Hi Alexander,

Your question is very interesting. I don't have any specific answer, but a couple of items that probably you should consider:

1. I can understand that you want to estimate entropy in a very short EEG time window (1 s), but I am not sure that it's a good idea to do the same in ECG. If one extracts 1 sec of regular EEG activity, it keeps certain acceptable stationarity level to calculate entropy, although the sample rate can also be a critical point to take into account. However, in ECG, you have to deal with the strong non-stationarity level marked by the QRS interval (assuming a cardiac cycle in 1 sec). I don't know if calculating entropy in this condition is actually useful.

2. What do you expect to characterize from your ECG signals applying entropy measures? As far as I know, if you want to work with nonlinear metrics, you can extract useful information from the R-R time series, not from the ECG raw data (ECG waveform) itself. If you go with the R-R time series, important information from the cardiac autonomic activity can be evaluated via heart rate variability. In that case, your entropy measure would work well.

3. In this work:

Article Nonlinear Recurrent Dynamics and LongTerm Nonstationarities ...

We estimated that a suitable epoch length in EEG signals for characterization with nonlinear metrics is 60 seconds, given the oscillatory behavior of nonlinear features observed in long-term EEG.

4. What do you mean by "heart irregularity"? is it heart rate variability? if the latter, then check this work:

Article An Overview of Heart Rate Variability Metrics and Norms

5. You can also evaluate the possibility to quantify the brain-heart connectivity as presented in this work in a study using polysomnography signals with Granger's causality:

Article Sleep apnea: Tracking effects of a first session of CPAP the...

6. From item 3, I think you should evaluate your multiscale entropy in ECG-EEG time windows of 40-60 seconds.

I hope it helps,

Alex C.

Hi Edwin,

first of all thank you very much for your answer which help a lot reconsidering some analysis aspects!

To 1 & 2.: Yes, I totally agree with the possibility of calculating HRV parameters. The plan of applying entropy measures directly on the "raw" ECG signal was based on the necessity of an equal amount of data points to calculate a cross entropy between EEG and ECG data.

I also found studies calculating ECG signal entropy, but mostly on a much longer time interval:

- Holzinger, A., Stocker, C., Bruschi, M., Auinger, A., Silva, H., Gamboa, H., & Fred, A. (2012). On Applying Approximate Entropy to ECG Signals for Knowledge Discovery on the Example of Big Sensor Data. In R. Huang, A. A. Ghorbani, G. Pasi, T. Yamaguchi, N. Y. Yen, & B. Jin (Hrsg.), Active Media Technology (Bd. 7669, S. 646–657). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-35236-2_64

- Liu, T., Yao, W., Wu, M., Shi, Z., Wang, J., & Ning, X. (2017). Multiscale permutation entropy analysis of electrocardiogram. Physica A: Statistical Mechanics and Its Applications, 471, 492–498. https://doi.org/10.1016/j.physa.2016.11.102

- Zhang, Y., Wei, S., Long, Y., & Liu, C. (2015). Performance Analysis of Multiscale Entropy for the Assessment of ECG Signal Quality. Journal of Electrical and Computer Engineering, 2015, e563915. https://doi.org/10.1155/2015/563915.

Zhang et al. suggest that according to ECG quality analysis, Multiscale Entropy for ECG is independent of data length for time intervals of minimum 10 seconds.

In my study design, I compare 4 different conditions of physical exercise conduction. I hypothesized that changes in ECG entropy between these conditions during recovery could indicate to different resting levels. Total recovery length is 25 minutes. I like to investigate the recovery process by means of an irregularity parameter (entropy) and in order to enlighten short changes in recovery, I decided to use these short time intervals.

To 3 & 5: Thank you very much for this article. I'm going to have a look on it.

To 4: No, I mean the interpretation of the entropy output, which is defined by a measure of signal (ir)regularity.

To 6: Thank you very much for the recommendation. Is there also a recommended amount of data points? Entropy calculating of such "long" time intervals needs plenty of time. I'm thinking of downsampling (to 256Hz) the data prior to the calculation. I'm also wondering, if the data length depends on the heart rate during the measurements. If I understood it correctly, measurements of the study related to 3 were conducted in absolute rest or even sleep. In my study case, subjects performed a physical exercise, which resulted in an average heart rate of around 150 bpm. Thus, subjects probably had much still higher heart rates in the following recovery as without a physical demand.

Thank you very much!

With best regards,

Alex

Hi Alexander,

Awesome! thank you very much for sharing your hypothesis. Regarding your last comment, I think there is no criterion to establish a number of data points, but maybe you can extrapolate the concepts from heart rate variability to entropy from raw ECG data, e.g. if you want to evaluate the cardiac parasympathetic activity, then epochs of 10-20 seconds would be fine. A sample rate at 256 Hz would be also acceptable, in any way, the higher a sample rate, the higher risk to get a bias in your entropy calculation. With a higher sample rate, you are prone to involve random processes (or high-frequency noise) in your signals. You could also perform an empirical analysis with variations of your epoch lengths: 10 sec, 20 sec, 30 sec.. etc, and see where you observe more interesting results. Obviously, the number of cardiac cycles will not be homogenous across patients, but I think for entropy evaluation the length of the time series across patients should be the same. Probably this is still an open question that you have a chance to answer with your research. I hope it helps...

Hi Edwin,

thanks a lot for the quick response and the helpful tips!

With best regards,

Alex