Figure 2.

Illustrations of the calculation of psychophysiological interaction (PPI) with deconvolution. The part figure (A) shows the time series a seed region. The time series (A) is deconvoved with the canonical hemodynamic response function (HRF) to form a neuronal level physiological variable (B). The part figure (C) shows a box‐car function representing task on (coded as 1) and off (coded as 0), which is then convolved with a canonical HRF to form a psychological variable at the BOLD (blood‐oxygen‐level dependent) level (D). A PPI term (F) is calculated by first point‐by‐point multiplication between the physiological variable (B) and psychological variable (C) (as shown in E), and then convolved with the canonical HRF to form a PPI term at the BOLD level. A PPI term (I) could also be calculated using a centered psychological variable (G). Because the psychological variable (C) contains a constant component, the resulting PPI (F) contains a component of the physiological variable. It could be illustrated by removing the PPI with centering (I) from the PPI without centering (F), which results in a residual of J. Even though the residual J is still highly correlated with the physiological variable (A), they are not exactly the same. The discrepancy is caused by imperfect deconvolution and convolution processes with the HRF. If the physiological variable is deconvolved with the HRF (B), and convolved back with the HRF, the resulting variable (K) is exactly the same as the residual J. Green color represents variables at the neuronal level, and blue color represents variables at the BOLD level. [Color figure can be viewed at http://wileyonlinelibrary.com]