Basis of executive functions in fine-grained architecture of cortical and subcortical human brain networks

Abstract Theoretical models suggest that executive functions rely on both domain-general and domain-specific processes. Supporting this view, prior brain imaging studies have revealed that executive activations converge and diverge within broadly characterized brain networks. However, the lack of precise anatomical mappings has impeded our understanding of the interplay between domain-general and domain-specific processes. To address this challenge, we used the high-resolution multimodal magnetic resonance imaging approach of the Human Connectome Project to scan participants performing 3 canonical executive tasks: n-back, rule switching, and stop signal. The results reveal that, at the individual level, different executive activations converge within 9 domain-general territories distributed in frontal, parietal, and temporal cortices. Each task exhibits a unique topography characterized by finely detailed activation gradients within domain-general territory shifted toward adjacent resting-state networks; n-back activations shift toward the default mode, rule switching toward dorsal attention, and stop signal toward cingulo-opercular networks. Importantly, the strongest activations arise at multimodal neurobiological definitions of network borders. Matching results are seen in circumscribed regions of the caudate nucleus, thalamus, and cerebellum. The shifting peaks of local gradients at the intersection of task-specific networks provide a novel mechanistic insight into how partially-specialized networks interact with neighboring domain-general territories to generate distinct executive functions.


Introduction
Executive function is an umbrella term for the processes necessary to manage diverse cognitive challenges. The range of "executive tasks" is vast and includes recalling or manipulating items in short-term memory, generating verbs under time pressure, withholding a habitual motor response, attending to specific stimuli and ignoring distractors, and solving tasks with constantly changing rules and following complex instructions (Miyake et al. 2000;Diamond 2013). Performance on executive tasks can identify severe cognitive deficits in patients with brain lesions, correlates with measures of general intelligence and predicts real life problem solving abilities (Duncan et al. 1996;Miyake et al. 2000;Roca et al. 2010;Friedman and Miyake 2017;Woolgar et al. 2018). Despite much progress, the underpinning of executive processes in the brain is still only partly understood.
One approach to identify executive processes examines individual differences in executive task performance. An influential "unity and diversity" model found that performance on all executive tasks tends to positively correlate, suggesting a common underlying process usually referred to as the "common executive function" (Miyake et al. 2000;Friedman and Miyake 2017) and linked to several constructs in theoretical models such as the central executive in working memory (Baddeley and Hitch 1974), the g-factor for general intelligence (Spearman 1904), proactive control in the dual mechanisms framework (Braver 2012) and energization (Stuss and Alexander 2000). To explain the remaining variance, the model also proposes several more specialized components, with the original model (Miyake et al. 2000) identifying three putative processes labelled as updating, set shifting and inhibition.
Recent replications have highlighted that fine-scaled division of components varies with diversity of the task battery, model chosen and the age of participants (Karr et al. 2018). Theoretical models thus suggest the existence of both domain-general and domain-specific brain processes to support executive task performance.
Another approach concerns brain lesion studies, the historical driver for the development of executive tasks. Relatively circumscribed lesions in frontal and parietal cortices are associated with widespread deficits in executive performance Woolgar et al. 2010Woolgar et al. , 2018, suggesting a domain-general process that has been compromised. A finer-grained view of lesion data, however, has often been used to argue that distinct executive functions are supported by distinct frontal lobe territories. For example, an authoritative review of two decades of brain lesion studies concluded that "there is no central executive". Instead, it attributed distinct executive processes to distinct territories: energization (dorsomedial), monitoring (right lateral), task setting (left lateral), emotional self-regulation (ventromedial) and metacognition (fronto-polar) (Stuss 2011). The spatially coarse nature of human brain lesions has hindered our ability to provide a comprehensive neurobiological explanation for the interplay between domain-general and domain-specific processes.
Functional magnetic resonance imaging (fMRI) studies in healthy participants have provided a more detailed picture. On the one hand, meta-analysis and withinsubject studies of diverse executive functions show circumscribed overlaps in the lateral and dorso-medial frontal cortices, insula, intraparietal sulcus and occipitotemporal junction. (Collette et al. 2005(Collette et al. , 2006Niendam et al. 2012;Fedorenko et al. 2013;Nee et al. 2013;Lemire-Rodger et al. 2019;Braver et al. 2021;He et al. 2021;Saylik et al. 2022;Friedman and Robbins 2022;Reineberg et al. 2022). These activations are usually linked to domain-general or multiple-demand (MD) areas that co-activate in association with many cognitively demanding tasks (Duncan 2010;Fedorenko et al. 2013;Assem et al. 2020;Shashidhara et al. 2020). On the other hand, several studies have fractionated activations based on the statistical strength of their engagements in different executive processes (Wager et al. 2005;Dosenbach et al. 2006;Dodds et al. 2011;Hampshire et al. 2012;Niendam et al. 2012;Lemire-Rodger et al. 2019;He et al. 2021;Reineberg et al. 2022). While such results are broadly in line with a picture of both unity and diversity, as yet there is no clear consensus on how domain-general and domain-specific executive processes combine.
Our recent work using high quality multi-modal imaging approaches of the Human Connectome Project (HCP) suggests a clearer path forward for investigating the putative unity and diversity of executive functions. HCP methods utilize surfacebased approaches and multimodal MRI features for accurate alignment of cortical regions across individuals ). Previously we used HCP data to refine the anatomy of MD activations, delineating 9 MD cortical patches per hemisphere distributed in frontal, parietal and temporal lobes   (Figure 1a). Within the 9 patches, using the HCP's recent multimodal cortical parcellation (HCP MMP1.0), we defined an MD core consisting of 10 out of 180 MMP1.0 areas per hemisphere, that are most strongly co-activated across multiple task contrasts, and most strongly functionally interconnected, surrounded by a penumbra of 18 additional regions [ Figure 1b; ]. This fine-grained picture of the MD system highlights several challenges for interpreting previous executive function studies. First, while executive activations often appear to overlap MD regions (Friedman and Miyake 2017), it remains unknown whether executive tasks engage penumbra or core MD regions, or additional nearby regions with more task specific responses. Second, links between executive activations and canonical resting state networks (RSNs) are uncertain.
Previous studies propose overlaps with the fronto-parietal network (FPN) (Power et al. 2011;Yeo et al. 2011;Blank et al. 2014;Ji et al. 2019;Assem et al. 2020;Cocuzza et al. 2020). In our previous study we have shown that core MD regions form a functionally integrated subset of the FPN . But in addition to further FPN regions, penumbra MD regions belong to three other canonical RSNs, the cingulo-opercular network (CON), the dorsal attention network (DAN) and the default mode network (DMN). We have hypothesized that such nearby nodes could act as communication channels between domain-specific and MD regions. It is currently unclear how different executive activations relate to RSNs. Third, previous studies have largely ignored subcortical and cerebellar contributions to executive functions (Niendam et al. 2012). Our previous work identified circumscribed MD regions in the head of caudate and localized patches in cruses I and II in the cerebellum as well as a putative MD region in the anterior and medial thalamus (Assem et al. , 2022. The relation between non-cortical MD regions and executive activations remains uncharted territory. To investigate executive activations and their relation to MD regions with high spatial precision, we collected a new dataset using HCP's multimodal MRI acquisition and analysis approach. We chose three classical paradigms targeting three putative executive functions: an n-back task (updating), a rule switching task (set shifting) and a stop signal task (inhibition). The same subjects performed all three tasks within the same session and within the same runs. In all three cases, a high-demand executive condition was contrasted with a low-demand baseline. This is a critical manipulation because MD regions are characterized by their strong response to task difficulty manipulations (Fedorenko et al. 2013;Assem et al. 2020).
Page 6 of 54 Our results explicate both unity and diversity of executive functions. The resulting scheme, however is quite different from classical views of distinct frontal territories and provides new mechanistic insights interlinking domain-general and domain-specific processes. The results show that the three executive tasks show overlapping activations at the single subject level within MD patches, suggesting a common role for MD regions in executive tasks. Yet each task's topography shifts within MD patches to form a unique intersection between core MD and adjacent finegrained RSNs. In this intersection, the strongest activations often arise at the border between a core MD region and an adjacent RSN. These results suggest a novel framework for how domain-specific areas recruit neighboring MD areas to generate distinct executive functions. They provide a new, fine-scale resolution of longstanding debates between domain-specific and domain-general views of executive function.  ): 2>0 n-back, hard>easy reasoning, math>story. (b) Extended MD system from . Core MD regions are colored in bright green surrounded by black borders. Penumbra MD regions are colored in dark green. Data available at: http://balsa.wustl.edu/r27NL (c) Flat cortical maps overlaid with group average activations for each executive contrast. Green borders surround core MD areas, with the nine coarser-scale patches labelled on the left hemisphere. Data available at: http://balsa.wustl.edu/x8M0q Results 50 subjects were scanned while performing three classical executive tasks in the same session: n-back, switch and stop signal. Data from 37 subjects were included in this report (see Materials and Methods for subjects' details). All tasks were visually presented and required button presses. Each task had two difficulty conditions. The n-back task consisted of 3-back and 1-back blocks (3>1 n-back). The switch task had two rule and one rule blocks (switch>no switch). The stop signal task had blocks with stop trials and blocks with no stop trials (stop>no stop). Participants performed 4 runs, each lasting 15 minutes and containing 4 easy and 4 hard blocks for each task, along with 12 fixation blocks. Additionally each subject underwent 30 minutes of resting state scans in a separate session. (Figure 2; see Materials and Methods for further task details).

Behavior
As expected, performance on the easy condition was better than the hard condition for all tasks (Table 1). For the targets in the n-back task, accuracy was higher and reaction times shorter for the 1-back condition than the 3-back condition (accuracy t 36 =6.6; reaction time (RT) t 36 =13.8, both ps<0.0001). Similarly, accuracy and RTs on the switch blocks were worse than the no switch blocks (accuracy t 36 =9.3; RT t 36 =27.2, both ps<0.0001). For the stop signal task, participants had more go omissions in the stop blocks (t 36 =3.0, p<0.01). In the stop block, participants successfully stopped on 44.7% (±10.6) of stop trials, with unsuccessful stop trial RTs faster than go trial RTs (Table 1). We first sought an overview of activations for each of the three critical contrasts (3>1 n-back, switch>no switch, stop>no stop). Figure 1c reveals broad similarities between the three tasks, with activations resembling the 9 MD patches from Assem et al. (2020), within and also adjacent to the 28 finer-scale core and penumbra regions (green borders). A partial exception is the temporal patch from Assem et al. (2020); though activations close to this patch were seen for all three contrasts (compare Figure 1a), they did not clearly overlap. The data also suggest that, in more detail, each task shows a unique pattern of activations. At the hemispheric level, there were stronger left hemispheric activations for switch, but right biased activations for stop. Within each hemisphere, exact activation patterns differed within and adjacent to MD regions. At a sub-areal finer grained level, for example, note activation patterns at the different edges of the right lateral prefrontal region p9-46v, with stop activations near its anterior-dorsal border, switch activations near its posterior-ventral border.
With this broad overview, it seems plausible that executive activations harbor both similarities and differences. In the next sections we explore the similarities, differences and fine-grained activations across these three tasks. Executive activations converge on a common MD core at the individual level First, we sought to statistically investigate conjunctions between the three executive contrasts at the coarse areal level. For areal definitions, we used the HCP's MMP1.0 . With the improved MSMAll alignment, previous work has shown that the HCP_MMP1.0 group-defined borders capture around 70% of the areal fraction of individually defined areas ) and produce closely matched results to those derived from subject-specific areal definitions (Assem et al.  Assem et al. (2020), which here we term 2020penumbra, along with 12 new regions that we call additional-penumbra. On the dorso-lateral frontal surface, we identify new areas FEF, 6a and 6ma near core MD region i6-8. More anterior, we identify areas 46 and 9-46d near core MD areas p9-46v and a9-46v. In the inferior frontal junction we identify PEF abutting core MD region IFJp. In the insular region, we identify area FOP4 next to core MD region AVI.
On the medial parietal surface, we identify a cluster of four areas next to POS2 (penumbra MD); these are 7Pm, 7PL, 7Am and PCV. All additional-penumbra regions were close to core MD regions. For each core MD, 2020-penumbra and additional-penumbra region, Figure   3b shows results of each individual task contrast (as above, one-sample t-test against zero, p<0.05 Bonferroni corrected for 360 areas). For core MD, the great majority of individual contrasts were positive. The same was true for the subset of 2020-penumbra regions that belonged to DAN or CON. By definition, additionalpenumbra regions showed significant contrasts for all tasks in at least one hemisphere, usually both, and notably, the majority of these also belonged to DAN or CON. A further notable result is that, among penumbra regions, those belonging to DAN tended to show greatest activation for switch, while those belonging to CON showed strongest activation for stop.
Next we investigate task overlaps at the finer-grained cortical vertex level. We performed this analysis within-subjects to confirm the existence of overlaps at the single subject level. For each subject, we identified the vertices that were significantly activated across the four runs for each of the three contrasts separately (p<0.05 FDR corrected for cortical vertices). Then we performed a conjunction to identify significant vertices in all three tasks creating a single map per subject. We then summed the maps across subjects to create a probabilistic subject overlap map ( Figure 3c). This revealed strong overlaps in 7 MD patches, weaker overlaps around the IFJp patch and almost no overlaps in the temporal MD patch (Figure 3c).
One intriguing finding is that overlaps lay near borders between core MD and adjacent RSNs in at least 7 locations. In the frontal dorso-medial patch (   Indeed, Figure 1c points to some differences between the tasks and Figure 3b hints that they might be linked to different RSNs. In this section we focus on functional preferences across the three tasks. To investigate these preferences at a finer grained level, we analyzed data at the vertex level. For each vertex, we compared its activations between the three tasks across subjects (paired t-tests) and assigned the vertex a task label if its activation was significantly stronger than each of the other two tasks ( To quantify the engagement of RSNs, we used the HCP-based whole-brain definitions of FPN, CON, DAN and DMN to compare activations between the three contrasts ( Figure 4c). We split the FPN into core MD and non-core MD portions.
Across the five networks, hemispheric asymmetries were pronounced. Collapsing across all networks, 3>1 n-back is right lateralized ( Together with the results of the previous section, the unity and diversity of each executive contrast can be conceived as a combination of core MD activations (the unity) and adjacent more specialized RSNs (the diversity), with different executive demands preferentially recruiting different RSNs. We also note that few areas of DAN and CON, those classified as 2020-penumbra MD (white borders in   Fine-grained core MD activations are shifted towards task-specific RSNs An interesting observation from the previous section is that executive preferences, which roughly map out canonical RSNs, surround core MD regions (Figure 4). Here we wondered whether this organization is related to the fine-scaled sub-areal activations within MD regions. We hypothesized that core MD activations for each task would be shifted towards the more specialized RSNs suggesting a strong interaction between domain-specific and the closest patches of MD regions.
For an initial overview of the fine-scaled preferences, we first selected all vertices that were significantly activated by any of the three contrasts (one-sample ttest against zero; p<0.05 FDR corrected for cortical vertices). Then we colored each vertex with the relative strength of its group average activation for each contrast (see

Materials and Methods). Figure 5a
reflects a mosaic of functional preferences, especially within core MD regions. For example, note how the colors form a rapidly shifting gradient within the right p9-46v.
Next we quantified these preferences within core MD regions. We compared activations between each pair of contrasts at the vertex level (paired sample t-test, p<0.05 FDR corrected for core MD vertices). To facilitate viewing gradients, we combined 3 frontal and parietal regions into two patches (mid-frontal patch: p9-46v, 8C and IFJp; parietal patch: PFm, IP2, IP1). We also visualize the territories for DAN, CON and DMN (Figure 5b-d).
Contrasting n-back vs switch (Figure 5b) revealed that each task's preferring vertices were shifted towards different RSNs. In the left hemisphere, switch vertices were spatially closer to DAN. N-back vertices were closer to DMN and more right lateralized. In the parietal patch, these preferences exist in a rough ventral (n-back) to dorsal (switch) gradient. A flipped (dorsal to ventral) gradient can be observed in the mid-frontal patch.
Contrasting switch vs stop (Figure 5c), again revealed a shift for switch vertices towards DAN prominent on the left hemisphere. Stop preferring vertices feature prominently on the right hemisphere and are spatially shifted towards CON.
These preferences form a similar rough dorsal (switch) to ventral (stop) parietal gradient that is flipped in the mid-frontal patch.

Contrasting n-back vs stop (Figures 5d) again revealed significant
preferences within core regions. While n-back activations were usually stronger, in the parietal lobe there was a cluster of stop preferring vertices, within PFm and shifted towards CON.
Altogether, these results demonstrate that fine-grained activations within core MD regions shift towards different RSNs in a task-specific manner. Further, task shifts in frontal and parietal cortex were systematically related. For example, a strong activation in the dorsal mid-frontal patch roughly predicts strong activation in the ventral parietal patch. In the next section we relate these task preferences to finergrained cortical connectivity. Executive functional preferences are recapitulated by fine-scaled core MD connectivity The above results reveal fine-scaled activation gradients within core MD regions.
Previously, we hypothesized that task preferences likely reflect differences in local MD connectivity with adjacent regions Duncan et al. 2020).
Thus, here we wondered whether core MD resting-state connectivity is related to activation shifts.
To illustrate, we first focus on the fine-grained preferences of one core MD region in the lateral prefrontal cortex: right p9-46v (Figure 6a). We utilized an independent resting-state data from 210 HCP subjects [the 210V validation sample from ]. Each subject underwent 1 hour of resting-state scans (minimally preprocessed, MSMAll aligned, spatial and temporal ICA+FIX cleaned; see Materials and Methods) to create a group average vertex to vertex connectivity matrix. We did not use the resting-state data of the current study's subjects to avoid circularity, as their resting-state data were also used for cortical alignment (MSMAll; see Materials and Methods). We then looked at the connectivity patterns of 3 seed vertices, manually placed within p9-46v (Figure 6a).
Seed 1 was placed close to the dorsal p9-46v border with area 46, where stop>no stop preferences peaked (first column in Figure 6a). Intriguingly, the connectivity of seed 1 strongly resembled core MD activations for stop>no stop. In the parietal lobe, for example, connectivity was strongest at the border between areas PFm and PF, with little connectivity to the more posterior IP1. This connectivity-activation similarity extended to other locations throughout the cortex in frontal, parietal and temporal patches (first column in Figure 6a). Next we placed seed 2 roughly in the middle of p9-46v (second column in Figure 6a). Now the connectivity map strongly resembled the n-back contrast activations. On the lateral parietal surface, for example, its peak connectivity lay within intraparietal sulcus area IP2. For seed 3, a vertex near the ventral border of p9-46v (third column in Figure 6a), the connectivity map resembled the switch contrast activations. This qualitative demonstration suggests that finegrained differences between task activation maps are matched by corresponding fine-grained differences in functional connectivity (Robinson et al. 2014;Tavor et al. Next, we quantified the connectivity-activation similarity across core MD regions at the single subject level. For each subject, we correlated (Pearson's correlation) the connectivity map of each core MD vertex ("seed vertices") with each of the three activation contrasts. The correlation was performed for seed vertices within core MD regions only. To limit the effect of local connections on driving any correlations, for each seed, we excluded from the correlation all vertices in the seed's own MMP1.0 region or any adjacent region, along with homologs in the opposite hemisphere. For each subject, we assigned each vertex showing a significant correlation greater than 0.2 with any of the task maps (FDR p<0.05) the label of the task it numerically most strongly correlated with. Then we created a subject probabilistic map for each task. To facilitate viewing the connectivity gradients within core MD regions, we used a winner-take all approach to assign each core MD vertex the label of the task with the greatest subject overlap (Figure 6b).
The results reveal fine-scaled systematic shifts in connectivity gradients. For example, replicating our manual seed demonstration, a dorsal to ventral task gradient (stop to n-back to switch) exists within the right mid-frontal MD patch. The gradient is reversed to a ventral to dorsal direction around parietal MD regions. In the insular patch, it becomes rostral to caudal. Note how seed preferences often follow the canonical RSNs; switch seeds closer to DAN (green), stop seeds closer to CON (blue) and n-back seeds closer to DMN (red).
Collectively, these results demonstrate fine-scaled topographies of each executive demand can be predicted by fine-scaled core MD connectivity. Hence, coactivated vertices within core MD form functionally connected networks. These findings further support the notion that each executive demand recruits a taskspecific network which in turn interacts most strongly with its immediately adjacent core MD territories.  Activations peak at borders between core MD and adjacent RSNs Within the fine-scale patterns that we have shown, borders seem especially important, including borders shared between core MD and other RSNs. For example (Figure 6), stop activations peak at the border between p9-46v (core MD) and area 46 (part of CON). Here we wondered whether there is a general pattern where peak activations fall on the borders between core MD and task-relevant adjacent networks.
First, we wanted to map out, at the single subject level, where the strongest activations lie for each contrast. For each subject and task separately, we selected the top 5% activated vertices across the whole cortex, binarised the map and summed it across subjects to create a probabilistic subject overlap map for each task. Vertices that overlap in more than 50% of subjects are shown Figure 7a. The strongest overlaps are concentrated around p9-46v, the parietal patch, and medial parietal patch. Stop>no stop vertices were closest to borders between core MD and CON, switch and n-back vertices were closest to borders between core MD and DAN.
To get a better picture of activations at border zones, we analyze borders between p9-46v and its surrounding three regions: 46, 8C, IFSp (Figure 7b; top).  (Figure 6).
On the medial frontal surface, our previous work ) noted a striking consistency across all tasks, with peak activation at the intersection of core MD area 8BM with SCEF (CON) (Figure 1). Probing this intersection in the current data (Figure 7b; bottom) indeed confirmed that activations for all three tasks peak near or at the 8BM/SCEF border bilaterally (all segment x task interactions F (30,1080) >78, p<0.0001).
As the above results rely on group-defined HCP_MMP1.0 borders, we sought to alleviate concerns that border activations might simply reflect an artefact due to individual differences in border locations or inherent MRI signal smoothness. To test this, we created a simulated dataset utilizing the subject-specific cortical parcellations of a randomly selected 37 HCP subjects from the 449 subjects dataset (see Materials and Methods). For each subject and for each area, we assigned all its vertices the activation value of the corresponding area and subject in the real data. This simulates the condition that activations are homogenous throughout the area. We created three datasets for our three contrasts. We then applied several degrees (4, 12, 20 mm FWHM) of surface smoothing to simulate the inherent blurriness of fMRI data at varying levels. Then we repeated the same analysis above, selecting the top 5% activated vertices for each subject and creating an overlap map across subjects. While the simulated maps showed activations in the same zones, none of the simulated maps replicated the sharp border activations. For example, comparing the simulated data (12 mm) with the real data shows much broader activations, with little focus on regional borders (Supplementary figure 3).
With 4 and 20 mm smoothing, results even less resembled the actual data.
These spatially precise results suggest that areal borders play a critical role in communication between MD and adjacent networks. Likely, it is at these borders that information is most intensively integrated between networks. Overlap and divergence in subcortical and cerebellar

MD regions
Finally we wondered whether executive overlaps and preferences extend to subcortical and cerebellar MD regions. We focus on the caudate, thalamus and cerebellum as those were the most prominent extracerebral structures that showed MD properties in our previous study  This avoids mixing of signals from the white matter or between different structures.
To identify overlaps at the voxel level, for each structure, we identified significantly activated voxels for each contrast (one sample t-test, FDR corrected for each structure separately, p<0.05, Bonferroni corrected for 3 structures) and then identified the conjunction of significant voxels across the three contrasts (Figure 8a).
For analysis transparency, we report that the initial results using the unsmoothed data (i.e. no additional smoothing over the standard 2 mm at the preprocessing stage) for the caudate and thalamus were patchy, likely due to the relatively low signal to noise ratio (SNR) of high spatial and temporal resolution fMRI for the subcortex at 3T because they are far from the head coil. Thus here we report the results after applying a 4 mm FWHM smoothing kernel limited within the major subcortical structures. This revealed a cluster of voxels in caudate head, extending to its body bilaterally, overlapping with caudate MD regions identified by Assem et al.
(2020) (Figure 8b). We were also able to identify a thalamic cluster that significantly overlapped with the putative MD thalamic region from Assem et al. (2020). For the cerebellar analysis we did not apply any additional smoothing, as the cerebellum is generally closer to the head coil. The analysis revealed clusters located mainly in cruses I and II, again mainly overlapping with MD cerebellar regions. Note however, that two of the previously-defined MD patch occupying the medial and lateral portions of the right crus I are missing in the current data. Investigating each contrast separately (Supplementary Figure 4) revealed that this is due to deactivations in this region for the stop>no stop contrast. These results largely replicate our prior findings of MD regions in subcortex and cerebellum.
We then wondered whether subcortical and cerebellar activations exhibit functional preferences within MD and adjacent RSNs. For this analysis we used unsmoothed data for all structures. We utilized our subcortical and cerebellar MD definitions (see Materials and Methods) and the DAN, CON and DMN subcortical and cerebellar network definitions from the same network parcellation we used for the cortical analysis (Ji et al. 2019). Any overlapping voxels between MD and RSNs were assigned to MD areas. We averaged the voxel activations for each network separately to give one parameter estimate per network x lateralization x structure x subject. To assess statistical significance, we applied a separate ANOVA for each structure with three factors: 3 tasks x 4 networks x 2 hemispheres. The caudate only had 3 networks as it did not have any voxels identified as DAN. All post hoc t-tests were evaluated at p<0.05 Tukey-Kramer corrected.
For the caudate (Figure 8c), the task x hemisphere x network interaction was For the thalamus (Figure 8d), the interaction task x hemisphere was significant (F (24,864) =38.7, p<0.0001). Across networks, stop was right lateralized while switch was left lateralized.
For the cerebellum (Figure 8e), we observed a significant interaction between task x hemisphere x network (F (24,864) =92.9). Across all networks, post hoc analysis showed left lateralized activations for stop>no stop, right lateralized for switch>no switch but no significant hemispheric preference for 3>1 n-back. These trends were especially strong in the MD area, which also showed strongest activations overall.
Note the flipped hemispheric preferences in the cerebellum due to the decussation of fibers across the midline in the brainstem.
All in all, the three executive tasks do share common activations that overlap with MD regions in the caudate, thalamus and cruses I and II in the cerebellum.
Within MD, hemispheric differences were more prominent than task preferences.
Outside of MD, DAN was preferentially activated by switch in the thalamus and cerebellum, while CON was predominantly activated by stop>no stop. Overall, these results parallel cerebral cortical findings, confirming that task overlaps and dissociations extend to subcortical and cerebellar components of brain networks. Our results using the high spatial resolution of HCP multimodal MRI approaches provide a novel framework supporting the unity and diversity model of executive functions and bridging it with detailed functional anatomy of the human brain.
Activations of three distinct executive functions showed overlapping activations (at the single subject and single vertex/voxel level) within cortical, subcortical and cerebellar domain-general MD regions. Surrounding this unity, each executive demand shows unique functional preferences within MD regions that extend to nearby canonical RSNs. Linking this unity and diversity are strong activations at the intersection of core MD and adjacent task-specific RSNs. We discovered these activations peaked at network borders defined using multimodal MRI criteria, suggesting a likely substrate for integration between networks. Our novel framework suggests domain-specific areas recruit adjacent MD areas from different spatial locations on the cortical sheet to generate executive functions, likely far more diverse than the three studied here. We elaborate on these points below.
MD patches: A consistent topology with task-specific shifts Using the precise HCP imaging approach, we have previously delineated 9 coarse cortical patches (Figure 1) co-activated by 3 cognitively demanding tasks . In this study we show that each of the three executive tasks strikingly coactivate roughly the same 9 MD territories (Figure 1). An exception was activity in the temporal patch, in which stop activations were more anteriorly-dorsally shifted than the other two contrasts. More generally, within the MD patches, each task showed detailed topological shifts. Our results showed that many of these shifts were unique for each task and varied in a systematic pattern across the cortex linked to the underlying fine-grained functional connectivity.
Executive unity at the intersection of MD core with adjacent networks We previously linked MD patches to a set of 10 core MD regions, which roughly outline the central portions of 7 out of the 9 patches. The conjunction of the three executive contrasts replicated 9 out of the 10 core MD regions, with the exception of posterior intra-parietal region IP1, confirming the strong domain-generality of MD core (Figure 3b). Surrounding MD core, the conjunction also identified a number of penumbra areas belonging to three RSNs: CON, DAN and non-core FPN (Figure 4).
At the finer grained vertex level, the most consistent conjunctions fell at the intersection of MD core with CON and DAN in 6 locations and at a 7 th location on the medial parietal patch between non-core FPN (POS2) and DAN. The location of these overlaps is reminiscent of an earlier study which argued for defining cortical integrative hubs at the points of intersection of multiple networks (Power et al. 2013).
A follow up study found that selective damage to these hubs is associated with large deficits in executive abilities (Warren et al. 2014). This suggests that our identified overlaps between these 3 networks are critical for supporting executive functions, at least the three components of executive function tested here.
Executive diversity reflects distinct interactions between domain-specific networks and core MD Many previous fMRI studies focused on dissociations between executive functions, suggesting they are supported by functionally distinct territories of the association cortices (Wager et al. 2005;Dosenbach et al. 2006;Dodds et al. 2011;Hampshire et al. 2012;Eisenreich et al. 2017). Such fractionated conceptions offer limited understanding for how executive processes are integrated and coordinated across the brain.
Instead of functional fractionations, our anatomically resolved results reveal a different picture of a common MD territory, defined by multimodal neurobiological criteria, which can be recruited from different spatial locations on the cortical sheet according to different task requirements. Here we summarize how each contrast's activation demonstrated this pattern in a spatially unique manner (Figures 4-7).
The stop>no stop activations were strongest in the right hemisphere. Many regions of CON showed stronger activation for stop than the other two tasks (Figure   4a, b), and within core MD regions, activations were often shifted towards adjacent CON regions, especially in parietal cortex ( Figure 5). In some cases activations peaked at the boundary between adjacent core MD and CON regions (Figure 7).
Previous studies implicate at least four cortical nodes in stop signal or similar paradigms: dorsal frontal regions, inferior frontal junction, temporal-parietal junction and dorsal anterior cingulate (Swann et al. 2012;Aron et al. 2014;Yeo et al. 2015;Suda et al. 2020;Isherwood et al. 2021;Sebastian et al. 2021). While an accurate comparison with our results is not possible, we show that these coarse nodes likely lie at the intersection between core MD and CON. We suggest that interaction between these two networks underlies the attentional re-orienting or "braking" processes involved in stop signal and similar paradigms.
The n-back contrast was slightly right lateralized, showing strong activation throughout core MD (Figures 4, 5) with strongest activations shifted mainly towards core MD-coreMD, coreMD-DAN or coreMD-DMN borders (Figure 7). N-back also showed the least deactivation of DMN (Figure 4). A recent study also demonstrated co-engagement of intermediate nodes between FPN and DMN in a 1-back>0-back task (Murphy et al. 2018). Murphy et al suggested the interaction between FPN and DMN plays a role in recalling detailed information from the immediate past. We speculate that the engagement of the intersection between PGs (DMN) and the parietal core MD patch reflects engagement of the episodic recall network (Rugg and Vilberg 2013) though this needs confirmation through a recall-focused paradigm investigated in a spatially precise approach similar to the current study.
Switch>no switch activations were left lateralized, with strongest activations in core MD and DAN (Figure 4c), in line with previous results highlighting dorsal frontoparietal activations (Braver et al. 2003;Crone et al. 2006;Tsumura et al. 2021).
Intriguingly, the switch contrast also showed strong activations in a band of lateral frontal regions ventral to core MD regions (Figures 2, 4). In a parallel analysis, we showed that seeds in these frontal patches show strong connectivity to the dorsal components of DAN, suggesting a ventral frontal component to DAN. The functional role of this ventral component remains unknown. On one hand, this patch of cortex is functionally heterogeneous with sensory-biased responses (Michalka et al. 2015; consistently engaged when comparing simple cognitive tasks to rest ). The left hemisphere bias and preference of ventral frontal regions may indicate a role for the phonological loop of working memory (inner speech) in managing task switching and wider cognitive tasks.
Thus, the diversity of executive task activations paints a picture of specialized recruitment of core MD regions from adjacent more domain-specialized networks.
This adds to accumulating evidence of other domain-specific language and sensory biased regions that also lie adjacent to MD regions (Fedorenko et al. 2012;Assem et al. 2022). These domain-specific regions likely form communication bridges with core MD, feeding in and out task-relevant information to support brain-wide cognitive integration . In line with this hypothesis, our functional connectivity analysis demonstrates activation shifts within core MD are mirrored by fine-grained shifts in whole-brain connectivity. These results echo previous demonstrations of pre-frontal activations being constrained by its intrinsic functional architecture (Tavor et al. 2016;Waskom and Wagner 2017).
In this study we looked at three traditional elements of the unity-diversity view.
An intriguing question concerns how the results might change with a more diverse set of tasks? Our conception of MD core as a domain-general territory commonly recruited from different spatial directions suggests that diversity is likely far greater than identified here. Activations for diverse cognitive demands are likely to intersect at different junctions between core MD and other RSNs.

Core MD borders are critical for executive functions
One of the most striking findings in this study is that the three executive contrasts showed peak activations overlapping with borders between core MD and adjacent RSNs (Figure 7). The implicated borders largely follow the RSNs most relevant to the contrast. Stop>no stop peak activations mostly overlapped with core MD-CON borders, while core MD-DAN borders were mostly crossed by switch>no switch peak activations. 3>1 n-back had a mixed preference towards core MD-core MD, core MD-DAN and core MD-DMN borders.
That said, there were also borders where the three contrasts peaked together.
Most prominently this occurred in the dorsomedial frontal patch at the border between 8BM (core MD) and SCEF (penumbra). We have also highlighted peaks at this border in our previous study that employed a different set of task contrasts (nback, reasoning, math>story) ). This striking consistency suggests a precise anatomical correlate for a domain-general process, and is most likely linked to response selection activations in the dorsal anterior cingulate cortex (Si et al. 2021;Seghezzi and Haggard 2022).
These findings are the most detailed in a growing body of evidence of activations lying at network borders (Nee 2021). For example, a recent study highlighted that FPN borders with other networks are the most predictive of individual differences in executive abilities (Reineberg et al. 2022). Why would activations peak at borders? The HCP MMP1.0 areal borders were defined using robust multimodal architectural and functional criteria including cortical curvature, myelin content, functional connectivity, and task activations as well as careful cross examination with previous cyto-architectural studies ) Task overlaps and divergences also extended to subcortical and cerebellar regions.
The three executive contrasts overlapped with MD regions in the head of caudate, the anterior and medial thalamus, and cerebellar cruses I and II (Figure 8). Our previous study  failed to find overlapping thalamic activations across diverse tasks, likely due to the low SNR of high spatial and temporal resolution fMRI in deeper brain regions ), but such overlap is clearly visible in the current data. Interestingly, RSN functional preferences also Page 36 of 54 extended into the subcortex and cerebellum, with hemispheric biases and RSN preferences largely matching those of cerebral cortex. These results strengthen the view that the MD system is brain-wide and tightly integrated. To examine finergrained shifts and link activations with specific subcortical/thalamic nuclei, higher resolution and higher SNR studies with 7T are needed.
Recruiting a common MD territory to create distinct executive functions Our results bring a fresh, anatomically precise perspective on brain systems underlying unity and diversity of executive functions. This perspective deviates from the broad differentiations typically observed in lesion studies and functional imaging investigations. We suggest that many cognitive demands, including traditional executive demands, recruit activity in a characteristic territory of 9 cortical patches, with associated subcortical and cerebellar activity. Different demands, however, shift the detailed pattern of activity within these patches, often towards adjacent, more specialized RSNs recruited by individual tasks. With MD territory at the center of multiple domain-specific networks, it is well placed to integrate the components of a cognitive operation to generate distinct executive processes. These protocols are substantially similar to those described in previous studies Smith et al. 2013;U urbil et al. 2013) but do differ in some respects. All subjects underwent the following scans over two sessions: structural (at least one 3D T1w MPRAGE and one 3D T2w SPACE scan at 0.8-mm isotropic resolution), rest fMRI (2 runs × 15 min), and task fMRI (5 tasks, 4 runs each, approx.

Subjects
100 min total). Whole-brain rest and task fMRI data were acquired using identical multi-band (factor 8) gradient echo EPI sequence parameters of 2-mm isotropic resolution (TR = 800 ms, TE=37 ms). Both rest and task EPI runs were acquired in pairs of reversed phase-encoding directions (AP/PA). Spin echo phase reversed images (AP/PA) matched to the gradient echo fMRI images were acquired during the structural and functional (after every 2 functional runs) scanning sessions to (1) correct T1w and T2w images for readout distortion to enable accurate T1w to T2w registration, (2) enable accurate cross-modal registrations of the fMRI images to the T1w image in each subject, (3) compute a more accurate fMRI bias field correction and (4) segment regions of gradient echo signal loss.

Data preprocessing
Data preprocessing was also substantially similar to the HCP's minimal preprocessing pipelines detailed previously

Task Paradigms
Each subject performed three tasks in the same scanning session: n-back, switch and stop signal (Figure 2). All three tasks were visual. Subjects performed two other tasks in a second session: an auditory version of the n-back task [previously reported in (Assem et al. 2022)] and a fifth task not relevant for this study. Before scanning, participants performed a short training session ensuring they understood the instructions and were performing above chance. This is particularly important for the stop signal task (see below).
Each subject performed four runs. Each run consisted of 36 blocks: 8 n-back, 8 switch, 8 stop and 12 fixation blocks. Each task consisted of 4 easy and 4 hard blocks. Each task block (30 s) started with a cue (4 s) followed by 12 trials (24 s, 2 s each) and ended with a blank screen (2 s) as an inter-block interval. Easy and hard blocks of one task were paired (easy followed by hard, or hard followed by easy) and the order was counterbalanced across runs and subjects. A fixation block (16 s) followed every two paired task blocks. For each trial in the task blocks, the visual stimulus was presented for 1500 ms, followed by 500 ms of a blank screen.
Responses were accepted at any moment throughout the trial. Stimuli were pictures of faces or houses (each category in a separate block). Face stimuli were selected from the Developmental Emotional Faces Stimulus Set (Meuwissen et al. 2017).
Faces were either males or females, children or adults, making a happy or sad face.
House stimuli were pictures of houses or churches, old or new, from inside or outside. There were 32 faces and 32 houses, each made up of 4 examples for each of the 2 x 2 x 2 possible feature combinations. Subjects were encouraged to use their right hand and respond to targets using a middle finger press and to non-targets using an index finger press but this was not enforced and several subjects found it more comfortable to use both hands for responses (index fingers or thumbs).

N-back task
For the 3-back condition (hard), subjects were instructed to press right for the target stimulus (i.e. current stimulus was the same as the one 3 steps back), and left for all non-target presentations. Similarly, for the 1-back condition (easy), subjects were instructed to press right for the target stimulus (i.e. current stimulus was an exact repetition of the immediate previous stimulus) and press left for all non-target stimuli.
In each block there were 1-2 targets and 2 lures (a target image but at the 2-back or 4-back positions).

Switch task
The switch rules were indicated by colored screen borders. The colors were either red or blue. For the 1-rule blocks (easy), the border color did not change throughout the trials of a single block. If the stimuli were faces, a red border indicated to the participant to respond whether the face was male (left press) or female (right press), while a blue border required a judgement if the face was that of a child (left press) or an adult (right press). If the stimuli were houses, for a red border participant responded whether the house was a standard house (left press) or a church (right press), while a blue border required a judgement if the picture was indoor (left press) or outdoor (right press). For the 2-rule blocks (hard), the colored borders would change randomly throughout the trials of a single block, ensuring an equal number of red/blue borders per block.  Barch et al. (2013). Briefly, autocorrelation was estimated using FSL's FILM on the surface (default parameters in HCP's task fMRI analysis scripts were used). Activation estimates were computed for the preprocessed functional time series from each run using a general linear model (GLM) implemented in FSL's FILM (Woolrich et al. 2001).

Stop signal task
For each of the tasks, 4 regressors were used (2 stimulus category x 2 task difficulty). Each predictor had a unitary height and covered the period from the onset of the cue to the offset of the final trial (28 sec). All regressors were then convolved with a canonical hemodynamic response function and its temporal derivative. 12 additional motion regressors were added to the model (3 translation, 3 rotation and their derivatives). The time series and the GLM design were temporally filtered with a Gaussian-weighted linear highpass filter with a cutoff of 200 seconds. Finally, the time series was prewhitened within FILM to correct for autocorrelations in the fMRI data. Surface-based autocorrelation estimate smoothing was incorporated into FSL's FILM at a sigma of 5mm. Fixed-effects analyses were conducted using FSL's FEAT to estimate the average effects across runs within each subject.
For further analysis of effect sizes, beta 'cope' maps were moved from the CIFTI file format to the MATLAB workspace. Beta maps were then converted to percent signal change as follows: 100*(beta/10000). The value 10000 corresponds to the mean scaling of each vertex/voxel's timeseries during preprocessing. Unless mentioned otherwise, parametric statistical tests were used.
For parcellating the cerebral cortex, the group-average HCP multi-modal parcellation (MMP1.0) was used , as the individualspecific areal classifier is not publicly available. Still, due to the superior cortical alignment approach of MSMAll, the areal fraction of individually defined parcels captured by group-defined borders reaches 60-70% ) and we have previously demonstrated that comparing areal classifier and group-defined borders showed similar results . Values of vertices sharing the same areal label were averaged together to obtain a single value for each area.
To create the RGB colors in Figure 5a, we converted each task's group average activation map to lie between 0 and 1 by normalizing their activations by the minimum and maximum activation value across all three contrasts. Each vertex was then assigned a color through a 1x3 vector [red green blue] with the value of each color ranging from 0 to 255. The color was assigned by combining the normalized activations of the three tasks as follows [n-back switch stop]*255.

Resting-state connectivity analysis
In this study we used a dense connectivity matrix (59k by 59k vertices) from 210 HCP subjects [the 210 validation group from ]. Each subject underwent 1 hour or resting-state scans. The analysis methods are described in detail in . Briefly, the pipeline was very similar to this current study with the addition of temporal ICA cleaning to remove global respiratory artefacts (Glasser et al. , 2019.

Borders analysis and simulation
We first calculated the geodesic distance between all cortical vertices using the connectome workbench function -surface-geodesic-distance-all-to-all using subjectspecific vertex areas and the midthickness cortical surface (derived from our 37 subjects). We then identified the vertices that belonged to the HCP_MMP1.0 borders using the workbench function -border-to-vertices. Vertices with each area were then sorted according to their distance from the border vertices and grouped into 5 distance groups by ensuring a similar number of vertices was included across all groups. Border vertices were included in this analysis.
To create the simulated data, we randomly selected 37 subjects from the 449 HCP subjects with each subject's cortex parcellated into 360 areas using a multimodal areal classifier . We then populated the vertices for each area and each subject with activation values derived from our 37 subjects; e.g. if the n-back average activation value for subject_1 for area p9-46v was 0.3, we populated the vertices belonging to area p9-46v in HCP_subject_1 with 0.3. We created three simulated datasets corresponding to the three executive contrasts. We then applied smoothing for each subject using workbench's function - For the voxel-wise conjunction analysis in subcortical structures, we applied an additional 4 mm FWHM to the data using the workbench function -ciftismoothing. All other analyses in this section, including all analyses of cerebellar activation, used unsmoothed data.
In Assem et al (2020) two versions of the subcortical/cerebellar MD masks were defined: One based on a conjunction of task activations and one based on rfMRI connectivity with cortical MD core. In this study, the caudate and cerebellar masks were based on task activations as they are slightly more spatially constrained than the rfMRI mask. The thalamic MD mask was based on rfMRI, as our previous study could not identify a task-based conjunction in the thalamus. The volumetric cerebellar results are projected on a flat cerebellar surface using SUIT software (Diedrichsen and Zotow 2015). Although this approach has the limitations of a volume-based analysis (and thus is done mainly to aid visualization), individual subject cerebellar surface reconstruction and registration is not yet easily available.

Supplementary figure 2. Connectivity (Pearson's correlation) of a seed in DAN (black borders)
shows connectivity to fine-grained regions ventral to the mid-frontal patch of core MD regions (white borders). Correlations are thresholded at 0.2. Correlations are average of the 210 validation HCP subjects . Data available at: http://balsa.wustl.edu/qxPk9 Supplementary figure 4. Activations (percent signal change) for each executive contrast in an axial slice of the subcortex (top row) and a flat map of the cerebellum (bottom row). MD areas as defined in  are surrounded by white borders on the cerebellar surface. Data available at: http://balsa.wustl.edu/w8g71