'Hierarchy' in the organization of brain networks

Abstract

Concepts shape the interpretation of facts. One of the most popular concepts in systems neuroscience is that of 'hierarchy'. However, this concept has been interpreted in many different ways, which are not well aligned. This observation suggests that the concept is ill defined. Using the example of the organization of the primate visual cortical system, we explore several contexts in which 'hierarchy' is currently used in the description of brain networks. We distinguish at least four different uses, specifically, 'hierarchy' as a topological sequence of projections, as a gradient of features, as a progression of scales, or as a sorting of laminar projection patterns. We discuss the interpretation and functional implications of the different notions of 'hierarchy' in these contexts and suggest that more specific terms than 'hierarchy' should be used for a deeper understanding of the different dimensions of the organization of brain networks. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Keywords: concerted cortical gradients; laminar projection patterns; spatial temporal scales; visual cortical hierarchy.

Figure 1.

Visual cortical hierarchy (VCH) based on the sorting of cortico-cortical projections according to their direction inferred from the laminar patterns of projection origins and terminations. (a) Example of an optimal arrangement of visual cortical areas of the primate (macaque) cerebral cortex, according to the sorting of oriented projections, where the orientation was inferred from the laminar patterns of projection origins and terminations [6]. In this framework, projections that originate predominantly from the upper, supergranular cortical layers are considered to be ‘forward’ projections (which are arranged to point up), while projections that originate predominantly from the deep, infragranular cortical layers are considered to be ‘backward’ projections (arranged to point down), following the convention of [2]. Generally, connections in the diagram reflect reciprocal relations of laminar projections. The three red connections indicate the minimal set of (six) laminar relations that are violated in the overall arrangement. Areas with boxes of the same colour maintain their relative level positions across all optimal arrangements, while areas with a shaded background (i.e. V1 and V2) are the only areas to stay fixed on the first and second level, respectively. For more details see [6]. (b) Map of the macaque visual cortex with areas forming part of the VCH shown in colour [2]. (c) The notion of a direction of projections that is associated with laminar patterns was derived from the observation that laminar projection origins and terminations show highly regular, repeating patterns as one proceeds from areas at the sensory periphery (A17, striate cortex, primary visual cortex) to more central areas of the brain (e.g. A18, A19) [7]. (Online version in colour.)

Figure 2.

Topological arrangement of sensory (visual and auditory) connections in the primate cortex. (a) Connections of visual cortical areas in the macaque brain, arranged by topological distance. Each concentric ring represents a different synaptic level, starting with primary sensory cortex on the outermost level 1. Any two levels are separated by at least one unit of synaptic distance. Nodes at the same level are reciprocally interconnected by the black arcs of the concentric rings. Figure and description adapted from [3]. (b) Progression of connections from the primary visual (green arrow) and auditory (blue arrow) areas of the primate cortex. Each new step is shown in black and the further connections of the new areas by light stippling or hatching. All sensory pathways converge in the depths of the superior temporal sulcus (STS, grey arrow). Adapted from [8].

Figure 3.

Visual cortical hierarchy versus topological sequence of primate visual cortical projections. The VCH diagram on the left was derived by optimization analysis of the laminar connectivity data between these structures using methods described previously [6]. Areas with near-simultaneous onset latencies are shaded. It is apparent that the stations with near-simultaneous onsets are on different levels of the hierarchy. An optimal topological diagram for the same network, on the right, derived by analysis of the shortest path to each structure from the retina. Stations with near-simultaneous onset latencies are shaded. It is apparent that the stations with near-simultaneous onsets are on the same level of the topological sequence, with the sole exception of the frontal eye fields (FEF). From [22].

Figure 4.

Sequential topology of the primate visual system connectivity versus benchmark networks. (a) Minimization of the sequential layout of the primate visual cortical network and comparison networks with the same number of nodes and edges around a circular layout. Areas are placed around a circle in such a way that the total sum of the distances of all connected areas becomes minimal. By the value of this cost function, the organization of the actual network was found to be more sequential than that of randomized networks or other comparison networks, but less sequential than that of strictly sequential networks in which connections are arranged such that they only link immediate neighbours. (b) Optimal sequential layout of the primate visual cortical network along a linear one-dimensional axis. The arrangement largely resembles the expected sequence through the system, from primary visual areas (on the left) to higher-order areas (on the right). (Online version in colour.)

Figure 5.

Architectonic gradients of the primate cerebral cortex and their relation to the organization of cortico-cortical connections. Less architectonically differentiated, agranular, cortical areas (yellow) are characterized by lower neuron density and different morphology of layer III pyramidal cells than more strongly differentiated, eulaminate, areas (dark green), with gradual changes across the spectrum. (a) Macroscopic and microscopic architectonic features show concerted changes along spatial gradients of the macaque cerebral cortex, indicating a natural axis of cortical organization. In particular, higher neuron density tends to correlate with smaller cross sections of the soma and the dendritic tree as well as with lower total spine count and lower peak spine density. (b) Relations of architectonic types with connection features. Connections exist predominantly between areas of similar cortical type; thus, agranular and dysgranular regions (yellow) tend to form more connections with each other than with eulaminate regions (dark green). Moreover, laminar patterns of projection origins are related to differences in architectonic differentiation. Connections between areas of distinct differentiation show a skewed unilaminar projection pattern, with projections originating predominantly in the infragranular or supragranular layers depending on the direction of the projection (agranular to eulaminate projections and eulaminate to agranular projections, respectively), while connections between areas of similar architectonic differentiation show a bilaminar projection origin pattern (connections between middle panels), where the dominating laminar compartment again depends on the connected areas’ relative differentiation. In summary, there are concurrent changes of macro- and microstructural cellular and connectional features across the cortical sheet, forming spatially ordered gradients, confirming and expanding observations from classic neuroanatomy studies (gradation principle of Sanides [29]). Figure adapted from [30].

Figure 6.

Schematic of hierarchical multi-level modular network organization. This nested module-within-module architecture can comprise diverse types of networks, for example, with (left) or without (right) central hub nodes. The nodes are also differentiated by scales of network access, distinguishing nodes with global access (hub nodes) from local nodes. Adapted from [53,54].

Figure 7.

Organization of the connectivity of the primate visual cortical system according to the architectonic type principle [30]. (a) Areas are arranged from higher types with dense, well-differentiated layers on the outer rings of the diagram proceeding to lower type areas on the inner rings of the scheme. Types are indicated by the shading of the rings, with lighter shading for higher and darker shading for lower types, as shown by the grey level scale. Connections, based on [2], between areas of the same or neighbouring types are drawn in black, between areas separated by two types in blue, and projections between areas separated by more than two types are shown in red. The predominance of black projections indicates the consistency of the structural model. (b) Comparison between average cortical hierarchy and structural types of the primate visual system. Left, diagram adapted from [12]; right, structural types. While there are small apparent differences between these figures, the overall picture is quite similar. This observation is owing to the fact that the architectonic type principle implies that structural type differences are correlated with laminar projection patterns, and, thus, the structural type scheme underlies the hierarchical arrangement of areas resulting from the sorting of the oriented projections. Figure adapted from [69].

Figure 8.

Overview of different concepts of ‘hierarchy’ in cortical brain networks as reviewed in the present paper. Depending on the chosen ‘hierarchy’ concept, the arrangement of the areas may vary substantially, also leading to different expectations of their functional properties. This overview is not exhaustive, and further notions of ‘hierarchy’ may be identified in the literature. (a) Sorting of areas by their ‘forward’ and ‘backward’ projections as classified from the laminar patterns of projection origins and terminations. (b) Arrangement of areas by the topological sequence of their connections, according to shortest paths from inputs at the bottom to outputs on the top. (c) Sorting of areas by feature gradients, for instance of cortical types or cellular density increasing from bottom to top. (d) Arrangement of areas by a progression of scales. Smaller neural systems are encapsulated in larger ones. For instance, laminar compartments are contained in cortical areas, which are in turn grouped into increasingly larger systems, such as the ventral and dorsal ‘streams’ of the primate visual system [73], by the arrangement of their connections and their functional properties. (Online version in colour.)