Inversion of a large-scale circuit model reveals a cortical hierarchy in the dynamic resting human brain

Abstract

We considered a large-scale dynamical circuit model of human cerebral cortex with region-specific microscale properties. The model was inverted using a stochastic optimization approach, yielding markedly better fit to new, out-of-sample resting functional magnetic resonance imaging (fMRI) data. Without assuming the existence of a hierarchy, the estimated model parameters revealed a large-scale cortical gradient. At one end, sensorimotor regions had strong recurrent connections and excitatory subcortical inputs, consistent with localized processing of external stimuli. At the opposing end, default network regions had weak recurrent connections and excitatory subcortical inputs, consistent with their role in internal thought. Furthermore, recurrent connection strength and subcortical inputs provided complementary information for differentiating the levels of the hierarchy, with only the former showing strong associations with other macroscale and microscale proxies of cortical hierarchies (meta-analysis of cognitive functions, principal resting fMRI gradient, myelin, and laminar-specific neuronal density). Overall, this study provides microscale insights into a macroscale cortical hierarchy in the dynamic resting brain.

Fig. 1. Automatic optimization of rMFM parameters yields stronger agreement between empirical and simulated RSFC.

(A) 68 × 68 empirical FC matrix of 68 ROIs from HCP test set (n = 226). (B) 68 × 68 SC matrix from the HCP test set. (C) Simulated 68 × 68 FC matrix using SC matrix from the test set and rMFM parameters estimated from the HCP training set (n = 226). (D) Correlation between inter-region simulated FC and inter-region empirical FC (ignoring diagonal elements of the matrices). Correlation between SC and empirical FC in the test set was 0.30. Correlation between simulated and empirical FC was 0.46.

Fig. 2. Strength of recurrent connections w and subcortical inputs I in 68 anatomically defined ROIs and their relationships with seven resting-state networks.

(A) Strength of recurrent connection w in 68 anatomically defined ROIs. (B) Strength of excitatory subcortical input I in 68 anatomically defined ROIs. Parcels correspond to the 68 Desikan-Killiany ROIs (26). Black boundaries correspond to the boundaries of seven canonical resting-state networks (19). (C) Seven resting-state networks (19). (D) Strength of recurrent connections w in the seven resting-state networks. (E) Strength of subcortical input I in the seven resting-state networks. Regions within sensory-motor systems exhibited strong recurrent connections and excitatory subcortical input, while those within the default network exhibited weak recurrent connections and excitatory subcortical input.

Fig. 3. Relationship between recurrent connection strength w and BrainMap cognitive components.

(A) 68 Desikan-Killiany ROIs are grouped into 10 zones spanning low to high recurrent connection strength w. (B) Twelve cognitive components derived from meta-analysis of 10,449 experiments (20) are ordered on the basis of the average normalized activation strength within each of the 10 zones. Zones with high recurrent connection strength were involved in sensory perception and motor actions (visual, auditory, hand, and face), while those with low recurrent connection strength were involved in cognitive functions, such as working memory, internal mentation, and reward.

Fig. 4. Associations of estimated rMFM parameters (strength of recurrent connection w and subcortical input I) with the first principal RSFC gradient and relative myelin content.

(A) First principal RSFC gradient obtained by diffusion embedding of the human connectome (6). (B) Association between recurrent connection w and first principal gradient. (C) Association between subcortical input I and first principal gradient. (D) T1w/T2w ratio map of estimated myelin content (21). (E) Association between recurrent connection w and myelin. (F) Association between subcortical input I and myelin.

Fig. 5. Associations between estimated rMFM parameters (strength of recurrent connection w and subcortical input I) and cytoarchitectonic measures (neuronal density and neuronal size) averaged across all cortical layers.

(A) Association between recurrent connection w and neuronal density averaged across all cortical layers. (B) Association between recurrent connection w and neuronal size averaged across all cortical layers. (C) Association between subcortical input I and neuronal density averaged across all cortical layers. (D) Association between subcortical input I and neuronal size averaged across all cortical layers.