A Complex Systems Perspective on Neuroimaging Studies of Behavior and Its Disorders

Abstract

The study of complex systems deals with emergent behavior that arises as a result of nonlinear spatiotemporal interactions between a large number of components both within the system, as well as between the system and its environment. There is a strong case to be made that neural systems as well as their emergent behavior and disorders can be studied within the framework of complexity science. In particular, the field of neuroimaging has begun to apply both theoretical and experimental procedures originating in complexity science-usually in parallel with traditional methodologies. Here, we illustrate the basic properties that characterize complex systems and evaluate how they relate to what we have learned about brain structure and function from neuroimaging experiments. We then argue in favor of adopting a complex systems-based methodology in the study of neuroimaging, alongside appropriate experimental paradigms, and with minimal influences from noncomplex system approaches. Our exposition includes a review of the fundamental mathematical concepts, combined with practical examples and a compilation of results from the literature.

Keywords: complexity science; emergence; evolution; multi-scale; neuroimaging; self-organization.

Figure 1.

The panels illustrate the vectors of z-scores calculated for each voxel by contrasting the activity of task-versus-baseline (positive values only). Maps were obtained from fMRI studies of simple/motor tasks (A) or more complex activities such as calculation, language comprehension and social cognition (B). The x-axis represents the logarithm of the z-score ranks. The red lines represent the same z-scores for the normal null distribution. The blue lines represent the James-Stein boundaries, that is, the minimal decay of a z-score distribution that would justify the use of statistical thresholds for the estimation of the z-scored vector for each contrast (see Equation 1). The boundary curve has been arbitrarily scaled to the maximum z-score value for the group of tasks for which the theory suggests the use of shrinkage estimators for all vectors with smoother decays.

Figure 2.

The panel above illustrates a simple linear growth model whereby the offspring of two rabbits is always twice the number of offspring of a single rabbit, whatever the number of iterations. In the logistic model below, a resource constraint makes the rabbits compete for resources and, this time, the offspring of two rabbits is not twice the offspring of one.

Figure 3.

A simple sand-pile experiment simulated on a 20 × 20 grid (left); each pixel represents a column where sand piles up and colors indicate the number of grains (blue = 0 to yellow = max number of grains = 4). Sand is dropped randomly on the grid, and it topples sideways, as well off the grid, when the set limit for the height of a sand column is reached. The right panel shows the total sand in the grid through time, as well as the size of the avalanches falling off it.

Figure 4.

A brain state consists in a set of regions with synchronized activity during a time interval. The three-dimensional plot represents the energy levels of each state and the red line with arrow on the energy landscape the dynamic trajectory of the brain moving from state to state, whereas “energy” here is a term derived from information criteria and not calculated from metabolic expenditure. Brain states are more or less likely to be visited by the dynamics over time based on their relative energy/stability (adapted from Gu and others 2018).