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

Abstract

Abstract-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, multipleinput 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.

Cerebrovascular Dynamics During Continuous Motor Task

“…We suggest that ETCO 2 at rest reflects blood partial CO 2 content, a relationship that might be less close and more variable while exercising (Brys et al 2003, JØrgensen et al 1992, Ogoh et al 2007, Robbins et al 1990). This could be relevant to explain the transfer function result differences between the two cycling studies and our investigation because CO 2 reacts slowly and amounts for a considerable fraction of CBFV variations, and hence spectral density, in the LF and VLF range (Kouchakpour et al 2010, Mitsis et al 2006, Panerai et al 2012, Panerai et al 2012a).…”

“…However, in terms phase, gain or impulse response as measure of comparison such models did not exhibit large differences from linear differential equations models (Kouchakpour et al 2014, Marmarelis et al 2014, Meel-van den Abeelen et al 2014, Panerai 1999a, Smirl et al 2015, Panerai et al 2001. Regarding non-stationarity present in the data, recordings over time periods of several minutes can average out non-stationary effects with the result that time-variant models and time-invariant models produce close results (Kouchakpour et al 2010, Marmarelis et al 2014, Nikolic et al 2015, Placek et al 2017.…”

“…When performing cognitive, motor or other tasks the blood supply to the activated brain areas is then further modulated regionally via vasoconstriction and dilation which are based on the metabolic demands. CA is assessable by: a) static methods which are characterized by measuring cerebral blood flow or its velocity [CBF(V)] under stable conditions before and after a vasodilatory/vasoconstrictory stimulus (Leenders et al 1999, Paulson et al 2010, Powers 1991, and b) by dynamic methods which analyze the interaction between CBF(V) and BP at spontaneous or induced slow oscillations present in CBF(V) and BP (Claassen et al 2016, Meel-van den Abeelen et al 2014, Müller and Österreich 2014, Zhang et al 1998. When CA fails an additional metabolic mechanism helps to keep oxygen concentration in the needed range by increasing the oxygen extraction rate as increasing the amount of the oxygen concentration released from hemoglobin (Leenders et al 1999).…”

“…CA is assessable by: a) static methods which are characterized by measuring cerebral blood flow or its velocity [CBF(V)] under stable conditions before and after a vasodilatory/vasoconstrictory stimulus (Leenders et al 1999, Paulson et al 2010, Powers 1991, and b) by dynamic methods which analyze the interaction between CBF(V) and BP at spontaneous or induced slow oscillations present in CBF(V) and BP (Claassen et al 2016, Meel-van den Abeelen et al 2014, Müller and Österreich 2014, Zhang et al 1998. When CA fails an additional metabolic mechanism helps to keep oxygen concentration in the needed range by increasing the oxygen extraction rate as increasing the amount of the oxygen concentration released from hemoglobin (Leenders et al 1999). In pathological conditions such as acute stroke the coordinated overlapping of these mechanisms seems to be disturbed (Caldas et al 2018, Maggio et al 2013, Reinhard et al 2012, Rivera-Lara et al 2017) which might be relevant for an early start of rehabilitation (Coleman et al 2017, Li et al 2018, Chi et al 2018.…”

A comparison of dynamic cerebral autoregulation across changes in cerebral blood flow velocity for 200 s

“…One suggestion of the origin of noise might be that the actual values of the phase, gain, and CVR are the sum of inverse and contradictory responses to changes in BP and EtCO 2 , and that these changes may differ between vessel types. Whether nonlinear, non-stationary, and/or time-varying approaches can help to overcome these difficulties is a question for future studies (Panerai et al, 1999b; Zhang et al, 2000; Giller and Müller, 2003; Serrador et al, 2005; Mitsis et al, 2006; Czosnyka et al, 2008; Hu et al, 2008; Dineen et al, 2010; Kouchakpour et al, 2010; Marmarelis et al, 2013; Kostoglou et al, 2014; Panerai, 2014). …”