Estimating the branching ratio in living neural networks

Experimental evidence suggests the cortex operates near a critical point (Cocchi et al., 2017) where information processing functions are optimized. Proximity to this point is measured by the branching ratio, which is the average number of neurons activated by one active neuron. If this ratio is one, the network is critical. If the ratio is above one or below one, the network is supercritical or subcritical, respectively. A new method for measuring the branching ratio corrects for subsampling (Wilting and Priesemann, 2018), but produces some puzzling results. It reports patients with epilepsy have a branching ratio less than one (Hagemann, Wilting et al., 2020), when models predict a branching ratio greater than one (Hsu et al., 2008). We investigated this in simulations of neural networks using both a naïve method that just looks at the first two time steps of an avalanche, and the new method that corrects for subsampling. We found that under certain conditions both methods seem to fail. Thus, more accurate ways of estimating the branching ratio are needed; they will help us monitor seizures in epilepsy patients, when a drug treatment works, and when a patient returns to consciousness.