## Abstract

Linear autoregressive (ARX) models are often used to describe the dynamic cerebral autoregulation in humans by relating cerebral blood flow velocity (CBFV) to beat-to-beat mean arterial blood pressure (MABP). For linear model estimation it is required that the input be persistently exciting. This study aimed to establish if the MABP is adequately persistently exciting for estimating to yield a linear model. Using ARX models with MABP as input and CBFV as output, linear models for 11 healthy normal subjects in supine position were obtained. The order of the models was allowed to vary between 1 to 10. For each subject, the model with the least mean squared error (MSE) value was selected, called M_{a}. M_{a} was then treated as the unknown model of the cerebral autoregulation to be estimated. M_{a} was separately subjected to the measured MABP as well as a pseudo random binary sequence (PRBS) to estimate two ARX models for it. The resulting estimates of Ma with the lowest MSE were selected as M_{e1} and M_{e2}, respectively. With the measured MABP as input, the MSE values between the resulting output of M _{e1} and M_{e2} and the measured CBFV were calculated. These MSE values were compared to the MSE value previously obtained for Ma to determine if M_{e1} that was obtained using MABP can estimate CBFV with the same level of accuracy as M_{e2}. This analysis was carried out both with the traditional 6 minutes data and was repeated by dividing the 6 minutes of data into four 1.5 minute sections, a total of 5 comparisons. The analysis showed that the computed MSE values for M_{a}, M_{e1} and M _{e2} were the same for each subject, irrespective of the duration of the data set used for the study. However, the orders of the models were not identical. For each of the three models the average MSE value for 11 subjects was 0.0200 for 6 minutes, 0.0235 for first 1.5 minute and 0.0263, 0.0278 and 0.0255 for second, third and fourth 1.5 minutes, respectively. Results suggest that 1.5 minutes of MABP sequence is adequate as input for estimating linear models of cerebral autoregulation.

Original language | English (US) |
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Title of host publication | Proceedings of the 2005 27th Annual International Conference of the Engineering in Medicine and Biology Society, IEEE-EMBS 2005 |

Pages | 5619-5622 |

Number of pages | 4 |

State | Published - Dec 1 2005 |

Event | 2005 27th Annual International Conference of the Engineering in Medicine and Biology Society, IEEE-EMBS 2005 - Shanghai, China Duration: Sep 1 2005 → Sep 4 2005 |

### Publication series

Name | Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings |
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Volume | 7 VOLS |

ISSN (Print) | 0589-1019 |

### Other

Other | 2005 27th Annual International Conference of the Engineering in Medicine and Biology Society, IEEE-EMBS 2005 |
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Country | China |

City | Shanghai |

Period | 9/1/05 → 9/4/05 |

## Keywords

- ARX estimation
- Cerebral autoregulation
- Linear models
- Mean arterial blood pressure

## ASJC Scopus subject areas

- Signal Processing
- Biomedical Engineering
- Computer Vision and Pattern Recognition
- Health Informatics