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. 2020 Mar 18;30(8):4607–4616. doi: 10.1093/cercor/bhaa063

Hierarchy of Connectivity–Function Relationship of the Human Cortex Revealed through Predicting Activity across Functional Domains

Dongya Wu 1,2,3,4,#, Lingzhong Fan 1,2,3,5,#, Ming Song 1,2, Haiyan Wang 1,2,3, Congying Chu 1,2, Shan Yu 1,2,3, Tianzi Jiang 1,2,3,5,6,7,8,✉
PMCID: PMC8248587  PMID: 32186724

Abstract

Many studies showed that anatomical connectivity supports both anatomical and functional hierarchies that span across the primary and association cortices in the cerebral cortex. Even though a structure–function relationship has been indicated to uncouple in the association cortex, it is still unknown whether anatomical connectivity can predict functional activations to the same degree throughout the cortex, and it remains unclear whether a hierarchy of this connectivity–function relationship (CFR) exists across the human cortex. We first addressed whether anatomical connectivity could be used to predict functional activations across different functional domains using multilinear regression models. Then, we characterized the CFR by predicting activity from anatomical connectivity throughout the cortex. We found that there is a hierarchy of CFR between sensory–motor and association cortices. Moreover, this CFR hierarchy was correlated to the functional and anatomical hierarchies, respectively, reflected in functional flexibility and the myelin map. Our results suggest a shared hierarchical mechanism in the cortex, a finding which provides important insights into the anatomical and functional organizations of the human brain.

Keywords: anatomical connectivity, dMRI, fMRI, functional activations, prediction

Introduction

Converging evidence indicates that spatial–temporal hierarchical organizations that span between the primary and association cortices exist in the primate cerebral cortex (Felleman and Van Essen 1991; Chaudhuri et al. 2015). This hierarchy strongly affects both the functional and anatomical organizations of the cortex. A spatial hierarchy has been found using the laminar patterns of anatomical projections (Markov et al. 2014) and was further indicated by the macroscale cortical myelin estimated using structural magnetic resonance imaging (MRI) (Burt et al. 2018). Two parallel modeling studies also indicated that heterogeneity of the anatomical cortical organization shapes the large-scale hierarchies of neural dynamics (Demirtas et al. 2019; Wang et al. 2019). As a temporal counterpart, a hierarchy of different timescales across the cortex has also been observed and modeled based on invasive tract-tracing connectivity in the macaque neocortex (Chaudhuri et al. 2015). Recently, taking advantage of the diffusion MRI and resting state functional MRI (fMRI), the links between anatomical connectivity and functional connectivity were characterized and also presented a macroscale gradient spanning from the cortical sensory to cognitive areas (Preti and Van De Ville 2019; Vazquez-Rodriguez et al. 2019). The above studies indicate that extrinsic anatomical connectivity plays an important role in supporting such inter-areal hierarchical heterogeneity.

It is well known that the function of a cortical region is constrained by the underlying extrinsic anatomical connectivity (Passingham et al. 2002). The early studies investigated whether the boundaries of distinct brain regions characterized by anatomical connectivity coincide with boundaries of functionally distinct regions (Johansen-Berg et al. 2004; Tomassini et al. 2007; Beckmann et al. 2009; Saygin et al. 2011). Recently, several studies investigated the extent to which the functional activation of a few visual contrasts could be predicted from anatomical connectivity at a voxel-wise scale (Saygin et al. 2012; Osher et al. 2016), but most of the brain regions that are activated in a few visual contrasts are only specialized for face processing or visual functions (Zeki et al. 1991; McCarthy et al. 1997; Kanwisher 2010). As is known to all, the primary somatosensory cortices differ from the high-order association cortices in terms of their laminar organization and afferent and efferent connections (Pandya and Seltzer 1982). Therefore, whether anatomical connectivity can predict functional activations in association cortex to the same degree is still unknown. In other words, the extent that the functional activation of a cortical region is shaped by anatomical connectivity, which can be termed as the connectivity–function relationship (CFR), has not been fully characterized across the whole cortex. Moreover, whether there is a hierarchy in the CFR across different types of cortical areas remains unclear.

The current study addressed the above questions by investigating the CFR in different cortical subregions based on the human Brainnetome Atlas (Fan et al. 2016). We used a prediction model to assess the CFR to ensure that the CFR captured by the multilinear model was not a result of overfitting. We adopted the Human Connectome Project (HCP) dataset, which includes seven functional domains, for two reasons: First, we aimed to test whether the CFR would be consistent across different task states. Second, because different tasks might activate different cortical regions, we wanted to include as many cortical regions as possible. Finally, to determine whether the pattern of the CFR had a specific meaning, we investigated whether the pattern of the CFR was also reflected in the functional and anatomical hierarchies of the cortex.

Materials and Methods

Human Connectome Project Data

We used the minimally preprocessed data (Glasser et al. 2013) provided by the HCP. We randomly selected 100 unrelated subjects from the S1200 release. The information about the 100 unrelated subjects is listed in Supplementary Table 1. Since we performed the analysis at the vertex level rather than at the subject level, the number of samples was far more than 100; these 100 subjects were sufficient to get a reliable prediction result. See Supplementary Figure 1 for the supporting evidence.

Acquisition parameters and processing were described in detail in several publications (Barch et al. 2013; Smith et al. 2013; Sotiropoulos et al. 2013; Ugurbil et al. 2013). Briefly, diffusion data were acquired using single-shot 2D spin-echo multiband echo planar imaging on a Siemens 3 Tesla Skyra system (Sotiropoulos et al. 2013). These consisted of three shells (b-values = 1000, 2000, and 3000 s/mm2), with 270 diffusion directions isotropically distributed among the shells, and six b = 0 acquisitions within each shell, with a spatial resolution of 1.25-mm isotropic voxels. Each subject’s diffusion data had already been registered to his or her own native structural space (Glasser et al. 2013). Task fMRI scans were acquired at 2-mm isotropic resolution with a fast time repetition sampling rate at 0.72 s using multiband pulse sequences (Ugurbil et al. 2013).

We used the task fMRI data that were projected into 2 mm standard CIFTI grayordinates space, and the multimodal surface matching (MSM) algorithm (Robinson et al. 2014) based on areal features (MSMAll) was used for accurate inter-subject registration. The task fMRI contained 86 contrasts from seven task domains (Barch et al. 2013), labeled as EMOTION, GAMBLING, LANGUAGE, MOTOR, RELATIONAL, SOCIAL, and WM (working memory).The paired negative contrasts are redundant for the regression modeling and were thus excluded (Tavor et al. 2016), resulting in 47 contrasts for further regression analysis. The z-statistics for each contrast were used to assess the functional activations.

Anatomical Connectivity Profile

We calculated anatomical connectivity based on the Brainnetome Atlas (Fan et al. 2016), which contains 210 cortical regions in both hemispheres. The volume-based Brainnetome Atlas was first projected onto the mid-thickness surface of Conte69 template using the workbench software, after which the holes were filled and the islands were removed. Each of the 210 cortical regions was used as a seed region. For every seed region, therefore, there were 209 target cortical regions. All the vertices within the seed region were characterized by the anatomical connectivity of the 209 dimensions, representing the connectivity of each vertex in the seed region to the remaining 209 target regions. The anatomical connectivity was determined via probabilistic diffusion tractography. The white matter surface mesh aligned using MSMAll was used as the seed. Fiber orientations were estimated per voxel (three fibers per voxel), and probabilistic diffusion tractography was performed using software toolbox FDT (FMRIB’s Diffusion Toolbox) of FSL (FMRIB’s Software Library) (Behrens et al. 2007) with 5000 streamline samples in each seed vertex to create a connectivity distribution to each of the remaining 209 target regions, while stopping tracking at the pial surface.

Model Training

To avoid overfitting, we separated the 100 subjects into a training group of 80 subjects and a testing group of 20 subjects. We only included the significant (P < 1 × 10−4, approximated by P = 0.05 with FWE correction) connectivity features on the training group for further prediction. The testing group was used to assess the training model. For each of the 47 contrasts, we performed a regression analysis on each of the 210 cortical regions using anatomical connectivity. The regression analysis was modeled as Inline graphic where Inline graphic is the z-statistical value of the contrast maps and the mean of Inline graphic is subtracted to remove the intercept term; Inline graphic represents anatomical connectivity; Inline graphic is the regression coefficient to be estimated from the regression model. To train the regression model on the ith cortical region, we concatenated all the vertices of the ith cortical region into a column across the training subjects. Assuming that the ith cortical region has Inline graphic vertices, Inline graphic is a single column vector of length Inline graphic, representing the functional activation of all the seed vertices; Inline graphic is a matrix of Inline graphic rows and 209 columns, representing the connectivity features of all the seed vertices to the remaining 209 target regions; Inline graphic is a single column vector of length 209, representing how each connectivity feature contributed to predicting a seed region’s functional activation. Similarly, we obtained a connectivity feature from the testing group. After estimating the regression model’s coefficients from the training group, we applied these coefficients to the testing group’s connectivity feature to get the predicted functional activation of the subjects in the testing group. To get the predicted functional activation for the entire cortex, we repeated the same procedure for every cortical region and then concatenated every region’s prediction.

Assessment of the CFR

The CFR was assessed using the prediction accuracy of each testing subject’s functional activation to avoid overestimation on the training data. We correlated the predicted activation of every subject in the testing group with the actual functional activation of the same subject to evaluate the accuracy of the predictions, and the prediction accuracies of all the testing subjects were further averaged. We used the correlation coefficients Inline graphic to assess the CFR instead of the mean squared error (MSE) or mean absolute error (MAE) because, unlike MSE and MAE, which are not standardized and un-bounded, Inline graphic is standardized and bounded between −1 and 1. In addition, under the least square conditions of the regression model, the square of the correlation coefficient equals the proportion of the variance in the functional activation that can be explained by the connectivity features. When used for statistical tests, the CFR was Fisher’s z-transformed.

Calculation of Task Activation and Threshold

Each region’s task activation profile was calculated by first averaging each vertex’s absolute activation within a training subject and then averaging each training subject’s mean activation. We removed some regions that had a low-activation level in the process of averaging the CFR within each of the seven functional networks. The threshold was determined by first estimating the density distribution of all regions’ task activations in each contrast using the “ksdensity” command in Matlab. Next, the density peak of the distribution was found, and finally, the right endpoint of the 5% interval of the density peak was chosen to be the threshold for removing regions that had a relatively low activation level in each contrast.

Calculation of Functional Flexibility

To calculate each region’s functional flexibility, we assessed the similarity of connectivity features between two tasks by first reshaping the connectivity features into a column vector and then calculating the Pearson correlation. The functional flexibility was calculated by averaging the similarities between all pairs of tasks and then subtracting from one. If different tasks have similar connectivity features, then the average similarity was close to one and the functional flexibility was close to zero, indicating a low functional flexibility; otherwise, if different tasks have different connectivity features, the average similarity was close to zero and the functional flexibility was close to one, indicating a high functional flexibility.

Statistical Analysis

The CFR assessed by correlation coefficient was Fisher’s z-transformed for further t-tests. The two-sample t-test was performed using custom Matlab command “ttest2.” We did 1000 random permutations to test the performance of the connectivity model statistically. We trained the models in the same manner, but the pairings between each vertex’s connectivity feature and its functional activation were shuffled. We then tested how these random models performed on the testing group. We got one mean prediction accuracy for the connectivity model and 1000 mean prediction accuracies for the random models. Then, we calculated whether the mean prediction accuracy of the connectivity model was higher than the 95th percentile of the mean prediction accuracy of the random models to test whether the performance of the connectivity model was statistically meaningful. One thing to notice here was that we only shuffled the data in the training group but not in the testing group. Since we had trained the regression model one region at a time, we shuffled the pairings within the seed region but not across the whole cortex.

Results

Comparison between Actual Activation and Predicted Activation

Since the CFR was assessed via the similarity between predicted activation and actual activation, we first investigated the anatomical connectivity’s predicted activation visually. We selected several representative contrasts and plotted the actual and predicted activations of subject 120 111 on the brain surface in Figure 1; more examples are shown in Supplementary Figure 2. The threshold values for the individual activation maps were based on a Gaussian-two-gamma mixture model (Hartvig and Jensen 2000; Beckmann and Smith 2004; Tavor et al. 2016). The overall pattern of the predicted activation was very similar to that of the actual activation. The similarities (evaluated by correlation) are quantitatively presented in the third column of Supplementary Table 2. Anatomical connectivity predicted the overall patterns of task activation in various functional domains. To ensure that the prediction results were not completely driven by the parcellation adopted, a direct quantitative comparison of the predictions based on the Brainnetome Atlas (Fan et al. 2016) and the HCP_MMP1.0 parcellation (Glasser et al. 2016) is shown in the fourth and fifth columns of Supplementary Table 2. The difference between the prediction accuracies based on these two parcellations is not significant (t(46) = 1.49, P = 0.14, paired-t test), and the similarities (evaluated by correlation) between the predicted activations based on these two parcellations were very high; thus the parcellation scheme had little influence on the prediction results.

Figure 1 .

Figure 1

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Comparison between the actual and predicted activations. The left column represents the predicted activation and the right column represents the actual activation. Different rows represent activations of different contrasts. We mapped the 98 percentiles of the most positive and negative data values to 1 and −1. The overall patterns of the predicted activation were very similar to those of the actual activation.

Statistical Tests of the CFR

The previous section showed that anatomical connectivity predicted the overall pattern of task activation, but to compare the CFR for each region, we must first examine the CFR of each region statistically. Statistical analyses using a permutation test that shuffled the pairings between connectivity features and task activations were performed to assess the reliability of the connectivity model. If the mean prediction accuracy of the connectivity model was higher than the 95th percentile of the mean prediction accuracy of the random models, we regarded the connectivity model as statistically better than random. We calculated the number of regions that had connectivity models statistically better than random (Supplementary Table 3). We found that the CFR was statistically better than random in many regions across most contrasts. We found that in all contrasts the regions that had predictions better than random had significantly higher (P < 0.05, two sample t-tests. With the highest P value being t(208) = 1.82, P = 0.035, and most P values are <0.001) task activations (defined in the Methods part) than regions that had predictions that were not better than random. The CFR for a few contrasts, such as PUNISH-REWARD, was better than random in only a few regions because these contrasts had a very low activation level throughout the whole cortex.

Additionally, distance may influence the connectivity model since regions that are closer together are more likely to be connected and coactivated. Therefore, an additional control analysis using a distance model was conducted to ensure that the performance of the connectivity model was not driven by the spatial relationships. Instead of using the connectivity strength of various vertices to other brain regions, the distance model used the Euclidian distance from the vertices to the center of other brain regions as features. A comparison of the prediction accuracy between the distance model and the connectivity model is shown in Supplementary Figure 3. Anatomical connectivity had a better prediction accuracy than the distance model. After regressing out distance from the connectivity profile, anatomical connectivity still had a prediction accuracy that was better than random in many regions (Supplementary Table 3).

Hierarchy in the CFR

The previous section indicated that the CFR was statistically meaningful across different domains, but regional differences in the CFR still existed. We investigated the regional differences based on both the Brainnetome Atlas and the seven functional networks (Yeo et al. 2011; see Fig. 2). The result based on the Brainnetome Atlas offers a fine distribution of the CFR, while the seven functional networks characterize the functional hierarchy of cortex and offer a summary of the result. We mapped each of the 210 cortical regions to one of the seven functional networks that achieved maximum overlap, and the CFRs in each of the seven functional networks were averaged. As shown in the previous section, the CFR was not statistically significant in regions that had low task activation; thus, we only included regions that had a task activation that was higher than a given threshold. The calculation of the task activation and the determination of the threshold are provided in the Materials and Methods section. The results show that the CFR in the sensory–motor networks was stronger than that in the association networks, with an exception that the CFR in the visual network was weak under the language story contrast because this task only included an auditory stimulus but not a visual stimulus. Since different task contrasts activated different brain regions, we could not directly compare the CFR between two regions that had totally different activation levels in the same contrast, such as between the motor and prefrontal brain regions in the motor contrast. Therefore, to allow for the comparison of the CFR between any two regions, we focused on the consistency of the CFR in all the contrasts instead of in a single one and averaged the CFR across all the contrasts (in Fig. 3), including only the activated regions (the same regions as in Fig. 2) in the averaging process. To assure that this selective averaging result was not dramatically driven by the threshold level, we verified that the result was consistent across different threshold levels (Supplementary Fig. 4). We found that a hierarchy existed in the CFR: The CFR was relatively high in the sensory–motor networks, moderate in the dorsal and ventral attentional networks, and relatively low in the frontoparietal, default, and limbic networks. The sensory–motor networks included regions such as the motor, auditory, and visual cortices, and the association frontoparietal and default networks included regions such as the lateral prefrontal cortex and temporal–parietal junction. The CFR in the sensory–motor networks was significantly (t(198) = 6.82, P = 5.3 × 10−11, two sample t-test) higher than that in the association networks.

Figure 2 .

Figure 2

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Spatial distribution of the CFR in different contrasts. (a) The seven functional networks of the cortex. The colors represent the mapping of the seven networks, namely the frontoparietal control (FPN), ventral and dorsal attention (vATN, dATN), default (DN), and limbic (LMB) networks that constitute the association networks and the motor–auditory (Mot) and visual (Vis) networks that constitute the sensory–motor networks. The spatial distribution of CFR and the rank of the CFR in the seven networks are shown in different subplots, with (b) EMOTION FACES, (c) GAMBLING PUNISH, (d) LANGUAGE STORY, (e) MOTOR T (Tongue), (f) RELATIONAL REL, (g) SOCIAL TOM, and (h) WM 2BK.

Figure 3 .

Figure 3

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Spatial distribution of the average CFR. (a) Spatial distribution of the average CFR in the Brainnetome Atlas. (b) The average CFR was ranked, and the color represented the mapping of the seven networks. The CFR was highest in regions that are located mostly in the Vis and Mot networks. (c) Rank of the average CFR in the seven networks. The star symbol indicates that the CFR in the sensory–motor networks was significantly (t(198) = 6.82, P = 5.3 × 10−11, two sample t-test) higher than that in the association networks.

Hierarchy in the CFR Was Related to Functional Flexibility

We revealed the hierarchy in the CFR in the previous section. Next, we explored the connectivity features that contributed to the CFR in the multilinear regression model. We extracted the significant (P < 1 × 10−4, approximated by P = 0.05 with FWE correction) connectivity features of each cortical region in predicting each task’s activations, and these connectivity features were further used to investigate the functional flexibility of each region. The functional flexibility was defined as the variation in connectivity features across different tasks, which was to assess whether a cortical region utilized similar or different patterns of connectivity features in predicting its task activations across different tasks. The calculation of functional flexibility is provided in detail in the Materials and Methods section, and the same threshold levels as in the previous section were used to identify the activated regions in each task. Examples of two regions (a sensory region and an association region) are presented in Figure 4. The region A37lv (in the fusiform, lateroventral Area 37) had a flexibility of 0.37 and had relatively similar patterns of connectivity features across different tasks, and the region A46 (in the lateral prefrontal cortex, Area 46) had a flexibility of 0.63 and had relatively different patterns of connectivity features across different tasks. The functional flexibility was also assessed in the seven functional networks, and the flexibility of the sensory–motor networks was significantly (t(196) = −4.93, P = 8.7 × 10−7, two sample t-test) lower than that of the association networks. Further, the flexibility of each region was negatively correlated (r = −0.63, P = 3 × 10−23) with the average CFR. Therefore, functional flexibility exhibited a hierarchy that was the inverse of the hierarchy in the CFR.

Figure 4 .

Figure 4

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The flexibility of the connectivity features was related to the CFR. (a) The blue arrows represent the significant connectivity features of region A37lv (in the fusiform, lateroventral Area 37) in two tasks. The cortical region name is viewed in an anticlockwise manner, with each name labeling the following cortical regions in the block. The abbreviations are included in the end of article. (b) The blue arrows represent the significant connectivity features of region A46 (in the lateral prefrontal cortex, Area 46) in two tasks. (c) The functional flexibility was ranked in the seven functional networks. The star symbol indicates that the flexibility of the sensory–motor networks was significantly (t(196) = −4.93, P = 8.7 × 10−7, two sample t-test) lower than that of the association networks. (d) The flexibility of each region was negatively correlated (r = −0.63, P = 3 × 10−23) with the average CFR.

Discussion

In the present study, we investigated whether a cortical hierarchy of the CFR exists throughout the cortex. Specifically, our results showed that the CFR was statistically better than random models in most regions across seven functional domains. Moreover, we revealed that the CFR in the sensory–motor networks was higher than the CFR in the association networks and that similar regional differences between the sensory–motor and association cortices were also reflected in the organization of functional flexibility and the myelin map, a finding which suggests that the CFR has a hierarchical structure throughout the cortex.

The CFR was assessed via the predictive ability of anatomical connectivity, and the rationality of this assessment was confirmed by the following points. Since the connectivity model outperformed the random control model in most regions across seven functional domains, the statistical significance of the CFR was confirmed in most cases. The regions in which the CFR failed to pass the statistical test had statistically lower activation levels than the regions in which the CFR passed the statistical test. Therefore, testing the CFR in task-relevant regions is necessary, so we adopted an HCP task fMRI dataset that incorporates a wide range of functional domains to cover as many region’s functions as possible. Previous studies have already showed that a close relationship exists between anatomical connectivity and visual functions via the predictive ability of anatomical connectivity (Saygin et al. 2012; Osher et al. 2016). Our result demonstrates that this CFR is not restricted to visual functions and that brain function is closely related to anatomical connectivity from the primary sensory and motor functional domain to the high-order cognitive functional domain, a finding which supports the assessment of CFR in high-order functions.

Moreover, we also revealed that the CFR was hierarchical across the whole cortex. The CFR was relatively high in the sensory–motor and visual networks, moderate in the attentional networks, and relatively low in the frontoparietal and default networks. This pattern of hierarchy in the CFR was further found to be negatively correlated with the functional flexibility of the anatomical connectivity profile. While the anatomical connectivity substrate is fixed, the functional repertoire of the brain is diverse. The connectivity–function relationship does not show a one-to-one correspondence (Misic et al. 2016), and the many-to-one mapping from function to structure suggests that a fixed structure can support flexible functions. Our result indicated that the association cortex is more flexibly involved in a variety of tasks than are the sensory–motor cortex, coinciding with a review that suggested that the divergence between structure and function is enabled more at the global integration level (Park and Friston 2013). This many-to-one mapping between function and anatomical connectivity may make the prediction of function from anatomical connectivity more difficult in the association cortex. In addition, hierarchy in the CFR was found to be positively correlated with the myelin map. Because functional flexibility was higher in the association cortex than in the sensory–motor cortex and the myelin map was negatively correlated with the anatomical hierarchical level of the cortex (Burt et al. 2018), the above finding suggests that the CFR decreases along both the functional and anatomical hierarchical axes from the sensory–motor to the association cortex. Because the attentional networks are spatially located between the sensory–motor–visual networks and the frontoparietal–default networks, the hierarchical structure in the CFR is very similar to the large-scale hierarchical gradients (Huntenburg et al. 2018) that span between the sensory–motor and association areas in various cortical organizations. For example, a previous study showed that concrete-to-abstract semantic gradients from the sensory–motor to the association cortices exist in the functional processing hierarchies (Huth et al. 2016). In addition, the gradients in functional processing hierarchies were likely to be supported by the gradients in connectivity (Margulies et al. 2016) and microstructure such as myelin (Huntenburg et al. 2017) and cortical thickness (Wagstyl et al. 2015), which were also likely to have a genetic basis in that gene expression has been shown to separate the sensory–motor cortices from the association cortices (Hawrylycz et al. 2012). Besides, a recent study (Vazquez-Rodriguez et al. 2019) showed that the relationship between anatomical and functional connectivity gradually uncouples in the association cortex, a finding which also supports our CFR hierarchy. Therefore, our finding may suggest a hierarchical gradient in the CFR that has genetic and microstructural bases.

We also revealed that the CFR was correlated with the myelin map, which can serve as a proxy for the anatomical hierarchy (Supplementary Fig. 5). The consistency between the hierarchy in the CFR with both the functional and anatomical hierarchies of the cortical organization implies a shared mechanism in the hierarchical structure of the human brain. A plausible explanation as to why these evidences are tied together is that compared to the sensory–motor cortex, the association cortex, which is late-developing in evolution (Kaas 2006) and human development (Clancy et al. 2000), is essential to more complex brain functions (Goldman-Rakic 1988) and acts as a hub of integration (Mesulam 1998), thus flexibly participating in multiple functions. The high functional load in the association cortex may require greater expansion (Hill et al. 2010; Reardon et al. 2018) and more complex structural substrates. For example, the association cortex exhibits more dendritic branching complexity and dendritic spine density (Elston 2003), which also influences the neuronal functional properties (Koch 2004). Using the myelin map as a proxy, Burt et al. (2018) verified that the number of spines on pyramidal cell dendrites increases along a hierarchical axis from the sensory to the association cortex, thus endowing the association cortex with more recurrent synaptic excitation in local cortical microcircuits that are critical substrates for evoking sustained neural spiking and supporting cognitive computations (Murray et al. 2014). This indication is also consistent with the hierarchical timing scale in cerebral cortex supported by an electrophysiological (Murray et al. 2014) and a dynamical model study (Chaudhuri et al. 2015). Overall, the evidence suggest that the complex functions in the association cortex are also supported by local microstructures and cannot be solely attributed to the source of their inputs determined by extrinsic connectivity (Elston 2003), thus extrinsic anatomical connectivity alone may explain relatively fewer functional activations in the association cortex due to the more complex structural substrates that underlie its functions, suggesting that more microstructural properties should be considered when studying the complex functions of the association cortex. This combination of factors behind the hierarchy in the CFR provides important insights into the understanding of the anatomical and functional organizations of the human brain.

In conclusion, we verified that the brain functions were constrained by anatomical connectivity heterogeneously across the cortex and revealed that the hierarchical structure in the CFR was related to both the functional and anatomical hierarchies in cortical organizations. We provided an extensive delineation of the relationship between functional activation and anatomical connectivity in the whole cerebral cortex across various functional domains. Investigating the cortical function with respect to anatomical connectivity improves our understanding of how the cortical function emerges from connectivity constraints. Future work can build more complex models that incorporate microstructural properties to better characterize brain functions.

Supplementary Material

SUPPLEMENTARY_bhaa063
Click here for additional data file. (2.6MB, docx)

Abbreviations of Cortical Labels

SFG

superior frontal gyrus

MFG

middle frontal gyrus

IFG

inferior frontal gyrus

OrG

orbital gyrus

PrG

precentral gyrus

PCL

paracentral lobule

STG

superior temporal gyrus

MTG

middle temporal gyrus

ITG

inferior temporal gyrus

FuG

fusiform gyrus

PhG

parahippocampal gyrus

pSTS

posterior superior temporal sulcus

SPL

superior parietal lobule

IPL

inferior parietal lobule

Pcun

precuneus

PoG

postcentral gyrus

INS

insular gyrus

CG

cingulate gyrus

MVOcC

medioventral occipital cortex

LOcC

lateral occipital cortex

Funding

Natural Science Foundation of China (grant Nos. 91432302, 31620103905, 81501179); Science Frontier Program of the Chinese Academy of Sciences (grant No. QYZDJ-SSW-SMC019); National Key R&D Program of China (grant No. 2017YFA0105203); Beijing Municipal Science & Technology Commission (grant Nos. Z161100000216152, Z181100001518004, Z171100000117002); Guangdong Pearl River Talents Plan (2016ZT06S220).

Notes

The authors thank Prof. Yuanye Ma and Prof. Simon B Eickhoff for their constructive suggestions that improved the manuscript and appreciate the editing assistance of Rhoda E. and Edmund F. Perozzi, PhDs. Data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) and funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research. Conflict of Interest: 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.

Availability of Code

The codes for implementing all the analyses are available upon request.

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