[Paper Review] On the scaling of avalanche shape and activity power spectrum in neuronal networks

Manoj Kumar Nandi, Alessandro Sarracino+2 more|arXiv (Cornell University)|Jun 29, 2022

Neural dynamics and brain functionNeuroscience60 references21 citations

TL;DR

This study investigates avalanche dynamics in integrate-and-fire neuronal networks with short-term plasticity, showing that at criticality, avalanche shapes collapse onto a universal profile as predicted by scaling theory. However, the power spectrum consistently follows Brown noise (f⁻²), while 1/f-like behavior (f⁻¹) emerges only slightly off-criticality, suggesting the power spectrum is a sensitive indicator of deviation from criticality.

ABSTRACT

Many systems in Nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as the scaling behaviour of the activity power spectrum as Brown noise. Recently, much attention has been given to the profile of neuronal avalanches, measured in neuronal systems in vitro and in vivo. Although a universal profile was evidenced, confirming the validity of the general scaling theory, the parallel study of the power spectrum scaling under the same conditions was not performed. The puzzling observation is that in the majority of healthy neuronal systems the power spectrum exhibits a behaviour close to $1/f$, rather than Brown, noise. Here we perform a numerical study of the scaling behaviour of avalanche shape and power spectrum for a model of integrate and fire neurons with a short-term plasticity parameter able to tune the system to criticality. We confirm that, at criticality, the average avalanche size and the avalanche profile fulfill the general avalanche scaling theory. However, the power spectrum consistently exhibits Brown noise behaviour, for both fully excitatory networks and systems with 30\% inhibitory networks. Conversely, a behaviour closer to $1/f$ noise is observed in systems slightly off-criticality. Results suggest that the power spectrum is a good indicator to determine how close neuronal activity is to criticality.

Motivation & Objective

• To test whether the general scaling theory for avalanche dynamics holds in neuronal networks, particularly regarding avalanche shape and power spectrum scaling.
• To resolve the discrepancy between theoretical predictions (Brown noise, f⁻²) and experimental observations (1/f noise, f⁻¹) in healthy brain activity.
• To investigate how inhibition influences the scaling behavior of the power spectrum and its deviation from Brown noise.
• To determine whether the power spectrum can serve as a reliable indicator of proximity to criticality in neuronal systems.

Proposed method

• Simulated integrate-and-fire neuronal networks with short-term plasticity to tune the system across critical and subcritical regimes.
• Used a scale-free connectivity pattern (P(kout) ∝ k⁻²) to model realistic functional neural connectivity.
• Varied the fraction of inhibitory neurons (0% to 30%) to probe the role of inhibition in spectral scaling.
• Applied avalanche detection via thresholding of activity bursts and computed average avalanche size, duration, and power spectral density (PSD).
• Performed scaling collapse of avalanche profiles using the exponent γ derived from <S> ∼ T^γ, and compared with PSD scaling S(f) ∼ f⁻β.
• Used the relation β = γ to test consistency between avalanche shape and power spectrum scaling under criticality.

Experimental results

Research questions

• RQ1 Does the general avalanche scaling theory hold for both avalanche shape and power spectrum in neuronal networks at criticality?
• RQ2 Why does the power spectrum in healthy neuronal systems often show 1/f-like behavior (β ≈ 1) instead of the predicted Brown noise (β = 2)?
• RQ3 How does the presence of inhibition (e.g., 30% inhibitory neurons) affect the scaling of the power spectrum?
• RQ4 Can the power spectrum exponent β serve as a quantitative indicator of how close a neuronal system is to criticality?

Key findings

• At criticality, the average avalanche size scales with duration as <S> ∼ T^γ, with γ ≈ 2.0, consistent with the general scaling theory.
• Avalanche profiles collapse onto a universal curve when scaled by duration, confirming the validity of the scaling theory for shape.
• The power spectrum consistently follows Brown noise scaling (S(f) ∼ f⁻²) at criticality, regardless of network composition (fully excitatory or 30% inhibitory).
• Slight deviations from criticality lead to a power spectrum exponent β ≈ 1.0, consistent with 1/f noise, observed even in networks with 30% inhibitory neurons.
• The power spectrum exponent β is a sensitive indicator of deviation from criticality: β ≈ 2 at criticality, β ≈ 1 off-criticality.
• Inhibition plays a crucial role in enabling the crossover from Brown noise to 1/f-like behavior in the power spectrum, even without tuning parameters.