Bayesian approach to uncertainty quantification for cerebral autoregulation index

Cerebral autoregulation refers to the brain's ability to maintain cerebral blood flow at an approximately constant level, despite changes in arterial blood pressure. The performance of this mechanism is often assessed using a ten-scale index called the ARI (autoregulation index). Here, $0$ denotes the absence of, while $9$ denotes the strongest, autoregulation. Current methods to calculate the ARI do not typically provide error estimates. Here, we show how this can be done using a bayesian approach. We use Markov-chain Monte Carlo methods to produce a probability distribution for the ARI, which gives a natural way to estimate error.