Optimal design for nonlinear estimation of the hemodynamic response function.

Subject-specific hemodynamic response functions (HRFs) have been recommended to capture variation in the form of the hemodynamic response between subjects (Aguirre et al., [ 1998]: Neuroimage 8:360-369). The purpose of this article is to find optimal designs for estimation of subject-specific parameters for the double gamma HRF. As the double gamma function is a nonlinear function of its parameters, optimal design theory for nonlinear models is employed in this article. The double gamma function is linearized by a Taylor approximation and the maximin criterion is used to handle dependency of the D-optimal design on the expansion point of the Taylor approximation. A realistic range of double gamma HRF parameters is used for the expansion point of the Taylor approximation. Furthermore, a genetic algorithm (GA) (Kao et al., [ 2009]: Neuroimage 44:849-856) is applied to find locally optimal designs for the different expansion points and the maximin design chosen from the locally optimal designs is compared to maximin designs obtained by m-sequences, blocked designs, designs with constant interstimulus interval (ISI) and random event-related designs. The maximin design obtained by the GA is most efficient. Random event-related designs chosen from several generated designs and m-sequences have a high efficiency, while blocked designs and designs with a constant ISI have a low efficiency compared to the maximin GA design.