Statistical Signal Properties of the Pressure-Reactivity Index (PRx)

The pressure-reactivity index (PRx) is defined in terms of the moving correlation coefficient between intracranial pressure (ICP) and mean arterial pressure (MAP) and is a measure of cerebral autoregulation ability. Plots of PRx against cerebral perfusion pressure (CPP) show a U-shaped behaviour: the minimum reflecting optimal cerebral autoregulation (CPPopt). However U-shaped behaviour may also occur by chance. To date there has been no evaluation of the statistical properties of these signals.

We simulated PRx/CPP distributions using synthetic ICP and MAP signals from Gaussian noise with known cross-correlation and calculated the statistical distribution of extrema in the PRx/CPP relationship.

The calculation of PRx on random data is statistically biased to show a U-shaped behaviour when the signals are positively cross-correlated (equivalent to PRx > 0). For PRx < 0, the bias is towards an inverse U-shaped behaviour. We demonstrate that this bias is eliminated by Fisher transforming the PRx data before CPPopt analysis.

Cross-correlated signals are biased to show a U-shaped distribution. A CPPopt-like behaviour will be observed more often than not even from random ICP and MAP signals that do not exhibit autoregulation, unless PRx is Fisher transformed. Care must be taken in interpreting CPPopt in terms of physiology calculated from untransformed data.