from different parcellation schemes to make unique contributions to the network. Although this promotes robustness in the graph, it can lead to the possibility that a given region of cortex can be assigned to multiple modules. Thus, it has the potential to complicate the interpretation of our results. In the analyses presented in our Results section, we take steps to address this later spatial overlap/multiple assignment issue.

To address the first issue and create a graph of frontal cortex at a single level of resolution, we extracted a subgraph consisting of the nodes and directed edges comprising the frontal cortex. We then removed redundant higher-level nodes from the graph (i.e., the frontal and prefrontal nodes) and binarized the resulting matrix leaving an undirected binary graph of the frontal cortex parcellated at a single level of resolution with 53 nodes and 269 undirected edges (Table 1). We take further steps to address the second, spatial overlap, issue in our analyses presented in the Results section.

Table 1.

Frontal Nodes Drawn from Modha and Singh (2010) Used for This Study

 Lateral Nodes Caudal, motor, and premotor regions Gu, 4c, PrCO, ProM, M2-HL, M2-FL, F2, F4, F5, F6, F7, 6Vb, 6Va Dorsolateral pFC 8Ad, L9, D9, 8B, PS, 9/46d, 46d, 46f, 46dr Ventrolateral pFC 44, 47/12, 9/46v, 45A, 45B, 46v, 46vr Frontal polar cortex 10v, 10d Medial Nodes Caudal regions SMAc, SMAr, 24d, 24c, 24b, 24a Mid to rostral regions 32, M9, 10m Orbital Nodes Caudal regions OFap, 13M, 13L, 13a Mid to rostral regions 12l, 12m, 12o, 12r, 11m, 11l, 14O, 14r, 10o
 Lateral Nodes Caudal, motor, and premotor regions Gu, 4c, PrCO, ProM, M2-HL, M2-FL, F2, F4, F5, F6, F7, 6Vb, 6Va Dorsolateral pFC 8Ad, L9, D9, 8B, PS, 9/46d, 46d, 46f, 46dr Ventrolateral pFC 44, 47/12, 9/46v, 45A, 45B, 46v, 46vr Frontal polar cortex 10v, 10d Medial Nodes Caudal regions SMAc, SMAr, 24d, 24c, 24b, 24a Mid to rostral regions 32, M9, 10m Orbital Nodes Caudal regions OFap, 13M, 13L, 13a Mid to rostral regions 12l, 12m, 12o, 12r, 11m, 11l, 14O, 14r, 10o

### Analysis

We applied Newman's modularity (Newman & Girvan, 2004) using simulated annealing (Guimerà, Sales-Pardo, & Amaral, 2004). This metric compares the number of within-module with between-module connections and thus reflects the strength of a graph's modular organization. Modularity, or Q, is defined as
$Q=∑i=1meii−ai2$
where eii is the fraction of edges that connect two nodes within a module i, ai is the fraction of edges connecting a node in module i to any other node, and m is the total number of modules. Modularity will be 1 if all edges fall within a module, and it will be 0 if there are no more connections within a module than would be expected by chance. According to Newman and Girvan (2004), typical values of Q range from 0.30 to 0.60 in relatively large and modular graphs (Newman & Girvan, 2004).
In subsequent analyses, we computed two nodal metrics that examine the roles of nodes within their module. The within-module degree (WMD) is a z-scored measure of the number of intramodule connections to each node. The WMD value for each node i, WMDi, is defined as
$WMDi=ki−k¯siσksi$
where ki is the number of connections between node i and other nodes in its module si, $k¯si$ is the average degree of all nodes in si, and $σksi$ is the standard deviation of the degree of all nodes in si. This gives a relative (z-scored) measure of how well connected any node is to other nodes within its own module (Guimerà & Nunes Amaral, 2005).
The participation coefficient (PC) is a measure of the number of intermodule connections for each node normalized by their expected value. The PC value for each node i, PCi, is defined as
$PCi=1−∑s=1NMkiski2$
where ki is the total number of connections to node i and kis is the number of connections between node i and nodes in module s. If a node has connections uniformly distributed to all modules, then its PC value will be 1; on the other hand, if its links are concentrated within its own module, its PC value will be 0 (Guimerà & Nunes Amaral, 2005).

## RESULTS

### First-Pass Analysis

Simulated annealing of the frontal graph produced an optimal Q of 0.315, which is in the typical range of values for modular graphs (Newman & Girvan, 2004). Three modules were detected roughly organized along the rostrocaudal axis of frontal cortex: one comprising mostly orbital and medial regions as well as some more caudolateral/motor regions (“orbitomedial + caudolateral module”: Figure 1A, yellow), one comprising mostly regions along the midlateral surface (“midlateral module”: Figure 1A, blue), and one comprising rostral and medial frontal regions (“rostral” module: Figure 1A, green).

Figure 1.

Results from the first pass (A) and second pass (B).

Figure 1.

Results from the first pass (A) and second pass (B).

To investigate whether this partition and corresponding Q value represents a better than a chance partitioning of the data, we performed Monte Carlo simulations, using 10,000 random partitions of the input graph, to ascertain a (null-hypothesis) probability distribution of Q values. Of the 10,000 iterations, the maximum Q value obtained was 0.08 (mean = −0.02 ± 0.01). Thus, it is highly unlikely (p < .001) that a random partition could provide a better fit to the data compared with our empirically derived partition of this brain graph.

We further interrogated this frontal cortex partition by calculating two nodal metrics: WMD and PC for each node (see Methods). WMD is a z-scored measure of the number of intramodule connections to each node. It provides a relative measure of how well connected any node is to other nodes within its own module. PC is the relative number of intermodule connections a node has. It is expressed as a ratio and indicates how important a node is for maintaining communication between modules. These metrics for every node in the brain graph are provided in Table 2.

Table 2.

WD, PC, and Degree for Frontal Nodes

 Region WMD PC Degree A. First Pass Caudal + orbital 12o 1.195 0.915 24 13L 0.995 0.997 17 12m 0.995 0.988 18 13a 0.995 0.988 18 11l 0.796 0.996 16 12r 0.796 0.996 16 13M 0.796 0.996 16 12l 0.796 0.859 24 10o 0.597 0.984 16 24b 0.597 0.931 19 24c 0.597 0.889 21 14r 0.199 0.980 14 10m 0.000 0.993 12 11m 0.000 0.976 13 24d 0.000 0.859 8 PrCO −0.398 0.967 11 6Va −0.398 0.938 12 6Vb −0.597 0.926 11 Gu −1.394 0.889 6 M2-FL −1.792 1.000 2 M2-HL −1.792 1.000 2 4c −1.991 1.000 1 Rostral 32 2.500 0.294 25 10d 0.000 1.000 1 OFap 0.000 1.000 1 14O 0.000 0.750 2 10v 0.000 0.556 3 B. Second Pass Dorsolateral SMAr 0.894 0.840 10 PS 1.342 0.910 10 46v 1.342 0.654 17 46d 0.894 0.889 9 8B 0.894 0.556 18 D9 0.000 0.750 8 M9 0.000 0.750 8 46dr −0.894 1.000 2 46vr −0.894 0.889 3 L9 −0.894 0.889 3 46f −1.342 1.000 1 SMAc −1.342 1.000 1 Ventrolateral 47/12 2.268 0.889 9 9/46v 1.512 0.972 6 8Ad 0.756 0.889 6 44 0.000 0.938 4 45A 0.000 0.938 4 9/46d 0.000 0.750 6 45B −0.756 0.750 4 ProM#2 −0.756 0.556 6 Premotor F2 1.200 0.840 10 F6 1.200 0.793 11 F5 1.200 0.609 16 F7 0.000 0.502 17 F4 −1.200 0.889 6 24a −1.200 0.490 14
 Region WMD PC Degree A. First Pass Caudal + orbital 12o 1.195 0.915 24 13L 0.995 0.997 17 12m 0.995 0.988 18 13a 0.995 0.988 18 11l 0.796 0.996 16 12r 0.796 0.996 16 13M 0.796 0.996 16 12l 0.796 0.859 24 10o 0.597 0.984 16 24b 0.597 0.931 19 24c 0.597 0.889 21 14r 0.199 0.980 14 10m 0.000 0.993 12 11m 0.000 0.976 13 24d 0.000 0.859 8 PrCO −0.398 0.967 11 6Va −0.398 0.938 12 6Vb −0.597 0.926 11 Gu −1.394 0.889 6 M2-FL −1.792 1.000 2 M2-HL −1.792 1.000 2 4c −1.991 1.000 1 Rostral 32 2.500 0.294 25 10d 0.000 1.000 1 OFap 0.000 1.000 1 14O 0.000 0.750 2 10v 0.000 0.556 3 B. Second Pass Dorsolateral SMAr 0.894 0.840 10 PS 1.342 0.910 10 46v 1.342 0.654 17 46d 0.894 0.889 9 8B 0.894 0.556 18 D9 0.000 0.750 8 M9 0.000 0.750 8 46dr −0.894 1.000 2 46vr −0.894 0.889 3 L9 −0.894 0.889 3 46f −1.342 1.000 1 SMAc −1.342 1.000 1 Ventrolateral 47/12 2.268 0.889 9 9/46v 1.512 0.972 6 8Ad 0.756 0.889 6 44 0.000 0.938 4 45A 0.000 0.938 4 9/46d 0.000 0.750 6 45B −0.756 0.750 4 ProM#2 −0.756 0.556 6 Premotor F2 1.200 0.840 10 F6 1.200 0.793 11 F5 1.200 0.609 16 F7 0.000 0.502 17 F4 −1.200 0.889 6 24a −1.200 0.490 14

The caudal + orbital module is composed of regions that fall along either the orbital/medial or caudolateral surface. Given this, we were interested in better understanding whether connections between either orbitomedial or caudolateral regions predominate and drive this module's structure. Examining the connections of caudolateral versus orbital/medial regions revealed that orbital/medial regions (10o, 10m, 11m, 11l, 12l, 12r, 12m, 12o, 13M, 13a, 13L, 14r, 24c, and 24b) are highly interconnected and make few connections to other modules. In contrast, caudolateral nodes (M2-FL, M2-HL, PrCO, 4c, 6Vb, and 6Va) maintain a balance of connections to other regions within the caudal + orbital module to premotor regions partitioned into the lateral module (see Figure 1). Thus, the connections to and between orbital/medial regions appear to predominate and drive the structure of the caudal + orbital module. To test this quantitatively, we used the nodal metric WMD, as it provides an index of the strength of membership for each node in a module. We compared WMD values of the caudolateral regions versus orbital/medial regions within the caudal + orbital module. We found that caudolateral nodes (M2-FL, M2-HL, PrCO, 4c, 6Vb, and 6Va) all had negative WMD values indicating that they were relatively weak members of the caudal + orbital module. In contrast, orbitomedial regions all had positive WMD values. These findings indicate that the preponderance of connections within the caudal + orbital module occurs to and between orbital and medial regions. Although caudolateral regions are connected to these orbital and medial regions, they are connected to premotor regions as well, and as such, these nodes are not strong members of the caudal + orbital module.

### Second-Pass Analysis

Given that most controversy in the field concerns the organization of the largest module, lateral frontal cortex, we applied a second pass of our modularity procedure to the midlateral module that produced an optimal Q of 0.324, which again is in the typical range of values for modular graphs. Three modules were detected: one comprising mostly dorsolateral regions (Figure 1B, light blue), one comprising mostly ventrolateral regions (Figure 1B, red), and one caudal comprising premotor and anterior cingulate regions (Figure 1D, orange).

In this second-pass partition of the lateral frontal module, it was evident that two regions typically considered as part of the dorsolateral frontal cortex partitioned with the “ventrolateral” module (e.g., 9/46d, 8Ad), and several regions typically considered as part of the ventrolateral frontal cortex (i.e., 46v, 46vr) and supplementary motor cortex (i.e., SMAc, SMAr) partitioned with the “dorsolateral” module. Thus, although the preponderance of nodes and edges is segregated along the dorsoventral axis, there are exceptions, most notably along convexity of the principal sulcus (e.g., Area 9/46d, 8Ad).

We further examined these exception cases along the principal sulcus convexity to better understand their roles in the lateral frontal network. Specifically, we were interested in testing whether these regions serve specialized roles within the lateral frontal network. To this end, we computed WMD and PC, which assess the roles nodes play with respect to communication between and within modules. For instance, nodes with a relatively high WMD but a moderate or low PC indicate that these regions are provincial hubs that facilitate mostly intramodule connections. Nodes with relatively high WMD and PC values indicate that a region acts as a bridge hub that links multiple modules to one specific module. In addition, a node with a low or moderate WMD but a high PC is considered a nonhub bridge node that links multiple modules together. Although these latter two hubs (bridges hubs and nonhub bridges) get assigned to modules, they are best thought of as contributing to multiple modules (Fornito, Zalesky, & Breakspear, 2015). The WMD z scores were 0.0 and 0.76 for 9/46d and 8Ad, respectively, and their PC values were 0.75 and 0.89, respectively (see Table 2B for WD, PC, and degree of all regions in the second-pass analysis). This indicates that these regions serve as bridge nodes with 8Ad acting as a bridge hub for the ventrolateral module and 9/46d acting as a bridge node that maintains connectivity similarly between modules.

Next, we examined the topology, WMD, and PC of other regions (PS, 9/46v, 46d, 46v, 46dr, 46vr) also located at or around the convexity of the principal sulcus. These regions all have relatively high PC values (see Figure 1) indicating a high level of between-module communication. The WMD z scores varied, with 9/46v, PS, 46v, and 46d having positive scores (1.51, 1.34, 1.34, and 0.89, respectively) and 46vr and 46dr having negative scores (both −0.894). Thus, overall, we see that regions situated along the convexity regardless of module assignment maintain high levels of between-module communication.

### Comparison with an A Priori Model of Frontal Organization

It is clear from the results above that the observed partitioning of the frontal network was similar to but not identical to an a priori model based solely on anatomical location (i.e., an idealized model that perfectly segregates dorsal from ventral and rostral from caudal). Next, we then examined (a) how similar our partition was to this idealized a priori model and (b) whether this similarity could have arisen by chance alone. To do this, we first created an a priori partition of the frontal cortex that perfectly segregated dorsal versus ventral and rostral versus caudal (see Table 1). We then computed the mutual information shared between this a priori partition and the observed partition. We obtained a value of 0.443, indicating that the observed partition was approximately 44% similar to the a priori partition. Next, we performed a Monte Carlo simulation to obtain a distribution of mutual information values and a 99% confidence interval around this distribution for hypothesis testing. On the basis of a 0.005 margin of error, 168 iterations were performed producing an average mutual information value of 0.408 and a critical value for the upper 99% confidence interval of 0.437. Thus, the observed partition's mutual information with the a priori model exceeded what would be expected 99% of the time compared with a random partition.

### The Impact of Spatial Overlap

As described in the Methods section, the brain graph we analyzed was generated by combining data from different parcellation schemes, and there are three cases in the first-pass analysis where overlapping regions of cortex are partitioned into different modules. For example, ventral premotor areas 6Va and 6Vb from Barbas and Pandya (1987) overlap with ventral premotor areas F4 and F5 from Matelli, Luppino, and Rizzolatti (1985), and these regions were partitioned into different modules in the first-pass analysis. Spatial overlap also exists between ventral premotor areas 4c/PrCO and PROM, between SMAs SMAc/SMAr and M2-FL/M2-HL, and between frontopolar areas 10o/10m and 10v/10d. The second-pass analysis did not produce any such cases of multiple assignments, and thus, the identified modules did not overlap.

The presence of spatial overlap in the first-pass analysis raises two potential issues regarding our results. First, given that there is an overlap between the ventral premotor nodes partitioned into the caudal + orbital module (6Va and 6Vb) and the ventral premotor nodes partitioned into the lateral module (F4, F5, PrCO), it raises the concern that the rostrocaudal organization evident in the first-pass analysis lacks robustness. Importantly though, as noted above, the caudolateral nodes, including 6Va and 6Vb, are relatively weak members of the orbitomedial + caudolateral module. Moreover, adding these nodes to the midlateral module does not drastically change the modularity value (Q = 0.282) of the brain graph. Thus, on the basis of the first-pass partition alone, evidence for a segregation of caudal nodes is mixed. However, in the second-pass analysis, there is no spatial overlap within premotor regions F4, F5, and PrCO, and these regions partition into a “premotor” module distinct from the midlateral frontal nodes. Thus, despite the inherent complications with spatial overlap in this data set, there are multiple sources of evidence for a rostrocaudal segregation.

Second, it is possible that spatial overlap between certain nodes or sets of nodes produced the observed results rather than true distinctions in the underlying anatomical organization. To rule out this possibility, two further analyses were performed. To examine the effect of spatial overlap between sets of nodes on community structure, eight graphs (see Figure 2 for four representative plots) were created in which different sets of seemingly overlapping nodes in premotor (6Va and 6Vb vs. F4 and F5) and supplementary motor (SMAc and SMAr vs. MII-FL and MII-HL) cortex were removed from the original graph and community detection analyses were then applied. In Graph permutation 1 (Figure 2, Column A), regions 6Va, 6Vb, MII-FL, and MII-HL were removed. In Graph permutation 2 (Figure 2, Column B), regions 6Va, 6Vb, SMAc, and SMAr were removed. In Graph permutation 3 (Figure 2, Column C), regions F4, F5, MII-FL, and MII-HL were removed. In Graph permutation 4 (Figure 2, Column D), regions F4, SMAc, and SMAr were removed (see Figure 2C for the four additional permutations). The first-pass community detection analysis on each of these graphs, similar to our original analysis, partitioned the pFC roughly along the rostrocaudal axis into either two or three modules (Figure 2, top). In all of these analyses, a module roughly corresponding to lateral pFC was detected. We then performed a second community detection pass on the lateral modules in these four graphs. This pass detected modules roughly organized along the dorsoventral axis. All community detection analyses at the second pass within lateral modules had Q ≥ 0.30. Thus, taken together, the pattern of results is very similar to the initial analyses (Figure 2, bottom).

Figure 2.

Depiction of community detection analysis results on brain map results after different sets of overlapping nodes have been removed. Macaque frontal cortical diagram adapted from Yeterian et al. (2012).

Figure 2.

Depiction of community detection analysis results on brain map results after different sets of overlapping nodes have been removed. Macaque frontal cortical diagram adapted from Yeterian et al. (2012).

To examine the effect of overlap between single node pairs, we examined the stability of the dorsolateral and rostrocaudal partitions after the removal of nodes. Specifically, we recomputed the first- and second-pass modularity analyses on an exhaustive set of frontal graphs for which a different individual node was removed from the original frontal graph. This resulted in 53 first- and second-pass partitions. The matrix in Figure 3 depicts the frequency for which node pairs co-occurred in modules through all 53 first- and second-pass community detection analyses. As can be seen, all nodes demonstrated a strong tendency toward stability, co-occurring in the same module, and the overall structure of the partitions matched that of a dorsoventral as well as a rostrocaudal organization. These results indicate that the modules that we detected in our main analyses remain stable after removing all potential cases of overlap.

Figure 3.

Stability of modules to removal of nodes. Plotted in each cell is the frequency for which each node pair co-occurred in the same module through 53 iterative passes of modularity. In each pass, one node was removed from the original graph.

Figure 3.

Stability of modules to removal of nodes. Plotted in each cell is the frequency for which each node pair co-occurred in the same module through 53 iterative passes of modularity. In each pass, one node was removed from the original graph.

## DISCUSSION

We examined the intrinsic white matter connections of the macaque frontal cortex using quantitative, observer-independent graph theory analyses. We found evidence that the intrinsic wiring of macaque frontal cortex reflects both a rostral–caudal and dorsal–ventral organization. The first pass of the community detection analysis algorithm uncovered a tripartite organization along the rostral–caudal axis. Interestingly, this specific segregation derived from an analysis of intrinsic frontal connections mirrors very closely the rostrocaudal organization proposed by Barbas and Pandya (1989) in their study of cytoarchitectonics of the frontal cortex. This segregation is also in accord with models of frontal cortical function (Buckley et al., 2009; Badre & D'Esposito, 2007; Petrides, 2005; Koechlin, Ody, & Kouneiher, 2003) based primarily on human neuroimaging results. In the second-pass analysis examining the lateral prefrontal module, distinct modules also emerged, organized along the dorsoventral axis. Again, this result is consistent with macaque (Meyer, Qi, Stanford, & Constantinidis, 2011; Baxter, Gaffan, Kyriazis, & Mitchell, 2009; Baxter, Gaffan, Kyriazis, & Mitchell, 2008; Passingham et al., 2002; Levy & Goldman-Rakic, 2000; Petrides, 2000; Petrides, 1995) and human (Hampshire, Duncan, & Owen, 2007; Blumenfeld & Ranganath, 2006; Petrides, 2005; D'Esposito & Postle, 1999; Courtney, Petit, Haxby, & Ungerleider, 1998) studies that propose distinct cognitive control functions along the dorsal–ventral axis.

The frontal cortex occupies nearly a third of the primate cortex. The intrinsic wiring of frontal cortex is immensely complex, and there is a growing realization that quantitative and observer-independent analyses of connectivity data are an essential tool that can lead to a better understanding of frontal cortex organization (Markov et al., 2014). Recent advances have made macaque white-matter connectivity data, and tools to analyze these data, widely available and accessible. For instance, the CoCoMac database, created and curated by the laboratory of Rolf Kötter (Bezgin et al., 2008; Kötter, 2004; Stephan et al., 2001; for ongoing support, see Bakker et al., 2012), is a Web-based repository of annotated macaque neuroanatomy data. CoCoMac houses an extensive amount of data: results from over 400 original reports and from Brodmann's 1905 work to studies published as recently as 2005, comprising more than 200 different mapping schemes and 30,000 anatomical connections. Computational techniques, such as coordinate-free registration (Blumenfeld et al., 2014; Stephan & Kötter, 1998), can be used to synthesize CoCoMac data to construct large-scale white-matter brain graphs of the macaque cortex. Here, we used one such graph, the current largest and most comprehensive published graph (Modha & Singh, 2010). Using these data coupled with a graph-theoretical community detection algorithm (Guimerà et al., 2004), our results indicate that the connections of frontal cortex are systematically and topologically organized into separate communities (i.e., rostral, caudal–orbital, dorsolateral, ventrolateral) that are maximally connected within their community and more sparsely connected between modules.

Our first-pass community detection results have bearing on the growing literature supporting a rostrocaudal frontal control hierarchy (Nee & D'Esposito, 2016; Blumenfeld, Nomura, Gratton, & D'Esposito, 2013; Taren, Venkatraman, & Huettel, 2011; Buckley et al., 2009; Race, Shanker, & Wagner, 2009; Badre & D'Esposito, 2007; Koechlin et al., 2003). These studies demonstrate that distinct regions along the rostrocaudal frontal axis, from premotor to midlateral to frontopolar cortex, are engaged in cognitive control processing at progressively higher levels of temporal or representational abstraction (e.g., from planning concrete motor actions in premotor cortex to forming abstract long-term goals in frontopolar cortex). Specifically, we found that regions within premotor cortex, within midlateral frontal cortex, and within frontopolar cortex form distinct subnetworks or modules. This indicates that regions within each of these modules are not only spatially adjacent but are highly interconnected. Moreover, the regions within each module tend to have a similar extent of differentiation (Barbas & Pandya, 1989), where the lamination of premotor (no Granule layer IV), midlateral prefrontal (very differentiated Granule layer IV), and frontopolar (Granule layer IV present but less differentiated) collectively differs. A major question that remains is how the architecture of frontal cortex can support a functional hierarchy. One proposal is that asymmetrical connectivity between nonadjacent frontal regions along the rostrocaudal axis gives rise to this processing hierarchy (Badre & D'Esposito, 2009). Alternatively, it is proposed that an anatomical gradient can be derived purely on the extent of Layer IV–VI lamination (Goulas, Uylings, & Stiers, 2014). Here, our first-pass results offer evidence for an anatomical model of frontal organization that does not rely on connectional asymmetry.

Our second-pass analysis found that dorsolateral and ventrolateral frontal subregions segregated into separate modules based on their intrinsic connections suggesting that dorsolateral subregions are much more strongly connected to each other than with ventrolateral subregions and ventrolateral frontal regions show the opposite pattern. This finding is consistent with an anatomical study by Barbas and Pandya (1989) showing that tracer-injected dorsal areas (i.e., dorsolateral and dorsomedial frontal cortex) exhibited slightly more spatially extensive staining with other dorsal frontal areas than with basoventral (i.e., ventrolateral and ventromedial) areas, whereas basoventral areas showed the opposite pattern. We can infer from this modular organization that dorsolateral and ventrolateral subregions likely perform separable functions. Macaque lesion (Buckley et al., 2009; Petrides, 1995; Passingham, 1975) and electrophysiological (Meyer et al., 2011; Constantinidis, Franowicz, & Goldman-Rakic, 2001; Funahashi, Chafee, & Goldman-Rakic, 1993) studies have proposed that primate ventrolateral pFC implements various first-order nonspatial cognitive control operations, such as selection, working memory maintenance, and retrieval of goal-relevant information, whereas dorsolateral frontal regions implement more spatial/second-order cognitive control processes such as working memory monitoring and relational processing of goal-relevant information. Similar results have also been found using human functional neuroimaging (Amiez & Petrides, 2007; Hampshire et al., 2007; Blumenfeld & Ranganath, 2006; Bor, Duncan, Wiseman, & Owen, 2003; D'Esposito & Postle, 1999; Courtney et al., 1998).

The first-pass analysis delineated frontal cortex into relatively large functional units, such as the lateral pFC, and the second-pass analysis was successfully able to subdivide this region even further into dorsolateral, ventrolateral, and premotor subnetworks. It is important to note that these partitions that were found at each pass represent the optimal solution found by simulated annealing for each of the input graphs. The number and size of these modules were not predetermined. Thus, this result is in line with prior theoretical work (Passingham, 2012; Petrides & Pandya, 1994) and empirical evidence (Averbeck & Seo, 2008; Passingham et al., 2002) that frontal networks have a modular organization at different spatial scales. This principle, termed “hierarchical modularity” (Meunier, Lambiotte, & Bullmore, 2010; Newman & Girvan, 2004), is a well-known property of complex biological networks. It is thought to allow a network to be highly robust and maintain a high level of integration while also allowing for flexibility and functional specialization. There is quantitative graph-theoretical evidence that whole-brain structural (Hilgetag, Burns, O'Neill, Scannell, & Young, 2000) and functional (Meunier, Lambiotte, Fornito, Ersche, & Bullmore, 2009; Zhou, Zemanová, Zamora, Hilgetag, & Kurths, 2006) networks demonstrate hierarchical modularity and copious amounts of anatomical tracing and cytoarchitectonic data that show that sensory and motor regions are hierarchically modular (Felleman & Van Essen, 1991). Our results are in line with these broad findings and provide additional evidence that the frontal cortex is decomposable into subnetworks at multiple scales.

A few studies focusing on the frontal cortex have been published using quantitative methods and CoCoMac, and these studies have bearing on our results. In a seminal review article, Passingham et al. (2002) showed that each prefrontal subregion has a unique connectional “fingerprint” by virtue of the fact that each region maintains a distinct pattern of intrinsic connections. Using hierarchical clustering, they additionally showed that frontal regions could be loosely grouped into connectional families based on connectional similarity between regions. The families that Passingham et al. (2002) found—a dorsal family, a ventral family, and an orbitomedial family—are similar to our results. More recently, Averbeck and Seo (2008) used a clustering approach to extend these original findings and identified five connectional families based on similarities in the long-distance pathways between frontal regions. These connectional families were roughly topologically organized into separate caudal–orbital, dorsomedial, ventromedial, dorsolateral, and ventrolateral clusters, a pattern consistent with prior observations in the neuroanatomy literature that prefrontal regions can be segregated based on inputs (Petrides & Pandya, 2002; Petrides & Pandya, 1999; Cavada & Goldman-Rakic, 1989; Seltzer & Pandya, 1989). In our study, we did not quantify connectional similarity or examine long-distance connections, but nevertheless, our results are convergent. Thus, taken together with these previous studies, we conclude that the intrinsic and extrinsic anatomical connections of the frontal cortex follow a rostrocaudal as well as a dorsoventral organization.

For our analyses, we used the largest and most comprehensive macaque brain graph available (Modha & Singh, 2010). Although every node has a unique connectivity fingerprint in this graph, there is the potential for spatial overlap between nodes and, with it, some redundancy between edges, which could impact community detection results. These issues arose from the fact that this graph was built by merging noncorresponding parcellation schemes. Importantly, the lack of correspondence between parcellation schemes (the “parcellation problem”) is a reality in large-scale brain graphs built from the macaque neuroanatomical corpus (Stephan et al., 2001; Stephan & Kötter, 1998), and although anatomical studies (Markov et al., 2014) and computational methods (Blumenfeld et al., 2014; Bakker et al., 2012) are being developed to address these issues, further work is still necessary. In our first-pass analysis, we addressed the issue of spatial/connectional redundancy by examining in partitions in multiple ways. We performed two additional analyses in which we removed spatial overlap and recomputed modularity. The results were similar to our original findings demonstrating that, regardless of spatial overlap, community detection analyses parcellate the graph into separate rostrocaudal and dorsoventral modules.

Our community detection analyses are “observer independent,” in that the size and number of modules that could be recovered were not constrained and were based purely on the presence or absence of community structure in the underlying data. The algorithm was free to detect any community structure in the data. The fact that the algorithm recovered a dual-axis topology suggests that such an organizational scheme is present in the data. We note though that, although community detection analyses are observer independent, the frontal graph that we used (Modha & Singh, 2010) relies on parcellation schemes and tracer results, which depend on the observation of skilled anatomists. One potential concern is that the parcellation schemes themselves introduce bias. For instance, whereas the vast majority of parcellations are based on cytoarchitectonics, some schemes additionally use patterns in tracer data to refine boundaries. Thus, there is some extent to which a region's connectivity is ipso facto part of its boundary and definition. Importantly though, these differences would not necessarily predict a dorsoventral or rostrocaudal organization. Therefore, we do not believe that using traditional parcellation schemes introduces bias. In addition, a major strength of CoCoMac and the Modha and Singh (2010) graph is that it does not depend on only a single parcellation scheme or results from a single study. Rather, all the data in CoCoMac are used in deriving both the connections and nodes of the graphs. Thus, the impact of any single “incorrect” or “biased” observation would be minimized (for discussion, see Blumenfeld et al., 2014).

It is clearly observable that not every node in the second-pass partition conformed to classical dual-axis anatomical organizational schemes. This was particularly obvious along the convexity of the principal sulcus. For example, “dorsal” areas 9/46d and 8Ad partitioned with ventral frontal nodes, and “ventral” areas 46v and 46vr partitioned with dorsal nodes. This creates some interpretative ambiguity. For instance, according to the most stringent criterion, whereby we only accept a perfect match between an a priori dual-axis parcellation and our observed data to reject the null hypothesis, based on our results, we would fail to reject this null hypothesis. However, on the basis of a mutual information criterion, our observed segregation was significantly more similar to the a priori idealized segregation than would be expected based on chance. In essence, although our results do not perfectly correspond to what would be expected based purely on an idealized dual-axis intrinsic model of frontal cortex, we can reject the null hypothesis that the intrinsic connections of frontal cortex have no dual-axis organization.

An alternative proposal supported by our findings is that a dorsoventral connectional organization exists but it is more graded and less dichotomous, especially along the principal sulcus. There are certainly data from human functional neuroimaging and nonhuman primate electrophysiology studies that have long supported this view (Duncan, 2010; Miller & Cohen, 2001; Duncan & Owen, 2000). With community detection analyses, regions are partitioned strictly into discrete modules; thus, all members within a module do not likely serve the same network role within the module. We examined the nodal characteristics of these principal sulcus regions to determine the strength of membership of nodes and the roles these nodes serve within their modules. We found that several of these regions (PS, 46f, 46dr, 46vr, and 9/46v) have high PC values, reflecting that they have a high proportion of between-module connections, being well suited for mediating communication between modules (so-called “connector hubs,” e.g., Guimerà & Nunes Amaral, 2005). Such wiring may be necessary for the frontal cortex as a whole to integrate multisensory and motivational signals in the service of goal-directed behavior.

## Acknowledgments

This work was supported by the National Institute of Health (grants F32MH087047 to R. S. B. and grants MH63901 and NS40813 to M. D.).

Reprint requests should be sent to Robert S. Blumenfeld, Department of Psychology and Sociology, California State Polytechnic University, Pomona, CA 91768, or via e-mail: rsblumenfeld@cpp.edu.

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