Averaging trick aligns cardiac output monitors for fair comparison

When two cardiac output monitors disagree, the problem may not be the devices themselves but the clock. Continuous cardiac output measured by pulmonary artery thermodilution delivers inherently delayed information because it relies on historical data, while newer beat-to-beat technologies built on blood pressure waveforms or bioimpedance respond far faster. Comparing their trending ability without accounting for that mismatch can make a good monitor look bad, or a poor one look acceptable. A study now published in BMC Biomedical Engineering by Yoshihiro Sugo and Ryoichi Ochiai argues that a simple signal-processing step, the moving average, can bridge that gap, and it quantifies exactly how long the averaging window needs to be.

The work was a single-center, retrospective, observational study conducted at a 916-bed university hospital, drawing on data originally collected from 20 patients undergoing kidney transplantation. The researchers analyzed arterial pressure cardiac index measured with a FloTrac/Vigileo system and estimated continuous cardiac index computed from pulse wave transit time, comparing both against continuous cardiac index derived from pulmonary artery thermodilution catheters. Data were collected at 1-minute intervals, yielding 5,027 data points over 83.8 hours. Because the analysis was a secondary use of data from a prior clinical study, no additional ethical approval was required, and the original study had been approved by the ethics committee of Toho University Omori Medical Center with written informed consent from all participants.

The core idea rests on the mathematics of the moving average itself. A moving average is a well-known low-pass filter, and when applied to a sinusoidal signal it produces two analytically predictable effects: the filtered signal is delayed by half the averaging time, and its amplitude is attenuated in a frequency-dependent way. That means two monitors using different averaging times will differ systematically in both timing and magnitude, even if they track the same underlying physiology. The authors reasoned that if the delay in thermodilution-based continuous cardiac output stems largely from moving average processing, then applying a suitably adjusted moving average to the faster monitor’s data should restore agreement, particularly in polar plot analysis, which is sensitive to such timing errors.

Polar plot analysis, described by Critchley and colleagues, evaluates trending ability by examining the direction of paired changes between a reference and a test signal. The team applied moving average windows ranging from 0 to 60 minutes in 1-minute increments to both test signals, generating 61 datasets each, and computed differences over time intervals from 1 to 60 minutes, for a total of 3,660 combinations per signal. Data pairs with an average change of less than 0.6 L/min/m², corresponding to 15 percent of the mean reference value, were excluded from the analysis. They also ran Bland-Altman analysis to assess bias, the standard deviation of differences, and proportional bias, since trending is a within-subject property that shows up in that variance.

The results were striking. With no moving average at all, the polar concordance rate at 30 degrees for estimated continuous cardiac index against the thermodilution reference was below 60 percent. Once the averaging window reached 17 to 30 minutes, concordance exceeded 90 percent, peaking between 20 and 30 minutes. Arterial pressure cardiac index behaved similarly but within a narrower window, reaching roughly 90 percent concordance between 21 and 27 minutes. The authors report that the concordance rate exceeded 92 percent for windows between 20 and 30 minutes for the estimated index, a level that meets the 92 percent threshold Critchley proposed for acceptable trending agreement when a 15 percent exclusion zone is used. The arterial pressure-based index did not quite reach that threshold but came close.

Crucially, the study did not stop at the standard moving average. The authors separately examined the two components of the operation: a pure time shift, in which the signal is simply delayed by half the window, and symmetric filtering, in which values from both sides of the current time point are averaged. When the estimated cardiac index signal was processed by time shift alone, the polar concordance rate peaked in the same 20-to-30-minute window but never exceeded 85.5 percent, showing that delay correction alone is insufficient. Filtering alone showed no similar window-dependent trend in concordance. Only the combination of the two, the true moving average, produced the full improvement, demonstrating that the observed delay reflects both time shift and signal smoothing.

The Bland-Altman results added a complementary picture. As the averaging window lengthened, the bias shifted in the negative direction for both test signals, with the smallest bias occurring with no averaging. The correlation coefficient between the difference and the mean, an index of proportional bias, started positive and crossed zero at 8 minutes for the arterial pressure index and 12 minutes for the estimated index. The standard deviation of the differences fell with increasing averaging time, reaching a minimum at 24 minutes for the arterial pressure signal and 21 minutes for the estimated signal, before rising again at longer windows. The mean polar angle also decreased with increasing averaging time, crossing zero at 19 minutes for the arterial pressure signal and 12 minutes for the estimated signal.

One apparent contradiction demanded closer inspection. Beyond 30 minutes of averaging, the polar angle standard deviation continued to fall while the Bland-Altman standard deviation rose. The authors resolved this by comparing polar plot analyses with and without an exclusion zone. Omitting the exclusion zone increased the polar angle standard deviation, and further analysis showed that as the averaging window lengthened, the amplitude of the estimated signal was attenuated and the time shift prolonged, increasing divergence from the reference. At the same time, the magnitude of changes in both signals shrank, so the exclusion rate rose, and a higher exclusion rate consistently yielded lower polar angle standard deviation values. The improvement at long windows was thus partly an artifact of excluding more data, not a genuine gain in agreement.

The study has clear limitations, which the authors state plainly. They lacked detailed information about the specific averaging algorithm inside the thermodilution monitor, so the inference that its response delay stems from moving average processing remains an assumption that motivated the method rather than a proven mechanism. The number of usable data points also varied across averaging windows, because larger windows delayed the start and hastened the end of available output, and any missing value within a window prevented the average from being computed. The analysis focused on a single trending metric, the polar concordance rate at 30 degrees, rather than the full set of criteria some authors recommend, such as keeping the mean polar angle within plus or minus 5 degrees and radial limits of agreement within plus or minus 30 degrees.

Within those constraints, the practical message is concrete. When comparing a monitor with minimal response delay against one with an inherent measurement delay, temporal adjustment is essential, and a moving average window of roughly 20 to 30 minutes appears to be the effective range for this dataset. The wide variability in effective averaging times also suggests that multiple factors contribute to the delayed response of thermodilution-based monitoring, including the thermal filament heating algorithm, clinical conditions such as mitral regurgitation, and physiological changes during bleeding or resuscitation. The authors note that no clinical study has demonstrated that this measurement delay has a negative clinical impact, and that cardiac output measurement itself has not been shown to improve patient outcomes in sepsis, major surgery, or mechanical ventilation for respiratory failure. The contribution here is methodological: moving average processing offers a practical way to make trending comparisons between cardiac output monitors with different response times more accurate, provided its filtering and time-shifting effects, and the data exclusions they induce, are kept in view.

Subject of Research: Using moving average processing to compensate for response time delays when comparing the trending ability of continuous cardiac output monitors

Article Title: Moving-average processing enables accurate quantification of time delay and compares the trending ability of cardiac output monitors with different response times

Article References: Sugo, Y., & Ochiai, R. (2025). Moving-average processing enables accurate quantification of time delay and compares the trending ability of cardiac output monitors with different response times. BMC Biomedical Engineering, 7(1), Article 14. https://doi.org/10.1186/s42490-025-00101-8

Image Credits: AI Generated

DOI: 10.1186/s42490-025-00101-8

Keywords: cardiac output monitoring, polar plot analysis, Bland-Altman analysis, moving average, esCCO, APCO, pulmonary artery thermodilution, response time delay, trending ability, hemodynamic monitoring, retrospective study, kidney transplantation