### 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 | Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings |

Pages | 5619-5622 |

Number of pages | 4 |

Volume | 7 VOLS |

State | Published - 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 |

### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Bioengineering

### Cite this

*Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings*(Vol. 7 VOLS, pp. 5619-5622). [1615760]

**Efficacy of using mean arterial blood pressure sequence for linear modeling of cerebral autoregulation.** / Gehalot, Piyush; Zhang, Rong; Mathew, Aby; Behbehani, Khosrow.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings.*vol. 7 VOLS, 1615760, pp. 5619-5622, 2005 27th Annual International Conference of the Engineering in Medicine and Biology Society, IEEE-EMBS 2005, Shanghai, China, 9/1/05.

}

TY - GEN

T1 - Efficacy of using mean arterial blood pressure sequence for linear modeling of cerebral autoregulation

AU - Gehalot, Piyush

AU - Zhang, Rong

AU - Mathew, Aby

AU - Behbehani, Khosrow

PY - 2005

Y1 - 2005

N2 - 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 Ma. Ma was then treated as the unknown model of the cerebral autoregulation to be estimated. Ma 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 Me1 and Me2, respectively. With the measured MABP as input, the MSE values between the resulting output of M e1 and Me2 and the measured CBFV were calculated. These MSE values were compared to the MSE value previously obtained for Ma to determine if Me1 that was obtained using MABP can estimate CBFV with the same level of accuracy as Me2. 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 Ma, Me1 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.

AB - 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 Ma. Ma was then treated as the unknown model of the cerebral autoregulation to be estimated. Ma 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 Me1 and Me2, respectively. With the measured MABP as input, the MSE values between the resulting output of M e1 and Me2 and the measured CBFV were calculated. These MSE values were compared to the MSE value previously obtained for Ma to determine if Me1 that was obtained using MABP can estimate CBFV with the same level of accuracy as Me2. 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 Ma, Me1 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.

KW - ARX estimation

KW - Cerebral autoregulation

KW - Linear models

KW - Mean arterial blood pressure

UR - http://www.scopus.com/inward/record.url?scp=33846923793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846923793&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33846923793

SN - 0780387406

SN - 9780780387409

VL - 7 VOLS

SP - 5619

EP - 5622

BT - Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings

ER -