Open AccessOptimal design for nonlinear estimation of the hemodynamic response function
Author(s) -
Maus Bärbel,
van Breukelen Gerard J. P.,
Goebel Rainer,
Berger Martijn P. F.
Publication year - 2012
Publication title -
human brain mapping
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.005
H-Index - 191
eISSN - 1097-0193
pISSN - 1065-9471
DOI - 10.1002/hbm.21289
Subject(s) - minimax , optimal design , mathematics , taylor series , nonlinear system , function (biology) , mathematical optimization , design of experiments , constant (computer programming) , control theory (sociology) , algorithm , computer science , mathematical analysis , statistics , artificial intelligence , physics , control (management) , quantum mechanics , evolutionary biology , biology , programming language
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. Hum Brain Mapp, 2011. © 2011 Wiley‐Liss, Inc.