This study was approved by the University of California, Irvine research ethics committee with waived written informed consent. All patients in the authors’ university hospital are informed that de-identified data may be collected for research purposes. All monitoring used in this study is considered part of standard care for patients.

### Patient selection

The inclusion criteria for study patients were as follows: adult patients greater than 18 years of age, undergoing elective open abdominal surgery, classified as ASA 2 or 3, equipped with a standard 5-lead EKG, and undergoing mechanical ventilation with constant respiratory frequency and in a volume control mode with at least 8 mL/kg tidal volumes. The major exclusion criteria were as follows: patients with cardiac arrhythmia, right ventricular failure, left ventricular ejection fraction <40%, PEEP >5 cmH_{2}O, and with a spontaneous breathing cycle detected on ETCO2 tracing. No modifications in anesthesia care were required for the study. A standard 5-lead electrocardiogram (EKG) was continuously displayed on a GE Healthcare monitor (GE Healthcare, Milwaukee, WI, USA) by standard monitoring electrodes (Novaplus, Irving, TX, USA). The standard 5-lead EKG placement used included the four limb electrodes (RA, LA, RL, LL) and the precordial lead V5. Extra care was taken to ensure that the standard 5-lead EKG placement was followed.

### Data acquisition and recording

EKG waveforms were collected on a laptop computer using an Ethernet port of the Solar 8000i anesthesia workstation and multiparameter bedside monitor (GE Healthcare, Milwaukee, WI, USA). Utilizing the data collection software (Visual Studio 2005, Microsoft, Redmond, WA, USA) developed by our research team for communication with the GE workstation, EKG waveforms were simultaneously digitalized and continuously recorded on the laptop computer with a sample rate of 240 Hz for a total of 10,000 samples (42 s) per data batch.

### Data analysis

From the recorded EKG waveforms, EKGv was calculated offline manually and by computer-automated algorithm. EKGv was defined as the relative difference in maximal (RDIImax) and minimal RDII (RDIImin) amplitude according to the following formula [6]:

\mathrm{EKGv}\phantom{\rule{0.25em}{0ex}}\left(\%\right)=100\phantom{\rule{0.75em}{0ex}}\times \phantom{\rule{0.75em}{0ex}}\frac{\mathrm{RDIImax}-\mathrm{RDIImin}}{\left(\left(\mathrm{RDIImax}+\mathrm{RDIImin}\right)/2\right)}

For manual determination, the manual EKGv calculator assumed *implied* respiratory cycles based on observed variations in the RDII amplitude. RDII amplitude was defined as the difference between a distinct RDII peak and respective trough. The manual EKGv calculator looked at the changing slopes of the RDII amplitudes and assessed where the maxima (RDIImax) and minima (RDIImin) of the slopes were to the best of his ability. He then chose three distinct RDIImax amplitudes that best represented the data batch and their respective adjacent RDIImin to calculate a total of three EKGv values per data batch (Figures 1 and 2). The median value was used as the representative of the manually determined EKGv (EKGv_{man}).

For automated determination, all RDII peaks and troughs were automatically detected and used in the calculation of EKGv (EKGv_{auto}) by an algorithm written in Matlab (Matlab R2011a, MathWorks Inc., Natick, MA, USA) (Figure 3). The steps of the algorithm are detailed below:

Step 1. *Set upper and lower limits for R peak detection*: An automatic R peak detection algorithm is used to detect every R peak in a given data batch of 10,000 samples. Peak detection begins by creating upper and lower limits for potential R peaks. The algorithm first performs the local maxima detection using MatLab’s max function on every 100 data points for a total of 2,000 data points or 20 local maxima. The mean ± standard deviation of this list of local maxima is then calculated, and any local maxima in this list not within those limits are considered noise and removed from further analysis. The R peak upper and lower limits are then calculated as the mean ± standard deviation of the final list of the first local maxima.

Step 2. *Peak detection*: The algorithm searches for the local maxima, or R peak, in every 100 data points using the calculated R peak upper and lower limits and identifies the sample location corresponding to the R peak. Then the algorithm looks to the closest neighbors of the detected R peaks to ensure the correct local maxima was detected and corrects the R peak and location or eliminates the detected R peak if necessary. The R peak detection limits, as well as this additional step, help to eliminate the identification of incorrect R peaks due to noise. If greater than half the number of detected R peaks were eliminated during this step, the data batch was considered unanalyzable by the algorithm. Heart rate is estimated as the total number of R peaks divided by the length of sample time (42 s).

Step 3. *Trough detection*: Recalling the list of identified R peaks, another algorithm searches for the trough preceding the peak. The algorithm takes relative slope information backwards from the R peak; from right to left of the signal, this would consist of first a negative slope (R to Q), followed by a positive slope (Q to trough), then a zero or negative slope (trough). If a trough is not detected, then a nearby data point from the identified Q point is used as an estimate of the trough.

Step 4. *RDII amplitude calculation*: The RDII amplitude is calculated from the difference between R peaks and corresponding troughs. Upper and lower limits of RDII amplitudes are the mean ± standard deviation of all calculated RDII amplitudes. If the standard deviation of the RDII amplitudes is very large, the upper and lower limits are used to eliminate any values outside of the limits.

Step 5. *EKG variability estimation*: Relative amplitudes and slope information are used to identify the minima and maxima (RDIImin and RDIImax) of the RDII amplitudes to estimate the respiratory cycles and calculate EKGvs. The EKGvs for each respiratory cycle are then calculated from the previously stated formula using corresponding RDIImin and RDIImax. All calculated EKGvs were then filtered through an upper and lower cut-off limit of the mean ± standard deviation and averaged for a final reported EKGv. The averaged value was used as the representative computer-automated algorithm calculation of EKGv (EKGv_{auto}).

### Statistical analysis

The normality of distribution of EKGv_{man} and EKGv_{auto} values was tested using the Kolmogorov-Smirnov test. In the case of a normal distribution, the parametric Pearson test was used to assess correlation. EKGv_{man} and EKGv_{auto} were also compared using Bland-Altman analysis [11]. A receiver operating characteristic (ROC) curve analysis was then performed for EKGv_{auto} varying the discriminating threshold of this parameter to determine the ability of EKGv_{auto} to discriminate between patients with an EKGv_{man} > 15% and EKGv_{man} ≤ 15%. This threshold was chosen based on a previous study by Lorne et al. which determined that the inconclusive limits of changes in stroke volume (ΔSV) ranged from 13% to 15%, and that EKGv > 15% was able to accurately predict ΔVTI > 15% [10]. In all cases, a *P* value less than 0.05 was considered statistically significant. All statistical analyses were performed using SPSS (SPSS 13.0, Chicago, IL, USA). Data are represented as mean ± standard deviation.