Please cite this article in press as: Kostoglou K, et al. Nonstationary multivariate modeling of cerebral autoregulation during hypercapnia. Med Eng Phys (2013), http://dx.doi.org/10.1016/j.medengphy.2013.10.011 ARTICLE IN PRESS G Model JJBE-2368; No. of Pages 9 Medical Engineering & Physics xxx (2013) xxx–xxx Contents lists available at ScienceDirect Medical Engineering & Physics jou rn al h om epage: www.elsevier.com/locate/medengphy Nonstationary multivariate modeling of cerebral autoregulation during hypercapnia Kyriaki Kostoglou a , Chantel T. Debert b , Marc J. Poulin c,d,e,f,g , Georgios D. Mitsis a,∗ a Department of Electrical and Computer Engineering, University of Cyprus, Nicosia, Cyprus b Department of Physical Medicine and Rehabilitation, Faculty of Medicine, University of Calgary, AB, Canada c Department of Physiology & Pharmacology, Faculty of Medicine, University of Calgary, AB, Canada d Department of Clinical Neurosciences, Faculty of Medicine, University of Calgary, AB, Canada e Faculty of Kinesiology, University of Calgary, AB, Canada f Hotchkiss Brain Institute, Faculty of Medicine, University of Calgary, AB, Canada g Libin Cardiovascular Institute of Alberta, Faculty of Medicine, University of Calgary, AB, Canada a r t i c l e i n f o Article history: Received 5 March 2013 Received in revised form 7 September 2013 Accepted 13 October 2013 Keywords: Cerebral hemodynamics Time varying systems CO2 reactivity Laguerre functions Recursive Least Squares Multiple forgetting factors a b s t r a c t We examined the time-varying characteristics of cerebral autoregulation and hemodynamics during a step hypercapnic stimulus by using recursively estimated multivariate (two-input) models which quan- tify the dynamic effects of mean arterial blood pressure (ABP) and end-tidal CO 2 tension (P ETCO 2 ) on middle cerebral artery blood flow velocity (CBFV). Beat-to-beat values of ABP and CBFV, as well as breath-to- breath values of P ETCO 2 during baseline and sustained euoxic hypercapnia were obtained in 8 female subjects. The multiple-input, single-output models used were based on the Laguerre expansion tech- nique, and their parameters were updated using recursive least squares with multiple forgetting factors. The results reveal the presence of nonstationarities that confirm previously reported effects of hyper- capnia on autoregulation, i.e. a decrease in the MABP phase lead, and suggest that the incorporation of P ETCO 2 as an additional model input yields less time-varying estimates of dynamic pressure autoregulation obtained from single-input (ABP–CBFV) models. © 2013 IPEM. Published by Elsevier Ltd. All rights reserved. 1. Introduction Cerebral autoregulation collectively refers to the ability of the cerebrovascular bed to maintain a relatively constant cerebral blood flow (CBF) in response to variations in several physiological variables. The most important of these variables is arterial blood pressure (ABP); therefore, the relation between ABP and CBF is typically used to characterize autoregulation. Accurate quantita- tive assessment of cerebral autoregulation and, more generally, hemodynamics, is important in the context of cerebrovascular disease diagnosis and monitoring [1,2]. Following the advance of transcranial Doppler ultrasound (TCD), which yields accurate mea- surements of CBF velocity (CBFV) [3], it is now well established that autoregulation is a dynamic, frequency-dependent phenomenon [4–6]. Dynamic autoregulation may be assessed from the CBFV response to step-like, externally induced ABP stimuli or from spontaneous physiological variability, as the latter exhibits suffi- ciently broadband characteristics. The majority of the studies that have assessed dynamic cerebral autoregulation from spontaneous ∗ Corresponding author. E-mail address: mitsis.georgios@ucy.ac.cy (G.D. Mitsis). variability have utilized univariate, linear techniques such as transfer function analysis [4]. However, in this latter study and other studies, low coherence values (<0.5) between spontaneous ABP and CBFV fluctuations in the frequency range below 0.07 Hz have been reported. Since coherence is a measure of linearity in the dynamic relation between ABP and CBFV, this suggests that nonlinearities and/or other physiological variables may have an important effect in this frequency range. In this context, it is well known that the cerebral vasculature is extremely sensitive to arte- rial CO 2 changes; for instance, spontaneous variations of end-tidal CO 2 (P ETCO 2 ) have been shown to influence CBFV as well as the BOLD fMRI signal [7,8]. Therefore, multivariate models of cerebral hemodynamics incorporating CO 2 as an additional input have been proposed in order to characterize autoregulation [7,9]. The pres- ence of nonlinearities has been also suggested [5,6], corroborating that the aforementioned low coherence between ABP and CBFV is due to both factors. In our previous studies, we have demonstrated that both dynamic nonlinearities and CO 2 variability account for a significant fraction of the low-frequency CBFV variability during resting conditions, orthostatic stress as well as ganglion blockade [7,10,11]. Collectively, these findings suggest that multi- variate and/or nonlinear modeling approaches yield more accurate quantitative descriptions of cerebral hemodynamics below 0.07 Hz. 1350-4533/$ – see front matter © 2013 IPEM. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.medengphy.2013.10.011