MIST: A multi-resolution parcellation of functional brain networks

Sample

All data were taken from the publicly available Cambridge dataset²¹, which is available from the 1000 functional connectomes project²². The Cambridge dataset consists of 198 subjects (123 female) between 18 and 30 years of age. Six minutes of rs-fMRI data (TR=3s, 119 time points) were recorded on a 3 Tesla Siemens Tim Trio Scanner (Siemens Medical Systems, Erlangen, Germany) at 3s TR using a 12-channel head coil. We have chosen this dataset due to the high quality of the imaging data, the low degree of in-scanner motion among individuals in the dataset, and because the acquisition parameters are representative of the average functional imaging study in the field in terms of spatial resolution and length of the scan. The sample is also shared without any access restrictions and has a moderate size, making it easy for other groups to attempt a replication or extension of our work.

Preprocessing

The data were preprocessed using the Neuroimaging Analysis Kit (NIAK) version 0.12.4²³, an Octave²⁴ based open source processing and analysis framework for imaging data. Each individual data set was corrected for differences in slice acquisition time. Head motion parameters were estimated by spatially re-aligning individual time points with the median volume in the series. This reference median volume was then aligned with the anatomical T1 image of the individual which in turn was coregistered onto the MNI152 template space²⁵ using an initial affine transformation followed by a nonlinear transformation. Finally, each individual time point was mapped to MNI152 space using the combined spatial transformations. For time points with excessive in scanner motion (> 0.5mm framewise displacement), the time point as well as the preceding and the two following time points were removed from the time series²⁶. Nuisance covariates were regressed from the remaining time series: slow time drifts (basis of discrete cosines with a 0.01 Hz high-pass cut-off), average signals in conservative masks of the white matter and the lateral ventricles as well as the first principal components (95% energy) of the six rigid-body motion parameters and their squares^27,28. Data were then spatially smoothed with a 3D gaussian kernel (FWHM = 6mm).

Quality control

The quality of the registration operations was visually inspected following an in-house developed quality control protocol²⁹. Specifically the registration between the individual T1 scans and the stereotaxic template space, as well as registration between the individual T1 and the median functional image were assessed. Subjects were excluded from the analysis in cases of failed coregistration with the template space or where less than 40 time points had acceptable amounts of head motion after scrubbing. A total of 190 subjects (119 female, mean age 21 years, SD 2.3) passed quality control criteria for inclusion in the analysis.

Generating the MIST parcellation

Functional connectivity was computed as the fisher-z transformed Pearson correlation between time series. Stable networks of functional connectivity were extracted from rsfMRI data using an implementation of the Bootstrap Analysis of Stable Clusters (BASC) algorithm¹⁸ within NIAK. The goal of the BASC process is to identify groups of brain regions that exhibit consistent and strong functional connectivity at the individual and group level. In brief, the process consists of three stages:

First, we apply a dimensionality reduction procedure using a region growing algorithm³⁰. The algorithm iteratively merges spatially contiguous voxels with highly correlated time series to form 1095 functional atoms (part of the release as MIST_ATOM). Second, we want to identify stable functional connections between these atoms at the level of individual subjects. To do so, we take 1000 bootstrap samples of the individual time series and then repeatedly cluster atoms by functional connectivity using hierarchical agglomerative clustering. We estimate how consistently two atoms are clustered together by averaging the binary adjacency matrices across bootstrap samples. This average adjacency matrix is called the individual stability matrix. Third, at the group level we want to identify connections that are consistently stable across individuals. To do so, we repeatedly sample subsets of individuals from the dataset and average their individual stability matrices. We then apply hierarchical agglomerative clustering on the average stability matrix within each subsample and binarize the resulting clustering assignment. Similar to the individual level clustering we average the binarized adjacency matrices across subsamples to obtain the group level stability matrix. Lastly, we generate the group level consensus partition on the group level stability matrix to identify clusters of stable group level connections. A more detailed description of the method can be found in the BASC paper¹⁸.

Selecting the resolution. The BASC process involves decisions about the spatial resolution, i.e. the number of groups that atoms are assigned to based on the stability of their connections. These spatial resolutions must be selected for the BASC process at the individual level, at the group level, and for the final decomposition of the group stability matrix into networks. Since the stability matrices at the individual and group level are generated by clustering atoms into discrete groups they are not resolution independent, i.e. changing the number of groups will change the stability matrix. The BASC process must therefore be repeated for every combination of individual, group and network level spatial resolutions.

Our goal for the MIST parcellation was to describe stable functional networks and how they break up into smaller functional assemblies across spatial resolutions. We used the the multiscale stepwise selection algorithm (MSTEPS) to identify those spatial resolutions that best reflect major transitions in network organization across resolutions³¹. This process identified nine representative group level resolutions [7, 12, 20, 36, 64, 122, 197, 325, and 444] that we included in the MIST parcellation. An additional parcellation was generated by splitting parcels of resolution 122 along the midline, which resulted in 210 fully lateralized parcels. To characterize the spatially contiguous nature of the parcels at this resolution and to distinguish it from the other parcellations we call this resolution the ‘ROI’ resolution and refer to the corresponding parcels as ROIs.

Parcels

Figure 1 provides an overview of the functional parcels identified at the different resolutions. The first step in resolution space from 7 to 12 sees the default mode network split into 3 parts, the downstream visual areas separate from the fronto parietal network, and the auditory network and insulae separate from the ventral attention network (to explore the MIST parcellations and their decomposition across resolutions, please refer to our interactive web viewer). Beyond resolution 12, parcels begin breaking up within these large scale networks. This is illustrated by the decomposition of the somatomotor network into 3 parcels at resolution 36 and 7 parcels at resolution 122 (see Figure 2).

Figure 1. Parcellation overview.

Parcellations MIST_7 through MIST_444 with slice coordinates denoted in MNI coordinates. Annotated parcellations are highlighted by orange parcellation names. Note that MIST_ROI is generated by splitting MIST_122 along the midline into fully lateralized ROIs. Parcel colors are random.

Figure 2. Decomposition of the Somatomotor network.

(Top row) MIST_7 rendered on the Civet³² standard surface for easier visualization. (Lower left) MIST_7 parcels highlighted over the sample-average atom by atom connectivity matrix. (Lower right) Zoomed in view on the surface and connectivity matrix representations of the Somatomotor network. Resolutions from top to bottom are: MIST_7, MIST_36, MIST_122. Surface parcel colors correspond to parcels overlayed on the atom by atom connectivity matrix.

Parcels at lower resolutions are exclusively bilateral and highly symmetric, and are generally made up of spatially discontinuous subregions. These subregions tend to separate first while remaining largely bilateral. The decomposition of parcels into left- and right-hemispheric subcomponents occurs more gradually (see Figure 3). Between resolutions 36 and 64, parcels tend to become less symmetric and more lateralized. At resolution 122, from which MIST_ROI is generated by forcing a split along the midline, more than 70% of parcels span both hemispheres. MIST_444 has 120 parcels (or ~27% of parcels) that encompass areas in both hemispheres.

Figure 3. Parcel properties across resolutions.

(Top row) Parcel symmetry across MIST resolutions. MIST_ROI is the lateralized version of MIST_122 and doesn’t have symmetric parcels. (Middle row) Parcel bilaterality scores across MIST resolutions. Higher values indicate a more bilateral parcel. Bilaterality scores are computed as 1 minus the absolute value of the parcel laterality. All parcels of MIST_ROI are by definition fully lateralized and hence have a bilaterality score of 0. (Bottom row) Internal homogeneity of parcels across MIST resolutions. Annotated parcels are highlighted in orange. Hover over individual data points to see additional information. The online version of this figure is interactive.

Hierarchy. While parcellations at each resolution have been generated independently from each other, we found that parcels at higher resolutions largely remain within the boundaries of their lower resolution parents. This allowed us to generate a pseudo-hierarchy by assigning each parcel at resolution R to the parcel at resolution R-1 with the highest overlap. This pseudo-hierarchy provides a decomposition tree of large scale functional networks into fine grained functional nodes at higher resolution. The majority of parcels have an overlap of close to 100% with their parent parcels. Our web viewer gives an interactive representation of the decomposition trees for the 7 functional networks at resolution MIST_7. However, a subset of parcels at higher resolutions does not overlap fully with the root of the pseudo-hierarchical decomposition tree it belongs to. These parcels are predominantly located at the interface of two low resolution functional networks and may represent more ambiguous boundary regions. Figure 4 provides the overlap of parcels at all resolutions with their root parcel (the MIST_7 parcel that the pseudo-hierarchy assigns them to). Note that we haven’t included MIST_ROI here as it is a transformation of MIST_122 and not an independent parcellation.

Figure 4. Overlap with root parcels in the pseudo-hierarchy.

The overlap with the corresponding pseudo-hierarchical root-parcel at MIST_7 is shown for parcels across resolutions. Overlap is represented in percent overlap of total parcel size. Higher values indicate an assignment more in line with the data derived pseudo-hierarchy. Annotated parcels are highlighted in orange. The online version of this figure is interactive.

Parcel nomenclature. Our goal in naming the functional parcels presented here was to provide an intuitive description of the general brain areas included in a parcel. Wherever appropriate, we tried to name parcels based on current terminology in the rsfMRI literature. For parcels that could not be described in their entirety by an established name, we listed the significant subcomponents of the parcel. Particularly at higher spatial resolutions, when parcels would encompass relatively small and well described areas, a functional name could sometimes not be justified. In these cases we named the parcel based on the underlying brain anatomy.

The parcel names included in this release are based on a systematic naming system (outlined below) to ensure consistency.

Naming template:

Naming example:

All fields except the {NAME} field are optional and only used where they add information to the name.

For each parcel name we also provide an abbreviated parcel label designed to take up less space while still being informative. The convention for labels follows that of names but uses different upper- and lowercase rules and values:

Label template:

Label example:

Suggested use, limitations and planned improvement of parcel names. It is important to note that the parcel names are intended to help navigate the parcellations by giving the reader a quick idea where in the brain a parcel is situated. They are not intended for precise delineation of a particular anatomical region or functional pathway. While the parcels names provided with this release are unique, they are also not intended as unique descriptors of individual parcels. We suggest that individual parcels are referred to by their integer ID and parcellation resolution. For example, the parcel 6 of the parcellation resolution 64 should be referred to as 6@MIST_64.

Parcel properties. Apart from individual labels we provide a set of quantitative properties for each parcel.

Quality of hierarchical decomposition

We assessed the accuracy of the hierarchical decomposition of parcels across multiple resolutions. We generated the hierarchy by assigning each parcel to the parcel of the next lower resolution it has the highest overlap with (see Methods for details). A good hierarchical decomposition would result in parcels that decompose into fully enclosed subparcels. We therefore tested the percent overlap of parcels with their parent parcels across the resolutions. Our interactive web viewer shows an overview of parcel overlap across resolutions. At every resolution, most parcels have a very high degree of overlap with their parent parcel. Parcels with lower parent overlap are predominantly located along the interface of parietal and occipital lobe and in the lateral prefrontal cortex. The parieto-occipital interface is also a transition area between two large scale functional networks at lower resolution and parcels along this interface could shift across resolutions along the stability gradient of this transition zone. The weighted average of parent overlap across resolutions is very high at 95%, indicating a generally excellent alignment of sub parcels with their parent parcel.

We finally looked at the entire hierarchical decomposition tree to find the overlap of parcels with the root parcel of their decomposition tree. The root parcels are the parcels in the MIST_7 parcellation for which decomposition across resolutions is tracked independently. While each parcel is assigned to the parcel of the next lower resolution it has the maximal overlap with, incremental non-complete overlaps can accumulate to a point where a parcel no longer has any overlap with the root parcel it is assigned to by our pseudo-hierarchy. Out of 1227 parcels across all nine resolutions (not including MIST_ROI) we identified 116 parcels that didn’t overlap with the root parcel of their hierarchical decomposition tree. Across the MIST resolutions we found parcels with no root overlap in MIST_36: 1 parcel (3%), MIST_64: 4 parcels (6%), MIST_122: 7 parcels (6%), MIST_197: 16 parcels (8%), MIST_325: 33 (10%), MIST_444: 55 parcels (12%). None of these parcels had root-parcels located in the somatomotor, visual or cerebellar networks of MIST_7. Figure 4 provides an overview of the root-parcel overlap across scales. While it is unclear what factors may cause the gradual shifts of these identified parcels it is important to note that most parcels have high degrees of overlap with both their immediate parent parcels as well as their root-parcels. The MIST pseudo-hierarchy thus captures meaningful cross-resolution relationships between parcels.

Multi-resolution parcellations

To our knowledge, there are only three other functional connectivity based multi-resolution parcellations available in the literature: those by Craddock and colleagues⁷ and by Shen and colleagues¹² both use approaches building on spectral clustering to derive volumetric, whole brain parcellations. Recent work by Schaefer and colleagues¹⁴ uses the similarity of functional connectivity in addition to local functional connectivity gradients to define brain parcels on the neo-cortical surface. All three of these multi-resolution parcellations have in common that they aim to provide very homogeneous functional areas at high spatial granularity that can be used as nodes in functional connectivity analyses. This leads to two important differences to the MIST atlas presented here. First, they either directly^7,14 or indirectly¹² force parcels to be spatially contiguous and, with the exception of the Craddock parcellation, lateralized to one hemisphere. Second, they provide parcellations at relatively high resolutions of 100, 200, and 300 parcels in the case of the Shen parcellation, 400 to 1000 parcels in increments of 200 in the case of the Schaefer parcellation, and 50 to 1000 parcels in increments of 50 in the case of the Craddock parcellation.

The objective of the MIST parcellation is related, but conceptually different as it aims to provide a multi-resolution decomposition of the brain beginning with large, spatially non-contiguous networks and ending with functional areas, the spatial resolution that the aforementioned parcellations aim to characterize. This is also reflected in the fact that no spatial constraint is imposed on the parcels of the MIST parcellation (with the exception of the MIST_ROI parcellation) which are markedly bilateral and non-contiguous up to the highest resolutions. Finally, we have relied on a data-driven method to automatically select the most descriptive resolutions of brain parcellations rather than selecting them at arbitrary intervals.

Yeo parcellation

Among the wealth of functional brain parcellations available at a single resolution, the works by Yeo³ and Glasser⁶ stand out due to their methodological rigor and the extent of their use in the field (more than 2500 and 720 citations to date respectively). They also stand at opposite ends of the spatial resolution spectrum covered by the MIST parcellation. They Yeo parcellations represent canonical functional connectivity networks while the Glasser parcellation represents small areas bounded by multi-modal agreement of boundaries.

Yeo and colleagues provide a partition of the cortical surface into large, distributed functional networks at spatial resolutions of 7 and 17 parcels that is based on the similarity of the seed based functional connectivity at 18700 surface vertices. In particular the 7 network parcellation is often considered a parcellation of reference for the canonical resting state connectivity networks that are reliably differentiable, and has informed the labeling of the MIST parcellation at low resolutions. While the Yeo parcellation is generated entirely on the cortical surface, the authors provide a projection into volumetric MNI space that we use to compare it with MIST parcellations of comparable spatial resolution: we compare the 7 Yeo networks to the MIST_7 parcellation, and the 17 Yeo networks to the MIST20 parcellation. Since the MIST parcellations cover the cerebellum and subcortical areas while the Yeo parcellations do not, we exclude those regions from the comparison and consider only regions in the intersection of the MIST brainmask and the non-zero voxels of the volumetric Yeo parcellation (1 region was removed from the MIST_7 parcellation, and 4 regions were removed from the MIST_20 parcellation).

We compare the parcellations in two ways: First, we determine the spatial overlap of networks by computing the maximal dice coefficient of each MIST network with the corresponding Yeo parcellation. Second, we detect and highlight the border regions between networks in each parcellation in order to qualitatively compare their spatial location.

The average dice coefficient of MIST_7 networks with Yeo_7 networks is 68%, with some regional variation (see Figure 5). The MIST_7 visual network has a high dice coefficient of 88% with the Yeo_7 visual network, while the MIST_7 network comprising the ventral attention and salience network has a lower dice coefficient of 49% with the corresponding Yeo_7 network (see Table 2 for a complete overview). Figure 5 (left side) gives a spatial representation of the parcel overlap. MIST_7 visual, somatomotor, default mode and mesolimbic networks show a high degree of spatial overlap with Yeo_7 parcels, whereas the fronto-parietal and the aforementioned ventral attention network show lower overlap. This is also reflected in the spatial alignment of network borders between the MIST_7 and Yeo_7 parcellations (Figure 5, right side). Borders of the visual, somatomotor, limbic and default mode networks of the MIST_7 parcellation are closely aligned while the detected boundaries in the Yeo_7 parcellation. By contrast, the frontoparietal and ventral attention network of the MIST_7 parcellation are intersected by estimated network boundaries of the Yeo_7 parcellation.

Figure 5. Similarity of MIST and Yeo parcellation.

Left column: MIST networks are color coded by their spatial overlap (dice) on corresponding Yeo networks⁵. Right column: the borders of the MIST networks (black line) are overlaid over the transition zones between Yeo networks to illustrate local differences in network outlines (black arrows). A: MIST_7 networks and Yeo_7 networks B: MIST_20 networks and Yeo_17 networks.

The average dice coefficient of MIST_20 networks with Yeo_17 networks is 55%, with considerable regional variation. The lateral and medial visual networks of the MIST_20 parcellation spatially overlap well with the corresponding Yeo_17 networks (visual A and visual B) by 85% and 81% respectively. On the other hand, the medial and lateral ventral attention networks of the MIST_20 parcellation both have dice coefficients with the Yeo_17 salience and ventral attention network of 33% and 38% respectively (see Table 3 for a full overview).

Several MIST_20 networks are situated inside larger Yeo_17 networks. The ventral somatomotor network of MIST_20 is 82% inside the Yeo_17 Somatomotor B network, yet has a dice coefficient of only 0.38 with this network. This is because the Yeo_17 Somatomotor B network extends ventrally beyond the somatomotor strip and includes a portion of the superior temporal lobe that is part of the auditory network in the MIST_20 parcellation. The MIST_20 auditory network is 60% inside the Yeo_7 Somatomotor B network. Other cases are less clear. The MIST_20 perigenual ACC and VMPFC network is 72% inside the larger Yeo_17 Default mode network A, but the three MIST_20 DMN sub-networks (anterior, posteromedial, and lateral DMN) do not align closely with the three Yeo_17 DMN sub-networks (Default Mode network A–C) (see Table 3). Figure 5 (B: right column) gives some indication for the reason behind this: the border of the MIST_20 posteromedial DMN sub-network extends further into the precuneus than that of the Yeo_17 Default Mode A network. Similarly, the border of the MIST_20 anterior DMN sub-network extends further ventrally and caudally along the medial surface than that of the Yeo_17 Default Mode B network (see black arrows).

Overall, visual, motor and limbic networks of the MIST_20 parcellation are well aligned with their Yeo_17 counterparts. The agreement of network boundaries is lower for the sub-networks of the DMN, the fronto-parietal and the ventral- and dorsal attention networks. The lower agreement between MIST_20 and Yeo_17 compared with the higher alignment of the MIST_7 and Yeo_7 parcellation are due to differences in the way large networks split into sub-sections at the higher spatial resolution (such as in the case of the Yeo_17 Somatomotor B network that includes temporal areas but otherwise aligns very closely to the MIST_20 ventral somatomotor network). Other differences are due to differences in alignment of network boundaries that may reflect instabilities of functional network membership in these areas, differences of methodology, or factors due to higher inter-subject variability of functional connectivity in these areas that influence the group level parcellations³³. Investigating these factors further goes beyond the scope of this work.

Glasser parcellation

Glasser and colleagues provide a widely used parcellation of the neo-cortical surface into homogeneous functional areas that is based on a combination of imaging modalities: resting state fMRI connectivity, task based fMRI activation, local myelination, and cortical thickness. The boundaries of functional areas in this parcellation are defined by overlapping gradient maxima in at least two of these modalities with additional weight given to gradients with contralateral homologues. The Glasser parcellation defines 360 functional areas, 180 per hemisphere. Like the Yeo parcellation, it is generated entirely on the cortical surface. While a projection to volumetric MNI space exists, the projection covers a very narrow band along the cortical ribbon and only covering only 51% of the volumetric parcels of the MIST_444 parcellation (excluding subcortical areas and the cerebellum, 387 parcels remain). A related difference that of size of the parcels when compared in their volumetric representations. The Glasser_360 parcels naturally follow closely the cortical surface, spanning different gyri. By contrast, the volumetric MIST_444 parcels are more localized in space and cover smaller areas on the cortical surface. As a result, when applying the consensus mask between both parcellations, the Glasser_360 parcels are on average more than twice as large.

Due to these differences, we attempted only a cursory comparison between the MIST_444 parcellation and the Glasser_360 parcellation. As the dice coefficient is not well suited to reflect alignment between parcels of very different sizes, we instead directly measured the maximal overlap of the MIST_444 parcellation with parcels in the Glasser_360 parcellation (i.e. we measured which percentage of the MIST_444 parcel is within the bounds of a Glasser_360 parcel of maximal overlap). The average overlap of MIST_444 parcels on Glasser_360 parcels is 50%, with a wide variability of values from 7% to 100% (the median is 47%). Figure 6 shows a projection of computed overlap of MIST_444 parcels onto the surface, revealing areas of higher parcel overlap within primary visual cortex, middle temporal gyrus, and sections of the dorsal ventromedial prefrontal cortex. Areas of low alignment are within the somatomotor strip, the precuneus and anterior cingulate cortex.

Figure 6. Similarity of MIST and Glasser parcellation.

The MIST_444 areas are projected onto the cortical surface and color coded by their spatial overlap (percent overlap) on the corresponding Glasser⁸ areas. Note that this comparison has limited practical value since the spatial extent of MIST and Glasser areas is very different.

It is worth pointing out, that the Glasser parcellation is methodologically very different from the MIST parcellation, in terms of spatial scope (cortical surface vs whole-brain volume), in terms of underlying data (high-resolution data of multiple modalities vs functional data of average resolution), and in terms of procedure (manually guided automatic parcellation based on local transition gradients vs unsupervised parcellation based on global similarity of connectivity). Nevertheless, both the Glasser_360 and the MIST_444 parcellations aim to provide a description of functional areas that can be assumed to be internally functionally homogeneous for the purposes of dimensionality reduction and node definition. Perhaps a more relevant metric is therefore the question of internal homogeneity of parcels. Here both parcellations perform very similarly with an average internal homogeneity of 0.5 for the MIST_444 parcellation and of 0.46 for the Glasser_360 parcellation (see Figure 7).

Figure 7. Comparison with other parcellations.

The standard deviation (SD) of homogeneity estimates across individuals in the HNU1 data set is shown as a function of the common logarithm of the average parcel size. Lower scores reflect lower variability in homogeneity estimates between individuals. Annotated parcellations are highlighted with an outline in orange. Random parcellations are shown as smaller white circles with a red outline for reference. The online version of this figure is interactive.

Other parcellations

To quantitatively compare the quality of our parcellations to other, existing functional connectivity parcellations we estimated the within parcel functional homogeneity, a common quality metric in the literature^11,34. A good functional brain parcel is expected to encompass voxels with reasonably similar functional activity. Here we estimate the functional homogeneity of a parcel as the average functional connectivity between its voxels. All other things being equal, smaller parcels will have higher internal homogeneity than larger ones, particularly when they are spatially contiguous. We therefore compute the global homogeneity of a parcellation as the size-weighted average of its individual parcels.

We compare our parcellations to a number of published brain parcellations in the literature (see Table 1). Parcellations that were generated on surface data were back-projected into MNI volumetric space. As a consequence, brain coverage differs between parcellations with some covering only the cortical ribbon while others also providing parcellations of subcortical regions and the cerebellum. A parcellation with only cortical coverage will on average have smaller parcels than a full brain parcellation of the same resolution. To account for parcel-size dependent differences in homogeneity, we therefore opted to compare parcellations based on the average size of their parcels (in voxels). Lastly, we included a random multi-resolution parcellation generated by Craddock and colleagues⁷. These random parcels are entirely driven by spatial proximity and since they have been reported to perform about as well as functionally defined parcels of similar size, we included them in this analysis as a point of comparison. All parcellations were resampled to 3mm isotropic voxels to allow for a direct comparison.

To conduct the quality assessments we used the openly available HNU1 dataset from the Consortium for Reliability and Reproducibility³⁵ that provides 10 repeat session of fMRI data acquired over the course of a month for 30 individuals. This dataset allows us to average our quality metrics across sessions per individual, giving a more stable estimate. In addition none of the compared brain parcellations has been generated on this data, providing an unbiased estimate of performance on other datasets. Data were preprocessed and quality controlled according to the protocol described above. 27 individuals (15 female, mean age 24.5 years, SD 2.4) were included in the analysis.

Figure 7 shows the global homogeneity of parcels over the logarithm of the average parcel size. The relationship between homogeneity and parcel size is clearly visible in the exponential decline of homogeneity with parcel size. Our multi-resolution parcellations compare well with other parcellations of similar parcel size, particularly at lower resolutions. A second question is how consistent the estimated homogeneity scores are across individuals. High consistency of homogeneity indicates that a parcellation generalizes well across individuals whereas a low consistency indicates a very case-dependent fit of the parcellation to the individual functional architecture. Figure 8 shows the standard deviation of homogeneity estimates across subjects as a function of the logarithm of average parcel size. Larger parcels show lower standard deviation of homogeneity across individuals. Again, our parcels fall well within the range of cross-subject consistency of other data driven atlases with comparable resolutions.

Figure 8. Consistency of homogeneity estimates as a function of parcel size.

Global parcel homogeneity of MIST parcellations and commonly used other brain parcellations of comparable size and focus. Homogeneity estimates are plotted over the common logarithm of the average parcel size. Higher scores reflect more homogeneous parcels. Annotated parcellations are highlighted with an outline in orange. Random parcellations are shown as smaller white circles with a red outline for reference. The online version of this figure is interactive.

The random Craddock parcellations we included as a point of comparison show homogeneity values with a strikingly logarithmic dependence on the average parcel size. At lower resolutions (i.e. larger parcel sizes), the random parcellations have lower internal homogeneity values than connectivity derived parcellations of similar resolution. Around a resolution of 120 parcels (i.e. parcels of around 473 3mm voxels) the internal homogeneity values of the random Craddock parcellations start to exceed those of connectivity driven parcellations. This change in relative performance is probably due the inability of a random parcellation to capture distributed, large scale functional networks at lower resolutions whereas at higher resolutions, a bias towards spatially contiguous parcels of similar size seems to be advantageous. The consistency of internal homogeneity estimates of the random Craddock parcels also shows a dependence on spatial resolution and is overall lower than that of the data driven parcellations. While the random Craddock parcellations were found to perform about as well as similar connectivity derived parcellations in previous work⁷, the strong performance at high resolutions observed here warrants further investigation.

Predictive performance

Another way to look at the generalizability of the MIST parcellation is to test its performance in real world applications. One of the most common applications for a functional brain parcellation is to define nodes in a functional connectivity analysis. A reasonable assumption is then that better parcels will lead to more generalizable models of functional connectivity. Dadi and colleagues have tested the impact of different brain parcellation methods (and other processing parameters) on the prediction of clinical traits based on the functional connectomes estimated from these parcellations^47,48. Prediction performance was compared across three pre-generated atlases (the Harvard-Oxford Atlas, the AAL atlas, and the MIST_64 parcellation) and a set of custom parcellations derived directly from the data using a range of methods (ICA, dictionary learning, K-means clustering, and Hierarchical clustering using Ward’s criterion). The authors found that across several prediction problems based on several datasets (including Schizophrenia on the COBRE dataset, Alzheimer’s disease based on the ADNI dataset, and Autism based on the ABIDE dataset), the MIST_64 parcellation performed consistently well, above the other pre-generated atlases and “almost as well as the best regions-extraction method applied to the rest-fMRI data of interest”.