fMRI activation maps based on the NN-ARx model

The most significant progresses in the understanding of human brain functions have been possible due to the use of functional magnetic resonance imaging (fMRI), which when used in combination with other standard neuroimaging techniques (i.e., EEG) provides researchers with a potential tool to elucidate many biophysical principles, established previously by animal comparative studies. However, to date, most of the methods proposed in the literature seeking fMRI signs have been limited to the use of a top-down data analysis approach, thus ignoring a pool of physiological facts. In spite of the important contributions achieved by applying these methods to actual data, there is a disproportionate gap between theoretical models and data-analysis strategies while trying to focus on several new prospects, like for example fMRI/EEG data fusion, causality/connectivity patterns, and nonlinear BOLD signal dynamics. In this paper, we propose a new approach which will allow many of the abovementioned hot topics to be addressed in the near future with an underlying interpretability based on bottom-up modeling. In particular, the theta-MAP presented in the paper to test brain activation corresponds very well with the standardized t test of the SPM99 toolbox. Additionally, a new Impulse Response Function (IRF) has been formulated, directly related to the well-established concept of the hemodynamics response function (HRF). The model uses not only the information contained in the signal but also that in the structure of the background noise to simultaneously estimate the IRF and the autocorrelation function (ACF) by using an autoregressive (AR) model with a filtered Poisson process driving the dynamics. The short-range contributions of voxels within the near-neighborhood are also included, and the potential drift was characterized by a polynomial series. Since our model originated from an immediate extension of the hemodynamics approach [Friston, K.J., Mechelli, A., Turner, R., Price C.J. (2000a). Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12, 466-477.], a natural interpretability of the results is feasible.