On the distinguishability of HRF models in fMRI

The problem of model falsification or model invalidation appears in several areas where we are interested in distinguishing among an eligible set of dynamic systems. In the context of fMRI studies of brain activity, modeling the haemodynamic response function (HRF) is a critical step. The estimation of the dynamic system describing a biophysical model of the HRF may leave much uncertainty on the exact values of the parameters. Moreover, the high noise levels in the data may hinder the model identification task. Therefore, this paper proposes a systematic tool to address the problem of the distinguishability among a set of physiologically plausible HRF models. The concept of absolutely input distinguishable systems is introduced and applied to the HRF model, by exploiting the structure of the underlying nonlinear dynamic system. A strategy to model uncertainty in the input time delay and magnitude is developed and its impact on the distinguishability of two physiologically plausible HRF models is determined, in terms of the maximum noise amplitude above which it is not possible to guarantee the falsification of one model in relation to the other. Finally, a methodology is proposed for the choice of the input sequence, or experimental paradigm, that should be used in order to maximize the distinguishability of the HRF models under investigation. The proposed approach may be used to assess the performance of HRF model identification techniques from fMRI data.