A model of variability in brain stimulation evoked responses.

The input-output (IO) curve of cortical neuron populations is a key measure of neural excitability and is related to other response measures including the motor threshold which is widely used for individualization of neurostimulation techniques, such as transcranial magnetic stimulation (TMS). The IO curve parameters provide biomarkers for changes in the state of the target neural population that could result from neurostimulation, pharmacological interventions, or neurological and psychiatric conditions. Conventional analyses of IO data assume a sigmoidal shape with additive Gaussian scattering that allows simple regression modeling. However, careful study of the IO curve characteristics reveals that simple additive noise does not account for the observed IO variability. We propose a consistent model that adds a second source of intrinsic variability on the input side of the IO response. We develop an appropriate mathematical method for calibrating this new nonlinear model. Finally, the modeling framework is applied to a representative IO data set. With this modeling approach, previously inexplicable stochastic behavior becomes obvious. This work could lead to improved algorithms for estimation of various excitability parameters including established measures such as the motor threshold and the IO slope, as well as novel measures relating to the variability characteristics of the IO response that could provide additional insight into the state of the targeted neural population.