IMPLICATIONS OF THE GENERAL LINEAR MODEL FOR THE DESIGN OF fMRI EXPERIMENTS

The Sensitivity for Detection of Weak Activations

The general linear model discussed in Chapter 18 is a powerful and highly flexible technique for analyzing Blood Oxygenation Level Dependent (BOLD) data to estimate the strength and significance of activations. In addition, it provides a useful framework for designing functional magnetic resonance imaging (fMRI) experiments and comparing the sensitivity of different experimental paradigms. For most fMRI applications, the goal is to detect a weak signal change associated with the stimulus, and a direct measure of the sensitivity is the signal-to-noise ratio (SNR) of the measured activation amplitude. Much of the discussion of the general linear model in Chapter 18 was geared toward deriving expressions for the SNR and for the associated statistical measures such as t and F. This chapter focuses on the implications of these SNR considerations for the design of fMRI experiments. From the arguments made in Chapter 18 for the case of a known hemodynamic response represented by a single model function M, the SNR is given by the simple expression aM/σ. The vector M is the unit amplitude response to the stimulus pattern with the mean removed, and M is the amplitude of M. The true amplitude of the response in the data is a, and σ is the standard deviation of the noise added in to each measurement. The intrinsic activation amplitude a is set by brain physiology, and the noise standard deviation σ is set by the imaging hardware and the pulse sequence used for image acquisition, so we can think of these as being fixed aspects of the experiment.