Testing the involvement of baroreflex during general anesthesia through Granger causality approach
Introduction
Arterial baroreflex function is an important short-term neural control system aiming at guaranteeing the homeostasis of the organism [1]. The characterization of baroreflex is based on the assessment of the baroreflex sensitivity derived as the variation of heart period, approximated as the time interval between two consecutive R peaks on the ECG (RR), per unit change of systolic arterial pressure (SAP) [2].
Usually during general anesthesia in humans baroreflex sensitivity is evaluated by administering vasoactive agents to importantly modify SAP and by observing the evoked RR changes. The application of this invasive technique allowed one to find out that arterial baroreflex is significantly attenuated during general anesthesia based on volatile anesthetics [3], [4]. The same depression of the baroreflex function was observed when intravenous anesthetics were utilized at relative high blood concentrations [5], [6].
Recently, several noninvasive techniques have been proposed for the estimation of the baroreflex sensitivity in more physiological conditions and without perturbing cardiovascular regulation. These techniques, based on the analysis of the spontaneous beat-to-beat RR and SAP variabilities [7], have been applied during general anesthesia [5], [8] but spontaneous baroreflex indexes were found inconsistent with pharmacological baroreflex gains [9]. Techniques exploiting spontaneous RR and SAP variabilities are helpful in assessing baroreflex sensitivity only when causality is along baroreflex (i.e. SAP changes contribute to RR variations) [10]. Unfortunately, this prerequisite is not properly tested. Usually, assessing the significance of squared coherence function between RR and SAP series is considered to be sufficient [11], but unfortunately coherence can be high even when RR variations contribute to SAP changes along the reverse causal direction [12] imposed by the Starling law (a longer RR induces a larger left ventricular filling and, in turn, a larger SAP at the next cardiac beat) and by the diastolic runoff (a longer RR induces a smaller diastolic pressure and, thus a smaller SAP at a given pulse pressure). Without testing causality from SAP to RR any estimate of the baroreflex sensitivity derived from spontaneous variabilities could be conversely related to the gain of the feedforward mechanical pathway linking RR to SAP [12]. We hypothesize that a lack of causality from SAP to RR could contribute to the disagreement between spontaneous and pharmacological baroreflex indexes [9].
The aim of this work is to assess the significance of the relation between RR and SAP along baroreflex during an experimental condition known to profoundly depress the baroreflex function (i.e. general anesthesia). This condition affects baroreflex function to such an extent that spontaneous SAP changes could not be sufficient to drive RR variations, thus preventing the exploitation of noninvasive techniques for the assessment of the baroreflex function. The presence of a significant causal relationship from SAP to RR was assessed using Granger causality approach [13] according to two traditional tests in the time domain (i.e. F-test and Wald test) [14], [15]. These two tests has three advantages: (i) they do not need to assume that the cardiovascular control mechanisms occur along specific temporal scales such as it needs when testing Granger causality in the frequency domain [12], [16], [17]; (ii) the percentage of false Granger causality detections can be rigorously kept under control by assigning the type I error probability accepted by the tests; and (iii) the distribution of the statistic assessing Granger causality under the null hypothesis of absence of a causal relationship between the two series follows a classical statistical distribution (i.e. the F distribution in the case of F-test and the χ2 distribution in the case of Wald test), thus allowing the analytical calculation of the critical value above which the null hypothesis is rejected.
Section snippets
Granger causality tests
A time series u={u(i), i=1,..,N} is said to Granger-cause the series y={y(i), i=1,..,N} (i.e. u⇒y), where i is the progressive sample count and N is the series length, if past values of u provide information on y above and beyond the information contained in the past values of y. More specifically, in a bivariate process u⇒y if the knowledge of a certain number of past values of y and u (and eventually even the current value of u) are more helpful to predict y than the exclusive knowledge of
Simulations
We generated processes characterized by a full or partial unpredictability to better understand whether different predictability levels played a role in producing false detections of Granger causality. WGN realizations were generated to simulate fully unpredictable processes. AR process realizations driven by WGNs were generated to simulate partially predictable processes. More specifically, we assigned the phase, φ, and the modulus, ρ, of the pair of complex and conjugated poles characterizing
Experimental protocol
Data belong to a database recorded during the NeuroMorfeo trial [19] designed to compare volatile and intravenous anesthetics for neurosurgical procedures in elective craniotomy. We make reference to [19] for more details about the inclusion criteria and anesthesiological strategies. Briefly, 37 subjects (age range from 18 to 75 years) were scheduled for craniotomy for supratentorial lesion. All subjects did not exhibit signs of intracranial hypertension, were in good physical state (ASA I-III,
Simulation results
In the case of WGN pairs the false rejection rate of the null hypothesis of absence of Granger causality relevant to the F-test and Wald test was 4%.
In the case of AR(2) type-1 simulation the false rejection rates of the F-test were 4%, 7%, 4% and 3% with Δφ equal to 0.01, 0.05, 0.15 and 0.40, respectively. The false rejection rates of the Wald test were not significantly different. In the case of AR(2) type-2 simulation the false rejection rates of the F-test were 5%, 5% and 4% with Δρ equal
Discussion
The main results of this study can be summarized as follows: (i) the two Granger causality tests had similar rates of false detections of Granger causality over short simulated signals (300 samples); (ii) the rates of false detections were independent of the complexity of the signals, the frequency of the dominant peaks and their sharpness; (iii) Granger causality from SAP to RR series was preserved during general anesthesia, thus allowing the use of techniques exploiting spontaneous
Conclusions
Since F-test and Wald test allow the simple and straight assessment of Granger causality from SAP to RR, they should be routinely utilized to assess the significance of the involvement of baroreflex in governing the RR–SAP variability interactions (i.e. SAP changes contribute to RR variations). We hypothesize that the routine application of these tests allows the rejection of data segments in which baroreflex is not significantly active as it occurs frequently in healthy humans during supine
Conflict interest statement
None declared
Acknowledgment
The Telethon Grant GGP09247 to A. Porta partially supported the study. The AIFA (Agenzia Italiana del Farmaco) Grant 2007-005279-32 fully financed the NeuroMorfeo trial.
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