A stochastic linear model of neurovascular dynamics in the BOLD signal

Introduction: The mapping from neuronal activation to measured blood oxygenation level dependent (BOLD) signal in fMRI involves a complex interplay between physiological and physical processes that is yet to fully elucidated. Methods that account for the variability of the hemodynamic response function (HRF) have, with few exceptions (eg.[1] and subsequent works), focused on parameterised, deterministic models of the HRF (eg. [2]). We propose a stochastic linear model (SLM) of the measured BOLD response, in which noise drives the neurovascular dynamics directly. The key difference between the SLM and the 'bilinear dynamical systems' approach [3] is that the SLM employs a fully stochastic model of the neurovascular response rather than attempting to separate stochastic neuronal activity from deterministic HRF's.