Stochastic accumulation by cortical columns may explain the scalar property of multistable perception

The timing of certain mental events is thought to reflect random walks performed by underlying neural dynamics. One class of such events--stochastic reversals of multistable perceptions--exhibits a unique scalar property: even though timing densities vary widely, higher moments stay in particular proportions to the mean. We show that stochastic accumulation of activity in a finite number of idealized cortical columns--realizing a generalized Ehrenfest urn model--may explain these observations. Modeling stochastic reversals as the first-passage time of a threshold number of active columns, we obtain higher moments of the first-passage time density. We derive analytical expressions for noninteracting columns and generalize the results to interacting columns in simulations. The scalar property of multistable perception is reproduced by a dynamic regime with a fixed, low threshold, in which the activation of a few additional columns suffices for a reversal.