Complex-number representation of informed basis functions in general linear modeling of Functional Magnetic Resonance Imaging.

Functional Magnetic Resonance Imaging (fMRI), measuring Blood Oxygen Level-Dependent (BOLD), is a widely used tool to reveal spatiotemporal pattern of neural activity in human brain. Standard analysis of fMRI data relies on a general linear model and the model is constructed by convolving the task stimuli with a hypothesized hemodynamic response function (HRF). To capture possible phase shifts in the observed BOLD response, the informed basis functions including canonical HRF and its temporal derivative, have been proposed to extend the hypothesized hemodynamic response in order to obtain a good fitting model. Different t contrasts are constructed from the estimated model parameters for detecting the neural activity between different task conditions. However, the estimated model parameters corresponding to the orthogonal basis functions have different physical meanings. It remains unclear how to combine the neural features detected by the two basis functions and construct t contrasts for further analyses. In this paper, we have proposed a novel method for representing multiple basis functions in complex domain to model the task-driven fMRI data. Using this method, we can treat each pair of model parameters, corresponding respectively to canonical HRF and its temporal derivative, as one complex number for each task condition. Using the specific rule we have defined, we can conveniently perform arithmetical operations on the estimated model parameters and generate different t contrasts. We validate this method using the fMRI data acquired from twenty-two healthy participants who underwent an auditory stimulation task.