Development of Top-Down Cortical Propagations in Youth

SUMMARY

Hierarchical processing requires activity propagating between higher and lower-order cortical areas. However, functional neuroimaging studies have chiefly quantified fluctuations within regions over time rather than propagations occurring over space. Here, we leverage advances in neuroimaging and computer vision to track cortical activity propagations in a large sample of youth (n=388). We delineate cortical propagations that systematically ascend and descend a cortical hierarchy in all individuals in our developmental cohort, as well as in an independent dataset of densely-sampled adults. Further, we demonstrate that top-down, descending hierarchical propagations become more prevalent with greater demands for cognitive control as well as with development in youth. These findings emphasize that hierarchical processing is reflected in the directionality of propagating cortical activity, and suggests top-down propagations as a potential mechanism of neurocognitive maturation in youth.

eTOC

Hierarchical processing requires activity propagating between higher and lower-order cortical areas. However, neuroimaging studies have chiefly quantified fluctuations within fixed regions over time rather than propagations over space. We used recent advances in neuroimaging and computer vision to demonstrate that top-down propagations become more prominent during task-demands and over neurodevelopment.

INTRODUCTION

The hierarchical organization of the cortex provides a scaffold for bottom-up sensory integration and top-down control^1–4. In humans, this hierarchical cortical organization is critical for cognitive control and executive function^5–7. However, recent evidence suggests that this cortex-wide hierarchical organization is not established at birth, but is instead a product of protracted development^8–10. Critically, the establishment of this cortical hierarchy is contemporaneous with both the development of top-down executive function^10,11 and the onset of psychiatric disorders^12,13. Understanding this neurodevelopmental window is crucial, as deficits in top-down control are associated with transdiagnostic psychopathology¹⁴, reduced quality of life¹⁵, and mortality in youth¹⁶. Although functional magnetic resonance imaging (fMRI) allows for noninvasive imaging of neurocognitive development, it has remained challenging to identify the precise spatiotemporal patterns of activity that support the development of top-down processing.

Notably, top-down hierarchical processing necessarily involves activity propagating through space from higher- to lower-order areas. However, most fMRI studies of hierarchical processing have quantified activity fluctuations in fixed regions over time rather than accounting for activity propagations over space. Recently, three studies have used a combination of fMRI in humans and intracranial recordings in macaques to show that slow but widespread activity systematically propagates up a putative cortex-wide functional hierarchy^17–19 known as the principal gradient²⁰. The observation of systemic propagations up the principal gradient provides a particularly compelling account of hierarchical activity for two reasons. First, the principal gradient itself reconciles several prominent theories of hierarchical cortical organization^20–24. Second, the observation of “bottom-up” propagations ascending the principal gradient aligns with proposed mechanisms of bottom-up hierarchical processing^4,21,23,24. Further, two recent studies documented top-down propagations, where alertness¹⁷ and arousal²⁵ were associated with the movement of activity from higher- to lower-order cortical regions. Together, these studies suggest that the direction of cortical activity over space (bottom-up or top-down) may be linked to hierarchical processing.

Despite these recent advances, important gaps remain. First, prior approaches to quantifying propagations have required summarizing activity across the entire brain in order to determine hierarchical directionality. Although these approaches can reveal whole-cortex hierarchical patterns of activity propagations, work in animal models suggests that cortical propagations may be predominantly localized phenomena. In contrast the large white matter bundles typically posited as the structural basis for functional network connectivity^26,27, cortical surface propagations utilize relatively shorter, horizontal projections^28–36. Second, developing noninvasive approaches that can capture local spatial directionality of activity propagations remains an important unmet need, as prior work has suggested that propagation directionality may be a central feature of stimulus encoding and task execution^{28–30,37–39}. Third, in addition to summarizing activity over the whole brain, existing fMRI approaches to delineating the procession of activity over space have typically required collapsing activity over many individuals. As a result, prior studies have not evaluated individual differences in cortical propagations at the local scale at which they are thought to occur. Individual differences are likely to be particularly informative for studies of brain development in youth, as top-down cognitive control improves dramatically in childhood and adolescence. However, it remains unknown whether top-down propagations become more prominent with development in youth.

Here, we fill this critical gap by applying a method that has been widely-used in computer vision – optical flow – to quantify the direction of activity propagations across the cortex in a large sample of youth. In contrast to other measures of fMRI signal fluctuations, optical flow enables quantification of the directional trajectory of activity over space on the surface of cortex. We applied optical flow to a large developmental dataset that included both high-quality resting-state and task fMRI data⁴⁰, and evaluated whether the direction of propagating signals aligned with the functional hierarchy (FH) established by the principal gradient. We hypothesized that our approach would reveal both intra- and inter-individual differences in bottom-up and top-down propagations. Specifically, we predicted that top-down propagations would become more prominent within individuals in response to a task that required cognitive control. Furthermore, we predicted that a comparison between individuals would reveal an increased prevalence of top-down hierarchical propagations with age in youth.

RESULTS

We capitalized upon advances in computer vision and a large sample of youth studied using fMRI at high temporal resolution to identify hierarchical propagations of cortical activity and delineate how they evolve with age. Specifically, our sample included n=388 participants ages 8–22 years old (204 females) from the Human Connectome-Development (HCP-D) project who had a large quantity (mean number of TRs per participant remaining after quality control = 1,255.7) of low-motion fMRI data acquired at rest. Spherical registration of these data enabled us to leverage spherical optical flow^41,42 to identify propagations of activity occurring across the cortical surface. Below, we first introduce the analytic framework for the application of optical flow and demonstrate that this technique can accurately identify activity propagations in simulated data with realistic noise properties where the ground truth is known. Using real data from HCP-D, we subsequently show that hierarchical cortical propagations can be found in every individual participant in this large dataset; we replicate this finding in a sample of densely-sampled adults. Next, we establish that tasks that require cognitive control are associated with more top-down cortical propagations and delineate increases in the prevalence of top-down propagations with age in youth. Finally, we present analyses that emphasize that these effects cannot be explained by developmental changes in functional connectivity and are robust to alternative definitions of the cortical hierarchy.

Measuring activity propagations across the cortical hierarchy with optical flow

Optical flow is a widely-used computer vision technique^43,44 that measures intensity differences between successive pairs of images, and estimates how intensity values in the image move from one frame to the next. Ultimately, this procedure yields a vector field between each frame; these vectors describe the direction of movement of intensity values between frames at each location in the image. We applied this approach to individual fMRI time series, where image intensity differences reflect differences in the blood-oxygen-level-dependent (BOLD) signal. As BOLD signal reflects local field potentials^{17,18,45–49}, the resultant vector fields described the direction of activity propagation between pairs of sequential fMRI volumes (Figure 1A). To evaluate whether fMRI activity propagates hierarchically, we compared the vector field derived from optical flow with a widely-used map of the cortical functional hierarchy²⁰ (Figure S1). We evaluated the spatial gradient (∇) of the functional hierarchy (FH) to derive a vector field that describes the direction of ascent up the hierarchy at each point on the cortex; we refer to this map of vectors as ∇FH. The directions described by ∇FH served as a reference that allowed us to describe the observed directional movement of activity quantified by optical flow as ascent or descent along the functional hierarchy. Specifically, we calculated the difference in the angle (in degrees) of the direction of activity estimated by optical flow compared to the direction of hierarchical ascent defined by ∇FH (Figure 1C). This comparison was repeated for each pair of timepoints, generating a time series of angles at each location that reflected the degree to which the estimated direction of activity propagations aligned with hierarchical ascent over time (Figure 1D). In this framework, alignment with the angle of hierarchical ascent (0° from ∇FH) indicated a bottom-up hierarchical propagation, whereas flow in the opposite direction (180° from ∇FH) indicated a top-down hierarchical propagation (Figure 1E, Figure S2, and Figure S3).

Figure 1: Measurement of hierarchical cortical propagations using optical flow.

A) To estimate the spatial directionality of activity across the cortex, all fMR images are projected to the fsaverage4 spherical surface. Specifically, for each pair of sequential images, we use optical flow to estimate the directions of signal propagations between each pair of successive images for each face on the cortical mesh. B) To estimate the direction of hierarchical ascent, the gradient vector field of a widely-used map of the functional cortical hierarchy²⁰ was extracted along the cortical surface (∇FH). This procedure yields vectors across the entire cortex, with each vector describing the most immediate direction of hierarchical ascent for any given face on the mesh. C) To quantify directional distributions, each optical flow direction was assessed relative to the ∇FH (direction of hierarchical ascent) over all sequential image pairs. D) This procedure was repeated for each face on the cortical mesh to yield a matrix of activity directions relative to ∇FH over time for each participant. E) Example bottom-up and top-down propagations: vectors were extracted from pairs of sequential BOLD images (white arrows) and overlaid onto the group-level FH (yellow-black shading). FH = Functional hierarchy.

Simulations reveal that optical flow captures cortical propagations

To ensure that our analytic framework was capable of accurately detecting cortical propagations in fMRI data, we generated simulations of cortical propagations where the ground truth was known. Simulated data were matched to the spectral content and noise properties of real fMRI data^17–19,50 (see Methods). Specifically, we generated a synthetic wave of activation that propagated in the posterior-to-anterior direction across the cortical surface (Figure 2A). To create a corresponding reference vector field (equivalent to ∇FH), we also created a scalar map that quantified the posterior-to-anterior position of each face on the surface of the cortex (Figure 2B) and calculated the gradient (∇) of this scalar map (∇PA, Figure 2C,D). Measurement of the vector fields obtained from the simulated data relative to ∇PA revealed prominent alignment of the directions recovered by optical flow with the known ground truth (92.3% of directions within 90 degrees of ∇PA, 8.49 S.D. from null directions, p < 0.001; Figure 2E); tighter alignment was limited by the realistic noise properties of the simulated data. These results from simulated data suggest that optical flow can accurately capture the directionality of cortical activity propagations.

Figure 2: Optical flow accurately recovers directional propagations in simulated fMRI data.

A) We simulated a wave that travels from the posterior pole to the anterior pole over ≈ 20 seconds. Realistic human BOLD spectral content was enforced in accordance with Laumann et al.⁵⁰. B) To create a reference direction equivalent to ∇FH, we use a scalar map of the posterior-to-anterior (PA) positioning of each point on the cortex. C) We calculated the gradient of this scalar posterior-anterior map (∇PA) over the cortical surface of to serve as a directional reference the cortex to calculate simulated propagation directionality. D) Example directional estimations of optical flow on the simulated wave. White arrows depict activity directionality as estimated by optical flow, and grey vectors depict ∇PA. E) Across cortical areas and timepoints, angular distances between the directions estimated by optical flow aligned with the expected ∇PA reference direction. Inset (top right) depicts the proportion of optical flow vectors within 90 degrees of ∇PA relative to 1,000 null-reference direction distributions (Observed = 0.923, 8.49 S.D. from null directions).

Optical flow reveals hierarchical propagations of cortical activity

Having verified that optical flow can accurately characterize the directionality of cortical propagations in simulated data, we next applied this approach to the real data from HCP-D. We expected to find both bottom-up propagations that aligned with the functional hierarchy (angular distances close to 0° compared to the ∇FH) as well as top-down propagations that flowed in the opposite direction (angular distances 180° from ∇FH). As hypothesized, we found a predominance of both bottom-up and top-down hierarchical propagations, which formed a bimodal distribution. These bimodal distributions were evident at both the group (Figure 3A) and participant-level (Figure 3B). To test whether propagations were enriched for bottom-up and top-down directionality, we quantified the presence of a bimodal distribution in each participant’s data using the dip statistic. We then compared this value to a null distribution generated using a conservative spin-based permutation test that persevered the spatial covariance structure of the data. This procedure revealed that the angular distributions of propagations were bimodal in every single participant in the HCP-D sample, far beyond what could be expected by chance (real data median SD from null distribution = 13.6 SD; p < 0.001 for all participants in the sample; Figure 3C). To further confirm that optical flow captured continuous propagations rather than differences between discrete activation patterns, we shuffled the temporal ordering of fMRI volumes for each participant. These temporal permutation tests confirmed that optical flow captured specific sequences of activity that were not present in temporally shuffled data (real data median SD from null distribution = 18.8 SD; p < 0.01 for 93% of participants in the sample; Figure 3D). These data suggest that bottom-up and top-down propagations are common and robust features of cortical activity.

Figure 3: Hierarchical propagation of cortical activity.

A) Across the entire sample, we found a bimodal distribution of angular distances between the ∇FH and vectors of directional activity estimated by optical flow (4.4 billion optical flow directions over all participants, locations, and timepoints). B) Directional distributions formed a bimodal distribution enriched for hierarchical ascent (0°) and descent (180°) within individual participants. The percentage axis is rescaled from panel A for detail, with the equivalent y-axis range demarcated across panels with dashed lines. The dip statistic was used to quantify the bimodality of each participant’s distribution of directional activity vectors and used in subsequent statistical testing. C) Spatial null models spun the reference directions provided from ∇FH, preserving the spatial covariance structure of the original map (left). Spatial null models were computed within participants (middle; participant #1 from panel B) by comparing the dip statistic obtained from permuted reference directions (black distribution) and the dip statistic from the real data (red line). Whereas 1.64 standard deviations from the mean is a common statistical threshold for significance, we found that the distribution of dip statistics from all the participants in the sample were approximately 13.6 standard deviations from the null distribution (right). D) Temporal null models shuffled the order of retained fMRI volumes in time, preserving complex spatial patterns found within individual images (left). Temporal null models were computed within participants (middle; participant #1 from panel B) by comparing the dip statistic obtained from permuted fMRI volume ordering (black distribution) and the dip statistic observed in real data (red line). Observed dip statistics were a median of 18.8 standard deviations from the null distribution (right). Note: 5 participants with positive outlier values are omitted for clarity (SDs = 166.7, 189.3, 258.9, 369.7, and 747.9).

Hierarchical propagations are also found in a dataset of densely-sampled adults

As a next step, we sought to replicate our findings using an independent dataset of adults. To this end, we applied the same procedures to the densely-sampled participants of the Midnight Scan Club (MSC) dataset. We found that hierarchical propagations were also present in all 10 MSC participants (Figure 4). This generalization is notable given the different age range, scanning hardware, and temporal qualities of the data (which included a nearly 3-fold decrease in temporal resolution in MSC compared to HCP-D). These results suggest that hierarchical activity propagations are a generalizable feature of cortico-functional activity in both youth and adults.

Figure 4: Cortical activity propagates up and down the cortical hierarchy in an independent sample.

Spatial null permutation testing reveals the presence of bimodal cortical propagations for all midnight scan club participants (black: spin-test permutations, red: true dip statistic).

Top-down cortical propagations increase during a task that requires cognitive control

Having described the presence of hierarchical activity propagations at rest, we next sought to determine whether they were modulated by the performance of a demanding cognitive task. Specifically, we hypothesized that the proportion of top-down cortical propagations relative to bottom-up propagations would increase when participants performed a task requiring cognitive control. To define the spatial distribution of bottom-up and top-down propagations, we quantified the percentage of propagations that could be characterized as bottom-up (< 90° from ∇FH) or top-down (> 90° from ∇FH) for each location on the cortex (Figure 5A). Notably, while all regions exhibited a mix of both bottom-up and top-down propagations, top-down propagations were enriched in regions such as the dorsolateral prefrontal cortex. At the participant-level, the percentage of top-down optical flow vectors was highly correlated with our statistical summary measure of bimodality (i.e., dip statistic, r = .70, p < 2.2×10⁻¹⁶; Figure 5B). Examining the percentage of top-down propagations allowed us to directly test whether top-down propagations became more common when participants performed a cognitive control task.

Figure 5: Top-down propagations differ across the cortex and individuals.

A) All faces exhibited a mix of both bottom-up (<90° from ∇FH) and top-down (>90°) propagations, but certain regions were enriched for bottom-up propagations or top-down propagations. For example, bottom-up propagations were more common in medial prefrontal cortex, whereas top-down propagations were more common in dorsolateral prefrontal cortex. B) Across participants, top-down propagations were strongly associated with a bimodal distribution of directional propagations quantified by the dip statistic (r = .70, p < 2.2×10⁻¹⁶). The 95% confidence interval of this linear relationship is indicated by the shaded area.

We compared propagations observed during rest to those present during a modified Go/NoGo task, where top-down control is required to suppress reflexive button-pressing⁴⁰ (Figure 6A). Mass univariate analyses revealed more top-down propagations during task than rest (n = 281, t_face = 2.37–13.97, p_fdr <0.05). While these effects were distributed across the cortex, increases in top-down propagations were particularly prominent in regions within the dorsal and ventral attention systems. Effects also localized to streams of cortical processing, such as the premotor pathway. Increases were maximal in the left upper-extremity subdivision of motor cortex, likely reflecting participants using their right hand to perform the task⁴⁰ (Figure 6B). These results suggest that task demands evoke increased prominence of top-down propagations within individuals.

Figure 6: A cognitive control task is associated with an increase in top-down propagations.

A) Schematic for Go/NoGo task where participants are asked to immediately press a button in response to certain shapes, and to withhold their response when presented with others. B) Map of significant differences in top-down propagations between task and rest (P_FDR < 0.05). Blue areas indicate faces where bottom-up propagations are more common during task demands (30% of statistically significant faces) and orange areas indicate faces where top-down propagations are enriched during task demands (70% of statistically significant faces). Insets (right) depict example task-rest differences at two cortical faces.

Top-down cortical propagations increase over development

Given that we observed an increase in top-down cortical propagations during a cognitive control task and that cognitive control abilities improve with age, we next evaluated whether top-down propagations became more prevalent with age in our sample of youth. Developmental effects were modeled with penalized splines that capture both linear and nonlinear effects; sex, number of frames available, and in-scanner head motion were included as model covariates. We found that older age was associated with widespread increases in the proportion of top-down propagations across the cortex (Δ Adjusted R² = 0.01 – 0.19, p_fdr <0.05, Figure 7A). These effects were particularly prominent in the anterior cingulate cortex, dorsal and ventral visual streams, as well as the medial and lateral premotor pathways. Age associations extended continuously between the canonical medial premotor pathway and inferio-medial prefrontal cortex, suggesting overlap in the maturation of regions in the default-mode network and maturation of the internally-driven medial premotor pathway. This increased prevalence of top-down propagations with age was quite evident even when measurements were averaged across the entire cortex (Δ Adjusted R² = 0.14, p = 1.7×10⁻¹⁴, Figure 7B; Table S1).

Figure 7: The prevalence of top-down propagations increases with age.

A) Top-down propagations become more prominent with age in youth (P_FDR < 0.05, more top-down with age in red). B) When averaged across the cortex, top-down propagations increase with age (smooth term effective degrees of freedom = 1.89). C) Whole-cortex directional distributions mature such that after adolescence, a greater percentage of propagations are top-down. This difference extends above and beyond the 95^th percentile of distribution differences observed in 1,000 equally sized, randomly selected subgroups of participants (gray band = 95% confidence threshold from bootstrap resamples).

Notably, the above analyses rely on a binarization of propagations into bottom-up or top-down. Next, we investigated how development is associated with shifts in the full distribution of directional propagations. To do so, we calculated the difference in the average angular distribution of propagations for the youngest (n = 127, mean age = 11.49, SD = 1.70 years) and oldest (n = 132, mean age = 19.76, SD = 1.39 years) tertiles of the data (Figure 7C). We then evaluated the significance of this difference of distributions by comparing the true difference to a null distribution created from random tertile splits (Figure 7C, gray band). We found that the angular distributions shifted monotonically towards top-down propagations with age: maximally top-down propagations increased with age the most, whereas maximally bottom-up propagations showed the largest declines with age. Together, these results suggest that top-down cortical propagations are a prominent feature of functional brain development.

Hierarchical propagations are robust to analytic parameter choices and choice of cortical hierarchy

Next, we conducted a series of sensitivity analysis to bolster confidence in our results. First, we sought to further confirm that the detection of hierarchical cortical propagations was not contingent upon a specific set of spatial regularization parameters used by the optical flow algorithm. To do so, we repeated our spatial permutation tests (as in Figure 3C) for all participants while applying a wide range of spatial regularization parameters. Across the HCP-D sample, we found that the angular distributions of propagations were specifically aligned with the functional hierarchy for every parameter choice that we evaluated (Figure S4). These results suggest that detection of bottom-up and top-down propagations is not dependent on specific analytic parameter choices.

Next, we sought to determine whether our findings would remain consistent if an alternate account of the cortical hierarchy was used. While the functional hierarchy is among the most widely used, a structural hierarchy (SH) defined by the presence of intra-cortical myelin is also broadly accepted. Prior work has demonstrated that this structural hierarchy defined by cortical myelin content aligns with hierarchical measures of tract-tracing and gene-expression^51,52. We used a myelin map derived from HCP-D that corrected for transmit field bias⁵³ and repeated our main analyses with ∇SH instead of ∇FH (Methods; Figure 8A). First, we evaluated whether cortical propagations traverse up and down the cortical hierarchy using the same conservative spatial permutation procedure. Observed dip statistics remained far (median = 8.6 standard deviations away) from our spatial null distribution, indicating that cortical propagations traverse up and down the structural hierarchy far more frequently than expected by chance (Figure 8B). Next, we compared propagations present during the cognitive control task to those present at rest using the structural hierarchy as the reference. The spatial distribution of results was highly similar to that observed when the functional hierarchy was used as a reference (Figure 8C). Similarly, when the structural hierarchy was used as a reference, we found that age was associated with greater prevalence in top-down propagations (Δ Adjusted R² = 0.10, p = 2.8×10⁻¹⁰; Figure 8D). Finally, as prior, we calculated the difference in the average angular distribution of propagations for the youngest and oldest tertiles of the data. When using ∇SH instead of ∇FH, we also found that the angular distributions consistently shifted towards fewer bottom-up and greater top-down propagations with age (Figure S5). Together, these results suggest that the existence of hierarchical propagations, the presence of task-evoked shifts in propagations, and observed associations with development are robust to definitions of the cortical hierarchy.

Figure 8: Defining the cortical hierarchy using a measure of intracortical myelin content yields convergent results.

A) Map of the structural hierarchy defined by cortical myelin content. B) Bottom-up and top-down propagation directions are also prominent across the structural hierarchy (∇SH), again forming a bimodal distribution for each participant (quantified with dip statistics). Dip statistics obtained for each participant were far greater than those obtained from a spatial null distribution obtained by spinning the myelin map (median SD of observed dip statistic from null distribution = 8.6). C) The proportion of bottom-up versus top-down propagations was systematically shifted when rest was compared to a cognitively demanding task and the structural hierarchy was used as the reference (p_fdr <0.05). D). The prevalence of top-down propagations increased with age when using cortical myelin content to define a structural hierarchy (Δ Adjusted R² = 0.10, p = 2.8×10⁻¹⁰)

The development of top-down activity propagations is distinct from the development of functional connectivity

Having demonstrated the presence of age-related increases in top-down propagations, we next conducted specificity analyses to evaluate if the observed development of top-down propagations were dissociable from previous descriptions regarding the development of functional connectivity. Notably, the spatial distribution of the principal gradient is collinear with the distribution of functional networks²⁰, and the age associations we report occur over the same age range as developmental functional network segregation^10,54. In particular, default mode network segregation has been among the most consistently reported aspects of adolescent functional connectivity maturation^10,54–61. Consequently, we sought to ensure that the development of hierarchical propagations was not attributable to differences in default mode segregation with age. Specifically, we quantified default mode network segregation in all participants (Methods) and repeated our developmental analyses of top-down propagations while covarying for individual differences in default mode network segregation. We found that the association between top-down propagations and age remained significant while covarying for default mode network segregation (Δ Adjusted R² = 0.14, p = 1.2×10⁻¹⁴) and was greater in magnitude than the association between age and default mode network segregation itself (Δ Adjusted R² = 0.05, p = 3.1×10⁻⁵; Figure S6). Next, we sought to verify that our findings were not attributable to developmental differences in the spatial localization of the principal gradient of functional connectivity. Accordingly, we derived principal gradients of functional connectivity for each age tertile of our sample, and re-calculated angular distances for each participant relative to the principal gradient for their respective tertile (Figure S7). Dip statistics derived from tertile-specific connectivity gradients were highly similar to those derived from the original group-level map (r = 0.87, p < 2.2×10⁻¹⁶), and the association between top-down propagations and age remained significant when using tertile-specific functional hierarchies (p = 9.5×10⁻⁴). Finally, to verify that age effects were not attributable to scanning-site differences, we harmonized fMRI data cross sites using ComBat and repeated our main developmental analyses. Developmental effects remained prominent when accounting for site differences with ComBat (Δ Adjusted R² = 0.12, p = 2.0×10⁻¹², Figure S8). Together, these analyses confirmed that our findings were not attributable to previously documented properties of functional neurodevelopment or scanner differences.

DISCUSSION

We capitalized on advances in computer vision and a large dataset of youth with high-quality neuroimaging to delineate functional propagations that traverse the cortical hierarchy in individual participants. Notably, we found that top-down propagations increased during performance of a demanding cognitive task and become more common with age in youth. These results implicate functional propagations as a mechanism of hierarchical processing and neurodevelopment.

Cortical surface propagations systematically ascend and descend the cortical hierarchy

Here, we describe the presence of bimodal cortical activity propagations in humans, which ascend and descend the cortical hierarchy. Conservative permutation testing emphasized that cortical activity disproportionately traverses up and down the cortical hierarchy far greater than expected by chance. Notably, both bottom-up and top-down propagations were present in all individuals, as evidenced by bimodal distributions of directional activity flow. Hierarchical propagations were robust to a range of analytic parameters (five orders of spatial regularization magnitude) and evident when either a functional and structural hierarchy was used as a reference. Importantly, we similarly found hierarchical propagations in every participant in a dataset of densely-sampled adults that was acquired using different scanning parameters with different temporal resolutions (TR = 0.8 seconds and 2.2 seconds). The generalizability and replicability of our results provides strong evidence of the prevalence of bottom-up and top-down propagations of cortical activity.

Decades of study of the BOLD signal and infraslow (0.01–0.1 Hz) cortical fluctuations provide important neurobiological context for the observed propagations. First, existing evidence suggests that BOLD signal fluctuations within a given region reflect infraslow fluctuations in local field potentials^45–49, and spatially propagating BOLD fluctuations reflect propagating local field potentials^17,18,49,62. Although infraslow field potentials have long been observed⁶³, they have only more recently been accepted as instrumental to functional cortical organization^64,65. Infraslow fluctuations manifest over larger portions of cortex than faster fluctuations^66–69 and recent studies provide multi-modal evidence that infraslow activity can entrain synchronization, spiking dynamics, and physiological arousal across the brain^{17,18,70–73}. Although infraslow entrainment has been repeatedly demonstrated for gamma-oscillations^{17,18,46,47,67,70}, we note that oscillations in other frequency bands bear more complex relationships to infraslow activity^62,74,75. Nonetheless, spatially-distributed facilitation and suppression of gamma-band activity may be one role of infraslow cortical propagations across individuals.

A central finding of this study is that the directionality of slow cortical propagations is systematically hierarchical. Our findings cohere with accumulating evidence from intracranial recordings that spatial directionality is a key feature of perception and task-execution in other mammals^{28–30,37,38,76} as well as reports of bimodal propagation directionality within circumscribed regions^30,34. Further, recent human neuroimaging studies suggest that macroscale structural brain networks are optimized to support neurotransmission in hierarchical directions^77,78. Our results cohere with this literature, and provide what is to our knowledge the first functional evidence of pervasive bottom-up and top-down propagations in individual humans. Our directional analyses suggest that the functional hierarchy captured by the principal gradient provides a potentially unifying account of infraslow propagation directionality across all cortical regions in humans. Although our results extensively demonstrate the presence of hierarchical propagations, our insights into the functional role of these propagations are preliminary. These initial results do suggest that hierarchical cortical propagations are involved in hierarchical processing, but the full suite of neurocognitive functions endowed by hierarchically structured propagations is likely to be complex. However, several existing experimental and theoretical accounts of complex spatiotemporal dynamics in cortical propagations provide intriguing evidence regarding why spatial directionality might be a key feature in cortical processing.

Studies focused on sensorimotor regions suggest that the spatial directionality of activity may interact with topographic representations in the cortex. During bottom-up visual processing, propagation directionality has been shown to underlie coordinated inter-regional stimulus encoding through distributed retinotopic propagations^35,79. In this context, the spatiotemporal trajectory of activity propagations across retinotopic mappings allows for continuous and synchronized activation of spatially-distributed but retinotopically-equivalent areas. Initial evidence suggests that an analogous pattern of structured activity propagations along topographically organized sensorimotor regions may underlie aspects of somatosensation and coordination of proximal-to-distal limb movements^80–82. Given the prominence of topographical representations across the cortical sheet^83–86 the observed spatiotemporal propagations may regularly interact with spatially-embedded topographical representations. However, propagations have been sparsely studied outside of sensorimotor cortices^87,88.

Although prior investigation of propagation directionality in higher-order cortices has been limited, the computational principles bestowed by cortical waves can provide insight into their roles throughout the cortex³⁶. First, as in visual cortex, the spatiotemporally distributed nature of propagations may facilitate the coordination and integration of information over large regions of the brain^31,39,76,79. Second, in contrast to older views endorsing neuron-specific information selectivity, information representation via distributed activity over time and space can be efficiently encoded^89,90, confer increased representational stability^35,73, and can better account for empirical observations of trial-to-trial variability in neuronal responses^35,73,89,91. Finally, if cortical propagations can encode sensory information^80,92, then local modulation of these propagations may serve to process sensory information⁹³. In studies of wave dynamics, the spatial and temporal history of a propagation can be recovered from “ripples” in the propagation medium at subsequent time points: this is true even in dissipative and chaotic conditions^36,94. For waves traversing up or down a cortical hierarchy, this suggests that local modulations to that wave would naturally ingrain modulation history into the wave. Consequently, where in the hierarchy the modulation came from, as well as when the modulation was made, could potentially be recovered from the form of the wave after modulation. As cortical hierarchies may be evolutionarily selected for precisely because they allow for integrating diverse signal modulations throughout the hierarchy⁴, such functionality would be invaluable for information transfer and hierarchical control. Indeed, recent evidence suggests that higher-order cortices act in a top-down fashion on lower-order cortices by priming them for rapid neurotransmission via modulation of ongoing activity fluctuations^93,95. Relatedly, we observed systematic modulation of cortical propagations in response to task-demands, potentially consistent with top-down processing. Together, our results suggest that bottom-up and top-down cortical activity propagations patterns may be important for hierarchical cortical information processing.

The development of top-down propagations

The prevalence of top-down propagations increased with age across the entire cortex as well as focally in several canonical processing streams. Specifically, we observed evidence for involvement of the dorsal stream, the ventral stream, and premotor pathways. Prior work in animals has revealed top-down propagations in canonical processing streams^38,76,96,97, suggesting that developmental increases in top-down propagations may to some degree occur where top-down propagations are common. However, the global age effect was nearly as strong as that of any single location on the cortex. This suggests that maturation may entail widespread increases in top-down propagations in addition to enhanced top-down propagations in specific canonical processing streams. In light of recent work highlighting individual differences in the localization of higher-order processes^10,98–100, the spatially-diffuse increases in top-down propagations we observed with age also suggests that top-down maturation may occur heterogeneously across the cortex for different individuals. Irrespective of spatial localization, our developmental results identify top-down propagations as a potential macroscale functional mechanism underlying the maturation of top-down cognition.

At the synaptic level, top-down cortical propagations may be facilitated by cholinergic neurotransmission. Although other neurotransmitters are likely to play important roles^101,102, convergent evidence from cell-staining^103–106, experimental loss-of-function studies^{105,107–110}, and group-average fMRI activation patterns^17,25,111 have consistently implicated cholinergic neurotransmitter systems broadly as causal in top-down cortical activity^112–116. Further, changes in cholinergic tone are sufficient to modulate cortical propagation dynamics¹¹⁷, and a recent report implicates cholinergic neurotransmission in the maturation of top-down processing in mice¹¹⁰.

One means by which cholinergic maturation may manifest at larger scales is by biasing allocation of attention. In hierarchical processing, cholinergic projections are able to enhance selective attention towards goal-directed behavior specifically because they induce top-down biasing of local sensory neurons^{97,115,118–120}. In instances where multiple salient stimuli compete for attention –such as cluttered visual scenes– top-down activity can bias conflict resolution within sensory cortices away from immediately salient stimuli in support of high-level goal pursuit^{96,97,115,120–123}. Notably, the gradual enhancement of proactive attention to long-term goals over reactivity to immediately salient stimuli is a critical feature of neurodevelopment^124,125. Here, we observed increases in top-down propagations during a cognitive task requiring attentional control to facilitate withholding (no go condition) over salient prepotent responses (go condition). Given that we also observed increases in top-down propagations in the same age range that the development of top-down attention has been ascribed to^11,121, our description of top-down propagation maturation aligns with the development of top-down attentional control. As such, the maturation of top-down propagations may play an important role in cognitive development by promoting goal-directed attention.

Limitations and Future Directions

Several limitations should be noted. First, the temporal resolution of fMRI restricted our analyses to infraslow frequencies. As prior studies have reported a wide variety of cross-frequency interactions among hierarchical and infraslow propagations^{17,18,62,72,75,76} future work examining propagation patterns across frequency domains may be able to further disentangle such interactions. Second, the cost function of optical flow is agnostic to the sign of the propagating signal: propagating decreases in BOLD signal are also captured by the resulting vector fields. Because hierarchically propagating infraslow activations and deactivations can facilitate or suppress faster rhythms^17,18, explicitly delineating activations from deactivations is an important step for future work. Third, respiratory ^18,126 and vascular^127,128 processes are known to contribute to BOLD signal propagations at similar frequencies. Further analyses of concurrently acquired physiological data^17,18,129 may serve to disentangle their contributions to observed propagations. Fourth, motion-related signal artifact is likely to impact functional propagations. Consequently, we erred on the side of being extremely stringent in quality assurance – using only low motion data and statistically controlling for residual motion artifact in all analyses. Finally, spatial resolution and computational burden hindered investigation into the role of the subcortex in functional propagations. Evidence across mammals, recording techniques, and experimental methods all suggest that subcortical structures, particularly the nucleus basalis and the thalamus, are extensively involved in top-down cortical propagations^{17,25,103–105,109,111,113,114,130}. Furthermore, the role of subcortical structures is likely to be highly complex. For example, in the thalamus, investigations have revealed hierarchical signaling is often bidirectional and context-dependent^131–134. Moving forward, computational advances in the optical flow algorithm and applications to volumetric fMRI with high spatial and temporal resolution data may allow investigators to delineate subcortical contributions to functional propagations.

These limitations notwithstanding, direct quantification of bottom-up and top-down activity on cortical surface holds substantial promise for several applications. First, induction of top-down activity remains a central goal of transcranial magnetic stimulation (TMS), but previously few direct measurements of top-down activity have existed¹³⁵. Concurrent TMS and fMRI-based optical flow may allow for more direct quantification of top-down activity induction across stimulation approaches. Relatedly, an explicit goal of neurofeedback protocols is to increase top-down cortical activity¹³⁶. Again, this goal is frustrated by lack of direct quantification of top-down activity in fMRI measurements. Real-time visualization of cortical propagations may facilitate more direct visualization of top-down activity. Third, top-down deficits have been implicated in the pathology of numerous neuropsychiatric disorders^14–16. Similarly, although increased top-down activity is common treatment target, lack of direct quantification of top-down activity has also hindered research into the etiology of and recovery from such conditions. Consequently, understanding if and how top-down deficits in psychopathology are associated with deficits in top-down propagations may allow for an improved brain-based understanding of these disorders. Although top-down cortical propagations may represent only one of many control mechanisms in the brain, the non-invasive quantification of top-down propagations described here may represent a broadly applicable measure for future research.

Conclusion

We demonstrated the presence of functional propagations that preferentially flow up and down the cortical hierarchy. Our observation that top-down propagations increase in response to top-down task demands suggests that such propagations are to some degree state-dependent. Finally, the development of top-down propagations with age suggests a potential role for cortical propagations in the development of top-down control in youth. Taken together, our findings suggest that the directionality of propagating cortical activity may be broadly relevant for studies of hierarchical cortical organization and neurodevelopment, with potentially important implications for our understanding of psychopathology and the design of neuromodulatory interventions.

STAR Methods

RESOURCE AVAILABILITY

Lead Contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Theodore D. Satterthwaite (sattertt@pennmedicine.upenn.edu)

Materials Availability

This study did not generate new unique reagents.

Data and Code Availability

HCP-D and the Midnight Scan Club are publicly available datasets^40,137. All analysis code and a step-by-step replication guide is available at https://github.com/PennLINC/DevProps.

METHODS DETAIL

Developmental dataset: HCP-D

To evaluate the maturation of cortical propagations, we used high-quality resting-state and task-fMRI data from the Human Connectome Project-Development 2.0 Release (HCP-D, n = 652, mean age = 14.4, SD = 4.1 years). Participants were scanned at four sites on 3 Tesla Siemens Prisma platforms. Structural scans consisted of high-resolution MPRAGE T1w images (0.8 mm³, TR/TI=2,500,1000 ms, TE = 1.8/3.6/5.4/7.2 ms, flip angle = 8°) and a variable-flip-angle turbo-spin-echo T2w sequence (0.8 mm³, TR/TI=3,200,564 ms, turbo factor = 314). Additionally, each subject underwent 26 minutes of resting-state scans across 4 runs, and 8 minutes of task-fMRI across 2 runs for our task of interest⁴⁰. Multiband acquisitions afforded sub-second temporal resolution for all functional images (2.0 mm³, TR/TE = 800/37 ms, flip angle = 52°).

Replication dataset: Midnight Scan Club

We sought to replicate findings of hierarchical functional propagations in the densely-sampled adults of the MSC. Imaging for each subject was performed on a Siemens TRIO 3T MRI scanner over the course of 12 sessions conducted on separate days, each beginning at midnight¹³⁷. Structural MRI was conducted across two separate days and included T1-weighted images (sagittal, 224 slices, 0.8 mm isotropic resolution, TE = 3.74 ms, TR = 2400 ms, TI = 1000 ms, flip angle = 8 degrees) as well as T2-weighted images (sagittal, 224 slices, 0.8 mm isotropic resolution, TE = 479 ms, TR = 3200 ms). In each session, thirty contiguous minutes of resting state fMRI data were collected, in which subjects visually fixated on a white crosshair presented against a black background. All functional imaging was performed using a gradient-echo EPI sequence (4.0 mm³, TR/TE = 2,200/27 ms, flip angle = 90°).

Image processing

Images from both datasets were processed with an updated version of the Human Connectome Project MRI pipeline^138–140. Specifically, all structural images underwent gradient distortion correction, bias field correction, and normalization to a standard template (MNI). Functional images underwent gradient distortion correction, re-alignment, EPI distortion correction, boundary-based registration, and normalization prior to being projected to the cortical surface and smoothed with a 2mm FWHM gaussian kernel. Functional images were then demeaned and de-trended. Subsequently, nuisance regressors included mean cifti timeseries signal, mean cerebrospinal fluid signal, mean white matter signal, as well as 3 translation (x,y,z) and 3 rotational (roll, pitch, yaw) motion measurements as well as their respective Volterra expansions (derivative, square, and derivative squared of regressor timeseries). Next, functional images were band-pass filtered between 0.008 and 0.09 Hz with a 2^nd order Butterworth filter. Framewise displacement was calculated after accounting for the influence of respiratory signal on framewise image realignment¹⁴¹. Noteworthy revisions to the standard HCP pipeline included usage of Advanced Normalization Tools (ANTs) for denoising, bias field correction, and diffeomorphic symmetric image normalization, which was selected due to consistently higher registration performance over previous methods¹⁴². Prior to image analysis, all functional images were downsampled to fsaverage4 with connectome workbench for computational feasibility.

HCP-D quality control and inclusion criteria

In order to be included in analyses, participants were required to have at least 600 TRs surviving three quality-control thresholds. First, in HCP-D frames were excluded if head motion exceeded 0.2 mm framewise displacement for that frame. Due to the slower sampling rate of the MSC data (TR = 2.2 seconds vs. 0.8 seconds in HCP-D), we relaxed our framewise displacement threshold to 0.4 mm for MSC rather than the 0.2 mm threshold used for HCP-D. Second, frames were excluded if they contained DVARS values that were > 3 standard deviations above the mean. Third, because we were interested in propagations across TRs rather than patterns within single, low-motion TRs, we excluded otherwise low-motion segments that were interrupted by moderate to high-motion frames. Specifically, if TRs that met the first two criteria were not part of a broader sequence of at least 10 consecutive low-motion TRs, these TRs were discarded. In HCP-D, 388 participants (mean age = 15.6, SD = 3.7 years) met the > 600 TR requirement after these quality assurance procedures.

As head motion is a major confound in neurodevelopmental imaging, we assessed associations between age and both the number of imaging volumes surviving quality-control and framewise displacement. As expected, age was positively associated with the number of retained imaging volumes (r =.35), and negatively associated with head motion within those remaining volumes (r = −0.36). As a result, we controlled for both the number of volumes retained and framewise displacement of retained volumes in all subsequent analyses.

Optical flow

Optical flow is a computer vision technique used to estimate the motion of signal intensity between successive images¹⁴³, which can be applied to neuroimaging to estimate the motion of activity^144,145. In the current study, we applied a spherical optical flow algorithm^41,42 to spherical registrations of each hemisphere of each participants’ cortical mantle^146,147. Specifically, we used an implementation of optical flow adapted to efficiently estimate biological data occurring on spherical surfaces by use of spherical harmonics and regularizing functionals⁴¹. This adaptation of optical flow minimizes the following formula:

$$||{\nabla }_{S}F\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}·\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}u\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}{\partial }_{t}F|{|}_{L^2\left(S\right)}^2+\hspace{0.17em}\hspace{0.17em}\alpha ||u|{|}_{{\mu }_n}^2$$

Where F is cortical BOLD signal represented via spherical harmonics, ${\nabla }_{S}F$ is the surface gradient of F upon the sphere, u is the vector field being solved for, t is a point in time, and ∂_tF is the partial derivative of the fit harmonics over time. L²(𝑆) and $\alpha {‖u‖}_{{\mu }_n}^2$ serve as norms, facilitating solvable and tractable flow derivations.

Notably, this operates under a brightness constancy assumption. As in image registration, the assumption is that a transformation function ϕ exists that can reconcile the spatial displacement between two images. Here, this assumption takes the form of:

$$F\left(t_n,\varphi \left(t_n,x\right)\right)=F\left(t_0,x\right)$$

Where t is a point in time, and 𝑥 is a point in space on the sphere. In our study, this assumption was approximated through the common practice of global signal regression (applied as part of pre-processing), which ensured that net signal was largely constant throughout the functional time series.

This spherical approach provided two primary advantages. First, spherical projection afforded the use of spherical harmonics. Spherical harmonics are a commonly adopted set of basis functions used to represent spherical data in diffusion-weighted imaging^148–150 and in other computational modeling applications^151–153. Here, we applied spherical harmonics to analytically represent BOLD signal at each spherically-projected hemisphere at each timepoint. In turn, this step provided computational efficiency to solve for the vector field u explaining the movement of signal between each pair of timepoints for each participant. Second, as 2-dimensional “patch” projections of the cortex incur prominent warping and large discontinuities between spatially adjacent cortices, our use of the spherical implementation of optical flow allowed us to analyze propagations continuously across the cortex with reduced spatial deformation.

Defining hierarchical ascent and descent

In order to estimate directions of hierarchical ascent and descent, we extracted the gradient vector field (∇) of an established map that defines the principal gradient (PG²⁰) of a functional hierarchy (∇FH) across the cortex. This approach is analogous to that taken in Tian et al.¹⁵⁴, but extracted across the cortical mantle rather than in subcortical volumetric space. The resultant vector field, describing hierarchical ascent at each face on the cortical mesh, was subsequently used as a common set of reference directions for each participant’s optical flow data.

Quantification of angular distances

In order to evaluate directional alignment between optical flow vectors and hierarchical vectors, we evaluated their angular similarities in degrees. Our primary metric of interest was the angle (in degrees) between hierarchical vectors and optical flow vectors. To derive these angles, the 3-dimensional cartesian (x,y,z) vectors describing both vector fields were converted to a spherical coordinate system (azimuth, elevation, rho) via cart2sphvec in MATLAB. Because the signal travels across the surface of the sphere rather than into or away from the surface, this conversion obviates the third coordinate (rho). Consequently, we retained azimuth and elevation only for each hierarchical and optical flow vector, which describe directionality on a 2-D tangent-plane at each cortical face (see Figure 1C). From this point, the angular distance was computed as the difference in directional orientation in degrees between ∇FH and the directional vectors returned by optical flow, with 0 degrees indicating perfect alignment (bottom-up flow) and 180 degrees indicating the maximum possible difference (top-down flow). By quantifying this angular distance between the observed direction of propagation and ∇FH, we were able to construct a timeseries of directional vectors that quantify top-down and bottom-up propagations at each cortical location, for each individual. In total, this yielded 4.4 billion directional measurements across all participants, locations, and timepoints.

Simulated data

To test whether optical flow could recover cortical propagations with known directionality, we simulated a wave of BOLD signal with a normal distribution over space traversing from the posterior pole to the anterior pole of the cortex. Temporal duration was set to match the ≈ 20 second hierarchical cortical propagations previously noted in group-averaged data^17–19. To ensure equivalence with real data, we adapted the code made available online by Laumann et al.⁵⁰ to match spectral content of our simulated data with that of a random fMRI scan from our sample. To examine whether our approach would approximate ground truth angular distances, we also generated a scalar map of the anterior-posterior coordinate of each vertex. After taking the gradient (∇) of this posterior to anterior map – ∇Posterior-Anterior – we calculated the angular distance between the optical flow vector fields in the simulated data and the ground-truth ∇Posterior-Anterior map. This provided an equivalent approach to quantifying angular distance from the ∇FH, but in a scenario where the ground-truth was known. To test the significance of the resultant alignment between the obtained optical flow vectors and ∇Posterior-Anterior, we employed conservative spatial null permutation tests. Specifically, we rotated ∇Posterior-Anterior around a sphere 1,000 times to generate null directional maps with conserved spatial covariance using the spin test¹⁵⁵. We then calculated the proportion of optical flow vectors estimated to be within 90 degrees of ∇Posterior-Anterior and within 90 degrees of the 1,000 rotated ∇Posterior-Anterior maps. Next, we evaluated the mean and standard deviation of these null proportions relative to the proportion derived from the true angular distribution, allowing us to quantify the degree to which angular alignment in the posterior-anterior direction exceeded alignment with similar directional maps. A p value was defined by the number of times (out of 1,000 rotations) that a randomly-aligned direction exhibited greater alignment than the posterior-anterior direction. Further information on the spin test is detailed in the section below.

Statistical testing of alignment with the functional hierarchy

In order to test whether hierarchical ascent and descent were both directional modes in the distribution of optical flow vectors, we employed Hartigan’s dip test. Specifically, we used the dip statistic to quantify the deviance of angular distributions from a unimodal distribution: a higher dip statistic indicates that a distribution is more likely bimodal (or multimodal) than unimodal. Subsequently, we compared this measure to dip statistics derived from spatial and temporal null models.

For spatial null models, optical flow angular distances were calculated relative to a spatially permuted ∇FH. By rotating or “spinning” the entire ∇FH continuously in space, local spatial properties of the original map are conserved¹⁵⁵. Consequently, this procedure yields a more realistic and conservative spatial null model than random permutations where the spatial covariance structure is lost. We performed 1,000 permutations, and 1,000 corresponding null dip statistics were obtained for each participant. The original medial wall and the resultant location to which the medial wall was spun was masked out of the angular distributions derived for each permutation. Finally, to extract a metric comparable across participants, we recorded the number of standard deviations between the true observed dip statistic and the mean of the 1,000 permutations.

For temporal null models, optical flow was re-calculated on temporally permuted data. Specifically, the temporal sequence of fMRI volumes surviving QC was shuffled iteratively for each participant. Because fitting optical flow for a pair of frames is computationally expensive, we were limited to 100 temporal permutations per subject (and required up to 1,883,000 optical flow decompositions per subject). This process yielded 100 sets of optical flow vectors for each participant’s shuffled data. These null sets of vectors were then subjected to the same angular distance calculation (relative to ∇FH), and 100 null dip statistics were subsequently obtained from these distributions. As for the spatial permutation testing, we evaluated the true vs. permuted dip statistics in terms of the number of standard deviations each participant’s true dip statistic separated from the null distribution.

Evaluation of Optical Flow Parameters

In order to evaluate if the alignment of propagations with the functional hierarchy was contingent upon a specific set of optical flow parameters, we conducted a parameter sweep across spatial regularizations (α). Specifically, we selected 4 alternative values for α spanning 5 orders of magnitude (0.01 for very low regularization, 0.1 for low regularization, 10 for high regularization, 100 for very high regularization). We then re-ran optical flow on each HCP-D participant with these new parameters. Subsequently, we evaluated the angular distance between optical flow vectors derived across these parameters and ∇FH. Next, we re-calculated our spatial null distribution at each new parameterization for each subject (Figure S4). As prior, we calculated the number of standard deviations that each participant’s dip statistic separated from the dip statistics from the null distribution of 1,000 permuted ∇FH maps; this was done for each of the four additional spatial regularization parameters.

Analysis of the impact of task demands

To evaluated how hierarchical propagations are modulated by task demands, we used data from Carit task included in HCP-D as it requires top-down cognitive control. The Carit task is a modified Go/No-Go task, where participants are instructed to make repeated button-presses in response to rapid, consistent visual stimuli (i.e., shapes), which are periodically interrupted by the display of a different stimuli. During these interruptions, the participant is instructed to withhold a button press, probing their ability to suppress their button-pressing response. Because fewer scans were allocated to this task within HCP-D, we relaxed the minimum TR requirement to 300 total TRs for task analyses only. As we compared propagations between task and resting conditions on a within-subject basis, only participants who passed both resting-state quality control (600 TRs, n = 388) and task QC (300 TRs, n = 281) were included for these analyses.

To test our hypotheses regarding shifts in top-down propagation prominence with task, we quantified the proportion of top-down propagations. Directional vectors that were greater than 90 degrees from ∇FH were considered top-down, while directional vectors that were less than 90 degrees were considered bottom-up. When averaged across timepoints, this procedure provided a measure of the prevalence of top-down propagations at each cortical face for each participant.

We next compared the proportion of top-down propagations during rest and under the cognitive control demands of the Carit Task. Specifically, we used a paired t-test to compare the proportion of top-down propagations at each cortical face. This procedure provided a t-statistic quantifying the degree to which faces exhibited more top-down propagations during the task than during rest. Multiple comparisons were controlled by the false-discovery-rate (FDR: q < 0.05).

Analysis of developmental effects

Developmental effects were estimated using generalized additive models (GAMs)^156,157 with penalized splines in R (Version 3.6.3) using the mgcv package. Non-linearity was penalized to avoid over-fitting, and fitting was optimized with restricted maximum likelihood¹⁵⁸. Participant sex, in-scanner head motion, and the number of frames passing quality assurance were included as covariates within each GAM. Four basis functions were specified as the maximum flexibility afforded to age splines in all models. To quantify the effect sizes of each age spline, we calculated the change in adjusted $R^2\left(\Delta {R^2}_{adj.}\right)$ between the full model and a nested model that did not include an effect of age. Statistical significance was assessed using analysis of variance (ANOVA) to compare the full and nested models¹⁵⁹. As above, multiple comparisons were controlled using the false-discovery-rate (q < 0.05). Finally, because $\Delta {R^2}_{adj.}$ describes effect size but not direction (i.e., increasing or decreasing top-down propagations with age) we extracted and applied the sign of the age coefficient from an equivalent linear model, as in prior work¹⁰.

To quantify developmental differences in the full distributions of angular distances between optical flow vectors and ∇FH, we compared the oldest and youngest tertiles of all participants. Specifically, we reduced each participant’s angular distribution to 18 bins, with each bin comprising a 10-degree span from 0–180 degrees from ∇FH. Each bin represents the percentage of optical flow vectors that fell within a 10-degree window of angular distances from ∇FH (0–10 degrees, 10–20 degrees, etc.). Across participants within each tertile split, the average of these percentages represents the average percentage of total propagations each 10-degree bin encompasses for each age tertile. To observe age-dependent differences, we subtracted the resultant value of each bin in the younger tertile from the resultant values in the older tertile. This approach provided a description of the difference in angular distributions between older and younger participants. However, that difference measure does not provide a statistical test of whether the difference is significant. To evaluate the statistical significance of age effects, we performed a bootstrap procedure, where tertile splits were determined randomly. We repeated the difference-of-distributions procedure described above for 1,000 random tertile splits, producing 1,000 random differences of distributions. Finally, we extracted the 95% confidence interval from these 1,000 distribution differences to obtain an estimate of distribution differences that could be expected by chance alone. Observed differences exceeding this confidence interval were interpreted as true group differences, exceeding those expected by selecting two groups of the same size when the age distribution was random.

Sensitivity analysis using structural hierarchy

We employed a group-level myelin map as an alternative hierarchy to confirm bottom-up and top-down directionality. We used the transmit bias-corrected myelin map derived from HCP-D⁵³ for a structural hierarchy⁵¹ (SH). We then extracted the gradient of this map (∇SH) to provide another reference map of hierarchical directionality at each point on the cortex. Because myelin tracks inversely with cortical hierarchy, top-down activity was quantified as optical flow vectors that were parallel with ∇SH rather than antiparallel, as for ∇FH. As prior, we first confirmed that cortical activity propagates up and down this hierarchy more than expected by chance with spin-test based spatial permutations. Next, we evaluated whether top-down propagations relative to ∇SH increased during a Go/No-Go task by re-calculating the equivalent paired-sample t-tests across rest and task data. Finally, we evaluated the average proportion of top-down propagations across the cortex for each participant, also using ∇SH as reference directions rather than ∇FH. We then applied the same developmental model to evaluate increases in top-down propagations with age.

Specificity and sensitivity analyses

We conducted several final analyses to confirm that our results were distinct from prior reported results and not driven by site effect. First, the age associations we report occur over the same age range as developmental functional network segregation^10,54. In particular, default mode network segregation has been among the most consistently reported aspect of adolescent functional connectivity maturation^10,54–61. To ensure that hierarchical development of cortical propagations was not explained by hierarchical development of cortico-functional networks that are typically measured using standard measures of functional connectivity, we repeated our analyses while controlling for developmental network segregation. To do so, we constructed a 17-network group-consensus atlas for the participants in our study with spatially regularized non-negative matrix factorization. Next, we calculated network segregation as prior¹⁰: the mean between-network coupling of a network with all other networks. We included this value as a model covariate in sensitivity analyses. Based on prior work, we identified which of the delineated networks are those most likely to exhibit developmental segregation. Previously, we have detailed that the functional networks undergoing the most dramatic developmental segregation are those lying at the top of the cortical hierarchy¹⁰, and other publications have similarly suggested that default-mode networks undergo developmental segregation^54–61. Accordingly, we evaluated each network for its hierarchical position and overlap with canonical functional networks, and selected the single network fulfilling both a priori criteria (high in hierarchy and overlapping with the canonical default mode). Segregation of this network (higher-order default-mode) comprised the metric of interest for our first sensitivity analysis. For tertile-specific principal gradients of functional connectivity, we followed the original procedure outlined in Margulies et al.²⁰. Specifically, average functional connectivity matrices were derived for each tertile, thresholded at the 90^th percentile, converted to cosine similarity matrices, and decomposed with diffusion map embedding. The gradient (∇) of the resultant first components from each tertile were calculated for use as tertile-specific functional hierarchy reference directions.

Finally, to ensure that the association between top-down propagations and age were not attributable to site effects, we harmonized top-down propagations across sites with ComBat^160,161. This provided a site-harmonized measure of the proportion of top-down propagations exhibited by each participant, which we then tested in the same GAM framework.

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
The Lifespan Human Connectome Project Development (HCP-D)	Somerville et al.40	https://humanconnectome.org/study/hcp-lifespan-development
The Midnight Scan Club	Gordon et al.137	https://openfmri.org/dataset/ds000224/
Software and algorithms
MATLAB	The MathWorks	Mathworks.com
R	The R Project	r-project.org
Python	Python Software Foundation	Python.org
ABCD-BIDS pipeline	Earl et al. 139	doi:10.17605/OSF.IO/89PYD
Spherical Optical Flow	Kirisits et al.41	zenodo.org/record/1238901#.Y8XO9f6SmUk
Freesurfer	Dale et al.146, Fischl et al.146	surfer.nmr.mgh.harvard.edu/
Hierarchical propagation approach	This paper	doi:10.5281/zenodo.7542444

Highlights.

• Cortical activity systematically propagates up and down a cortical hierarchy

• Bottom-up and top-down propagations are common in all participants across datasets

• Top-down propagations are more common during cognitive demands

• Top-down propagations become more prominent with development in youth