2.1.

Diffuse Optical Device

The hybrid diffuse optical device used the combination of TRS and DCS and is described in detail in Refs. 5758.–59. Near-infrared light was sent into the tissue through a set of fibers incorporated into a combined DCS/TRS-BIS probe with a source-detector separation ($\rho$) of 25 mm for both optical modalities. Diffuse optical data were measured unilaterally on the left frontal lobe during extracranial surgical procedures due to the fact that the BIS signal was retrieved from this cerebral hemisphere. The combined DCS/TRS-BIS probe is shown in Fig. 1. The probe was designed around the BIS sensor while providing a compact housing for the source and detector fibers of both modalities, as shown in Fig. 1. It was 3D printed in TangoBlack shore 27 material (Stratasys Ltd., Eden Prairie, Minnesota) and incorporated in a head strap that was wrapped around the patient’s head. A Coban bandage (CobanTM, 3M TM) was used to keep stable the probe placement.

Fig. 1

(a) Bottom view of the 3D printed combined BIS-TRS/DCS probe. The first three electrodes of the BIS sensor are placed on the subject’s left forehead followed by the black fiber pad which fits around the BIS sensor. The fourth electrode is attached next to the patient’s left eye. Source (top) and detector (bottom) fiber tips are placed in between the first and second electrodes, surrounded by TangoBlack shore 27 material. (b) TRS and DCS acquired data in alternation. The intensity autocorrelation curves were calculated for 2.5 s, while the system switched through all three TRS lasers with an acquisition time of 800-ms per wavelength.

Briefly, the device consists of a single longitudinal mode laser operating at a wavelength of 785 nm for DCS measurements (DL785-120-SO, CrystaLaser, Reno, Nevada) and with pulsed light sources at 690, 785, and 830 nm for TRS measurements (BHLP-700, Becker & Hickl GmbH, Berlin, Germany). At the DCS detection site, a set of four single-photon counting avalanche photodiode collected the diffuse photons. A fiber bundle collected the TRS light and guided it into a hybrid photomultiplier detector, operated by a control card (HPM-100-50 and DCC-100 Becker & Hickl GmbH, Berlin, Germany). The detector signal was processed by a single photon counting card and a manufacturer-provided software (SPC-130 and SPCM, Becker & Hickl GmbH, Berlin, Germany).

The TRS and DCS modalities were multiplexed by an optical switch (Piezosystem Jena GmbH, Jena, Germany), so the DCS data could be acquired during 2.5 s, while a TRS measurement (800-ms per wavelength) was carried out alternately. Figure 1 shows the acquisition of TRS and DCS data. The entire device was controlled by a PC.

Events such as patient movement, substances injection, failures, etc. were recorded both by a marking routine included in the software, that recorded it in the data files of the hybrid device, and by detailed notes on measurement protocols, to be able to trace-back and relate such eventualities in the post-processing phase.

2.2.

Clinical Data and Patient Medications

In addition to the recordings provided by the hybrid diffuse optical setup, ${\mathrm{SpO}}_2$, heart rate (HR) and mean arterial pressure (MAP) were extracted from either an anesthesia monitor (Datex-Ohmeda Aisys™, GE Healthcare, Little Chalfont, United Kingdom) by the open-source VitalSigns capture (VScapture) program⁶⁰ or from a general monitor (Philips IntelliVue MX800, Koninklijke Philips N.V.). The BIS data were acquired by a BIS sensor (BIS Vista™, Medtronic plc, IRL). These signals were recorded by the same monitor with the same timestamps and were synchronized with the optical signals with a precision of 1 s and according to the beginning of the measurement.

General anesthesia was performed under total intravenous anesthesia with propofol at a concentration of 1% (Propofol Fresenius^®, Fresenius Kabi Deutschland GmbH, Bad Homburg, Germany) using the Schneider model of target-controlled infusion anesthesia⁶¹ based on age, height, weight, and gender of the patient^3,62 implemented in a TIVA system (Alaris Asena^® PK, Becton, Dickinson and Company, Franklin Lakes, New Jersey). After induction and tracheal intubation, pulmonary volume-controlled ventilation was maintained with a fraction of inspired oxygen (${\mathrm{FiO}}_2$) of 0.5, a tidal volume of 6 to $7\mathrm{mg}/\mathrm{kg}$, a respiration rate between 12 and 16 breaths per minute, a positive end-expiratory pressure of 4 to 6 mmHg, and a MAP between 60 and 80 mmHg.

It should be noted that the patients received further medications, such as fentanyl for analgesia,^63–65 atropine sulfate, atracurium besylate, or rocuronium bromide to obtain neuromuscular blockade, remifentanil, neostigmine, lidocaine, and midazolam. Some of them are known to influence cerebral hemodynamics (i.e., fentanyl,^63–65 midazolam,⁶⁶ remifentanil,⁶⁷ atropine sulfate,⁶⁸ and lidocaine⁶⁹). Our study is not designed to investigate these interactions and it is not trivial to consider these effects since they are not well known. Since the primary goal of the study the direct comparison of the optical and BIS signals, we have decided to remove the duration of their administration from all the signals as described in the following section.

2.3.

Data Evaluation

The data were first evaluated by fitting the respective semi-infinite medium solutions of the photon diffusion equation to the optical measurements.^70–72 The fitting was done using the downhill-simplex or Nelder-Mead method in MATLAB™’s implemented fminsearch function.^73,74 Further data analysis was then carried out in R⁷⁵ (v4.0.1, R Core Team, 2019) and the integrated development environment RStudio (v1.1.5042, RStudio, Inc., Boston), especially for the calculation of OEF and ${\mathrm{CMRO}}_2$,⁷⁰ artifacts removal and data re-sampling. Data collected during patient movements in the surgery were excluded from the dataset. When further medications clearly changed the optical signals or BIS, they were generally recorded with a mark and were excluded as well during post-processing. The data were grouped in 5 s bins for each patient to match the BIS sample size.

The oxy and deoxyhemoglobin (${\mathrm{HbO}}_2$ and Hhb) contents were calculated using the wavelength-dependent absorption coefficients (${\mu }_{\mathrm{a}}$) from TRS measurements (see Sec. 2.1). Three main tissue constituents (${\mathrm{HbO}}_2$, Hhb, and ${\mathrm{H}}_2\mathrm{O}$) were considered. The tissue oxygen saturation (${\mathrm{StO}}_2$) was calculated as the ratio of ${\mathrm{HbO}}_2$ concentration over the sum of ${\mathrm{HbO}}_2$ and Hhb concentrations.

Assuming that blood volume percentage in the venous compartment ($\gamma$)⁷⁶ does not change (${\gamma }_1={\gamma }_2$), the measures of ${\mathrm{StO}}_2$ were converted into relative OEF (rOEF) and ${\mathrm{CMRO}}_2$ (${\mathrm{rCMRO}}_2$) changes using the relation:^{48,70,76–78}

2.4.

Statistical Analysis

The hypotheses of this study were: (1) after propofol induction, CBF and ${\mathrm{CMRO}}_2$ decrease (as BIS does) with respect to the initial baseline; (2) after propofol reduction, CBF and ${\mathrm{CMRO}}_2$ increase (as BIS does); (3) during the beginning of the surgery, the time of the changes in CBF, OEF and ${\mathrm{CMRO}}_2$ shows a correlation with the times of change of BIS; and and (4) during the end of the measurement, the time of the changes in CBF, OEF, and ${\mathrm{CMRO}}_2$ shows a correlation with the times of change of BIS.

Relevant R packages exploited for this purpose and data visualization were nlme (v. 3.1-152), lme4 (v. 1.1-27), lmerTest (v. 3.1-3), and stats (v. 3.6.3).

First, the times corresponding to the induction of TIVA and the end of propofol infusion were identified for all measurements on BIS time-traces according to the marked events.

Short periods (100 s) around these times were selected for each measurement session as including the LOC and ROC. A total of four windows of interest were then defined during these two periods, two for the initial period and two for the final period. All windows had a duration of 100 s and they were chosen and labeled as follows. The “before anesthesia onset” window was defined just before the event of propofol injection. The before anesthesia onset was the baseline for the initial period and thus used to normalize all data for the entire initial period, providing relative values ($r{\mathrm{BIS}}_i$ where the index “$i$” stays for induction). The “after stabilization” window following the anesthetics induction was symmetrically centered around a point that was automatically identified as the minimum value after BIS decreased at least below 40 and over a range of the signal that included the arrival at a stable condition after LOC. The “recovery” window (recovery and used as a second baseline) was selected after the maximum point that was automatically identified after BIS increased at least up to 65. The recovery window was the baseline for the second period and was used to normalize all, providing relative values ($r{\mathrm{BIS}}_r$ where “$r$” stays for recovery). The “before end of anesthesia” window was taken just before the event marking the end of propofol infusion. The choice of using two baselines was made to focus just on the initial and final parts separately, discarding all the changes that occurred during the whole surgery and artifacts. The same four temporal windows were then applied to the optically derived relative time-traces ($r{\mathrm{CBF}}_i$, $r{\mathrm{CBF}}_r$, $r{\mathrm{OEF}}_i$, $r{\mathrm{OEF}}_r$, $r{\mathrm{CMRO}}_{2i}$, and $r{\mathrm{CMRO}}_{2r}$).

Afterward, the median of all relative time-traces was calculated separately over the windows and divided into four groups according to the window of origin (before anesthesia onset, after stabilization, before end of anesthesia, and recovery). Medians were chosen over means to account for any remaining outliers that may influence the mean. Boxplots for each group of medians and each variable were then depicted for data visualization purposes. To test hypotheses, Wilcoxon paired samples tests (Wilcoxon signed-rank test) were used to compare groups two by two: data for groups after stabilization were then compared to the data for group before anesthesia onset, while before end of anesthesia to recovery. For ${\mathrm{rBIS}}_i$, ${\mathrm{rCBF}}_i$, ${\mathrm{rOEF}}_i$, and ${\mathrm{rCMRO}}_{2}i$, it was tested the alternative that the after stabilization group was lower than the baseline group before anesthesia onset. On the contrary, ${\mathrm{rBIS}}_r$, ${\mathrm{rCBF}}_r$, and ${\mathrm{rCMRO}}_{2}r$ were tested for the alternative that the recovery group was greater than the baseline group before end of anesthesia; while for ${\mathrm{rOEF}}_r$ it was tested if the recovery group was lower than the before end of anesthesia one. A similar approach was taken also with the other physiological variables (MAP, HR, and ${\mathrm{SpO}}_2$), as explained in Appendix 6.2.

Furthermore, a percentage of change was calculated to quantify the amount of change per each time-trace with respect to the baseline. This percentage was expressed as the ratio between the absolute value of the difference of the median value of the group after stabilization or recovery and the median value during the baseline before anesthesia onset or recovery respectively multiplied by 100 and the median of the corresponding baseline period again. Similarly were calculated their respective interquartile ranges (IQR) as a percentage.

Then, the time-traces per each measurement session were considered separately, aiming at testing the same hypotheses on an individual basis. Unpaired Wilcoxon test was used to test whether the difference between the window of after stabilization or before end of anesthesia and the mean of their respective baseline window before anesthesia onset or recovery was different from zero. The test was repeated for both single-sided cases, greater or lower than zero. A change was considered significant if the p-value was lower than 0.05. When the difference was significantly greater than zero, it was acknowledged as a positive change, an increase; on the contrary, as a negative change, a decrease. If none of the tests was significant, it was marked as constant, “no change.” Whenever a change was found to be significant, its direction, either as an increase or a decrease with respect to baseline, was counted and the prevalent direction for the non-invasive signals compared to the BIS one.

Finally, the correlation in time between non-invasive hemodynamic profiles and the BIS was investigated by verifying whether they were subject to concomitant changes. In this regard, the times at which the time-traces for each measurement session exhibited a change were identified. The initial period focused on the data around the LOC, starting 100 s before the TIVA induction and lasting until a new stable level of the time-trace was reached. The final period was selected starting 100 s before the end of propofol infusion and lasting until the end of the measurement session.

The identification of the moments of change was performed automatically by exploiting the Lavielle method^79,80 (function lavielle in R), which is capable of detecting the moment when a statistical change occurs in a time-dependent signal and is exemplified in Fig. 2. The number of segments into which the algorithm divides a time-trace (either initial or final) was set to three, to match the expected three periods, i.e., baseline, transition, and new stable level. As a consequence, two points of change were identified for the initial period and two for the final one. They were labeled as “anesthesia onset” and “time to reach stabilization” for the initial transition, while as “end of anesthesia onset” and “time to reach plateau” for the waking up transition.

Fig. 2

Exemplification of the automatic segmentation by the Lavielle method. (a) The period of LOC for the variables of relevance (${\mathrm{rBIS}}_i$, ${\mathrm{OEF}}_i$, ${\mathrm{CBF}}_i$, and ${\mathrm{CMRO}}_{2i}$) in time is depicted. The period includes an initial baseline, a transition period and then another period that reaches a stable condition. The moments in the time axis where the segments split the time-traces are then collected. In the LOC, the anesthesia onset corresponds to the change point between the initial baseline and the beginning of the transition; while the time to reach stabilization coincides with the moment in which the transition ends and the new stability level is reached. (b) Similarly, on the right there is an example focused on the ROC. Here, the end of anesthesia onset and time to reach plateau are identified.

The four points were collected for the four variables of interest (rBIS, rCBF, rOEF, and ${\mathrm{rCMRO}}_2$) per measurement session and grouped according to the four labeled times. Some cases were discarded, as detailed in Appendix 6.1. Then, each group of points was used to check the correlation in time between rBIS points and the optically related ones using R Pearson correlation coefficients, which were computed and reported together with $p$-values (significant when lower than 0.05). Additionally, to visualize the relation, rBIS was plotted versus rCBF, rBIS versus rOEF and rBIS versus ${\mathrm{rCMRO}}_2$ and linear regression lines were depicted with the 95% confidence interval.

3.1.

Study Population

About 29 patients were enrolled in this study, but six had to be excluded from the analysis because of missed recording of the propofol induction and final recovery. Details about data unavailability and discarded subjects are reported in Appendix 6.1. About 23 patients (15 men and 8 women) were included for further analysis. For this population, the average (standard deviation) age was 55.2(11) years and the body mass index (BMI) was $28.5(4)\mathrm{Kg}/{\mathrm{m}}^2$. Demographic and clinical data are provided in Table 1.

Table 1

Demographic table related to the included subjects and reporting the sex (M: male, F: female), age, BMI, and surgery type. The discarded subjects were not included in this table, and for this reason, the identification (ID) numbers of the subjects are not sequential.

3.2.

Optical Data

Figures 3 and 4 show examples of time-traces during anesthesia induction and over the wake-up phase. The relative changes in BIS, OEF, ${\mathrm{CMRO}}_2$, and CBF from the left cerebral hemisphere are represented as well as absolute ${\mathrm{StO}}_2$ and BIS.

Fig. 3

Representative time evolution of the (a) BIS; (b) tissue oxygen saturation (${\mathrm{StO}}_2$); (c) rBIS. (d) The relative oxygen extraction fraction (rOEF); (e) the relative cerebral metabolic rate of oxygen extraction change (${\mathrm{rCMRO}}_2$); and (f) the relative CBF change (rCBF) during anesthesia induction ($t_0$ 3 minutes) by propofol (1%).

Fig. 4

Representative time evolution during ROC of the (a) BIS; (b) tissue oxygen saturation (${\mathrm{StO}}_2$); and (c) relative BIS (rBIS). The relative changes of (d) the oxygen extraction fraction (rOEF), e) the cerebral metabolic rate of oxygen extraction (${\mathrm{rCMRO}}_2$) and (f) the CBF (rCBF) are also shown at the end of the surgery performed under TIVA with propofol (1%) ($t_{\text{end}}$ 207 minutes).

In Fig. 3, the above-mentioned parameters are plotted around the initiation of general anesthesia by TIVA of propofol at $t_0$ 3 minutes and are excerpts from the entire procedure from subject 13.

In this example, the BIS value decreases from around 90 to about 30 [Fig. 3(a)], which represents a characteristic BIS drop due to induction of general anesthesia by TIVA with propofol. The ${\mathrm{StO}}_2$ starts from around 68%, rises to 71% and then decreases to 66%. rBIS has a drop of 66% [Fig. 3(c)] if the baseline value is considered as 100%. Relative OEF shows an upward tendency after induction. Similarly to the observed BIS change, the ${\mathrm{rCMRO}}_2$ and the rCBF [Fig. 3(f)] decreased by about 60% [Fig. 3(e)] referred to a 100% baseline. The baseline relative values for the optical variables were equal to 1 (100%). After the change, during the selected window that was used for the following analysis, the relative values of the median (standard deviation) were: 0.29(0.03) for the rBIS, 0.35(0.05) for rCBF, 0.32(0.05) for rCMRO₂ and 0.92 (0.09) for rOEF.

In Fig. 4, a characteristic time evolution of BIS, ${\mathrm{StO}}_2$, rBIS, rOEF, ${\mathrm{rCMRO}}_2$, and rCBF are plotted during the ROC phase of subject 29. The propofol perfusion was stopped at $t_{\text{end}}$ 207 minutes.

BIS increases from around 40 to 50 to about 70 as a reaction to the end of the general anesthesia by TIVA with propofol [Fig. 4(a)]. ${\mathrm{StO}}_2$ increases from around 55% up to 67% [Fig. 4(b)]. In this case, a window after the TIVA end is averaged and defined as a new reference as previously described. An rBIS raise of about 55% is observed [Fig. 4(c)] if the new reference is set as 100%. ${\mathrm{StO}}_2$ increases, and since the ${\mathrm{SpO}}_2$ did not show a change for this subject, rOEF decreased by about 27% [Fig. 4(d)]. ${\mathrm{rCMRO}}_2$ and rCBF showed a positive change recovering of up to 100%.

In Fig. 5, on the left, the results of the group analysis are reported. For the initial part of the measurement, focused on the LOC, ${\mathrm{rBIS}}_i$, ${\mathrm{rCMRO}}_{2i}$, ${\mathrm{rCBF}}_i$, and ${\mathrm{rOEF}}_i$ all showed a significant decrease for the corresponding after stabilization window with respect to their before anesthesia onset ($p<0.0001$, $p<0.01$, $p<0.01$, and $p<0.01$, respectively). The amount of percentage change calculated considering the baseline as 100% was $-67\%$ ($\mathrm{IQR}-62\%$ to $-71\%$) for ${\mathrm{rBIS}}_i$, $-33\%$ ($\mathrm{IQR}-18\%$ to $-46\%$) for ${\mathrm{rCMRO}}_{2i}$, $-28\%$ ($\mathrm{IQR}-10\%$ to $-37\%$) for ${\mathrm{rCBF}}_i$ and $-5\%$ ($\mathrm{IQR}-1\%$ to $-18\%$) for ${\mathrm{rOEF}}_i$.

Fig. 5

Data group visualization by boxplots for the periods of LOC and ROC. Both periods include the data distributions for the four variables (rBIS, rCBF, rOEF, and ${\mathrm{rCMRO}}_2$) around the group median and are all compared to their respective baseline period (either before anesthesia onset or recovery), which equals one and is represented by a dashed gray line. Percent changes of the medians are also reported close to arrows that show the direction (higher-up or lower-down) with respect to baseline. $P$-values for testing the difference of the group median with respect to baseline are reported. Asterisks indicate significant $p$-values. Subjects are color-coded in the same way for all variables.

Similarly, the group results for the final part regarding the ROC phase are on the right part of Fig. 5. ${\mathrm{rBIS}}_r$, ${\mathrm{rCMRO}}_{2r}$, ${\mathrm{rCBF}}_r$, and ${\mathrm{rOEF}}_r$ all showed a significant change for the corresponding before end of anesthesia window with respect to the recovery window ($p<0.0001$, $p<0.05$, $p<0.01$, and $p<0.001$, respectively). This change was an increase for the first three variables, with a percentage of +48%(IQR +38% to +55%) for ${\mathrm{rBIS}}_r$, +29%(IQR +17% to +39%) for ${\mathrm{rCMRO}}_{2r}$, and +30% (IQR +10% to +44%) for ${\mathrm{rCBF}}_r$. Instead, ${\mathrm{rOEF}}_r$ decreased by −7%(IQR −20% to −1%) during the final period.

We did not find any significant change in the other monitored systemic parameters.

The tests results of the subject-by-subject analysis of the direction of change are summarized in Table 2. For ${\mathrm{rBIS}}_i$, all after stabilization to before anesthesia onset comparisons lead to a significant decrease (21/21). For ${\mathrm{rCBF}}_i$, 14/18 comparisons led to a significant decrease, while 4/18 to a significant increase. For ${\mathrm{rCMRO}}_{2i}$, after stabilization windows showed a significant decrease with respect to before anesthesia onset for 12/18 measurements, a significant increase in 4/18 and showed no change in 2/18 cases. ${\mathrm{rOEF}}_i$ decreased significantly in 10/19 comparisons, increased significantly in 3/19 and showed no change in 6/19.

Table 2

Summary of single subjects results. For all variables, the number of events was counted and reported against the total number of measurements included for that subject. For the initial part, related to the LOC, after stabilization-mean(before anesthesia onset) windows were tested against zero; while for the final part, related to the ROC, before end of anesthesia-mean(recovery) windows were tested against zero. For the beginning, the majority of the cases for all variables present a significant decrease. Instead, rCBF, rCMRO2, and rBIS show a majority of increases for the final part, while rOEF an increase.

The evaluation of the variables during the ROC showed that ${\mathrm{rBIS}}_r$ had a significant increase for all measurements (23/23). $\mathrm{rCBF}r$ had a significant increase in 19/21 cases and a significant decrease in 19/21. ${\mathrm{rCMRO}}_{2r}$ decreased significantly in 13/18, stayed constant in 2/18 and increased in 3/18 subjects. ${\mathrm{rOEF}}_r$ increased in 5/19 measurements, did not vary significantly in 4/19, while it decreased significantly in 10/19.

In relation to the analysis of the correlation in time, a total of 12 plots with the linear regressions and $R$ Pearson correlation values are shown in Fig. 6. The results for the initial period are reported in the first two columns of plots: all cases showed a $p$-value lower than 0.05. For the anesthesia onset, Pearson coefficients $R$ were 0.94 for CBF-BIS time, $R=0.78$ for OEF-BIS time and $R=0.95$ for ${\mathrm{CMRO}}_2$-BIS time. For the time to reach stabilization, $R$ was equal to 0.87 for CBF-BIS time, $R=0.69$ for OEF-BIS time and $R=0.9$ for ${\mathrm{CMRO}}_2$-BIS time. $R$ is always higher than 0.6 and positive. For the final part of the surgery, all cases showed a $p$-value lower than 0.05 and are reported in the third and fourth columns in Fig. 6. For the end of anesthesia onset, Pearson coefficients $R$ were 0.99 for CBF-BIS time, $R=0.99$ for OEF-BIS time and $R=1$ for ${\mathrm{CMRO}}_2$-BIS time. For the time to reach plateau, $R$ was equal to 0.99 for CBF-BIS time, $R=0.99$ for OEF-BIS time and $R=1$ for ${\mathrm{CMRO}}_2$-BIS time.

Fig. 6

Linear regression plots for the four automatically retrieved time points identifying a change in the time-traces for all four variables of interest. BIS time is plotted versus CBF time, then versus OEF time and finally versus ${\mathrm{CMRO}}_2$ time. Pearson correlation coefficients $R$ and $p$-values are reported for each plot. Gray areas represent a 95% confidence interval built around the regression line.

6.1.

Discarded and Unavailable Data Details

As reported in Sec. 3, some subjects were excluded from further analysis. Six patients had to be excluded because the recording of the LOC and ROC were missed. About 23 measurements were included.

Unfortunately, some more time-traces were partially discarded, since the quality of the data was not sufficient, especially for TRS data.

For TRS, one quantitative criteria for rejection was the signal-to-noise ratio (SNR) calculated as the ratio between the maximum value of the light pulse and the standard deviation taken within a portion of the signal prior to the pulse, the background. The threshold set was $\mathrm{SNR}<10$. Qualitatively, the shape of the TRS laser pulse was also considered as an important feature to reject data.

For DCS, a minimum of 10 kHz for the count-rate was set as a threshold for rejection. The main cause of poor data quality or its deterioration was postural changes during surgery, which led to a loosening of the probe. Over time, the quality generally suffered from this and data points were lost towards the end of the measurements. The main consequence is reflected in the higher exclusion rate for the ROC periods. Often, data rejection corresponded to marked events over time and notes were inspected to verify their origin. The repercussions of the removal on the data were different for the different moments of the analysis. The numbers of available measurements evaluated in each analysis are reported in the following Table 3.

Table 3

Details of the number (N) of measurements included for each analysis type according to the period (LOC or ROC) and by physiological signal (NBIS, NCBF, NOEF, and NCMRO2).

6.2.

Additional Physiological Variables

The monitored systemic parameters were ${\mathrm{SpO}}_2$, HR, and MAP. The successful measurements with valid recordings were for the LOC: N MAP = 12, N HR = 21, and N ${\mathrm{SpO}}_2=23$; while for the ROC: N MAP = 10, N HR = 18, and N ${\mathrm{SpO}}_2=23$. For most of the measurements, in fact, we had no data points and most of the times this was due to a failure in the recordings after patient movement.

For these variables, we have carried out a group analysis in the same fashion as BIS and the optical parameters, meaning that we have taken the median values over the same windows and built a dataset for each variable, separating LOC and ROC. Then, we tested with the same Wilcoxon test, to check whether the distributions between the values post-induction or pre-recovery were different from their baseline.

In summary, during LOC we did not find any significant difference (LOC: $p$-value MAP = 0.07, $p$-value ${\mathrm{SpO}}_2=0.8$, and $p$-value HR = 0.6) between the groups. Instead, during the ROC, we found that the median value after recovery was significantly higher for HR ($p=0.004$) and MAP ($p=0.02$), while no significant change for ${\mathrm{SpO}}_2$ ($p=0.48$).