INTRODUCTION

Cerebral blood flow (CBF) autoregulation refers to the physiological mechanisms that preserve CBF and brain tissue oxygenation despite changes in blood pressure (BP) [1,2]. The lower limit of autoregulation (LLA) is the mean arterial pressure (MAP) below which CBF is reduced with further MAP reduction, a phenomenon called ‘pressure passivity’. For BP measured invasively from the radial artery, the duration of MAP reductions below the LLA has been independently associated with acute kidney injury [3], and major morbidity and operative mortality after cardiac surgery [4]. Moreover, recent data demonstrate that targeting a MAP greater than the individual patient's LLA during cardiopulmonary bypass (CPB) may reduce the incidence of delirium after cardiac surgery [5]. Thus, maintaining MAP in the cerebral autoregulatory range is beneficial in patients presenting for cardiac surgery and perhaps other procedures, wherein current care is based on empirically choosing MAP targets. Importantly, the LLA was demonstrated to vary markedly between individuals over a wide range of pressures (40--90 mmHg) [6], and the sensitivity of predicting the MAP level for the LLA based on preoperative MAP showed wide confidence intervals and low specificity [6].

These observations and the lack of commercially available methods to determine the LLA noninvasively led Obata et al.[7] to investigate whether this metric could be predicted using a measure called the Ambulatory Arterial Stiffness Index (AASI) that can be determined from any type of repeated BP reading. The AASI, originally derived from 24-h ambulatory BP readings [8], has been shown to predict cardiovascular and stroke mortality, and is believed to be determined in part from the mechanical properties of the vasculature [9]. The properties of the AASI are further elucidated later on in the Discussion. Obata et al.[7] determined the AASI using intraoperative SBP and DBP measured invasively at the radial artery before initiation of the CPB, and showed that the AASI varies directly with the LLA [7]. Limitations of that study were that variables that might influence the AASI, such as peripheral vascular resistance and stroke volume, were not considered.

Given the importance of maintaining a MAP above the LLA during surgery and in critically ill patients, the main objective of the present study was expanding the previously identified predictive capacity of the LLA using intraoperatively determined AASI in the following way: finding independent characteristics from the given demographic, preoperative and intraoperative characteristics, other than AASI, which correlated with the LLA in a statistically significant way (‘single predictors’). Then, combine these predictors with AASI to generate novel composite predictors with improved performance on predicting LLA. These single predictors could provide a physiological basis for MAP targets. A second aim of this study was to evaluate predictors’ level indicating whether the MAP is above or below the LLA during cardiac surgery and try to explain the underlying physiological view.

MATERIALS AND METHODS Study population

The data of 181 patients included in this analysis were made available from a prior prospective observational study that determined the limits of cerebral autoregulation during cardiac surgery prior to CPB [4,6,7,10]. These data were previously used in the retrospective cohort study of Obata et al.[7]. The parent protocol was approved by the Johns Hopkins Medicine Institutional Review Board (IRB00070516). Written informed consent was obtained from all participants. Eligibility criteria for the present analysis included the availability of an LLA measure, good quality intraoperative BP data, over five BP readings with pulse pressure (PP), defined as SBP minus DBP, greater than 15 mmHg, DBP-SBP correlation coefficient (Rds) within the range of 0.4 to 1, and availability of the preoperative characteristics of age, sex, BMI, status of diabetes mellitus, and mean SBP, DBP and heart rate. All patients received routine intraoperative care [7].

Measurements Blood pressure and related measures

Arterial pressure signal obtained directly and continuously from the radial artery over the time extending from the insertion of the arterial line until the initiation of CPB (‘intraoperative’). The pressure signal was analysed to obtain BP readings (SBP and DBP) from each of the pulse waveforms that were stored in the electronic medical record. A single BP reading was extracted from this record every 1 min (whichever is the current on) that referred as ‘BP measurement’. The median duration of the intraoperative phase was 140 min with interquartile range of 114–168 min [7], which also represents the number of BP measurements (1 reading/minute). In addition, all set of vital signs was taking in the preoperative holding area prior to the receiving any medications.

From the BP readings taken before the initiation of the CPB during the intraoperative phase, we calculated the average intraoperative SBP, DBP, MAP (equals DBP+PP/3), and PP, referred to hereafter as ‘BP measures’. Note that BP readings with a PP 15 mmHg or less were excluded in order to exclude artifacts from the arterial blood sampling. The term ‘BP-related measures’ refers to variables calculated from the BP measures, including BP variability (standard deviations [SD] of SBP, DBP, MAP and PP), SBP coefficient of variation (SBP_cv), defined as SD(SBP)/(average SBP) and similarly DBP_cv, MAP_cv and PP_cv. The AASI was defined as 1 minus the DBP-on-SBP slope obtained using standard regression that applied to the BP readings [8]. We replaced AASI by 1-AASI for preferring LLA predictors reported in this study to correlate positively with the LLA.

Determination of the lower limit of cerebral autoregulation

The LLA was determined as previously described [3,6,11,12]. Briefly, during the whole intraoperative phase, CBF velocity was monitored at the bilateral middle cerebral arteries by transcranial Doppler (TCD) ultrasonography via two 2.5-MHz transducers fitted on a headband, simultaneously with the radial BP continuous readings before CPB. MAP data and TCD signals were digitized at 60 Hz and then integrated over time as nonoverlapping 10-s mean values, and resampled at 0.1 Hz. This eliminated high-frequency noise originated from the respiratory and pulse frequencies, while allowing for the detection of oscillations occurring below 0.05 Hz. The signals were further high-pass filtered with a cutoff of 0.003 Hz to remove slow drifts. Thus, limiting analysis to the frequency of slow vasogenic waves (0.05 to 0.003 Hz), which are relevant to autoregulation. A continuous, moving Pearson correlation coefficient for the relationship between MAP and CBF velocity (‘mean velocity index’, Mx) was calculated during the intraoperative phase. Each Mx value was determined using consecutive, paired, 10-s averaged values of MAP and CBF velocity from 300 s duration, thus incorporating 30 data points for each index, where MAP data were placed in 5 mmHg bins. The LLA was defined as the MAP at which Mx increases from less than 0.4 to at least 0.4, or as the lowest observed MAP in case Mx was not less than 0.4. Mx less than 0.4 and Mx at least 0.4 characterize, respectively, cerebral autoregulation and pressure passivity [7]. The LLA determination was feasible due to MAP variation during the procedure.

Statistical analysis

Sample size of convenience was taken from the prior referenced study [7]. Univariate analysis was applied to each demographic, preoperative and intraoperative characteristic, where the LLA was taken as the dependent variable. Results identify single characteristics that were associated with the LLA in a statistically significant way.

Explaining the LLA by multiple characteristics using multivariate linear regression analysis necessitated limiting the analysis to a subset of all characteristics shown hereafter to be independent variables (‘the full model’), where LLA was taken as the dependent variable. The variables independency was required for minimizing potential collinearity, and implemented by calculating Pearson correlation coefficient r between all possible pairs of the continuous characteristics, keeping only characteristics for which |r|<0.45 when paired with any other characteristic. Handling this elimination process for a group of characteristics, in which each member was correlated by |r|≥0.45 with at least one other group member, for example SBP, DBP, MAP and PP, is described in the Supplemental Results, https://links.lww.com/HJH/C280.

Identification of independent characteristics that may explain the LLA in a statistically significant way (‘single predictors’) was achieved by applying to the full model of independent characteristics a multivariate linear regression procedure using a backward elimination technique with a enter/remove P value of 0.05. The group of independent characteristics from the full model, not identified as single predictors by this procedure, were used for adjustment (‘adjustors group’) when calculating hazard ratios.

In accordance with the study objective, we generated new predictors, which were expected to be superior to single predictors in explaining LLA. This was done by generating new variables, each representing a different combination of all the single predictors, called hereafter ‘composite predictors’. In this study, we defined and evaluated two such predictors: an additive LLA predictor X (‘COMP_sum’) defined by the outcome of the multivariate linear regression with the backward elimination, being LLA = α+β·X, where X is a weighted sum of all the single predictors X1, X2, X3…, and a multiplicative LLA predictor (‘COMP_mult’) generated by multiplying all the single predictors, for example X1·X2·X3·…

Logistic regression was applied for determining the odds ratio (OR) of a binary outcome equals 1 for MAP<LLA and 0 for MAP≥LLA, as associated with a ‘binary risk’ defined using the median level of a single or composite LLA predictors (‘Median’), equals 1 and 0 for Predictor<Median and Predictor≥Median, respectively. With these definitions, we assume that the LLA and any of its tested predictors are negatively correlated. The ORs of the single or and composite predictors was reported both unadjusted, and adjusted to the adjustors group, thus establishing a sensitivity test for the effect of the adjustment. We also calculated the area under the receiver operating characteristic (ROC) curve (AUC) that measures the ability of a classifier to distinguish between a MAP<LLA and a MAP≥LLA using the predictors.

All analyses were performed using SYSTAT 12 (SYSTAT Software Inc., San Jose, California, USA). Statistical significance was a two-sided P value of less than 0.05.

RESULTS Patients’ characteristics

Table 1 summarizes demographic, preoperative and intraoperative characteristics of the 181 enrolled patients. The LLA range was 35–95 mmHg, where 17, 43 and 40% of patients had the LLA ranges of less than 55, 55–65 and more than 75 mmHg, respectively. Table 1 also summarizes that the only listed characteristics () identified by the univariate analysis to associate with the LLA, not including the composite variables, were BMI, 1-AASI, SBP_cv, MAP_cv (P < 0.001 for all), DBP_cv (P = 0.003) and PP_cv (P = 0.012). It is noteworthy that SBP, DBP, MAP and PP were significantly lower in the intraoperative phase than in the preoperative phase (P < 0.001 for all).

TABLE 1 - Demographics and perioperative characteristics and the parameter β and its P value characterizing their relationship with the lower limit of cerebral autoregulation obtained using univariate analysis Variable Results (n = 181) β Mean [95%CI] P Demographic and preoperative data  Age (years) 71 ± 8 [58,84] −0.04 [−0.28,0.21] 0.75  Male, n (%) 123 (68.1) 0.14 [−4.1,4.4] 0.95  Pre-SBP (mmHg) 137 ± 20 [106, 175] −0.03 [−0.07,0.13] 0.55  Pre-DBP (mmHg) 72 ± 11 [54,90] 0.09 [−0.08,0.27] 0.28  Pre-MAP (mmHg) 94 ± 13 [74,116] 0.07 [−0.08,0.23] 0.35  Pre-PP (mmHg) 65 ± 16 [41, 98] −0.00 [−0.12,0.12] 1.00  Pre-HR (bpm) 65 ± 15 [49, 87] −0.06 [−0.19,0.08] 0.40  BMI a (kg/m2) 29.6 ± 6.1 [21.4, 40.7] −0.59 [−0.90,−0.27] <0.001  Diabetes mellitus, n (%) 86 (47.5) −0.08 [−4.0,3.9] 0.97 Intraoperative data (prebypass mean)  SBP (mmHg) 117 ± 11 [101,135] −0.06 [−0.12,0.33] 0.52  DBP (mmHg) 57 ± 8 [46, 74] −0.16 [−0.40,0.09] 0.21  MAP (mmHg) 77 ± 8 [65, 92] −0.07 [−0.32,0.18] 0.59  PP (mmHg) 60 ± 11 [46, 79] 0.15 [−0.03,0.34] 0.10  HR (bpm) 73 ± 19 [48, 100] −0.06 [−0.19,0.08] 0.40  LLA (mmHg) 64.3 ± 13.0 [43, 85] LLA predictors derived from the intraoperative BP measurements  1-AASI a 0.43 ± 0.11 [0.25, 0.62] −31.2 [−48,−14] <0.001  SBP_cv a 0.17 ± 0.04 [0.11, 0.24] −84.9 [−131,−38] <0.001  DBP_cv 0.18 ± 0.07 [0.11, 0.28] −40.1 [−68,−14] 0.003  MAP_cv 0.15 ± 0.04 [0.10, 0.22] −87.3 [−132,−43] <0.001  PP_cv 0.21 ± 0.06 [0.12, 0.31] −42.8 [−76,−9.4] 0.012  COMP_mult (kg/m2) 2.1 ± 1.0 [0.95, 3.9] −5.6 [−7.4,−3.8] <0.001  COMP_sum (kg/m2) 77.8 ± 11.1 [62.0, 97.9] −0.52 [−0.68,−0.36] <0.001

Results are expressed as mean ± SD [5th to 95th percentiles] or as n (%). Univariate analysis of the characteristics, taking the LLA as the dependent provides and a characteristic as the independent variable provided the β coefficient, that is the estimated rate of the LLA change per 1 unit of the variable, and its P value. AASI, the Ambulatory Arterial Stiffness Index defined by 1 minus DBP-on-SBP regression slope obtained by applying standard regression to the repeated BP readings; COMP_mult, a composite multiplicative predictor of the LLA equals BMI (1-AASI) SBP_cv; COMP_sum, a composite additive predictor of the LLA expressed by BMI+51.7 (1-AASI)+156·SBP_cv HR, heart rate; LLA, the lower limit of cerebral autoregulation; MAP, mean arterial pressure; PP, pulse pressure; Pre; refers to Preoperative; SBP_cv, SBP coefficient of variation equals SD(SBP)/(average SBP) and similarly defined DBP_cv, MAP_cv and PP_cv; .

Single and composite predictors of the lower limit of cerebral autoregulation

Starting with Table 1, the independent characteristics identified using the procedures described in Materials and methods and Supplemental Results, https://links.lww.com/HJH/C280, that is the full model, were age, sex, diabetes mellitus, BMI, preoperative DBP, preoperative PP and intraoperative MAP, PP, heart rate, 1-AASI and SBP_cv. The continuous, independent and statistically significant predictors of the LLA, that is single predictors, identified by applying to the full model multivariate linear regression with the backward elimination were BMI, 1-AASI and SBP_cv. The rest of the independent characteristics in the full model (‘adjustors group’) are given in the legend of Table 2. The outcome of this procedure was a linear relationship between LLA and a weighted sum of these single predictors given by LLA = Constant-a·BMI-b·(1-AASI)-c·SBP_cv (P < 0.001), where mean [95% CI] (P value) of Constant, a, b and c were, respectively, 104.7 [92,117] mmHg (P < 0.001), 0.52 [0.22, 0.8] mmHg/kg per m2 (P < 0.001), 26.9 [11,43] mmHg (P = 0.001) and 81.3 [38,125] mmHg (P < 0.001). This relationship can be re-written in the ‘univariate form’ LLA = 104.7–0.52·COMP_sum, where COMP_sum = BMI+(b/a)·(1-AASI)+(c/a)·SBP_cv = BMI+51.7·(1-AASI)+156·SBP_cv. Following Methods, the composite multiplicative LLA predictor was defined as COMP_mult = BMI·(1-AASI)·SBP_cv.

TABLE 2 - Odds ratio for the dichotomized predictors by median (‘exposure’) and the mean arterial pressure minus lower limit of cerebral autoregulation dichotomized with reference to zero (‘outcome’) Predictor Median Unadjusted OR
Mean[5%-95%](P-value) AUC Adjusted OR
Mean[5%-95%](P-value) AUC BMI (kg/m2) 28.9 3.49 [1.65,7.34](0.001) 0.649 3.54 [1.57,8.01](0.02) 0.698 1-AASI 0.42 2.14 [1.05,4.34](0.035) 0.594 2.17 [1.01,4.7](0.048) 0.649 SBP_cv 0.16 2.59 [1.27,5.30](0.009) 0.616 3.05 [1.39, 6.69](0.005) 0.686 COMP_mult (kg/m2) 1.95 6.11 [2.64,14.2](0.00003) 0.700 6.33 [2.65, 15.1](0.00003) 0.747 COMP_sum (kg/m2) 76.2 6.30 [2.72,14.6](0.00002) 0.703 6.13 [2.70,15.6](0.00003) 0.748 Data are unadjusted and adjusted odds ratios calculated using logistic regression with dichotomized outcome equals 1 for MAPth to 95th percentiles] (P-value). AUC, the area under receiver operating characteristic (ROC) Curve (see Fig. 3); MAP, intraoperative mean arterial pressure. The adjustors group included age, sex, diabetes mellitus, preoperative DBP and pulse pressure, and intraoperative PP and heart rate (see Supplemental Results, https://links.lww.com/HJH/C280).

Table 3 reports for both the single and the composite LLA predictors, the parameters α & β determined using the regression model LLA = α + β[Predictor], and additional aspects of this relationship and predictors properties not mentioned in Table 1. The table shows that the correlation with the LLA of the independent predictor variables was similar (|r| = 0.26--0.27), but much weaker than that of the composite LLA predictors COMP_sum and COMP_mult (r = −0.41 and −0.43, respectively). Table 3 also reports the median level of these predictors, and the correspondingly estimated LLA ranging between 64.4 and 65.4 mmHg, which contained the observed LLA median of 65 mmHg.

TABLE 3 - Properties of the single and composite predictors of the lower limit of cerebral autoregulation and parameters obtained using the univariate regression model lower limit of cerebral autoregulation = α+β·[Predictor] Predictor r α (mmHg) β a Predictor median Estimated LLA by median Predictor threshold BMI (kg/m2) -0.27 81.5 [72,91]∗∗ −0.59 [−0.90,−0.27]∗∗ 28.9 64.4 37.3 1-AASI -0.26 77.5 [70,85]∗∗ -31.2 [−48,−14]∗∗ 0.42 64.4 0.59 SBP_cv -0.26 78.4 [70,86]∗∗ −84.9 [−131,−38]∗∗ 0.16 64.8 0.24 COMP_mult (kg/m2) -0.41 76.1 [72,80]∗∗ −5.6 [−7.4,−3.8]∗∗ 1.95 65.2 2.75 COMP_sum (kg/m2) -0.43 105 [92,117]∗∗ −0.52 [−0.68,−0.36]∗∗ 76.2 65.4 84 Data are the Pearson correlation coefficient (r) between LLA and a predictor, α and β are mean [95% Confidence Interval], where the stars mark the P-value: The single LLA predictors BMI, 1-AASI, and SBP_cv (defined Table 1legend) were identified as the independent continuous characteristics that predicted the LLA with statistical significance. COMP_sum and COMP_mult are, respectively, the additive- and multiplicative LLA predictors defined in the text as COMP_sum = BMI+51.7 (1-AASI)+156·SBP_cv and COMP_mult = BMI·(1-AASI)·SBP_cv. a The units for β are mmHg-m2/kg for BMI, COMP_mult and COMP_sum and mmHg for the other predictors. The Predictor Threshold is the highest value of the predictor for which MAP Fig. 3). ∗P∗∗P

Figure 1 shows plots of the LLA dependence on the predictors BMI, 1-AASI and COMP_sum, defined in Table 1. The plots of the LLA versus SBP_cv and versus COMP_mult (not shown) appear similar to that of the LLA versus 1-AASI and versus COMP_sum, respectively. It is noteworthy that the two outliers in (B) and (C) marked by arrows belong to morbidly obese patients (#258 and #286 with BMI 49 and 55 kg/m2, respectively).

FIGURE 1: Plots of the lower limit of cerebral autoregulation versus three predictors defined in Table 1 using intraoperative data of individual patients collected prior to the cardiopulmonary bypass (n = 181). The parameters of the regression lines (dashed) are given in Table 3. The arrows in B and C point to deviant data of two morbidly obese patients. The Pearson correlation coefficient r is marked.

Table 4 reports the quality of estimating the LLA by its single and composite predictors using the regression coefficients given in Table 3. For all predictors, the absolute deviation of the estimated LLA from the observed LLA was smaller than 10 mmHg in 50--58% of the patients for all predictors, and greater than 15 mmHg in 24--27 and 18--20% of the patients using the single and composite LLA predictors, respectively.

TABLE 4 - The number (percentage) of patients for whom the deviation of the lower limit of cerebral autoregulation estimated from the univariate analysis of the various predictors (Table 2) from the observed lower limit of cerebral autoregulation level was found in a given range Predictor n (%) for [LLA (estimated) – LLA(observed)] range Range (mmHg) → <−15 <−10 −10 ≤ to <10 ≥10 ≥15 BMI 24 (13.3%) 46 (25.4%) 99 (54.7%) 36 (19.9%) 24 (13.3%) 1-AASI 24 (13.3%) 47 (26.0%) 91 (50.3%) 43 (23.8%) 27 (14.9%) SBP_cv 24 (13.3%) 46 (25.4%) 99 (54.7%) 36 (19.9%) 24 (13.3%) COMP_mult 18 (9.9%) 43 (23.8%) 100 (55.2%) 38 (21.0%) 19 (10.5%) COMP_sum 17 (9.4%) 37 (20.4%) 105 (58.0%) 39 (21.5%) 20 (11.0%)

Supplemental Table 1, https://links.lww.com/HJH/C280 shows that the LLA, 1-AASI and SBP_cv (and also DBP_cv, MAP_cv and PP_cv) were correlated significantly (r > 0.15, P < 0.05) with at least three of the four BP variability measures SD(SBP), SD(DBP), SD(MAP) and SD(PP), where each variability measure highly correlated with at least two other BP variability measures by r > 0.6 (P < 0.00001). Therefore, the LLA correlated in a statistically significant way with the BP variability measures SD(SBP), SD(DBP), SD(MAP), but neither with SD(PP) nor with BP itself (|r|≤0.12, P > 0.05). BMI was not correlated with any of the BP variability measures (|r| < 0.05), but correlated with DBP, which was marginally significant (r = 0.16, P < 0.05).

Implications of mean arterial pressure-to-lower limit of cerebral autoregulation difference as outcome

Next, we identified additional indicators to determine whether MAP is lower or higher than the LLA. Figure 2 shows that there was no case, in which MAP was lower than the LLA for either MAP more than 87 mmHg or LLA less than 65 mmHg. MAP < LLA was detected in 42 patients. For LLA <65 mmHg, there were 87 patients with positive MAP-LLA only (4–53 mmHg), and for MAP > 87 mmHg, 16 patients with positive MAP-LLA only (9–53 mmHg). Eight patients displayed both LLA < 65 and MAP > 87 mmHg, leaving 95 patients displaying LLA < 65 or MAP > 87 mmHg.

FIGURE 2:

The mean arterial pressure-to- lower limit of cerebral autoregulation difference plotted versus MAP (a) and the LLA given in 5 mmHg bins (b) for the individual patients (n = 181). The MAP<LLA region is darkened. The dashed line in (b) connects the points of the low fifth percentile of the MAP-LLA distribution calculated for each LLA value.

Figure 3 (a--c) depicts MAP-to-LLA difference versus the LLA predictors 1-AASI, BMI and COMP_sum, respectively. The plots for SBP_cv and COMP_mult (not shown) resemble the plots (a) and (c) for 1-AASI and COMP_sum, respectively. There were 42 patients (23%) at risk for having a MAP<LLA. A domain of special interest included patients for whom predictors exceeded ‘Threshold’ levels, above which MAP≥LLA (values given in Table 3). This domain was most populated when using the composite predictors (details for all predictors are found in the Fig. 3 legend).

FIGURE 3: The MAP-to-LLA difference plotted versus the LLA predictors 1-AASI (a), BMI (b) and COMP_sum (c) for the individual patients (n = 181), and the corresponding ROC (receiver operating characteristic) curves (d)--(f) generated using logistic regression. In (a)--(c), the MAPTable 3. The data of the remaining 139 patients, for whom MAP≥LLA, are distributed between the predictor values Table 3, as follows: 132 and 7 for SBP_cv; 128 and 11 for 1-AASI, 123 and 16 for BMI, 102 and 37 for COMP_mult, and 92 and 47 for COMP_sum, respectively. Panels (d)--(f) that correspond to (a)--c), respectively, represent some results of logistic regression applied to MAP-to-LLA difference (DIF). The odds ratio (OR) for the DIF sign (Outcome = 1 for DIF≤0) and predictor-minus-median sign (Exposure = 1 for Predictor ≤ Median) were either adjusted (ROC curves solid line) or unadjusted (dashed line). The axes of the ROC curves were ‘sensitivity’ and ‘1-specificity’ representing, respectively, the ‘true positive’ and the ‘false positive’ rate of diagnosing MAPTable 2. Adjustment included the following adjustors: age, sex, diabetes mellitus, preoperative DBP and pulse pressure, and intraoperative PP and heart rate (see Supplemental Results, https://links.lww.com/HJH/C280).

Table 2 reports the unadjusted and adjusted OR quantifying the association between ‘Exposure’ and the ‘Outcome’ calculated using logistic regression. Outcome was defined as the MAP-to-LLA difference (=1 for MAP<LLA and = 0 for MAP≥LLA), and Exposure was the difference between the predictor median and the predictor level (=1 for Predictor<Median and = 0 for Predictor≥Median. All predictors displayed statistically significant ORs, but the ORs for the composite variables were similar and higher than the ORs for the predictor variables BMI, 1-AASI and SBP_cv (about 6.3–6.5 versus 2.2–3.5, respectively). Adjustment slightly increased the ORs, but none of the adjustors (listed in the table legend) had a statistically significant OR. Figure 3 (d--f) shows the ROC curves, corresponding to the (a)-(c) panels, obtained from the logistic regression and used for the OR determination (unadjusted and adjusted) reported in Table 2. The area under the continuous ROC curve (AUC), which quantifies how accurately one can discriminate between a MAP<LLA and MAP≥LLA (see values in Table 2), reached 0.70–0.75 for the composite predictors (for both adjusted and unadjusted values), where the range of 0.7–0.8 is considered acceptable [13]. The AUC for the single predictors was lower.

DISCUSSION

This study expanded the previously reported association between the LLA of CBF and the vascular measure arterial ambulatory stiffness index AASI [7] as follows: BMI and SBP coefficient of variation (SBP_cv) displayed a positive and significant association with the LLA independently to that of 1-AASI. The association became much stronger when combining these three predictor variables into multiplicative and additive composite LLA predictors COMP_mult, and COMP_sum, respectively (Table 3 and Fig. 1). The LLA, 1-AASI and SBP_cv (but not BMI) were associated with measures of BP variability (Supplemental Table 1, https://links.lww.com/HJH/C280). The composite predictors displayed better quality of the LLA estimation than each of the predictor variables (Table 4). It is understandable that additional composite predictors could be defined and tested in the same way. In that respect, the present study demonstrated the feasibility of this approach.

The risk of losing CBF autoregulation that occurs when MAP is lower than the LLA was found in 42 (23%) of the 181 patients, while 95 (52%) of the patients, who satisfied the preferred lower-risk condition MAP≥LLA displayed either MAP at least 87 mmHg or LLA less than 65 mmHg (Fig. 2). High MAP beyond the CBF autoregulation range may result in hyperperfusion [19]. This is usually not an issue during the present procedure, in which the main focus of BP management is on avoiding hypotension. As the LLA is not routinely measured during cardiac surgery, getting more indications to whether MAP<LLA or MAP≥LLA by using the LLA predictors is clinically significant. Figure 3 shows that each of the LLA predictors had a threshold level above which MAP<LLA did not occur. The number of patients with lower risk, detected in this way, was two to four-fold greater when using the composite predictors, compared with using the single predictor (Fig. 3 legend). The OR showed a statistically significant association between the sign of MAP minus LLA (‘Outcome’) and the sign of the difference between a predictor and its median (‘Exposure’), as detailed in Table 2, wherein much stronger association was found for the composite predictors than for the predictor variables. Our findings may enable improved LLA estimation from routine perioperative data of an individual prior to the CPB (Table 4), albeit requiring more sophisticated data analysis and processing. The new predictors, especially the composite ones, may assist in modifying the perioperative management strategies aiming to maintain the cerebral autoregulation during CPB by keeping MAP greater than LLA.

Why is the lower limit of cerebral autoregulation associated with blood pressure variability?

Cerebral autoregulation is effective for MAP≥LLA but ≤ the upper limit of autoregulation. This process involves cerebral arterioles that minimize changes in CBF, in response to MAP changes, by actively changing tension developed by the vascular smooth muscles in the arteriolar walls, and thus the vessels lumen [14]. A reduction in the arterial pressure below the critical closing pressure of these arterioles leads to CBF reduction manifesting pressure passivity [15]. The CBF-pressure relationship also has a dynamic aspect: It can take about 10 s for a vascular smooth muscle to change its tension in response to BP change to ensure steady CBF [16]. Thus, cerebral autoregulation is effective for very slow BP fluctuations at the range of 0.02–0.07 Hz, that is about 50 to 14 s to complete one oscillation [14]. In fact, the main spectral power of both arterial pressure and CBF falls in this frequency range [17,18]. In contrast, faster BP changes, such as those generated by cardiac and/or respiratory activity, during postural changes, coughing or physical activity become temporally coherent with CBF to a point where CBF becomes directly related to BP changes [1,16,18]. This frequency-dependent relationship between oscillations in arterial pressure and CBF referred to as dynamic autoregulation [19] resembles a high-pass filter, wherein higher-frequency BP oscillations are more linearly transferred to the cerebral circulation than the lower frequency ones [20].

Consistent with the above description, we do believe that there is a room for speculating that LLA level may be affected by slow MAP oscillations, as follows: if average MAP is slightly below LLA, then it is expected that a large-enough amplitude of oscillation in the arterial pressure would cause MAP to exceed the LLA during part of the oscillation period and become higher than the LLA. Therefore, the CBF-pressure relationship would oscillate between pressure-passive (MAP<LLA) to autoregulation (MAP≥LLA). In this case, more time would be spent at a MAP≥LLA for larger amplitude pressure oscillation (for the same mean MAP). Therefore, the LLA practically marks the MAP value, at which the CBF-pressure relationship undergoes a transition between autoregulation and pressure passivity. Thus, it is likely that if the MAP is close to, but lower than the LLA, inducing or increasing BP oscillations would shift the LLA to lower values following the LLA definition (see Materials and methods). As BP variability is a measure for the mean amplitude of the pressure oscillation, we may conclude that the LLA is associated with SD(MAP), as observed (Supplemental Table 1, https://links.lww.com/HJH/C280). The occurrence of MAP oscillations that cross LLA is supported by the finding that in our study, 29 (16%) of the patients had an average MAP<LLA and (MAP+SD)>LLA, and 44 (24%) had an average MAP>LLA and (MAP-SD)<LLA. Modification of the CBF-MAP relationship by an oscillatory lower body negative pressure was demonstrated by Tan et al.[14].

Explaining the association of lower limit of cerebral autoregulation with its predictors

Our finding that the LLA is associated with BP variability may explain its association with predictors, in which BP variability is part of their definition. This includes SBP_cv defined by