Dynamic Modeling Of Cerebral Blood Flow Autoregulation Using ARX And Windkessel Models

Linear lumped parameter models like ARX and Windkessel models are simple, easy to solve, and find their application in real time modeling. The present study is focused on employing single input single output ARX and Windkessel models to beat-to-beat mean arterial blood pressure (MABP, mmHg) considered as input to the model, and cerebral blood flow velocity (CBFV, cm/sec) considered as output of the model. For some models and modeling methodologies, the data consisted of cerebral perfusion pressure (CPP, mmHg, estimated from MABP) and CBFV. The data was measured from 10 healthy normal subjects while the subjects performed Valsalva maneuver with and without the ganglion blockade by the use of trimethaphan. The main objective of this study was to examine the relative performance and limitations of the above mentioned linear modeling options and to demonstrate newer modeling methodologies for them. Also, since for linear model estimation it is required that the input be persistently exciting, the present study aimed to establish the efficacy of MABP for estimation of linear models and tested if a short data segment of 1.5 minute duration is adequate for the same, as compared to the traditional 6 minutes data.

Two ARX modeling schemes investigating up to 10th order models, and three schemes for Windkessel modeling involving the 3-element model and four of its modified versions of 4 or 5 elements, were employed in the present study. Even though the study was not restricted to lower order systems or simple Windkessel models, results indicate that lower order ARX models (1st, 2nd, and 3rd order ARX models) and the 3-element Windkessel model are adequate. Among the ARX and Windkessel methodologies, ARX modeling schemes proved more promising. The results of using CPP-CBFV data were not better than the results of using MABP-CBFV data.

It is clear that the models used for the present study had very basic mechanisms and structures, but were still able to reproduce the measured data. Also, tests involving the 1.5 minute MABP using the ARX models and results from the Monte-Carlo simulations of Windkessel models using two schemes suggest that a segment of 1.5 minute duration of MABP is effective and adequate for estimating linear models of cerebral autoregulation.