Meaningful design and contrast estimability in FMRI.

Optimising the efficiency of an experimental design is known to be of great importance. However, existing methods for calculating design rank deficiency and contrast estimability (an important aspect of experimental design) relate to computational precision rather than image noise and are therefore not very meaningful. For example, a contrast between two experimental conditions may be mathematically "estimable" while requiring a huge differential BOLD response for statistical significance to be reached. In this paper we formulate standard efficiency equations in terms of required BOLD effect, and use this to generate measures of rank/estimability which are meaningful. This takes into account the strength and smoothness of the timeseries noise and is applicable to complex contrasts; we show how to re-express several regressors and an associated contrast vector as a single equivalent regressor, so that we can calculate the contrast's effective peak-peak height unambiguously. We also present some example results on typical designs, and characterise noise results from a range of typical FMRI acquisitions, in order to allow experimenters to apply efficiency estimation in advance of acquiring data.