Scaling errors in measures of brain activity cause erroneous estimates of effective connectivity

Effective connectivity (EC) is the collective term for various measures of the interaction between the nodes in a network of neurons or neural populations during a certain experimental condition. Here, I investigated three types of EC that differ with respect to signal normalization, and therefore measure different aspects of neural interactions. Unnormalized EC measures pure connection strength. Amplitude-scaled EC measures the combined influence of signal amplitude and connection strength on neural activity. Finally, normalized EC measures the influence of one node on the activity of another relative to all influences on that node. With a theoretical analysis, I investigated the sensitivity of EC to signal scaling (the ratio of the amplitude of the measured signal and the underlying neural activity) and found that scaling affects the conclusions of the analysis of unnormalized EC severely, whereas normalized EC is not affected by the scaling problem. In an analysis of previously published hemodynamic response functions (Handwerker, D. A., Ollinger, J. M., D'Esposito, M., 2004. Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses. Neuroimage 21, 1639-1651), I tested the predictions of the theoretical analysis. The empirical analysis indicated that signal scaling contributes to a large extent to measurement errors of unnormalized EC, although hemodynamic response function shape variability also contributed. Normalized EC, on the other hand, was only affected by shape differences and not by scaling. In addition to being more accurate, normalized EC is also an appropriate type of measure of neural interactivity if one is interested in the relative influence of one node on another, rather than absolute connection strengths per se.