Optimal experimental designs for fMRI via circulant biased weighing designs

Abstract

Functional magnetic resonance imaging (fMRI) technology is popularly used in many fields for studying how the brain reacts to mental stimuli. The identification of optimal fMRI experimental designs is crucial for rendering precise statistical inference on brain functions, but research on this topic is very lacking. We develop a general theory to guide the selection of fMRI designs for estimating a hemodynamic response function (HRF) that models the effect over time of the mental stimulus, and for studying the comparison of two HRFs. We provide a useful connection between fMRI designs and circulant biased weighing designs, establish the statistical optimality of some well-known fMRI designs and identify several new classes of fMRI designs. Construction methods of high-quality fMRI designs are also given.

Circulant Partial Hadamard Matrices: Construction via General Difference Sets and Its Application to fMRI Experiments

“…We propose a criterion to quantify a GDS and apply it as DVA to find the GDS of an r-H(m × n). We depict 0-H(m × n) and 2-H(m×n) constructed from specific GDSs, and 0-H(m×n) is proved as universally optimal for estimating the HRF of a stimulus type and for comparing HRFs of two stimulus types (Cheng and Kao (2015)). We have searched the CPHMs when n > 52, see Table 2.…”

Efficient orthogonal functional magnetic resonance imaging designs in the presence of drift

“…These designs (when a 2 is replaced with 0) satisfy orthogonality properties and remain optimal for the estimation of HRF when there is only one stimulus type. 16 Subsequently, Lin et al 6 also obtained orthogonal designs using circulant (almost) orthogonal arrays. The designs based on extended m-sequences, Paley difference sets, or circulant Hadamard matrices require n to be necessarily a multiple of 4.…”

D-optimal chemical balance weighing designs with diagonal covariance matrix of experimental errors

“…Some applications of weighing designs are presented in Banerjee (1975), Harwit andSloane (1979), Graczyk (2013), Cheng and Kao (2015). Moreover, Cheng (1980) proposed to apply the results on weighing designs to the setting of 2 fractional factorial designs.…”