Network connectivity modulates power spectrum scale invariance

- We use power spectrum scale invariance to quantify signal complexity in a negative feedback loop.
- Within this loop, we model network connectivity, and show its effect on complexity of signal outputs.
- We introduce a simple nonlinear extension to model the hemodynamic filter, with similar results.

Measures of complexity are sensitive in detecting disease, which has made them attractive candidates for diagnostic biomarkers; one complexity measure that has shown promise in fMRI is power spectrum scale invariance (PSSI). Even if scale-free features of neuroimaging turn out to be diagnostically useful, however, their underlying neurobiological basis is poorly understood. Using modeling and simulations of a schematic prefrontal-limbic meso-circuit, with excitatory and inhibitory networks of nodes, we present here a framework for how network density within a control system can affect the complexity of signal outputs. Our model demonstrates that scale-free behavior, similar to that observed in fMRI PSSI data, can be obtained for sufficiently large networks in a context as simple as a linear stochastic system of differential equations, although the scale-free range improves when introducing more realistic, nonlinear behavior in the system. PSSI values (reflective of complexity) vary as a function of both input type (excitatory, inhibitory) and input density (mean number of long-range connections, or strength), independent of their node-specific geometric distribution. Signals show pink noise (1/f) behavior when excitatory and inhibitory influences are balanced. As excitatory inputs are increased and decreased, signals shift towards white and brown noise, respectively. As inhibitory inputs are increased and decreased, signals shift towards brown and white noise, respectively. The results hold qualitatively at the hemodynamic scale, which we modeled by introducing a neurovascular component. Comparing hemodynamic simulation results to fMRI PSSI results from 96 individuals across a wide spectrum of anxiety-levels, we show how our model can generate concrete and testable hypotheses for understanding how connectivity affects regulation of meso-circuits in the brain.