Nonlinear responses in fMRI: The balloon model, volterra kernels, and other hemodynamics

There is a growing appreciation of the importance of nonlinearities in evok ed responses in fMRI, particularly with the advent of event-related fMRI. T hese nonlinearities are commonly expressed as interactions among stimuli th at can lead to the suppression and increased latency of responses to a stim ulus that are incurred by a preceding stimulus, me have presented previousl y a model-free characterization of these effects using generic techniques f rom nonlinear system identification, namely a Volterra series formulation. At the same time Burton ct al. (1998) described a plausible and compelling dynamical model of hemodynamic signal transduction in fMRI. Subsequent work by Mandeville et al. (1999) provided important theoretical and empirical c onstraints on the form of the dynamic relationship between blood flow and v olume that underpins the evolution of the fMRI signal. In this paper we com bine these system identification and model-based approaches and ask whether the Balloon model is sufficient to account for the nonlinear behaviors obs erved in real time series. We conclude that it can, and furthermore the mod el parameters that ensue are biologically plausible. This conclusion is bas ed on the observation that the Balloon model can produce Volterra kernels t hat emulate empirical kernels. To enable this evaluation we had to embed th e Balloon model in a hemodynamic input-state-output model that included the dynamics of perfusion changes that are contingent on underlying synaptic a ctivation. This paper presents (i) the full hemodynamic model (ii), how its associated Volterra kernels can be derived, and (iii) addresses the model' s validity in relation to empirical nonlinear characterisations of evoked r esponses in fMRI and other neurophysiological constraints. (C) 2000 Academi c Press.