Intraoperative short-term blood pressure variability and postoperative acute kidney injury: a single-center retrospective cohort study using sample entropy analysis

Abstract

Background

To investigate if intraoperative very short-term variability in blood pressure measured by sample entropy improves discrimination of postoperative acute kidney injury after noncardiac surgery.

Methods

Adult surgical patients undergoing general, thoracic, urological, or gynecological surgery between August 2016 to June 2017 at Seoul National University Hospital were included. The primary outcome was acute kidney injury stage 1, defined by the Kidney Disease: Improving Global Outcomes guidelines. Exploratory and explanatory variables included sample entropy of the mean arterial pressure and standard demographic, surgical, anesthesia and hypotension over time indices known to be associated with acute kidney injury respectively. Random forest classification and L1 logistic regression were used to assess four models for discriminating acute kidney injury: (1) Standard risk factors which included demographic, anesthetic, and surgical variables (2) Standard risk factors and cumulative hypotension over time (3) Standard risk factors and sample entropy (4) Standard risk factors, cumulative hypotension over time and sample entropy.

Results

Two hundred and thirteen (7.4%) cases developed postoperative acute kidney injury. The median and interquartile range for sample entropy of mean arterial pressure was 0.34 and [0.26, 0.42] respectively. C-statistics were identical between the random forest and L1 logistic regression models. Results demonstrated no improvement in discrimination of postoperative acute kidney injury with the addition of the sample entropy of mean arterial pressure: Standard risk factors: 0.81 [0.76, 0.85], Standard risk factors and hypotension over time indices: 0.80 [0.75, 0.85], Standard risk factors and sample entropy of mean arterial pressure: 0.81 [0.76, 0.85] and Standard risk factors, sample entropy of mean arterial pressure and hypotension over time indices: 0.81 [0.76, 0.86].

Conclusion

Assessment of very short-term blood pressure variability does not improve the discrimination of postoperative acute kidney injury in patients undergoing non-cardiac surgery in this sample.

Introduction

Acute kidney injury (AKI) occurs in approximately 9% of cases after surgery and is more common in patients with multiple comorbidities undergoing high-risk surgery [1]. AKI is associated with both short and long-term complications including longer hospital length of stay and increased mortality, up to 10 years after the index surgery [2, 3]. The cause of perioperative AKI is multifactorial including both patient and procedural-specific factors [4, 5]. Identifying patients at higher risk of postoperative AKI can facilitate early risk stratification and appropriate evidence-based interventions.

Mean arterial pressure (MAP) below threshold values (e.g., < 60–65 mmHg) for prolonged periods of time, is a common and well-described pathway for AKI by causing reduced blood flow and oxygen delivery to the kidney [1, 6, 7]. However, recent studies have suggested that MAP below 60–65 mmHg is not associated with a higher rate of postoperative AKI [8, 9]. Current ‘MAP below blood pressure threshold over time’ approaches also exclude informative features such as patterns of blood pressure changes over time and waveform beat-to-beat features from the arterial pressure tracing. An alternate, novel approach to ‘MAP below blood pressure threshold over time’ analysis is evaluating the impact of blood pressure variability (BPV) on postoperative outcomes. BPV describes the dynamic and continuous change of blood pressure over defined epochs of time. BPV can be classified into very short-term (seconds to minutes), short-term (over 24 h) or medium-term variability (between days).

Very short-term BPV represents a plausible mechanistic pathway for AKI, owing to the rapid fluctuations in blood pressure occurring within exceedingly brief intervals of time, overwhelming the myogenic and tubuloglomerular feedback control mechanisms. During such intervals, the kidney may encounter challenges in autoregulation, impeding the maintenance of a consistent blood flow and potentially increasing the risk of AKI [10, 11]. Park et al. demonstrated that increased BPV intraoperatively, measured using standard deviation, coefficient of variation, variation independent of mean, and average real variability of MAP, increased the risk of postoperative AKI by 7–13% [12].

Principle indices of short and long term BPV typically include measures of sequence or dispersion of MAP. An alternate index used to quantify very short-term BPV within the context of time series data is sample entropy (SampEn). SampEn serves as a robust indicator of the degree of disorder or 'surprisability' inherent in a system and provides meaningful information on very short-term BPV [13, 14]. SampEn of heart rate variability has previously been shown to predict the risk of neonatal sepsis [15].

In this study, we investigate if intraoperative SampEn of MAP, a measure of very short-term BPV, improves discrimination for postoperative AKI after non-cardiac surgery. Our null hypothesis was that SampEn of MAP would not improve discrimination for developing AKI stage 1, compared to standard demographic, surgical and anesthetic risk factors.

Methods

Study design

This is a retrospective, observational study which follows the STROBE-RECORD reporting guidelines.

Ethics statement

The acquisition and free disclosure of the data used in this study was approved by the Institutional Review Board of Seoul National University Hospital, Seoul, South Korea (H-1408–101-605). The need for consent to participate was waived by the Institutional Ethics Committee of Seoul National University Hospital, Seoul, South Korea, due to anonymity of the data.

The data collection was also registered at clinicaltrials.gov (NCT02914444) on 30 August 2016. Data collection was performed in accordance with relevant guidelines and regulations of the Institutional Ethics Committee of Seoul National University Hospital, Seoul, South Korea. Data was accessed on January 18th, 2023.

Data source

We utilized the VitalDB data set from the PhysioNet database (https://physionet.org/content/vitaldb/1.0.0/) (accessed 06/28/2023). VitalDB is an open-source, freely available perioperative dataset from Seoul National University Hospital, designed to facilitate the development and testing of waveform bio-signal data. Information on the development and validation of the dataset has been previously reported and published [16].

Study population

We included patients undergoing non-cardiac (general abdominal, thoracic, urological, and gynecological) surgery from August 2016 to June 2017 with invasive arterial blood pressure data. Cases performed under local anesthesia only, American Society of Anesthesiologist (ASA) Physical status 5, cases with missing preoperative creatinine values or waveform data were excluded.

Primary outcome

The primary outcome was AKI stage 1, defined by the Kidney Disease: Improving Global Outcomes guidelines as a serum creatinine increase of at least 0.3 mg/dl within 48 h after surgery or an increase of at least 1.5 times from baseline within 7 days after surgery [17]. Urine output was not used to define AKI due to the inconsistent documentation of this variable.

Exploratory variable

Prior to calculating the SampEn of MAP, a blood pressure artifact reduction algorithm was implemented. This algorithm has been previously utilized and validated [1].

SampEn relies on two parameters: m and r. m is referred to as the “embedding dimension” or “template length”, and r is referred to as the “tolerance” or “noise filter”. SampEn is the sum of the natural logarithm of the number of times any m contiguous blood pressure values are similar to another, different, m contiguous values, within a tolerance of r. Higher values of m allow for more complex wave shapes to be matched to one another but requires more data in each wave to discern. The tolerance r is similar. Lower values of r restrict matches to only those which are very close to the template, but also lowers the total number of matches, meaning that more data is needed to find matches. A simplified, visual explanation of SampEn is provided in S1 Appendix.

SampEn is calculated as follows: for a given time window size m, construct all possible “templates” of length m of contiguous data points from the arterial waveform. (Example: [1, 2, 3, 4, 5] with m = 2 generates [[1, 2], [2, 3], [3, 4], [4, 5]]). Then, compute a distance metric between all templates using the Chebyshev distance, which is defined as the maximum of the absolute differences between the elements of two vectors. Next, let r be an a priori defined threshold value. Define B = the number of times the distance metric between any two templates was less than r, excluding the distance between a template and itself, which is always equal to 0. Repeat the above process but increase the window size (m) by 1. Define A = the number of times the distance metric between any two templates of size m + 1 is less than r, excluding the distance between a template and itself, which is always 0. Finally, SampEn is computed as the negative natural logarithm of A/B. SampEn was reported as values between 0 to infinity, with higher values indicating more stochasticity or ‘suprisability’ [13, 18].

The hyperparameters r and m were selected and optimized by maximizing the Kolmogorov–Smirnov test statistic between the distribution of SampEn of those who developed AKI against those who did not. Because the Kolmogorov–Smirnov statistic provides a distance between the empirical distributions of two variables, we can find m and r which provide the greatest separation between the SampEn of each of our target classes.

SampEn measurements can be sensitive to the “stationarity” of the data. “Weakly stationary” refers to time series data where mean and covariance are not a function of the time domain. Non-stationarity of the data causes templates which would otherwise match one another in shape to reject due to the magnitude of their values being different, leading to an unnecessarily high tolerance parameter r.[13] We evaluated for weak stationarity by linearly detrending our data and performing the augmented Dicky-Fuller test on each wave in our dataset. An infographic is provided in S2 Appendix explaining how SampEn was calculated, optimized and operationalized for our models.

Explanatory variables

The following patient and procedural variables were included in the analysis: age, sex, body mass index, ASA Physical status, hypertension, diabetes, emergency surgery, total intraoperative blood loss, total number of red blood cell units transfused, case length and surgical approach type (open, videoscopic or robotic). We created five cumulative hypotension over time variables which quantified the duration and severity of intraoperative hypotension: (1) percent of case time that a patient’s MAP was less than 60 mmHg, and (2–5) number of discrete hypotensive episodes where a single episode is defined as x ∈ [1, 5, 10, 15] or more contiguous minutes where MAP is less than or equal to 60 mmHg. We chose a threshold MAP below 60 mmHg, based on the Perioperative Quality Initiative guideline which suggests maintaining MAP above 60–70 mmHg during surgery and is a clinically relevant target for anesthesia providers [19]. Finally, to understand the relationship between BPV measures of dispersion and SampEn, we calculated the standard deviation of the MAP for each case.

Statistical analysis

Descriptive statistics were used to assess the distribution of all demographics, surgical, and intraoperative variables. Continuous variables were summarized with means, standard deviations, medians, and interquartile ranges, where appropriate. Categorical variables were summarized with counts and percentages. Histograms and x–y plots were used to visualize the distribution of SampEn in the study population. The relationship between SampEn of MAP and standard deviation of MAP was visualized using a scatterplot with locally estimated scatterplot smoothing.

To determine whether SampEn of MAP improves the prediction of AKI beyond the standard predictors, random forest classification and L1 normalized logistic regression were used to assess four models for postoperative AKI. By using both a non-linear (random forest) and a linear classifier (L1 normalized logistic regression), we could determine if there were variables which had a non-linear relationship with AKI. With both random forest classification and L1 normalized logistic regression, all continuous variables were normalized, and standardized, and missing values were dealt with by imputing the median value. Binary variables were one hot encoded and missing categorical values were dealt with by imputing the most common value.

Exploratory and explanatory variables were used to fit the four models for both the random forest and L1 logistic regression models. The four models included: (1) Standard risk factors which included age, sex, body mass index, ASA Physical status, hypertension, diabetes, emergency surgery, total intraoperative blood loss, total number of red blood cell units transfused, case length and surgical approach type (open, videoscopic or robotic) (2) all variables in the first model (the standard subset of variables) and cumulative hypotension over time (all five hypotension variables) (3) the standard risk factors and the SampEn of MAP (4) the standard risk factors, cumulative hypotension over time, and the SampEn of MAP [1, 12, 20]. Model 1 provides a baseline for the discriminative capability of a model with no hemodynamic predictors, Model 2 provides a benchmark for a model that utilizes time dependent threshold MAP values (< 60 mmHg X time) including standard risk factors, Model 3 tests whether the addition of SampEn provides an increase in discrimination to a model which accounts for the standard risk factors, and Model 4 tests whether the addition of SampEn provides an increase in discrimination to a model which accounts both for the standard set of risk factors, as well as an established set of time dependent threshold MAP values (< 60 mmHg X time). Standard risk factors are based on variables that are known to be associated with AKI.

For hyper-parameter selection in the random forest classifiers, we divided our data into an 80/20 train test split and optimized it by maximizing the C statistic on the test dataset. The c statistic is an accuracy metric for a classification model that is equal to the average probability that a patient which developed AKI was given a higher probability of developing AKI by the model that those which did not develop AKI. It is also equal to the area under the receiver operating characteristic (ROC) curve. The parameters which we optimized for in the random forests were the forest's maximum depth, minimum samples per leaf, number of trees, number of features to randomly select at every split, and criterion to measure the quality of splits.

ROC curves with 95% confidence intervals were created to evaluate the difference between the discriminative capabilities of the models. In addition, we used precision, recall and F1 score to evaluate and compare performance of our models. Precision is the number of true AKI events the model correctly identified divided by all the observations the model predicted were AKI events. Precision quantifies how accurate the model is when it predicts a case will develop AKI. Recall is the number of true AKI events the model correctly identified divided by the total number of true AKI events in the dataset. Recall quantifies the proportion of all AKI events that were correctly identified. The F1 score serves as a type of average between the precision and recall of a model. They were computed as follows: precision = TP/ (TP + FP), recall = TP/(TP + FN) and F1 = 2TP/ (2TP + FP + FN), where TP, FP, FN, TN are the number of true positives, false positives, false negatives and true negative, respectively.

Finally, because the number of patients in the database who developed AKI was small, error metrics could potentially suffer from instability and dependence upon the specific test/train split we used. To alleviate this potential problem, and to gain a more robust understanding of the model performance, we trained each model 500 times using a randomized test/train split of 30/70, effectively obtaining a random sample from the distribution of possible precisions, recalls, c statistics, F1, and accuracy metrics.

Because the AKI and non-AKI classes were very imbalanced, all models were trained with balanced class weights which increase the penalty of making a wrong prediction for smaller classes and decrease the penalty of making a wrong prediction for larger classes. This means that the model will weight AKI predictions much higher than non-AKI predictions.

All analysis was performed with Python using the pandas, numpy, seaborn, pingouin, optuna and sklearn packages. SampEn calculation was optimized using an implementation in the Rust programming language [21,22,23,24].

Results

Overview and standard predictors

The original dataset includes 6,388 non-cardiac surgical cases. After applying the pre-defined exclusion criteria, we had 2, 880 cases in the final cohort. Two hundred and thirteen (7.4%) cases developed postoperative AKI. Demographic, surgical, and anesthetic variables, by the risk of developing AKI is reported in Table 1. Patients who developed AKI were more likely to be male, have preoperative hypertension and diabetes, undergo emergency surgery, higher intraoperative blood loss, ASA III-IV and undergo open surgical procedures.

Table 1 Demographic, anesthetic, and surgical variables with and without acute kidney injury

Mean arterial pressure below threshold

The number of discrete episodes of hypotension by minutes and percentage time MAP was below 60 mmHg by AKI status is reported in Table 1 and Fig. 1. The distribution of the discrete hypotensive episodes and percentage time of hypotension is right-skewed. The percent of case time where MAP < 60 mmHg was higher in the AKI group (Median: 4, IQR [1, 12]) compared to the non-AKI group (Median: 1, IQR [0, 4]).

Fig. 1

Boxplots for the number of discrete hypotensive episodes and the percentage of case time where mean arterial pressure is less than or equal to 60 mmHg between those with and without acute kidney injury

Sample entropy

Optimization yielded an embedding dimension of m = 9 (the length of the templates) and a tolerance of r = 0.0477 (the noise filter). The Dicky-Fuller test results for weak stationarity demonstrated that 80.6% of the waves in the dataset were weakly stationary, and the p-value of the tests were linearly unrelated to the development of AKI. Because our value of r was relatively low at 0.0477, the likelihood that the non-stationary waves affected our results is very low.

The median and interquartile range for MAP SampEn for the cohort was 0.34 and [0.26, 0.42] respectively. Bivariate visualization of SampEn and the risk of AKI is demonstrated in the box plot in Fig. 2. This demonstrates no significant difference in SampEn scores between the groups that did and did not develop AKI (two-sided t-test: AKI versus No AKI [-0.05, 0.0]).

Fig. 2

Boxplot for the sample entropy of mean arterial pressure values by acute kidney injury status

Relationship between standard deviation and SampEn of MAP

The standard deviation of MAP between those with and without AKI is demonstrated in S3 Appendix, which demonstrates no difference between the AKI and no AKI groups. To understand how measures of dispersion and SampEn are related, S4 Appendix demonstrates the relationship between MAP SampEn and standard deviation of MAP. This shows a nonlinear relationship between standard deviation of MAP and SampEn of MAP.

Model prediction

ROC curves and c-statistics with 95% confidence intervals for the random forest and L1 logistic regression models, trained on the four subsets of predictors are demonstrated in Table 2 and Fig. 3. C-statistics for the L1 logistic regression models were identical to that of the random forests. The consensus between the random forest and logistic regression models on each of the four subsets of variables suggests there are no non-linear effects in the explanatory variables captured by the random forests.

Table 2 C statistic with 95% confidence interval for the four prediction models

Fig. 3

Receiver operating characteristic (ROC) curves with 95% confidence intervals for the four prediction models. A Random Forest Model, B L1 Normalized Logistic Regression Model

ROC curves and c-statistics were identical for the models indicating that the addition of hypotension over time or SampEn of MAP did not improve discrimination of AKI compared to the standard risk-factors, which included preoperative demographic, surgical and anesthetic variables. Finally, precision, accuracy, recall and F1 score distributions for the four models are shown in Fig. 4. The precision for all models is low, while in contrast their recall is high. This is due to incorporating balanced class weighting during model training. The addition of hypotension lowered the model recall, while slightly improving the precision. However, when averaged into an F1 score, we noted that this tradeoff did not produce an improvement in discrimination at a 95% level of confidence.

Fig. 4

Panel 1 (L1 Logistic Regression Model) and Panel 2 (Random Forest Classification) with F1 (A), Accuracy (B), Precision (C), and Recall Scores (D) for predicting postoperative acute kidney injury

Discussion

In this single-center retrospective study, we demonstrate that very short-term BPV measured by SampEn of MAP did not improve discrimination for the development of postoperative AKI stage 1 after non-cardiac surgery in adults.

There are several approaches for quantifying BPV: measures of frequency, dispersion, sequence, or stochasticity. There are currently no standards to guide which measures to employ when analyzing BPV. Parati et al. suggested that measures of sequence and dispersion are more appropriate for analyzing short (over 24 h) to medium-term variability (between days), while spectral analysis of waveform data is more appropriate for very short-term BPV (seconds to minutes) [25]. In our study we analyzed 2-s arterial waveform data to measure BPV, hence the use of SampEn, which aligns with very short-term BPV analysis.

There are currently limited studies on the impact of BPV on AKI. Park et al. demonstrated that standard deviation, coefficient of variation, average real variability, and variation independent of mean of intraoperative blood pressure, measures of dispersion and sequence, were all independently associated with postoperative AKI after non-cardiac surgery, when controlling for intraoperative hypotension [12]. They demonstrated that average real variability was associated with both postoperative AKI (adjusted odds ratio, 1.13 per 1 standard deviation increment; 95% CI, 1.07 to 1.19) and critical AKI (adjusted odds ratio, 1.13 per 1 standard deviation increment; 95% CI, 1.02 to 1.26). However, it is important to note that in their cohort without intraoperative hypotension, high BPV was not associated with AKI [adjusted OR: 0.98 (CI: 0.87, 1.27) p = 0.91]. This suggests that BPV below autoregulatory ranges might impose a greater risk of AKI, compared to BPV within normal autoregulatory ranges. Furthermore, it is important to note that the addition of average real variability measures in the continuous monitoring sub-cohort in the Park study (those with an arterial line and 2-s wave form data) only improved the prediction for AKI by 1% (CI: 0.2–1.8%), which is negligible and in keeping with our findings. In summary, based on the Park study and our work, the association of very short-term BPV and AKI is weak in the absence of intraoperative hypotension. Additionally, measures of very short-term BPV do not improve discrimination for developing AKI compared to standard demographic, surgical and anesthetic risk factors.

The impact of intraoperative BPV beyond AKI has also been studied. The effect of intraoperative BPV on mortality is inconclusive, with studies demonstrating mixed results. Mascha et al. demonstrated that low generalized average real variability of MAP intraoperatively is associated with a 14% higher rate of 30-day mortality, compared to patients with high generalized average real variability of MAP, after controlling for intraoperative hypotension [26]. Similarly, James et al. reported that decreased number of episodes where the fractional mean pressure is greater than 15%, increased postoperative mortality as a mediation factor for frailty [27]. Amongst patients with preoperative hypertension, increased intraoperative lability has also been shown to be associated with decreased mortality. All these studies posit autonomic dysregulation and reduced BPV as presumptive mechanisms for increased mortality. In contrast, in a prospective cohort study in patients undergoing gastrointestinal, gynecological, and neurosurgical surgery, higher coefficients of variation of systolic, diastolic, and mean blood pressure were all associated with increased mortality [28]. A limitation of the latter study was that intraoperative hypotension was not included in their model. Controlling for this confounding variable is important to isolate the true effect of BPV on postoperative mortality.

Our study has several limitations. We utilized a publicly available, well curated dataset from a single medical center in South Korea. The homogenous population in this cohort may not be reflective of a more diverse, heterogeneous population with different risk factors for cardiovascular disease, diabetes, and AKI and hence our findings may not be generalizable to other population group. Secondly, we did not have data on inotrope and/or vasopressor medication use in this dataset, which can have a significant impact on BPV. Future work in this field should include how BPV is mediated by inotropes and vasopressor therapy and its impact on postoperative outcomes. In addition, unmeasured confounders might still bias our findings. We only reported AKI stage 1 in this study, however there are multiple studies that have demonstrated the consequences of milder stages of AKI on the long-term morbidity and mortality [2, 3, 29]. Due to the absence of a standardized measure of BPV, findings may differ based on the tool used to measure variability.

Due to class imbalance in the data, class weighting was used to train the models. This technique was employed to ensure that the model learned predictive information from the features themselves rather than adopting the higher accuracy policy of always predicting the majority class. However, class weighting also decreases the model's precision. This is because class weighting will cause the model to overpredict the minority class (postoperative AKI), resulting in higher recall at the cost of precision on new data [30]. Finally, external validation using an independent dataset would be essential to demonstrate the robustness of our findings. Major strengths of our study include validation of an alternate measure of very short-term BPV, using time series data. In addition, we evaluated the relationship between BPV measures of dispersion and stochasticity, which we demonstrated are nonlinear in nature. Future work on BPV and its impact on organ-specific outcomes should include measures of both dispersion and stochasticity.

In conclusion, in this study using 2-s arterial waveform data, SampEn MAP was no better than standard demographic, anesthetic and surgical risk factors in discriminating postoperative AKI. Additional studies utilizing a larger, heterogeneous population with intraoperative vasopressor and inotrope data is required to better elucidate the impact of BPV on AKI and mortality. Understanding the importance of very short-term BPV intraoperatively is clinically relevant, as it will allow anesthesia providers to intervene earlier and potentially reduce the risk of postoperative AKI.