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

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. 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 M-a 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 M-a 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.