On the nature and use of models in network neuroscience

Abstract

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.

FIG. 1.. Schematic of network models used in neuroscience.

(Left) The simplest and most commonly used network model for neural systems is one that represents the pattern of connections (edges) between neural units (nodes). More sophisticated network models can be constructed by adding edge weights and node values, or explicit functional forms for their dynamics. Multilayer networks can be used to represent interconnected sets of networks, and dynamic networks can be used to understand the reconfiguration of network systems over time. (Right) Common measures of interest include: degree, which is the number of edges emanating from a node; clustering, which is related to the prevalence of triangles; cavities, which describe the absence of edges; hubness, which is related to a node’s influence; paths, which determine the potential for information transmission; communities, or local groups of densely interconnected nodes; shortcuts, which are one possible marker of global efficiency of information transmission; and core-periphery structure, which facilitates local integration of information gathered from or sent to more sparsely connected areas.

FIG. 2.. Three dimensions of network model types.

(a) We posit that efforts to understand mechanisms of brain structure, function, development, and evolution in network neuroscience can be organized along three key dimensions of model types. (b) The first dimension extends from data representation to first-principles theory. (c) The second dimension extends from biophysical realism to functional phenomenology. (d) The third dimension extends from elementary descriptions to coarse-grained approximations.

FIG. 3.. Illustrations of different categories of model assessment.

(a) Descriptive validity addresses the question of whether the model resembles in some key way(s) the system it is constructed to model. For network models, descriptive validity naturally aligns with questions about how well the specific patterns of nodes and edges (circular inset) matches the anatomical and/or functional data that it represents (main panel). (b) Explanatory validity focuses on a theoretical construct that is ultimately used to develop statistical tests and support conclusions drawn from the use of the model. A network model can be considered to have explanatory validity if its architecture can be justified in terms of brain data and if it can then be used to test for causal relationships to dynamics or behavior based on that architecture. Here we show a formal model of network node dynamics (circular inset) that can be used to test for causal relationships with dynamics in the true system (main panel). (c) Predictive validity occurs when there is an organism-model correlation in response to a perturbation, such as a drug, electrical or chemical stimulation, neurofeedback, or training. Here we show the model’s response to perturbation (circular inset) matching the organism’s response to perturbation (main panel).

FIG. 4.. Bridging model types in network neuroscience.

There are many ways to bridge model types. One natural path begins with fine-scale and coarse-grained information drawn from real systems (left) to create network models as data representations, which in turn are used to inform first-principles theories (middle). These theories then predict observed patterns of functional or structural connectivity (right).