Abstract
Models of large-scale brain networks that are informed by the underlying anatomical connectivity contribute to our understanding of the mapping between the structure of the brain and its dynamical function. Connectome-based modelling is a promising approach to a more comprehensive understanding of brain function across spatial and temporal scales, but it must be constrained by multi-scale empirical data from animal models. Here we describe the construction of a macaque connectome for whole-cortex simulations in TheVirtualBrain, an open-source simulation platform. We take advantage of available axonal tract-tracing datasets and enhance the existing connectome data using diffusion-based tractography in macaques. We illustrate the utility of the connectome as an extension of TheVirtualBrain by simulating resting-state BOLD-fMRI data and fitting it to empirical resting-state data.
Background & Summary
Linking cellular and circuit-level neural activity with macroscopic signals collected using noninvasive imaging techniques remains a significant challenge to understanding the underlying mechanisms associated with BOLD-fMRI and M/EEG signals. TheVirtualBrain (TVB) is an open-source software platform developed to meet this challenge through simulations of whole-brain network dynamics constrained by multimodal neuroimaging data1,2. TVB models link biophysical parameters at the cellular level with systems-level functional neuroimaging signals3. This linkage across spatial and temporal scales needs to be constrained by multi-scale data available from animal models. Recently, simulations of whole mouse brain dynamics have been made available in TVB4. In addition to rodents, nonhuman primates have become a valuable animal model for studying large-scale network interactions5,6. With unique similarities in brain, cognition, and behaviour to humans7–9, nonhuman primate models are well poised to bridge multiple scales of investigation. Here, we describe the development of a macaque structural connectome as an initial step towards establishing a multi-scale macaque model in TVB.
Simulations of large-scale network dynamics in which neural mass models are coupled together depend on neuroanatomical connectivity to define the spatial and temporal interactions of the system10,11. The connectome is a critical aspect of these models, with its white matter fiber tract capacities (i.e., weights) and tract lengths acting to scale network interactions. However, the construction of any individual connectome is nontrivial and, in the macaque, can be approached using a variety of datatypes. Neuroanatomical data from axonal tract-tracing studies are commonly considered the gold standard and are publicly available from a few sources. One, for example, is the CoCoMac database12,13, which can be queried for any number of cortical and subcortical brain regions14,15. It offers extensive coverage of the macaque brain but its description of fiber tract capacities is limited to categorical assignments. In another tracer dataset, Markov and colleagues16 provide a fully-weighted description of the macaque connectome. The edge-complete connectome, however, describes only 29 of 91 brain regions of a single hemisphere and its utility for whole brain simulations is limited. Alternatively, connectome construction could be performed using tractography on diffusion weighted imaging (DWI) data, as is commonly done for human subjects17. Probabilistic tractography has been shown to yield reasonable estimates of fiber tract capacities in macaques18–20 and can also provide estimates of tract length. But the resulting connectomes are undirected and therefore unable to capture the known impact of structural asymmetries on functional network topology21,22 and dynamics23. Moreover, connectomes derived from probabilistic tractography are tainted by a large number of false positive connections24,25 that can dramatically change the topology of the reconstructed network20,26,27.
We approached the problem of constructing a fully-weighted whole-cortex macaque connectome by synthesizing the information available from both tracer and tractography data (Fig. 1). We took advantage of the specificity of tracer connectivity and enhanced a whole-cortex tracer connectome with weights estimated from tractography. Since the accuracy of tractography algorithms varies as a function of their parameter settings20,28–30, we first optimized the tractography algorithm to best reproduce the fully-weighted but partial-cortex tracer connectome from Markov and colleagues16 before estimating whole-cortex connectome weights. We also estimated connectome tract lengths using tractography, which for tracer datasets is usually limited to Euclidean or geodesic distance estimates between ROI centers.
The connectome presented here will allow us to simulate whole-brain dynamics in the macaque across different modalities and scales (e.g., LFP, M/EEG, fMRI). Simultaneous recordings of neural signals at different spatial and temporal scales in the macaque are already possible35–37 and these types of data paired with TVB simulations will allow us to assess our understanding of brain dynamics across scales. In conjunction with existing macaque empirical data and open-access neuroimaging sharing initiatives like PRIME-DE38, the virtualized macaque brain will be a solid step forward in our efforts to model structure-function mapping in the whole brain.
Methods
Tracer data
Two independent tract-tracing datasets were used in the construction of the whole-cortex macaque connectome. The first was a whole-cortex structural connectivity matrix of 82 regions-of-interest (ROIs) as described in Shen et al22. This connectivity matrix follows the Regional Map (RM) parcellation of Kötter and Wanke39 and was derived from the CoCoMac database of axonal tract-tracing studies [cocomac.g-node.org]12–14. The matrix is directed and includes interhemispheric connectivity. Its edge weights are categorical (‘weak’, ‘moderate’, or ‘strong’).
The second tract-tracing dataset was the edge-complete connectivity matrix of 29 ROIs as described in Markov et al16 (Fig. 2A) [data available at core-nets.org]. This connectivity matrix represents intrahemispheric connectivity between a subset of regions in a 91-ROI parcellation. Its edges are fully weighted, spanning six orders of magnitude. This connectivity matrix was used to optimize tractography within the macaque brain. For the purposes of comparison with diffusion-derived connectivity matrices, the tracer matrix was symmetrized by taking the mean of the edge weights of both directions between pairs of ROIs.
ROI parcellations
Volumetric parcellations corresponding to both tracer-based connectivity matrices were defined on the F99 macaque atlas40. Both parcellations were registered to each subject’s diffusion data to define ROIs for tractography (see preprocessing section below). The RM parcellation was also used for defining ROIs in the resting-state BOLD-fMRI data in order to compute functional connectivity. For the RM parcellation, ROIs were first drawn on the F99 surface41 and converted to a labelled volume with a 2 mm extrusion22 using the Caret software package42 [http://brainvis.wustl.edu/wiki/index.php/Caret:About]. The 29-ROI parcellation and the F99 macaque atlas were both obtained from the SumsDB database [http://brainvis.wustl.edu/wiki/index.php/Sums:About].
Neuroimaging data acquisition & preprocessing
Neuroimaging data from 9 male adult macaque monkeys (8 Macaca mulatta, 1 Macaca fascicularis) were used for the construction and validation of the macaque connectome. These neuroimaging data were a subset of data presented in previous studies20,43. All surgical and experimental procedures were approved by the Animal Use Subcommittee of the University of Western Ontario Council on Animal Care and were in accordance with the Canadian Council of Animal Care guidelines.
Surgical preparation and anaesthesia44 as well as imaging acquisition and preprocessing protocols20,43 have been previously described. Briefly, animals were lightly anaesthetized before their scanning session and anaesthesia was maintained using 1-1.5% isoflurane during image acquisition. Images were acquired using a 7-T Siemens MAGNETOM head scanner with an in-house designed and manufactured coil optimized for the non-human primate head45. Two diffusion weighted scans were acquired for each animal, with each scan having opposite phase encoding in the superior-inferior direction at 1 mm isotropic resolution. For six animals, data were acquired with 2D EPI diffusion while for the remaining three animals, a multiband EPI diffusion sequence was used. In all cases, data were acquired with b = 1000 s/mm2, 64 directions, 24 slices. Four resting-state BOLD-fMRI scans were also acquired for each animal using a 2D multiband EPI sequence (600 volumes, TR = 1000 ms, 42 slices, resolution: 1 × 1 × 1.1 mm). Finally, a 3D T1w structural volume was also collected for all animals (128 slices, resolution: 500 µm isotropic).
The Brain Extraction Tool (BET) from the FMRIB Software Library package (FSL v5) was used to extract the brain from skull and soft tissue for all image modalities prior to all other preprocessing steps. Diffusion-weighted images were preprocessed using FSL’s topup, eddy and bedpostx tools for image distortion correction and modelling of fiber directions. Both parcellations in F99 atlas space were nonlinearly registered to each animal’s T1w structural volume and then linearly registered to diffusion space using the Advanced Normalization Tools (ANTS) software package46.
FSL’s FEAT toolbox was used for preprocessing the fMRI data, which included motion correction, slice timing correction, high- and low-pass filtering, registration, normalization and spatial smoothing (FWHM: 3 mm). Global white matter and cerebrospinal fluid signals were linearly regressed using AFNI’s (Analysis of Functional NeuroImages) 3dDeconvolve function.
Tractography optimization for fiber tract capacity estimates
Tractography was performed between all ROIs of the 29-ROI parcellation using FSL’s probtrackx2 function. Seed and target ROI masks were defined as the white matter voxels adjacent to each gray matter ROI. Exclusion masks were defined as the gray matter voxels adjacent to each seed mask. As the parcellation was defined in the left hemisphere, an exclusion mask of the right hemisphere was also applied. Tractography parameters were set to 5000 seeds per voxel, a maximum of 2000 steps, and 0.5 mm step length. Paths were terminated if they looped back on themselves and rejected if they passed through an exclusion mask. Tractography was performed repeatedly with various curvature thresholds (0.2, 0.4, 0.6, 0.8) as well as with and without distance correction.
Fiber tract capacity estimates (i.e., ‘weights’) between each ROI pair were taken as the number of streamlines detected between them and dividing by the total number of streamlines that were sent from the seed mask, with the exclusion of those streamlines that were rejected or excluded. A structural connectivity matrix of all ROI pairs was generated with these capacity estimates and symmetrized by taking the mean of the estimates of both directions between ROI pairs. This procedure was repeated for the various tractography settings and resulted in a total of eight connectivity matrices (4 curvature thresholds × 2 distance correction options) for each subject. Each of these eight matrices were then thresholded by discarding the lowest capacity estimates in increments of 5%, resulting in a total of 160 connectivity matrices for each subject.
The optimal set of tractography parameters for each subject was determined by computing the area-under-the ROC curve (AUC) of the 160 matrices in comparison with the “ground truth” tracer-derived connectivity matrix (see Fig. 2B-F for an example subject). The set of tractography parameters yielding the maximum AUC was determined for each subject. In all cases, the maximum AUC value was obtained without distance correction. Optimal curvature thresholds ranged between 0.2 and 0.8, while the optimal percentage of weak connections to discard ranged between 0 and 35% (Table 1).
Tractography was repeated for the RM parcellation using the optimal set of tractography parameters for each subject in the same manner as described above. For intrahemispheric tracking in the RM parcellation, exclusion masks of the opposite hemisphere were applied. Structural connectivity matrices were symmetrized and thresholded to each subject’s optimal threshold for discarding weak weights (Table 1). Tractography between all ROIs of the RM parcellation was then repeated with the distance correction option in probtrackx2 in order to estimate tract lengths. This was done by first dividing the number of streamlines detected between a seed voxel and the target ROI in the distance corrected tractography by the number of streamlines when distance correction was not used. The median value across all seed voxels was taken as the tract length between the seed and target ROIs.
Macaque connectome construction
Tractography-derived structural connectivity matrices in the RM parcellation were averaged across subjects. These averaged fiber tract capacity estimates were applied to the corresponding nonzero elements of the tracer-derived matrix. The resulting matrix represents a whole-cortex macaque connectome that is both directed (as informed by tracer data) and weighted (as informed by diffusion imaging data) (Fig. 3A; Data Citation 1). For technical validation, the weights were fit with a lognormal function and visualized using MATLAB’s Distribution Fitting Tool from its Statistics Toolbox (MATLAB R2011b).
Tract length estimates were averaged across subjects and the matrix symmetrized. Only those tract lengths with corresponding nonzero elements in the tracer-derived matrix were kept (Fig. 3B; Data Citation 1).
Functional connectivity
Functional connectivity (FC) for each subject was computed by first calculating a weighted average time series22 for each ROI in the RM parcellation for each resting-state fMRI scan. The pairwise Pearson correlation coefficients between time series were determined and a Fisher z-transform was applied to each resultant FC matrix. FC matrices were then averaged within subjects to obtain individual FC for each subject. FC matrices were also then averaged across subjects to obtain an overall average FC for the group.
TVB simulations
Large-scale network dynamics were simulated using TheVirtualBrain (TVB) software platform (thevirtualbrain.org) based on previously described methodologies32,47,48. For input to TVB, the connectome’s weights matrix was normalized to its maximum value but not thresholded.
The Reduced Wong-Wang32 dynamic mean field model, implemented using C code for efficient parameter exploration49, was used to model the local dynamics of each brain region. This mean field model consists of excitatory and inhibitory populations coupled together by excitatory (NMDA) and inhibitory (GABA) synapses. The strength of the coupling from the inhibitory population on the excitatory population was scaled by a feedback inhibition control parameter (Ji). The 82 mean field models, one for each brain region, were then coupled together according to the macaque connectome’s weights matrix and scaled using a global coupling parameter (G). Conduction velocity was fixed across the network so that time delays between regions were governed by the connectome’s tract length matrix. The uncorrelated Gaussian noise of each region was scaled in amplitude by a single noise parameter (sigma).
Model fitting was performed by a parameter space exploration in which G and sigma were varied systematically to optimize the fit between empirical and simulated functional connectivity. These parameters were chosen because previous studies have shown how they are crucial to determining the dynamics of the model32 and have been implicated in brain disease47,48. G was varied between 0.1 and 5 in 100 equally-sized steps while sigma was varied between 0.01 and 0.1 in 30 equally-sized steps for a total of 3000 iterations of the parameter search. Excitatory population firing rates have been reported to be in the range of 5 ± 5 Hz in the macaque50–53. Tuning the excitatory neural mass models with Ji to constrain their firing rates to ∼3 Hz is known to result in better models of FC with biologically-plausible dynamical properties32. Therefore, within each parameter search iteration, Ji was first tuned for each region individually to constrain its excitatory population firing rate to ∼3 Hz32. Ji tuning was performed for up to 100 iterations as described by Schirner and colleagues49. Simulations in which 100 iterations of Ji tuning still resulted in unrealistic excitatory population firing rates (mean >= 10 Hz across regions) were not considered for analysis. Conduction velocities in the macaque brain have been estimated to be in the range of 3-10 m/s54,55 and were set to 4 m/s in our simulations to reflect the median of the distribution reported by Girard and colleagues54. All other parameters of the model were the same as those from Deco and colleagues32. Resting-state BOLD-fMRI data with the same duration (10 mins) and sampling rate (TR = 1 s) as the empirical BOLD-fMRI data were then simulated by applying a Balloon-Windkessel hemodynamic model33,34 to the excitatory synaptic activity of each region. Simulated FC was computed and the cosine similarity (aka uncentered Pearson correlation32) between the upper triangles of the simulated and empirical FC matrices was used to determine the goodness of fit. The simulated data with values of G and sigma giving the maximum cosine similarity to empirical FC was used for further analysis. The statistical significance of our goodness of fit measure was assessed by creating a distribution of 1000 shuffled networks using the empirical FC. This was done by randomly rewiring the empirical network using the ‘null_model_und_sign’ function from the Brain Connectivity Toolbox (BCT; https://sites.google.com/site/bctnet/), which preserved the degree-, weight- and strength-distributions from the empirical network. The cosine similarity between each of the 1000 shuffled networks and the simulated FC was then computed to create a null distribution of cosine similarity values. A p-value was computed as the proportion of the null distribution with a cosine similarity value greater than or equal to the observed value.
A principal component analysis (PCA) was performed on the simulated timeseries data to identify the dominant networks in the simulated resting-state data. The first three components were chosen for interrogation as together they explained 79.1% of the covariance in the data. We arbitrarily selected the 10 nodes with the highest loadings within each component for the purpose of visualization.
As the best fit simulated network had only positively-weighted edges, comparison of its topology with that of the empirical network was done by first thresholding the empirical network to only the positive weights using the BCT function ‘threshold_absolute’ and then thresholding the simulated network to have the same density as the empirical one using the BCT function ‘threshold_proportional’. The sum of each node’s weights within each network were then calculated using the ‘strengths_und’ BCT function to derive the nodal strengths for comparison.
To test the extent to which our average macaque connectome can be used for modelling any individual macaque’s brain dynamics, we repeated our fitting procedure using the empirical FC matrix from each individual subject. To assess the goodness of fit for each subject, we repeated the shuffling procedure on each individual FC matrix to produce nine sets of 1000 shuffled networks. We additionally tested the extent to which using an individual’s structural connectome for simulations could provide a better fit to that individual’s empirical FC by repeating the entire simulation procedure using each animal’s optimized structural connectome (based solely on DWI tractography). As before, weights matrices were normalized to their maximum value but not thresholded.
Significant testing for correlations was done using permutation tests, whereby the the correlation coefficient between two variables x and y was recalculated after randomly shuffling y 1000 times to produce a null distribution of correlation coefficients. The p-value was taken as the proportion of the null distribution with a correlation coefficient greater than or equal to the observed coefficient.
Code availability
Custom code written in MATLAB for the generation of the macaque connectome, including wrapper scripts for neuroimaging preprocessing and DWI tractography, is available upon request from the corresponding author. The C code for the Reduced Wong-Wang model in TVB is available at https://github.com/BrainModes/The-Hybrid-Virtual-Brain.
Data Records
The macaque connectome dataset is openly available for download from Data Citation 1: Zenodo https://doi.org/10.5281/zenodo.1471588. Available files for download include:
weights.txt: Weights matrix representing a directed and weighted connectome in the 82-node RM whole-cortex parcellation; ROI order as presented in the look-up table
tract_lengths.txt: Tract length matrix, in mm
TVBmacaque_RM_LUT.txt: Look-up table for RM parcellation; includes ROI ordering, label indices, ROI names and abbreviations
RM_inF99.nii.gz: labelled volume of gray matter ROIs of RM parcellation, in F99 macaque atlas space; labels as specified in the look-up table
surf_faces.txt, surf_vertices.txt, surf_labels.txt: F99 macaque atlas surface and corresponding RM parcellation labels; labels as specified in the look-up table
Technical Validation
Tractography was used to estimate the fiber tract capacities of the macaque connectome via an optimization procedure that selected the tractography and connectome threshold parameters that produced the most accurate connectome for each subject, as assessed by comparison with tracer data (Figure 2). The average 29-ROI connectome that resulted from this optimization procedure had weights that were correlated with the tracer weights (r = 0.71, p < 0.001)also see ,20, suggesting that the optimized tractography parameters for each subject could reasonably be applied to the estimation of fiber tract capacities across the whole brain.
Tractography was therefore repeated using the whole-cortex RM parcellation and the average weights and tract length estimates across subjects were applied to the tracer-derived RM connectivity matrix to generate a canonical macaque connectome (Fig 2A-B). As reported in tracer studies, macaque fiber tract capacities follow a lognormal distribution16,31. We fit our tractography-derived weight estimates with a lognormal function (mu=-5.07, sigma=1.92) and found that they also generally follow a lognormal distribution (Fig 3C). As expected, tract length estimates were correlated with the Euclidean distance between ROI pairs (Pearson correlation, r = 0.72, p < 0.001; Fig. 3D), with tract length estimates (median: 38.8 mm) being on average longer than Euclidean distances (median: 31.4 mm; Wilcoxon rank sum test, p < 0.001). Tract length estimates were also significantly shorter on average for intrahemispheric connections (median: 33.2 mm) than interhemispheric ones (median: 51.4 mm; Wilcoxon rank sum test, p < 0.001) (Fig 3E).
For the purposes of validating the connectome and demonstrating a use case for the dataset, we simulated macaque resting-state BOLD-fMRI data in TVB. A parameter space exploration that fit the simulated FC to the overall grand average empirical FC across a range of G and sigma values was performed. The best fit simulated FC occurred with parameter values G = 0.298 and sigma = 0.0255 (Fig. 4A-C). This corresponded with a cosine similarity fit of 0.75, which was significantly greater than the cosine similarity fits with null networks (p < 0.001). This best fit simulation was chosen for further analysis. Example simulated BOLD timeseries from five randomly chosen ROIs are shown in Figure 4D. We inspected the top 10 nodes from the three most dominant networks identified using a PCA on the simulated BOLD timeseries. The first network (59.3% of the covariance) was comprised of lateral prefrontal and anterior cingulate regions bilaterally as well as left intraparietal area (Fig 4E, red). The second network (12.3% of the covariance) included superior and central temporal cortical regions, primary and secondary auditory cortices, as well as the insula bilaterally (Fig 4E, green). The third (7.6% of the covariance) was composed of V1, V2 and exstrastriate visual cortices bilaterally (Fig 4E, blue). These networks are similar to the frontal, superior temporal, and visual resting-state networks previously reported in macaques44,56,57. We additionally computed the nodal degree (sum of weights, or strengths) of the simulated and empirical FC networks to compare their topologies. The strength of each node in the simulated network was correlated with its strength in the empirical network (r = 0.51, p < 0.001; Fig. 4F).
To determine whether a canonical macaque connectome could be used to simulate resting-state BOLD-fMRI of individual macaques, we fit the set of 3000 simulations generated from the parameter space search to the empirical FC of each of our subjects. The best fit cosine similarity for each animal (range: 0.47 – 0.80; Fig. 5A) was significantly greater than the fits with each animal’s null FC distribution (all p < 0.01). Using each subject’s individual connectome for simulations resulted in similar fits to individual empirical FC (cosine similarity: 0.47 – 0.79; Fig. 5A) that were not significantly different from the fits obtained using the canonical connectome (paired t-test, p = 0.35). Together with the observation that structural connectomes exhibit far less variance than functional ones58, this suggests that a canonical macaque connectome can be used in simulations to capture some aspects of individual macaque whole-brain dynamics.
While the fits of the individualized simulations to empirical data may be no better than when using the canonical connectome, an examination of the best-fit simulation parameters under each condition suggests that individual specificity may instead be captured within the biophysical parameters of the model (Fig. 5B). In the case of the canonical connectome simulations, 4 of 9 subjects had identical G and sigma parameters. For individualized connectome simulations, however, all parameter sets were different across subjects. This is in line with our recent findings that individualized TVB model parameters are better at predicting cognitive status in dementia than the coupling between structural and functional connectivity47 and suggests that generative models based on individual connectomes may be able to capture subject-specific characteristics that are not identifiable from the empirical data alone. The modelling approach may therefore extract the portion of the measured variance in the empirical data that is most closely related to the underlying biophysics, increasing the sensitivity to individual differences.
Usage Notes
In the technical validation section above, we described an example of how the macaque connectome dataset can be used for region-based simulations. However, the dataset also includes a labelled cortical surface, allowing for surface-based simulations such as those presented by Proix and colleagues59. Further information on the TVB software platform, including the download package, documentation and tutorials can be found at https://www.thevirtualbrain.org (also see https://github.com/the-virtual-brain).
Our choice to construct the macaque connectome using the RM parcellation was a deliberate one, as the parcellation was intended to harmonize cytoarchitectonic, topographic and functional definitions of brain regions across primate species39. As such, the application of the RM parcellation to the human brain allows for direct cross-species comparisons. The RM parcellation, with the addition of 14 subcortical regions, and the corresponding connectome in humans is already available in TVB60.
Acknowledgements
This work was supported by a grant from the Canadian Institutes of Health Research (CIHR) to SE. We thank Amanda Easson, Tyler Good, John Griffiths, Zheng Wang and Marmaduke Woodman for technical advice.
Author contributions
K.S. and A.R.M. designed the study. G.B. and S.E. collected the data. K.S. analysed the data and prepared the first draft of this manuscript. All authors contributed to the subsequent revisions of the manuscript.
Competing interests
The authors declare no competing interests.
References
Data Citations
- 1.