Multiple-Model Set-Valued Observers: A new tool for HRF model selection in fMRI

This paper proposes a new approach for the selection of a biophysical model describing the haemodynamic response function (HRF) measured in BOLD-fMRI data, based on model falsification techniques. Specifically, the novel method of Multiple Model Set-Valued Observers (MMSVOs) is introduced. The observers consider that the initial state lives in a set, the linear time-varying dynamic system obtained from a bilinear approximation of the nonlinear HRF model about the nominal input signal is uncertain, and the output measurements are corrupted by bounded noise. It is shown, both theoretically and through simulation, that the proposed method is able to successfully distinguish the correct HRF model among a set of physiologically plausible alternatives. Moreover, the feasibility of the technique is demonstrated by its application to an empirical dataset. In summary, the results obtained clearly indicate that the proposed methodology is potentially well-suited to be used in the modeling of BOLD-fMRI data.