title: Optimal design for nonlinear estimation of the hemodynamic response function.
abstract: 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.
authors.affiliation: Department of Methodology & Statistics, Faculty of Health, Medicine and Life Sciences, Maastricht University, Maastricht, The Netherlands. baerbel.maus@maastrichtuniversity.nl
authors.forename: Bärbel
authors.initials: B
authors.lastname: Maus
authors.forename: Gerard J P
authors.initials: GJ
authors.lastname: van Breukelen
authors.forename: Rainer
authors.initials: R
authors.lastname: Goebel
authors.forename: Martijn P F
authors.initials: MP
authors.lastname: Berger
mesh_terms: D000465:Algorithms; D002560:Cerebrovascular Circulation / Q000502:physiology*; D003198:Computer Simulation; D006439:Hemodynamics / Q000502:physiology*; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging / Q000379:methods*; D017711:Nonlinear Dynamics