## Tiecks autoregulatory index

Cerebral autoregulation (CA) can be evaluated by measuring relative blood flow changes in response to a steady-state change in the blood pressure (static method) or during the response to a rapid change in blood pressure (dynamic method). The dynamic cerebral autoregulation response to transient hypotension is commonly assessed using Tieck’s Autoregulatory Index (ARI).

The ARI was initially developed using the rapid thigh-cuff deflation technique (1,2). This procedure involved 6 min of bilateral supra-systolic (220 mmHg) thigh-cuff inflation, followed by rapid cuff deflation. The integrity of CA is graded between 0 (absence of dynamic CA) to 9 (strongest dynamic CA) by applying a second-order linear differential equation defined as:

where dPn is the normalized change in MAP relative to the control value (MAPbase), adjusted for the estimated critical closing pressure (CCP) of 12 mmHg (35), x2n and x1n are state variables (equal to 0 at baseline), mVn is modeled mean velocity, MCAvbase is baseline MCAvmean, f is the sampling frequency (10 Hz), and n is the sample number. The mVn generated from 10 predefined combinations of parameters T (time constant), D (dampening factor), and k (autoregulatory gain) are fitted to the actual MCAvmean recording within a specified window (typically 30 s) to identify the best fit model associated with the minimum error or highest correlation. The unconstrained ARI ranging between 0 (absence of CA) to 9 (strongest CA) is typically derived via interpolation (2).

### Analysis outputs

Parameter | Definition |
---|---|

ARI | Autoregulatory index. |

iARI | Interpolated autoregulatory index. |

Model fit | Minimum MSE or maximum correlation. |

### Settings definitions

Parameter | Definition |
---|---|

Output signal | Doppler velocity channel. Default is Doppler 1. |

dPn start and length | dPn is the normalised change in mean arterial pressure relative to the control blood pressure value adjusted for the estimated critical closing pressure. Start and length determine the start and the length of the analysis window. The recommendation is to set the start to correspond to the initial drop in mean blood pressure (default is 0), and the window to 30 (1) or 35 (2). |

Method | Interpolation method |

MAP window | Window for determining MAPbase. Default is 5. |

CCP | Estimated critical closing pressure. Default is 12 mmHg. |

f | Sampling frequency. Default is 10 Hz. |

### Graph Definition

Graph | Definitions |
---|---|

MAP | Mean arterial pressure |

Flow velocity | Blood flow velocity |

ARI model fits | Modelled flow velocity calculated from Tieck's second-order linear differential equation. |

MSE | Model fit based on mean squared error of the differences between observed vs. modelled flow velocity. |

Correlation | Model fit based on Pearson’s correlation between observed vs. modeled flow velocity. |

## References

(1) Tiecks FP, Lam AM, Aaslid R, Newell DW. Comparison of static and dynamic cerebral autoregulation measurements. Stroke. 1995 Jun;26(6):1014-9.

(2) Tzeng YC, Lucas SJE, Atkinson A, Wilie CK, Ainslie PN. Fundamental relationships between arterial baroreflex sensitivity and dynamic cerebral autoregulation in humans. J Appl Physiol 108: 1162–1168, 2010.