Neural physiological modeling towards a hemodynamic response function for fMRI

The BOLD signal provided by the functional MRI medical modality measures the ratio of oxy- to deoxy- haemoglobin at each location inside the brain. The detection of activated regions upon the application of an external stimulus, e.g., visual or auditive, is based on the comparison of the mentioned ratios of a rest condition (pre-stimulus) and of a stimulated condition (post-stimulus). Therefore, an accurate knowledge of the impulse response of the BOLD signal to neural stimulus in a given region is needed to design robust detectors that discriminate, with a high level of confidence activated from non activated regions. Usually, in the literature, the hemodynamic response has been modeled by known functions, e.g., gamma functions, fitting them, or not, to the experimental data. In this paper we present a different approach based on the physiologic behavior of the vascular and neural tissues. Here, a linear model based on reasonable physiological assumptions about oxygen consumption and vasodilatation processes are used to design a linear model from which a transfer function is derived. The estimation of the model parameters is performed by using the minimum square error (MSE) by forcing the adjustment of the stimulus response to the observations. Experimental results using real data have shown that the proposed model successfully explains the observations allowing to achieve small values for the fitting error.