Abstract
Patientventilator asynchronies can be detected by close monitoring of ventilator screens by clinicians or through automated algorithms. However, detecting complex patientventilator interactions (CPVI), consisting of changes in the respiratory rate and/or clusters of asynchronies, is a challenge. Sample Entropy (SE) of airway flow (SEFlow) and airway pressure (SEPaw) waveforms obtained from 27 critically ill patients was used to develop and validate an automated algorithm for detecting CPVI. The algorithm’s performance was compared versus the gold standard (the ventilator’s waveform recordings for CPVI were scored visually by three experts; Fleiss’ kappa = 0.90 (0.87–0.93)). A repeated holdout crossvalidation procedure using the Matthews correlation coefficient (MCC) as a measure of effectiveness was used for optimization of different combinations of SE settings (embedding dimension, m, and tolerance value, r), derived SE features (mean and maximum values), and the thresholds of change (Th) from patient’s own baseline SE value. The most accurate results were obtained using the maximum values of SEFlow (m = 2, r = 0.2, Th = 25%) and SEPaw (m = 4, r = 0.2, Th = 30%) which report MCCs of 0.85 (0.78–0.86) and 0.78 (0.78–0.85), and accuracies of 0.93 (0.89–0.93) and 0.89 (0.89–0.93), respectively. This approach promises an improvement in the accurate detection of CPVI, and future study of their clinical implications.
Introduction
Invasive mechanical ventilation (MV) is a lifesupport measure administered to patients who cannot breathe on their own. Patientventilator asynchronies occur when there is a mismatch between the ventilator’s setting and patient’s breathing pattern. Recent studies have emphasized the impact of asynchronies upon clinical outcomes^{1,2,3,4,5}, focusing on the incidence of specific subtypes of asynchronies or on the asynchrony index, and also on their distribution over time given that they occur in clusters within prolonged uneventful periods^{1,2,3,4,5,6}. Importantly, in most of these studies ventilator’s waveforms were analysed visually^{2,5,7,8}; only a few analyses have been based on automated algorithms^{1,4,6,9,10} or, more recently, on machine learning algorithms incorporating not only ventilator waveforms but also clinical data^{11}.
Asynchronies are difficult to define when supported only by visual assessment carried out by inexperienced personnel, since different types may develop in a short time period or may even overlap with each other. Furthermore, asynchronies, which are by nature timelimited and transient, lead to patient distress, impede the ventilator’s effectiveness in decreasing the work of breathing, increase the time on mechanical ventilation and have a negative impact on outcome^{1,2,4,7,12}. Additionally, sometimes patient’s drive only becomes evident due to an increase in the respiratory rate itself^{13,14,15,16}, which, given its irregular and complex behaviour, may be overestimated by visual observation or dedicated algorithms. Therefore, it would be extremely useful to have access to a method for assessing irregularity and complexity which could detect Complex PatientVentilator interactions (CPVI), including not just asynchronies of any kind but also changes in the respiratory rate, in an automated, noninvasive and personalized fashion.
Normal physiological data are nonlinear^{17}. The complex behavior of a nonlinear system cannot be characterized by the sum of its inputs, and the study of these systems requires methods that take into account the nonlinear physiological response to a given stimulus. These methods could provide insights into organsystem interconnectivity, regulatory control, and complexity in time series during disease^{17,18,19}.
Entropy is a nonlinear method derived from the theory of complex systems which measures the randomness and predictability of stochastic processes. Various types of entropy have been used in clinical monitoring^{20,21,22}. Sample Entropy (SE) is a measure of complexity and regularity, defined as the negative natural logarithm of the conditional probability that two sequences similar for m points will remain similar at the next point, where selfmatching is not included^{23}. Thus, a lower SE value indicates more selfsimilarity in a time series.
SE has proved to be an effective tool for investigating different types of time series data derived from various biological conditions in the human body. Examples of these conditions include the activation of inspiratory muscles in COPD patients^{24,25}, the analysis of atrial fibrillation on electrocardiograms^{26}, background electroencephalograms in Alzheimer’s patients^{27}, heart rate variability^{28,29}, human postural sway^{29} and seizure termination during electroconvulsive therapy^{30}.
Interestingly, only a few entropy approaches have been applied in the respiratory system to study breathtobreath variability and its components as predictors of successful separation from MV during spontaneous breathing trials (SBT)^{19,31,32,33,34}. Breathtobreath approaches suggest that increased irregularity of the respiratory system may be a marker of pulmonary health^{19} and may serve as a weaning predictor^{32,33,34,35}, opening up the possibility that a certain degree of irregularity may be normal^{3,36}. However, these studies rely on the detection of the appropriate respiratory cycle. Hence, the performance of automated algorithms in breathing cycle detection may be jeopardized when transient asynchronies occur during patientventilator interaction or even overlap with each other. In this respect, other authors have applied the SE to the entire signal, as is the case of Sá et al.^{37} who evaluated the respiratory changes by applying SE upon the entire airway flow signal providing an early and sensitive functional indicator of interstitial asbestosis.
We hypothesized that analyzing transient complexity of CPVI may provide clinically relevant information during MV. Therefore, we sought to develop and validate a noninvasive method based on SE measurement using the entire airway pressure (Paw) and airway flow (Flow) waveforms to detect CPVI, defined as the occurrence of asynchronies and changes in the respiratory rate.
Methods
Defining complex patient ventilator interactions
We defined CPVI as a > 50% change in the respiratory rate^{13,35,38,39} and/or > 30% asynchronous breaths of any type (ineffective expiratory efforts, double cycling, premature cycling, prolonged cycling, or reverse triggering) over a 3min period. A recent study found that 38% of mechanically ventilated patients had clusters of ≥ 30 ineffective expiratory efforts in a 3min period (i.e., ≥ 50% of all breaths in a patient with a respiratory rate of 20 breaths per minute), and that the median duration of these clusters was 20 min^{4}. Another study found that 59.7% of patients had clusters in which > 10% of all breaths in a 3min period were double cycled, with a mean cluster duration of 15.5 min^{6}. Figure 1 shows a representative example of different CPVIs consisting of increased respiratory rate, asynchronies, or a combination of these phenomena.
Data acquisition and data analysis
The Better Care system (Better Care, Barcelona, Spain. US patent No. 12/538,940) continuously records Paw and Flow signals at a sample frequency of 200 Hz from intubation to liberation from MV^{9}. Better Care uses drivers specifically designed to interact with output signals from mechanical ventilators and bedside monitors rather than directly with patients, synchronizing recorded signals and storing them for further analysis. We used MATLAB (The MathWorks, Inc., vR2018b, Natick, MA, USA) for signal processing, data analysis, and visual assessment. Signals were decimated at a sampling rate of 40 Hz before entropy calculation.
Study population
The findings presented in this paper represents an ancillary analysis on an ongoing clinical study (ENTROPYICU, ClincalTrials.gov NCT04128124) designed to assess the feasibility of using SE to identify CPVI during MV. Data from 27 patients were obtained from an ongoing database at two centers in Spain. The database was constructed prospectively for the development of a connectivity platform (Better Care) to interoperate signals from different ventilators and monitors and subsequently compute algorithms for diagnosing patientventilator asynchronies (ClinicalTrial.gov, NCT03451461). The Comitè d’Ètica d’Investigació amb medicaments at the Corporació Sanitària Parc Taulí and the Clinical Research Ethics Committee of Fundació Unió Catalana d’Hospitals approved the database and the study protocol. The need for informed consent was waived because the current study was an ancillary analysis with anonymized data. The guidelines followed in this study were according to the applicable Spanish regulations (Biomedical Research Law 14/2007). This type of study must be evaluated and approved by at least one Institutional Review Board (IRB). Parc Taulí’s IRB approved this study to be carried out in all participating centers. The IRB approved the study allowing it to be carried out without the explicit request of informed consent from each participant given that it is a study with retrospective data. Spanish regulations allow studies to be carried out with this condition as long as they are approved by an IRB.
The SE analysis was performed on the complete set of Flow and Paw data collected during the two hours before selfextubation. Selfextubations, defined as extubations performed by the patient himself, are included in unplanned extubations but its mechanisms differ from accidental extubations^{40}. Clinical and demographic data were obtained from medical charts (Table 1).
Visual validation of CPVI
Experts’ visual assessment was considered the gold standard. Three critical care physicians with extensive experience in analyzing ventilator waveforms visually reviewed 92 15minlong segments of Flow and Paw recordings from the twohour period immediately before selfextubation. The 15min window was selected based on two previous studies evaluating clusters of asynchronies, in which mean cluster duration was 15.5 and 20 min respectively^{6,10}. An expert in MV selected the segments to ensure a balanced proportion of different ventilation modes (grouped into pressure support ventilation (PSV) or assistcontrol ventilation (ACV) modes, comprising volume assistcontrol and pressure assistcontrol ventilation) and of segments with and without CPVIs. Every patient contributed both CPVI and nonCPVI segments with at least one 15min segment of each type; however, some patients contributed more segments than others. In order to ensure that the most valuable CPVI events were not missed, all the 15min segments immediately preceding selfextubation were included. To ensure masking of the scorers, Flow and Paw tracings were randomly ordered in MATLAB prior to visual analysis. To standardize scoring criteria, scorers were provided with written descriptions of the characteristics of CPVI before visual analysis. Scorers were asked to determine whether CPVI were present in each segment. No time limitations were imposed.
Sample entropy
SE is a nonlinear technique that measures the randomness of a series of data^{23}. Compared to other approaches, SE’s main advantage is that it provides consistent results even in short and noisy medical time series^{19,23}. To calculate SE, three parameters are necessary: the embedding dimension, m (a positive integer); the tolerance value or similarity criterion, r (a positive real number); and the total length of the series, N. Briefly, SE is defined as the negative logarithm of the conditional probability that two sequences of patterns of m consecutive samples that are similar to each other within a tolerance r will remain similar when one consecutive sample is added (\(m + 1\)), excluding selfmatches. SE is calculated as follows^{23}:
Given a time series of N samples \(\left\{ {x\left( n \right) = x\left( 1 \right),x\left( 2 \right), \ldots ,x\left( N \right)} \right\}\), a subset of \(N  m + 1\), overlapping vectors \(X_{m} \left( i \right)\) of length \(m\) are defined:

1.
Form m vectors defined by \(X_{m} \left( i \right) = \left[ {x\left( i \right),x\left( {i + 1} \right), \ldots ,x\left( {i + m  1} \right)} \right],{ }i = 1,2, \ldots ,N  m + 1\). These represent \(m\) consecutive \(x\) values.

2.
Then, define Chebyshev distance between vectors \({ }X_{m} \left( i \right)\) and \(X_{m} \left( j \right)\), i.e., the maximum absolute difference between their scalar components:
$$d\left[ {X_{m} \left( i \right),X_{m} \left( j \right)} \right] = \begin{array}{*{20}c} {max} \\ {k = 0, \ldots ,m  1} \\ \end{array} \left[ {\left {x\left( {i + k} \right)  x\left( {j + k} \right)} \right} \right].$$(1) 
3
For a given \(X_{m} \left( i \right)\), count the number of j \(\left( {1 \le j \ge N  m,i \ne j} \right)\), denoted as \(B_{i} \left( r \right)\), such that the distance between \(X_{m} \left( i \right)\) and \(X_{m} \left( j \right)\) is less than or equal to a threshold \(r\).
$$\begin{gathered} \hfill \\ B_{i}^{m} \left( r \right) = \frac{{B_{i} \left( r \right)}}{N  m  1}, \\ \text{Then, for}\, 1 \le i \ge N  m, \hfill \\ \end{gathered}$$(2) 
4.
Defined \(B^{m} \left( r \right)\) as
$$B^{m} = \frac{1}{N  m}\mathop \sum \limits_{i = 1}^{N  m} B_{i}^{m} \left( r \right)$$(3) 
5.
This previous procedure is repeated, increasing the dimension to \(m + 1\) to calculate \(A_{i} \left( r \right)\) as the number of \(X_{m + 1} \left( i \right)\) within \(r\) of \(X_{m + 1} \left( j \right)\), where \(j\) ranges from 1 to \(N  m\left( {i \ne j} \right)\). Then,\({ }A_{i}^{m} \left( r \right)\) is defined as:
$$A_{i}^{m} \left( r \right) = \frac{{A_{i} \left( r \right)}}{N  m  1}$$(4) 
6.
Set \(A^{m} \left( r \right)\) as
$$A^{m} = \frac{1}{N  m}\mathop \sum \limits_{i = 1}^{N  m} A_{i}^{m} \left( r \right)$$(5)
Thus, \(B^{m} \left( r \right)\) is the probability that two sequences will match for \(m\) samples, whereas \(A^{m} \left( r \right)\) is the probability that two sequences will match for \(m + 1\) samples. Finally, sample entropy is then defined as
which is estimated by the statistic:
The m parameter is generally taken as 2, while the r parameter normally ranges between 0.1 and 0.25 times the standard deviation (SD) of the segment analyzed of length N. In this study, SE was calculated over the Flow (SEFlow) and Paw (SEPaw) signals using a 30s sliding window (N = 1,200 samples) with 50% overlap. SE was explored using m from 1 to 20 and with r values equal to 0.1, 0.2, 0.3, and 0.4 times the SD of each sliding window. To reduce noise and to increase the consistency of the results, we applied an 8periodlong exponential moving average filter to the SE series.
Automatic CPVI detection
We devised an automated algorithm based on SE to detect CPVI events (European patent application number EP19383116). Figure 2 summarizes the algorithm in a flowchart. Detection of a CPVI depends on whether the percentage of change (PC) in SE with respect to the patient's own SE baseline value during the 15min period is greater than a predefined threshold of change (Th). We calculated PC for SEFlow and SEPaw in each 15min period in two ways, using the following derived features (the mean SE value [SEFlow_{mean} and SEPaw_{mean}], and the maximum SE value [SEFlow_{max} and SEPaw_{max}]), applying different values of Th (15%, 20%, 25%, 30%, 35%, 40%, 45%, and 50%). We hypothesized that SE values would be higher in periods with CPVI than in periods with regular patientventilator interactions. Periods were considered to contain a CPVI event when PC exceeded the Th. The optimal Th for CPVI detection was selected during the SE setting optimization procedure (explained below).
KeimMalpas^{41} recently proposed that alert thresholds derived from continuous analytic monitoring should be based on the degree of change from the patient’s own baseline, rather than on general cutoff thresholds. In our study there was no single baseline value common to all patients; each patient had their own baseline.
The baseline value of each SE feature was initialized with the value calculated in the first 15min period. This value was updated with each new 15min segment if the SE feature of the new one was lower than the current baseline.
Statistical analysis
Fleiss’ kappa coefficient was used to assess the reliability of agreement among scorers for visual assessment^{42}. The automated CPVI detection algorithm was applied over the SE series derived from the same Flow and Paw tracings previously used for visual assessment. To evaluate the performance of the automated algorithm with respect to the gold standard visual assessment, we calculated sensitivity, specificity, positive and negative predictive values (PPV and NPV respectively), accuracy, and the Matthews correlation coefficient (MCC)^{43}. Widely used in biomedical research, the MCC is considered a balanced measure of the confusion matrix of true and false positives and negatives^{44,45,46}. Calculation of the MCC is based on all four elements of the confusion matrix: true positive (TP), true negative (TN), false positive (FP), and false negative (FN) values, as follows:
MCC values can range from − 1 to + 1. An MCC value of − 1 suggests perfect disagreement between the predictions and the gold standard, and a value of 1 suggests perfect agreement between the predictions and the gold standard; a value of 0 indicates that the prediction is no better than random. The MCC index was used as the measure of effectiveness during the process to optimize SE settings so as to achieve the most robust CPVI estimation.
Optimization procedure (selection of m, r, and Th)
In entropy studies, determining the optimal settings to robustly extract the randomness of a series of data is an important step^{47,48}. To select the optimal settings for the SE parameters m and r and the optimal Th for estimating CPVI, we used a repeated holdout crossvalidation method with the MCC as a measure of effectiveness.
Figure 3 depicts the steps involved in the optimization and the validation procedure. Once the experts had visually validated the set of 92 observations, it was randomly divided into two subsets: 70% of the data for optimization and the remaining 30% of the data for validation. This optimization procedure was repeated a total of 15 times using different subsets (randomly selected each time) to capture as much relevant information as possible and to minimize the potential bias resulting from fitting the settings on a single partition. The MCC metric was computed for all combinations of m, r, and Th for each repetition. Finally, the maximum mean MCC value determined the optimal combination of SE settings and Th among all possible combinations. The optimization procedure was individually applied to the features derived from SEFlow (SEFlow_{mean}, SEFlow_{max}) and SEPaw (SEPaw_{mean}, SEPaw_{max}) in order to determine the respiratory signal and features that best reflect CPVI.
In addition, a sensitivity analysis by using a small grid search of r values (step = 0.01) around the optimal value in the best features derived from SEFlow and SEPaw was performed to compare regions of confidence and to investigate whether the selected r value is a robust local maximum.
To assess the robustness of the optimization procedure, we computed the medians and interquartile ranges of all measures of performance (MCC, sensitivity, specificity, accuracy, PPV, and NPV) considering the optimal combination for both the optimization and validation subsets.
Results
Visual CPVI analysis by experts
The experts visually assessed a total of 92 periods: 45 periods of PSV (22 with CPVI and 23 without) and 47 periods of ACV (24 with CPVI and 23 without). Fleiss’ kappa for interrater agreement was 0.90 (0.87–0.93), indicating almost perfect agreement.
Detecting CPVI with SE
The exponential moving average filter reduced the noise in SE series and generated a smoothed SE version suitable for detecting CPVI (see Supplementary Methods and Supplementary Fig. S1). Figure 4 shows representative examples of respiratory signal tracings with the corresponding SEFlow (m = 2 and r = 0.2) and SEPaw (m = 4 and r = 0.2) tracings. SE was highly sensitive to changes in the irregularity of the respiratory pattern occurring during ventilation.
Optimization of SE settings, Th detection using a repeated holdout crossvalidation procedure
Figure 5 shows the procedure used to optimize SE settings and Th for CPVI detection. We calculated the mean MCC value for each combination of m, r, and Th for all derived features analyzed (SEFlow_{mean}, SEFlow_{max}, SEPaw_{mean}, and SEPaw_{max}). In general, SEPaw features exhibit much less sensitivity to m parameter selection than SEFlow features. SEFlow_{max} and SEPaw_{max} features yielded the highest mean MCC values. The highest MCC values for SEFlow_{max} were found for values of m = 2, r equal to 0.2 and 0.3, and Th between 20 and 35%, whereas for SEPaw_{max} were found for values of m equal to 3 and 4, r = 0.2, and Th between 25 and 30%. The optimal SE settings for SEFlow_{max} were m = 2, r = 0.2, and Th = 25%, and for SEPaw_{max} m = 4, r = 0.2, and Th = 30%. As regards the optimal SE settings, SEFlow_{max} at Th = 25% (SEFlow_{max}25) yielded the highest mean MCC value (0.84) and SEPaw_{max} at Th = 30% (SEFlow_{max}30) yielded the highest mean MCC value (0.86). Both SEFlow_{max}25 and SEPaw_{max}30 yielded their highest MCC values in 13 of the 15 repetitions. The sensitivity analysis conducted for the SEPaw_{max} and SEFlow_{max} features around the optimal value of r = 0.2 is shown in Supplementary Figure S3. Once we had determined the settings that best detected CPVI, we evaluated the performance of the algorithm in the 15 repetitions of the crossvalidation procedure. Figure 6 displays the algorithm’s performance statistics. The median values of all the parameters observed in the optimization subset were slightly higher than those observed in the validation subset (Supplementary Table S1); this is a common consequence of the repeated holdout crossvalidation process. The performance of SEFlow_{max}25 and SEPaw_{max}30 stratified by ventilator modality (grouped into pressure support ventilation and assistcontrol ventilation modes) is shown in Supplementary Table S2.
For comparative purposes, we also carried out the procedure for optimizing SE settings and Th over the unfiltered SE series. The Supplementary Methods and the Supplementary Figure S2 show the results obtained in this case.
Discussion
Our automatic algorithm for detecting CPVI from ventilator signals proved highly sensitive and specific in individual patients. Using nonlinear analysis of SE to measure irregularity and randomness in the entire set of physiological Flow and Paw signals, the algorithm compared data from different periods in each patient’s interaction with the ventilator to detect CPVI. In our analyses the maximum changes of SE in both Flow and Paw signals yielded the most accurate results at different thresholds and settings. The most accurate results for SEFlow_{max} were obtained with a threshold of change of 25% with m = 2, r = 0.2, and for SEPaw_{max} with a threshold of change of 30% with m = 4 and r = 0.2.
The recognition of the hidden information contained in physiological time series draws attention to the extraordinary complexity of physiological systems^{49}. Several nonlinear techniques have been developed to study the irregularity and complexity of these physiomarkers^{18,23,50,51,52,53}. Previous studies have used methods based on approximate entropy and sample entropy using breathtobreath variability and derived indices^{19,23,32,33,34}, which relies on the detection of the appropriate respiratory cycle.
The main advantage of our approach is that it does not require the detection of each single breathing cycle to measure irregularity in Flow and Paw waveforms and thus identify the development of a CPVI. This approach makes a fundamentally different assumption about where complexity occurs in the physical signal, focusing on transient Flow and Paw complexity rather than breathtobreath complexity in order to accurately identify changes in the respiratory rate and asynchronies which by their nature are transient and timelimited.
To our knowledge, no recommendations are currently available for the estimation of respiratory dynamics by applying an entropy approach to the entire dataset of Flow and Paw tracings during MV^{23,52}. Recently, Sá et al.^{37}, used SE estimation upon entire Flow signal without optimized parameters. Thus, one important contribution of our study is the description of a set of optimization and validation procedures based on a repeated holdout crossvalidation method used in machinelearning models, which we used to obtain the optimal m, r and Th values. Ensuring the robustness of the validation procedure.
Our study also applied a personalized threshold to determine the occurrence of a CPVI event based on a proportional change from the patient’s own baseline value, which is continuously updated. Continuous predictive analytics monitoring achieves early detection of changes in status over time in previously stable patients. KeimMalpas et al.^{41} recently suggested that an absolute threshold of change from baseline values may not be clinically significant in realworld settings and could lead to a high rate of falsepositives in patients with high baseline values^{54}. In our study, thresholds of change of 25% and 30% from SEFlow_{max} and SEPaw_{max} respectively, proved to be the most accurate for CPVI detection. The optimization procedure found that r = 0.2 is suitable for detecting CPVI events using SEFlow_{max} (m = 2, Th = 25%) or SEPaw_{max} (m = 4, Th = 30%) features. Additionally, the sensitivity analysis indicates that r = 0.2 proved to be a more robust local maximum for SEFlow_{max} feature. This might suggest that the algorithm predictions seems to be not influenced by small changes in underlying unknown parameters (i.e., different dataset, different measurement equipment or ventilator waveforms) when using SEFlow_{max} (m = 2, r = 0.2, Th = 25%), and therefore, could be a more suitable feature than SEPaw_{max} (m = 4, r = 0.2, Th = 30%).
Interestingly, both SEFlow_{max}25 and SEPaw_{max}30 performed well in detecting CPVI in AssistControl Ventilation, while SEFlow_{max}25 performed slightly better than SEPaw_{max}30 in Pressure Support Ventilation mode. The reason for the latter finding may be that during PSV the pressure is constant, and it is the flow waveform that exhibits more changes in accordance with patient’s demand and the mechanical properties of the diseased lung. However, due to the small sample size these subanalysis results should be interpreted with care, and further research is needed.
Our study has several limitations. First, our algorithm responds to changes in the respiratory rate based on transient changes of Flow and Paw waveforms detected by SE, but not on inspiratory effort. This means that respiratory drive, the intensity of the neural output from the respiratory center that regulates the magnitude of inspiratory effort^{55}, may not have been fully assessed^{15,56,57}. Unfortunately, although many techniques have been proposed^{55,58,59,60} none have been implemented at the bedside to monitor drive and effort. Our proposed algorithm does not include measurements of effort; nevertheless, whenever a diaphragmatic contraction occurs unassisted by the ventilator, and an asynchrony develops our algorithm is able to detect it.
Second, although our method does not rely on the detection of breathing cycles to measure irregularity and is based on changes in SE of Flow and Paw waveforms, none of the features deriving from breathtobreath variability were considered. Therefore, their potential importance in detecting CPVI is yet to be assessed.
Third, while the dataset used for the repeated hold out crossvalidation method was paired between segments with and without CPVI, most of them were from tracings of patients who selfextubate, in whom the occurrence of events of poor patientventilator interactions is highly unpredictable. For that reason, the clinical meaning of CPVI in critically ill patients is yet to be determined and requires more research. Additionally, in the current study we have only examined SE, and other promising measures of entropy may also provide adequate diagnostic tool. For instance, multiscale entropy analysis^{61,62}, Fuzzy approximate entropy^{63}, conditional entropy^{64} and distribution entropy^{65} could be others potentially useful entropy measures to be investigated.
Finally, we did not analyze data from proportional modes of MV. Thus, although it is tempting to speculate that ventilatory modes that adapt to patients’ efforts and variability might induce higher changes in SE, the performance of our algorithm in patients ventilated in these modes may differ substantially, and it should not be implemented in these modes until validated by future research.
Conclusion
Our noninvasive method based on SE measurement of Paw and Flow is able to detect CPVI, defined as the occurrence of transient asynchronies and changes in the respiratory rate, with high accuracy. Clinical relevance and usefulness of identifying Complex PatientVentilator Interactions in different clinical scenarios deserves to be explored.
Data availability
The datasets generated and analyzed in the current study are available from the corresponding author on reasonable request.
Change history
09 November 2020
An amendment to this paper has been published and can be accessed via a link at the top of the paper.
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Acknowledgments
This work was funded by projects PI16/01606, integrated in the Plan Nacional de R+D+I and cofunded by the ISCIII Subdirección General de Evaluación y el Fondo Europeo de Desarrollo Regional (FEDER). RTC201761931 (AEI/FEDER UE). CIBER Enfermedades Respiratorias, and Fundació Parc Taulí.
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Study concept and design: L.S., J.A.E., R.M., C.d.H., and L.B. Data acquisition: L.S., J.A.E., C.d.H., C.S., M.B., G.G., A.O., and R.F. Data processing and interpretation: L.S., J.A.E., R.M., J.L.A., R.F., and L.B. Statistical analysis: L.S., R.M., and M.R. Figure preparation: L.S., J.A.E. and R.M. Drafting of the manuscript: L.S., J.A.E., and R.M. Revision of manuscript for important intellectual content: L.S., J.A.E., R.M., C.d.H., J.L.A., R.F., and L.B. Study supervision: L.S., J.A.E., R.M., C.d.H., A.O., R.F., and L.B. Data access and responsibility: L.B. had full access to all of the data in the study and takes full responsibility for the integrity of the data and the accuracy of the data analysis. L.S. and J.A.E. contributed equally to the study. All authors reviewed the manuscript.
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L.S., J.A.E., R.M., C.d.H., J.L.A, and L.B. have been named in a provisional European patent application number EP19383116 owned by Corporació Sanitària Parc Taulí: “A device and method for respiratory monitoring in mechanically ventilated patients”. L.B. is inventor of a US patent owned by Corporació Sanitària Parc Taulí: “Method and system for managed related patient parameters provided by a monitoring device”, US Patent No. 12/538,940. L.B. own stock options of BetterCare S.L., a research and development spinoff of Corporació Sanitària Parc Taulí. The remaining authors have no conflicts of interest.
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Sarlabous, L., AquinoEsperanza, J., Magrans, R. et al. Development and validation of a sample entropybased method to identify complex patientventilator interactions during mechanical ventilation. Sci Rep 10, 13911 (2020). https://doi.org/10.1038/s41598020708144
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