Nonlinear, multiple-input modeling of cerebral autoregulation using Volterra Kernel estimation

Autoregulation refers to the automatic adjustment of blood flow to supply the required oxygen and glucose and remove waste, in proportion to the tissue´s requirement at any instant of time. For the brain, cerebral autoregulation is an active process by which cerebral blood flow is controlled at an approximately steady level despite changes in the arterial blood pressure. Robust assessment of the cerebral autoregulation by a model that characterizes this system has been the goal of many studies, searching for techniques that can be used in clinical scenarios to detect potentially dangerous impairment of control. Multiple input, single output (MISO) models can be used to assess autoregulation, and system parameters can be estimated from spontaneous beat-to-beat variations in arterial blood pressure (ABP) and breath-by-breath end-tidal carbon dioxide (P_ETCO2) as inputs, and cerebral blood flow velocity (CBFV) as the output. In this study a non-linear, multivariate approach, based on Volterra-type kernel estimation models is employed. The results are compared with linear models as well as nonlinear single-input single-output (SISO) models. The normalized mean squared error was used as the criteria of performance of each model in assessing cerebral autoregulation. Our simulation results indicate that for relatively short signals (around 300 sec), nonlinear, multiple-input models based on Volterra systems performed best, though the benefit varied considerably between subjects. When using a fixed model for all recordings, a linear SISO model with ABP as input provided the smallest average modeling error.