From Maps to Multi-dimensional Network Mechanisms of Mental Disorders

Abstract

The development of advanced neuroimaging techniques and their deployment in large cohorts has enabled an assessment of functional and structural brain network architecture at an unprecedented level of detail. Across many temporal and spatial scales, network neuroscience has emerged as a central focus of intellectual efforts, seeking meaningful descriptions of brain networks and explanatory sets of network features that underlie circuit function in health and dysfunction in disease. However, the tools of network science commonly deployed provide insight into brain function at a fundamentally descriptive level, often failing to identify (patho-)physiological mechanisms that link system-level phenomena to the multiple hierarchies of brain function. Here we describe recently developed techniques stemming from advances in complex systems and network science that have the potential to overcome this limitation, thereby contributing mechanistic insights into neuroanatomy, functional dynamics, and pathology. Finally, we build on the Research Domain Criteria framework, highlighting the notion that mental illnesses can be conceptualized as dysfunctions of neural circuitry present across conventional diagnostic boundaries, to sketch how network-based methods can be combined with pharmacological, intermediate phenotype, genetic, and magnetic stimulation studies to probe mechanisms of psychopathology.

Keywords: brain imaging; control theory; dynamic networks; generative models; graph theory; mental disorders; multilayer networks; network neuroscience; psychiatry; schizophrenia.

Figure 1. Graphical Overview of Network Approaches Discussed

Traditional tools from the mathematical discipline of graph theory have emerged as particularly useful in describing structural and functional brain networks. Multilayer network approaches extend this static representation by adding an additional dimension to the 2D graph, such as time or data modality. Generative network methods can be used to study the mechanisms by which brain networks have evolved or have been shaped over development. Network growth is simulated based on some predefined rules and is then compared to a real (brain) network. Finally, network control theory offers a mechanistic explanation for how activation patterns in the brain are controlled based on the underlying structure.

Figure 2. Multilayer Network and Generative Modeling Approaches

Generative network models investigate possible underlying mechanisms that contribute to the development or evolution of brain networks. (A) A generative network model is created by adding links to a network in a stepwise fashion based on a predefined rule (here preferential attachment: higher likelihood for links to appear at already highly connected nodes). The final network is then compared to a real (brain) network and evaluated in terms of several topological metrics, for example, by using Kolmogorov-Smirnov statistics. (B) Vértes et al. (2012) showed that functional resting-state brain networks have evolved under an economic trade-off between minimizing wiring length and persevering topological complexity. Schizophrenia patients showed a lower penalty for wiring cost, suggesting a differential regulation of neuronal migration, differentiation, and axon guidance. (C) Betzel et al. (2016a) tested various growth rules based on several topological measures as well as Euclidean distance between regions. They demonstrated that penalization of distance and a preference for a normalized topological measure of overlap in two nodes’ neighborhoods are dominant drivers of the observed structural connectome but that their relative contributions change in healthy aging. Boxes are interquartile ranges (IQR). The whiskers (error bars) define the full range of the distribution, excluding outliers (more than 1.5 IQRs beyond the top/bottom of box). These outliers are plotted as individual points. (D) Hypothesized neurobiological mechanisms contributing to altered network generation in developmental disorders that can be directly instantiated in generative models: altered neuronal migration by distance-dependent guidance factors (top); activity-dependent wiring of neurons that share a nearest neighbor (middle); and degeneration of existing links by excitotoxicity (bottom).

Figure 3. Network Control Theory Approaches

(A) Based on a structural network backbone, A, network control theory models how the network transitions from an initial state x₀ (left side, active nodes in blue) to a final target state x_t (right side, active nodes in blue). The particular nodes that exhibit control, B, over the network are selected (middle, red arrows), and the minimum amount of control energy u(t) in each control node that is necessary to drive the network from x₀ to x_t is computed by finding the optimal solution to the minimization problem of the corresponding Hamiltonian. (B) Gu et al. (2015) investigated the controllability of structural brain networks. Regions within the default-mode network supported transitions into easy-to-reach brain states (average controllability), while cognitive control areas facilitated transitions into hard-to-reach states (modal controllability). (C) First evidence for altered controllability in disease was demonstrated for mild traumatic brain injury (TBI) by Gu and colleagues (Gu et al., 2017). Although healthy and TBI subjects showed a high overlap in brain areas contributing to controllability, the TBI group showed a significant reduction in mean control energy. Error bars indicate SEM. (D) Applications of network control theory to clinical populations can offer the possibility to mechanistically understand perturbation/therapeutic interventions, such as medication, transcranial magnetic stimulation (TMS), transcranial direct current stimulation (tDCS), or deep brain stimulation on a brain circuit level, to prevent transition to pathologic states and steer the brain toward more favorable conditions.

Figure 4. Graphical Summary of Multilayer Network Approaches and Developmental Applications

(A) Temporal network approaches link connectivity matrices that represent a networks’ connectivity pattern at a particular time in an ordinal fashion as follows: node i in layer s (time window) is linked to node i in the adjacent time windows, s – 1 and s + 1. Multilayer network approaches can then be used to find time-resolved patterns of coherent connectivity over time. Two essential model parameters determine the temporal cohesiveness (ϖ) and the structural scale of resolution (γ). (B) Fair et al. demonstrate a shift from local, anatomically arranged organization to a more functionally distributed network architecture during development; adapted from Fair et al. (2009). (C) Braun et al. (2016) used temporal networks to investigate the time-resolved reconfiguration of functional brain networks during a working memory task. Schizophrenia patients (SZ) and first-degree relatives (REL) showed more inefficient reconfiguration than healthy controls (HC), as measured by a network flexibility metric. Interestingly, such a high-flexibility state could be induced in healthy controls by administering an NMDA receptor antagonist (DXM), pointing toward a critical role of glutamate in the development of less stable network patterns in schizophrenia. Error bars indicate SEM. (D) A schematic representation of changes in community structure in typically developing (TD) and autism spectrum disorder (ASD) subjects, as assessed by multilayer community detection tools.