Weaning from Mechanical Ventilation: On the Improvement of the Prediction of Patients’ Readiness with Cardiopulmonary Coupling Indices

The ideal moment to withdraw respiratory supply of patients under Mechanical Ventilation (MV) at Intensive Care Units (ICU), is not easy to be determined for clinicians. Although the Spontaneous Breathing Trial (SBT) provides a measure of the patients’ readiness, there is still around 15-20% of predictive failure rate. This work explores both Heart Rate Variability (HRV) and Cardiopulmonary Coupling (CPC) estimates as complementary information for readiness prediction. The CPC is related to how the mechanisms regulating respiration and cardiac pumping are working simultaneously, and it is deﬁned from HRV in combination with respiratory information. Three different techniques are used to measure CPC, including Orthogonal Subspace Projections, Dynamic Mutual Information and Time-Frequency Coherence. 22 patients undergoing SBT in pressure support ventilation are analysed in the 24 hours previous to the SBT. 13 had a successful weaning and 9 failed the SBT or needed reintubation –being both considered as failed weaning. Results illustrate that traditional variables such as heart rate, respiratory frequency, and the parameters derived from HRV do not differ in patients with successful or failed weaning. However, signiﬁcant statistical differences are found for the novel CPC parameters, throughout the whole recordings, comparing the values of the two groups. In addition, the night prior to SBT is the moment where differences are higher, probably because patients with failed weaning might be experiencing more respiratory episodes, e.g. apneas during the night, which is directly related to a reduced RSA. Therefore, results suggest that the traditional measures could be used in combination with these novel CPC biomarkers to help clinicians better predict if patients are ready to be weaned.


Introduction
Most of the patients admitted to Intensive Care Units (ICU) present symptoms of respiratory failure and need the support of Mechanical Ventilation (MV). MV is a procedure of artificial respiration that supplies or collaborates with a patient's respiratory function, in order to have an efficient gas exchange and reduce the respiratory effort. As the respiratory muscles and the nervous system recover, patients are prepared to maintain normal breathing autonomously, making the respiratory support unnecessary.
This process of withdrawing MV is known as "Weaning" and is a challenging and very delicate procedure. The American Thoracic Society (ATS) and the American College of Chest Physicians (CHEST) identify weaning as an investigation priority anonymous and encrypted to ensure privacy. The guidelines followed in this study were according to the applicable Spanish regulations (Biomedical Research Law 14/2007).
Patients with neurological disorder, dementia or focal brain injury at ICU admission were excluded from the analysis. In addition, only those patients ventilated with assist/support ventilation modes were considered, i.e., excluding patients that were in controlled ventilation modes in the 24 hours previous to the SBT. Data during the 24 hours prior to the SBT were obtained from 22 patients. For this subset, the most common MV mode was Pressure Support Ventilation (PSV), but also some patients spent some time in Continuous Positive Airway Pressure (CPAP). Excluding controlled-MV modes implies that respiration may be more irregular, and apnoea or periodic breathing could happen. An example of the respiratory pattern in PSV mode is shown in Figure 1.

Criteria for weaning readiness
The following criteria were used to determine if a patient was presumably ready to be weaned, i.e., if a patient was ready to perform the SBT 19 Criteria for successful SBT Subsequently, patients presumably ready to be weaned, had to perform the SBT. The SBT was carried out by a low-level inspiratory pressure support or by a T-tube test. The criteria listed in this section show the indicators used to evaluate the success of the SBT, in order to decide if MV could finally be withdrawn.
The following criteria were used to assess if SBT was successful 19

Patient classification and demographics
When the health condition of a patient improved enough, they are probably ready for weaning 19,20 . Then, these patients must perform the SBT. Patients presenting at least one item of the intolerance criteria for successful SBT 19 , were not ready for discontinuation and weaning failure was considered. These patients belong to the F-group. Patients who passed SBT 19 , belong to the S-group. However, 2 patients that passed the SBT required orotracheal intubation or reconnection to non-invasive MV within 48 hours after SBT. These 2 patients were reclassified in the F-group. Refer to Fig.2 for the patient classification scheme. With all these premises, there are 13 patients in the S-group and 9 in the F-group. Accordingly, for the analysed subset, actual weaning readiness is for the 54% of patients, and the SBT was incorrect for the 13% of the tests that passed.  Figure 2. Algorithm for the definition of the weaning success. Patients are classified into the S-group or F-group after the Spontaneous Breathing Trial (SBT). The S-group stands for the group of patients successfully weaned (successful SBT and no need of reintubation). F-group stands for the group of patients with SBT failure and patients with SBT success but with the need of reintubation after 48 hours of weaning. Numbers in parentheses represent the number of patients according to the respective criteria.
The demographics of patients are summarized in Table 1. The variables available include: age, gender, Acute Physiology and Chronic Health Evaluation II (APACHE II), Sequential Organ Failure Assessment (SOFA), reason for MV, MV duration, ICU length of stay, ICU mortality and In-hospital mortality. , is a proprietary system for data collection designed to interact with output signals from mechanical ventilators and bedside monitors rather than directly with patients. It was firstly developed to interoperate signals from different ventilators and monitors, and subsequently compute algorithms for diagnosing patientventilator asynchronies (ClinicalTrial.gov, NCT03451461). Better Care standardizes, synchronizes and stores the signals of all the bedside monitors and ventilators at 200 samples per second, from intubation in the ICU to liberation from MV. It uses drivers specifically designed to interact with output signals from mechanical ventilators and bedside monitors rather than directly with patients. Different biomedical signals were recorded, including the three bipolar leads of the electrocardiogram (ECG), as well as the respiratory signals: air flow and airway pressure. In addition, pulse photoplethysmography, blood pressure via invasive catheter, and SpO 2 were also recorded.
The onset of inspiration for each breath, i, labelled as n I,ON i , was delineated using an algorithm implemented in the Better Care platform. For each respiratory cycle, information on the type of ventilation mode, the trigger of respiration and the appearance or absence of asynchronies, such as ineffective efforts or double cycling, were also given 51,52 . Notice that PSV mode forces spontaneous breathing, so no breath was automatically triggered by the MV.

Methods
Methodologies are based on the signal processing of the ECG and respiration. First, HRV and respiratory information are estimated. Afterwards, the indices of CPC, based on TFC, ID and OSP, can be obtained.
All these different measures are used in this work to characterize the evolution of the ANS function or the CPC mechanisms. However, the algorithms do not extract the information in the same way, and the different indices may have different temporal resolution. For this reason, the average value in consecutive 30-minutes periods is considered for each index, in order to be able to compare all the different estimators through the 24-hour recordings.

HRV and respiratory information estimation
The baseline-corrected tidal volume signal, r(t), is obtained integrating the instantaneous air flow signal followed by baseline subtraction. The baseline is estimated by modified Akima piecewise cubic Hermite interpolation of the n I,ON series estimated at the integrated air flow signal. This ensures that each tidal volume breath begins and ends with zero litres, as depicted in Figure 1. The respiratory frequency signal, F r (t), is derived from the estimation in each breath by computing the inverse of the instantaneous respiration-to-respiration difference, F r , from the n I,ON series. After that, r(t) and F r (t) are resampled at 4 Hz, to obtain the tidal volume signal, r(n), and the respiratory frequency signal, F r (n), respectively.
The lead II of the ECG is upsampled at 1000 Hz with cubic spline interpolation, to ensure that HRV analysis is not compromised by the effect of low sampling frequency 53,54 . Then, the QRS-complexes are detected by means of a waveletbased method 55 . The time between two successive R waves defines the RR interval. Ectopic beats and miss-detections are corrected as described in 56 . The exclusion of non-normal RR intervals, that do not represent the ANS function, results in the normal-to-normal (NN) interval series.
The temporal indices of HRV are calculated from the NN series 43 , and the ones used in this work are the standard deviation of the NN intervals (SDNN), and the root mean-square of successive differences of adjacent intervals (RMSSD). SDNN is the "gold standard" parameter of HRV for medical stratification of cardiac risk, when recorded over a 24-hours period 43 .
Afterwards, the HR is represented to produce a signal which accurately reflects the HRV, so that classical HRV indices in the frequency domain can be derived. In this work, the HRV is estimated using the Time-Varying Integral Pulse Frequency Modulation model (TVIPFM) 57 . Given a particular beat time occurrence series, the instantaneous HR, d HR (t), can be expressed, from the TVIPFM, as d HR (t) = (1 + m(t))/T (t). The term 1/T (t) represents the time-varying mean HR and m(t) represents the modulating signal of interest, which is assumed to contain the ANS modulation of the sinoatrial node. The instantaneous mean HR, d HRM (t) = 1/T (t), is obtained by low-pass filtering d HR (t) at 0.03 Hz. The HRV signal is represented by the term d HRV (t) = d HR (t) − d HRM (t). Finally, the modulating signal is estimated as m(t) = d HRV (t)/d HRM (t) and the evenly sampled version of the modulating signal, m(n), is obtained by resampling m(t) at 4 Hz.
It is known that respiration affects HRV. Therefore, the frequency domain analysis of the HRV is performed guided by respiration 58 . In order to do so, the High Frequency (HF) band is redefined to be centred at the respiratory frequency: 15]Hz, and the HF power, P HF , is defined as the power within this band. Low Frequency (LF) power, P LF , is defined as the power in the classic LF band 43 : Ω LF = [0.04, 0.15] Hz. The use of the modified HF band was also encouraged by the increased F r observed in some mechanically ventilated patients, who had a respiratory frequency above 24 rpm, i.e., 0.4 Hz, that could lead to an underestimation of the power using the classical HF band. The balance between the Sympathetic Nervous System (SNS) and Parasympathetic Nervous System (PNS) activity, the so-called sympathovagal balance 59 , is represented by the power normalized in the LF band P n LF = P LF /(P LF + P HF ).
Since most of the power of HRV in a 24-hour recording resides in the frequencies below HF and LF power, the Very Low Frequency (VLF) power, P VLF , is also studied. The P VLF is accounted for by fluctuations in NN intervals that have a period larger than 25 seconds: Ω VLF = (0, 0.04] Hz. The physiological role of P VLF is still not clear, but it is believed to be related to the circadian rhythms, core body temperature, and metabolism 60 .
These frequency domain parameters are calculated using a TF distribution belonging to the Cohen's class 44 . A time and frequency resolution of 11.25 s and 0.039 Hz, respectively, is used.

Time-frequency analysis
The respiratory influences on HRV can be captured based on TF coherence, which is given by: f ) are the auto-power spectral densities calculated by means of the Cohen's Class Wigner Ville Distribution 44 of respiration, here represented by its surrogate tidal volume r(n), and HRV, represented by m(n), respectively.Ŝ r,m (t, f ) is the cross-power spectral density. An illustrative example of the TFC performance can be seen in Figure 3. A significant coherence level of coupling between HRV and respiration is set by the signal-independent threshold, γ TH (t, f ; α). It is established based on a surrogate data analysis 44 , with α = 5% risk that both signals are coupled when real coupling does not exists γ TH (t, f ; 0.05) = γ 0 . The region Ω r,c HF (t, f ), from which the coherence is estimated, is identified as the region where the TF coherence is significant within the HF band centred at the respiratory frequency, Ω r HF (t): . Time-frequency maps of HRV, respiration and spectral coherence of a five minutes period. The TF map of the respiratory signal,Ŝ r (t, f ), is on (top) and the TF map of the HRV modulating signal,Ŝ m (t, f ), is in the (middle). The TF map of the quadratic spectral coherence between respiration and HRV,γ 2 (t, f ), is in the (bottom). The white-dotted lines in the TF map ofŜ m (t, f ) andγ 2 (t, f ), represent the HF band centred at the respiratory frequency, Ω r HF (t). The regions of coherence with statistical significance within the HF band centred at the F r , Ω r,c HF (t, f ), are the red-colored area in theγ 2 (t, f ) map. For further information, see 44 .
To characterize the temporal evolution of the local coupling between the spectral components of the signals, the index C HF (t) is defined as: This index takes into account the magnitude of the local coupling, averaged in the HF band. Now, if the mean significant coherence, C HF (t), is averaged in a period of time, it yields to the definition of C HF :

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Finally, for all the time course, the existence of significant coupling at any frequency in the whole band Ω r HF (t) is identified as: Once the "mask" T HF (t) is defined, the percentage where TFC is significant in a period of time, T HF , can be defined as: The index of CPC used from this framework is calculated using Eq. (3) and Eq. (5). This index is noted as C T HF and is composed taking into account the mean significant coherence averaged in a period of time, C HF , with the percentage of time where TFC is significant in that same period, T HF : As for the estimation of the HRV frequency domain parameters, the same TF maps are used to obtainŜ r (t, f ),Ŝ m (t, f ) and S r,m (t, f ), using the TF distribution belonging to Cohen's class 44 . As mentioned before, the time and frequency resolution is fixed to 11.25 s and 0.039 Hz, respectively, for the TF distribution.

Dynamic mutual information
It is known that the RSA defines a causal relationship from respiration to HRV, since respiration drives acceleration/deceleration in the HR. This relationship implies that the uncertainty about HRV, can be resolved not only by knowing itself, but also by taking into account the information transferred from respiration. This resolution of entropy, or uncertainty, can be quantified using measures of predictive information 45 .
Let's denote r n and m n as the scalar random values obtained by sampling the process r(n) and m(n), respectively, at the present time, n. If the information carried by the HRV is split into components related to respiration and others, the predictive information leads to the definition of the Cross Entropy (CE) term, C E r↔m . This term quantifies the amount of information shared at a certain time, n, between the present value of HRV, m n , and the past of respiration, r − : where I(·; ·) quantifies the mutual information, H (m n ) expresses the amount of information carried by the process in terms of the average uncertainty about m n , the so-called Shannon entropy. H (m n |r − ) denotes the conditional entropy and it quantifies the average uncertainty that remains about m n when r − is known 45 .
The computation of C E r↔m is done using the approach presented in 45 , using the link between information theory and predictability. It is possible to describe the dynamics of the system using a linear vector autoregressive model.
The model order, M, is defined as the minimum amount of delays obtained using both the Minimum Description Length principle and the Akaike Information Criterion. The maximum possible delay is set to 10 seconds in order to avoid over-fitting. The minimum possible delay is set to the period equivalent to the lowest frequency of the respiration bandwidth in order to avoid a too-simple model.

HRV decomposition
By using subspace projections, the HRV can be decomposed into two different components 46  The OSP projects m onto the subspace V. The matrix V is constructed as a time-delay embedding of r, that spans the subspace V, using M delays. Therefore, the subspace V is defined by all variations in r, in order to extract all dynamics of the

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HRV that are linearly related to respiration. Once the matrix V is constructed, the HRV can be projected onto the respiratory subspace V, by means of the projection matrix P: with the projection matrix, P, obtained from V as: As a result, all dynamics of HRV linearly related to respiration are described in m r . The orthogonal component, m ⊥ , computed as the residual, m ⊥ = m − m r , is explained by all other HR modulators not linearly related to respiration. An example of the HRV decomposition can be seen in Fig.4. It is denoted as m r (n) and m ⊥ (n), when it is necessary to refer generically to those vectors in time.
After decomposing the HRV, the relative power of the respiratory component, P m r , is computed as an estimate of the CPC 46 :

Long-term assessment and statistical analysis
First, since SDNN is the state-of-art index for medical stratification of cardiac risk in long-term analysis, the SDNN is calculated for the whole period of 24 hours before the SBT. The Mann-Whitney U-test is also used to compare the value for the S-group vs. F-group.
After that, the evolution of the common clinical parameters, HRV and CPC indices, through the 24 hours before SBT are analysed, in order to determine if circadian rhythms could be affecting the regulatory mechanisms and the interpretation of the results. However, it must be considered that the SBT's are generally performed in the morning, but not at the same exact time for all patients. For this reason, all the recordings are segmented from 08:00 p.m. to 10:30 a.m. of the SBT day, so that the same time interval is considered for all the patients. This means that it is being considered only some part of the circadian rhythm.
At this point, the average value in consecutive 30-minutes periods is considered, for the representation of the evolution through the day and for the statistical analysis. To this end, each HRV and CPC indices are calculated separately using different temporal resolutions:

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• The parameters F r and HR are unevenly sampled at the inspiration onset and heart beats occurrence, respectively. Therefore, the mean value in each half hour is computed. • For the computation of C E r↔m , P m r , and the temporal HRV parameters -SDNN and RMSSD-, sliding windows of 3-min-length with 75% of overlap are used. For these, there is a sample each 45 seconds and a total of 1920 samples in 24 hours. So, the mean of 40 overlapped windows in each 30-minutes period is computed, for each parameter and for each patient. • Finally, the C T HF and the frequency domain parameters of HRV -P VLF , P HF and P n LF -are calculated using the TF distribution belonging to Cohen's class 44 . Therefore, these indices are calculated at the resampling frequency, F s = 4 Hz, and thus the average value of 7200 samples, i.e., 30 minutes, is obtained. Finally, the averaged values for the S-group vs. F-group are compared with the non-parametric unpaired Mann-Whitney U-test, for all the parameters. Differences are considered significant for a level of p ≤ 0.05. Table 2 shows the median and quartiles 1 and 3 of the SDNN, calculated in the whole recordings of 24 hours. Higher SDNN is visible for the S-group patients, and although the difference is not significant, the p-value approaches 0.05. As expected, the SDNN values are higher considering the 24-hours recordings (see Tab.2), than considering the averaged 3-minutes windows (see Fig.6), for the same group of patients. The evolution of the patients throughout the day before SBT, from 08:00 p.m. to 10:30 a.m., are illustrated in the Figs. 5, 6 and 7. The commonly-used clinical variables respiratory frequency, F r , and heart rate, HR, -shown in Fig.5-, can be compared to the parameters of HRV -in Fig.6-and the CPC estimators -in Fig.7.

Results
Looking at Fig.5, both F r and HR rely within the limits of criteria for weaning readiness. In general, patients of the F-group have little higher HR and F r . The F r is significantly higher only at 9:00, moment when HR differences are larger between both groups. However, no big differences throughout the recordings, during night or day, are appreciable.  Figure 5. Evolution of the common clinical indices for weaning readiness before SBT. The mean respiratory frequency, F r , and mean HR, are represented. Green and Red boxplots represent the patients of the S-group and the F-group, respectively. The p-value comparing each half hour is represented in the right axis, from 0 to 1, and the dotted line represents the p = 0.05 threshold. The asterisks indicate statistical significance with p ≤ 0.05. Fig.6 shows the evolution of the HRV parameters. The RMSSD is higher in the S-group during the entire recording since midnight, apparently the moment when patients fall asleep. In particular, after waking up, at around 7:00 a.m., significant differences are found. Correspondingly, looking at the P n LF , an increment can be seen for the F-group, starting at 00:00, compared to the slight decrease for the S-group. This increment for the F-group can be associated with a SNS activation, in view of the sudden increase of the P HF and P VLF at the very same time. Curiously, sudden changes can sometimes be found on the P VLF , especially for the F-group. However, much variability exists for the P VLF power, and neither significant differences nor appreciable patterns on the P VLF evolution can be found. . Evolution of the HRV indices before SBT. The temporal parameters SDNN and RMSSD, and the frequency parameters, P VLF , P HF and P n LF are represented. Green and Red boxplots represent the patients of the S-group and the F-group, respectively. The p-value comparing each half hour is represented in the right axis, from 0 to 1, and the dotted line represents the p = 0.05 threshold. The asterisks indicate statistical significance with p ≤ 0.05.
The evolution of the CPC estimates is illustrated in Fig.7. As said, CPC estimators are computed considering respiration to be the system driving changes in the HRV. Clear differences exist in the CPC mechanism comparing the patients that were successfully weaned, S-group, and the patients reintubated or that still needed time in MV, F-group. The C T HF index quantifies the mean coherence normalized by the amount of time in coherence, in the HF band centred at the respiratory frequency. It is higher when HRV and respiration have components at the same frequencies, taking into account that these components have different physiological origin. Differences are significantly higher, particularly during the night. The C E r↔m term, that represents the amount of information shared between respiration and HRV, is larger for the S-group. This amount of information shared is higher during the night than in the morning before the SBT, especially for the S-group. The P m r represents the relative power of the respiratory component inserted within the HRV. It is also higher for the S-group than for the F-group. Remark that the p-values since 9:00 a.m. approximately, right before the SBT, increases abruptly for the 3 CPC indices. This means that the differences between the two groups are less substantial for the time before performing the SBT.

Discussion
HRV and CPC have been analysed for a total of 22 patients presumably ready for weaning, in the 24 hours before the SBT. Statistical differences have been found comparing patients who needed reintubation or required more time in MV, the so-called F-group, and patients with a successful extubation process, S-group. These differences are especially appreciable for the parameters estimating the CPC. The fact that the CPC changes so much with respect to the S-group can be related to a more unstable regulatory system. By monitoring this in the night, or in a continuous way, clinicians can obtain additional information Evolution of the CPC estimators before SBT. The CPC parameters C T HF ,C E r↔m and P m r , are represented. Green and Red boxplots represent the patients of the S-group and the F-group, respectively. The p-value comparing each half hour is represented in the right axis, from 0 to 1, and the dotted line represents the p = 0.05 threshold. The asterisks indicate statistical significance with p ≤ 0.05. of this stability that can help to make the decision to wean a patient from MV.
The patients of the S-group have higher values of SDNN, calculated over 24 hours (see Tab.2). A major component of SDNN is due to a higher variability and day-night difference of the HR. This shows a better adaptability of the heart to changes, for patients actually ready for weaning, S-group.
Remark that the SBT is not performed at the same time for all the patients. Hence, in order to have all recordings of the patients aligned in time, some segments had to be omitted at the start and end of the recordings for some patients.
The mean respiratory frequency, F r , was always above 9 rpm, i.e., 0.15 Hz. However, for some patients, it was above 24 rpm, i.e., 0.4 Hz (see Fig.5). Moreover, in other studies like 61 , they found that HRV analysis guided by respiration improved the ability of HRV to discriminate cognitive stress in healthy subjects. Therefore, the need to centre the HF band in respiration is crucial to make a proper and more powerful interpretation of the results in the frequency domain.
The evolution of the currently-used clinical variables, HR and F r , is very similar for both groups. It is clear that these parameters are not giving useful information to predict weaning readiness. On the contrary, some HRV parameters seem to better discern both groups. The temporal parameter RMSSD has higher values for the S-group, in accordance with the fact that this index quantifies parasympathetic modulation of NN intervals driven by respiration and vagal modulations 60 .
These modulations of the vagal activity are also quantified by P HF . Notice that the P HF is much higher for some patients of the F-group, around 11 p.m., and around 8:00 a.m. The rest of the time, mainly during sleep at night, P HF is higher for the S-group, in agreement with the results of 28 . The time when P HF is higher for the F-group, occurs before going to sleep and waking up. However, the P VLF and P n LF are also higher, so strong vagal modulations are in conflict with strong sympathetic activations. Moreover, this sudden increase in the P HF for the F-group, that could be interpreted as an increase of the vagal activity, is not present in the CPC parameters. These patients are an example where the frequency content in the HF band does not contain only respiratory information (see Fig.4). These HF components can be a consequence of the non-linear effects of respiration transferred to the HR. These non-linear influences could be mediated by the respiratory pacemaker in the central nervous system 62 through SNS modulations 63 , and the CPC estimates used in this work are unable to detect them. Further investigation is required using techniques able to take both linear and non-linear effects into account. Methodologies that are able to quantify up to second order interactions by detecting and quantifying the quadratic phase coupling 64 could account for this fact or also techniques based on least-squares support vector machines formulated for non-linear function estimation 65 .
The P n LF is the standard measure of the sympathovagal balance. However, it has already been proven that P n LF is not an appropriate measure of the vagal and sympathetic modulations 46,66 , and that maybe is why only slight differences can be appreciated during the night. Therefore, in this context of the ICU, where patients are continuously monitored, P n LF is not recommended as an index to use as a reliable weaning predictor. At this point, results of the CPC parameters were encouraging. First, the TFC exhibited illustrative results. The C T HF , is the CPC estimator which exhibits larger differences between S-group and F-group patients. These results are also in agreement with those obtained using mutual information, where higher C E r↔m values were found in the S-group than in the F-group. Finally, there are also visible differences looking at the relative power of respiration, P m r , inserted into the HRV: patients of the S-group had a relative power around the 25% of respiration, but those of the F-group had it around 5%. Altogether, this illustrates that those patients who are actually ready for weaning, have good levels of RSA and that their CPC system is ready to work, in contrast with the patients who did not pass SBT or needed reintubation. Therefore, these CPC estimators are promising as additional indexes to improve the weaning readiness criteria.
Moreover, these differences in the CPC parameters are more evident during sleep than right before the SBT, what could be due to the loop gain. In other words, patients with failed weaning might be experiencing more apnoea events during the night, which is directly related to a reduced RSA and a higher cardiovascular risk 40,67 . In fact, the PNS activity is well known to be predominant during sleep at night. Consequently, it is in this moment when the CPC is stronger. Results suggest that the proper moment to test readiness is during the night, more than during the early morning. Probably, it would be better to check at night how the patient behaves to decide whether to wean. However, one limitation is that the patients in the ICU may not keep similar sleep patterns. Nowadays, clinicians assess whether the patients can perform SBT when they are awake in the morning and conscious. The patients, knowing that they have to prepare for the SBT, can generate high levels of stress and anxiety, and this can alter their biomarkers (HR, F r , CPC estimates, SpO 2 , HRV, etc.), towards more alert-related values. In point of fact, less clear differences are found at this time, in the morning right before the SBT.
The computational cost for obtaining P m r is low and it may be obtained in real time in the same way as the standard clinical parameters. On the other hand, the computational cost for obtaining C E r↔m or C T HF is higher, but they could also be obtained in quasi-real time. Therefore, these algorithms can be implemented in the ICU monitors, and the CPC status could be assessed continuously, together with the well-known clinical variables.
In a preliminary analysis of this study, other CPC estimators were also explored, like the other entropy measures from the ID framework, the bandwidth of the TFC and the unconstrained sympathovagal balance from the HRV decomposition. However, the indices with best performance were the ones presented here, namely P m r , C E r↔m and C T HF . Interestingly,the study in 50 analyses the best methods for RSA estimation in a simulation study, and concludes that the same three parameters are the best estimators of the CPC.
Other works compare the values of the indices obtained right before the SBT with the values obtained after the SBT 17,27,28,30 , and all of them found some differences in the HRV parameters. The very important difference of the present study with the state-of-the-art is that the indices and evolution of the patients are obtained only before the SBT and using the long-term information. The fact that the weaning readiness prediction can be improved using CPC indices could only have been revealed using long-term analysis.
In 68 , they stress the importance of the P VLF power in the weaning scenario. The P VLF power, partially related with the circadian rhythms 60 , could provide useful information of the neurohumoral regulatory mechanism 69 . On the contrary, here it is illustrated that the P VLF power is not so relevant in the analysis of the 24 hours prior to SBT. Nevertheless, some patients in this MV and ICU context showed strong characteristic VLF oscillations, possibly also related with sleep disorders, that must be further studied. These sudden changes cause non-stationarity, and this is the reason why 3-minute sliding windows and TF analysis are used to calculate the indices.
Further studies should be performed including controlled MV modes, in order to obtain a complete knowledge of the CPC regulation mechanisms during the whole weaning process. As said, only patients in CPAP or PSV modes are analysed in this study as these MV modes force spontaneous breathing. Therefore, there is no influence of the ventilator into the CPC mechanisms, through automatized respiration driven by the ventilator. Perhaps, in the controlled MV modes, it is the ventilator the one controlling respiration -not the ANS-, and the HRV would be the driving system, since the ventilator would be the one regulating respiration externally. This might lead to a different impact on the CPC estimators, since synchronization and coordination of the regulatory mechanism could change.
The clinical utility of this, and future studies, is that if HRV and CPC are actually proven to predict weaning failure, they might be incorporated as screening parameters. In other words, HRV and CPC could be calculated or assessed before weaning, in a multimodal index combined with the current parameters to reinforce the prediction of weaning success or failure. In fact, looking at Tab.1, patients with failed weaning had a higher mortality rate, and spent more days in MV and in the ICU. Therefore, this multimodal index could help to reduce these weaning failure rates and the very adverse effects associated with reintubation, to thereby result in better clinical outcomes.
Finally, it must be kept in mind that patients in the ICU are admitted from very diverse diagnostics. Taking this into account, two patients with the same characteristics and similar evolution may get different outcomes. Hence, sometimes, a patient who does not meet the readiness criteria can be also successfully weaned, and viceversa 15 . This is why clinicians take the criteria for

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weaning readiness and SBT performance as one among several considerations rather than rigid requirements. Such uncertainty can be reduced by implementing new research and technologies to daily clinical practice 70,71 , and this study is other step forward in the field of predictive precision medicine, that exploits the capabilities of the CPC estimates.

Conclusions
This study analysed the evolution of patients undergoing weaning from MV in the 24 hours before the SBT, considering that all patients were "ready" for discontinuation from MV. Furthermore, this evaluation was done looking only at the results before performing the SBT, but because of this, it was needed a long-term analysis.
None of the parametric measures currently used as clinical criteria for weaning readiness showed noticeable differences between the patients actually ready for weaning and the patients who did not pass the SBT or those who needed reintubation. However, it was revealed that patients successfully weaned exhibited higher CPC values, assessed with the variables C T HF , C E r↔m and P m r , specially, during the night prior to the SBT. In addition, it was shown that some differences exist for the HRV parameters, but not as strong as for the CPC indices.
As it was stated, the information that clinicians are handling in the ICU at this moment is not enough to decide weaning readiness. By way of conclusion, it was found that these CPC indices have information of the weaning readiness, but even before performing the SBT. The potential predictive value of these CPC indices should be considered and further studied, in order to implement this technology into the daily clinical practice, integrating software systems like Better Care in the ICU's. This will help to reduce weaning failure rates, the very adverse effects associated with the reintubation process and thereby result in better clinical outcomes.