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I have some ECG data where I am estimating the average beginning of the action potential. I am interested in the discrete Fourier analysis of joint t-f HRV when input data is ECG. Frequency domain method here - a simplification of the joint t-f HRV. However, I am uncertain how this method works because I see several limitations and mistakes in designs of several systems. There are also several publications about the topic, but little has been peer-reviewed. Also little data and research systems are publicly available for reviews. According to @Christiaan (see comments), ECG shows compound action potential which is most likely detected by detecting R peaks. In HRV analysis, they do currently

Estimate R-R interval in time and frequency domains:
Consider an estimate of R peaks. 
It is not always the maxima. 
There can be two peaks of equal length at maximum. 

I think, in including two R peaks, they think they cancel the error of estimating the start of R peak, although the uncertainty actually increases. I think this is wrong in ignoring the uncertainty about the estimate of the start of R-R or simplifically the start of AP. I think we should be able to estimate the precise location of action potential better. They are using commonly exclusion principles which lose much original signal and decrease sensitivity

  • by excluding small time, frequency $|x|, |\eta| \in \mathbf R$ by choosing the window $w$ such that $w(t) \approx 0 \approx \hat{w}(\eta)$.
  • by excluding one beat normal beat before and after each ectopic beat.
  • system fails if more than 20% of ectopic beats.
  • system fails in 24h recordings because of computational issues of longer segments - so limiting to 5 minutes and averaging.

My Exclusions and Hypothesis

To detect the exact beginning of the action potential $s$ value $s(x) \in \mathbf R$ at exact instance $x \in \mathbf R$ is unpractical. Instead, I measure some averages of the signal: $A_{\sigma} s(x) := \int_{\mathbf R} x(y) \varphi_{0,\sigma}(y-x) dy$ where $\varphi_{0,\sigma}$ is 0-average-valued $\sigma$-variance of normal density function.

  • $A_{\sigma} s(x) := \int_{\mathbf R} x(y) \varphi{0,\sigma}(y-x) dy$.
  • No windowing function so including also small time, frequency $|x|, |\eta| \in \mathbf R$.

Processes limiting to detect the beginning of action potential

  1. Technical processes (fine with these)
  2. HR Saturation process.
  3. HR Recovery process.

I am very interested in how you can characterize HR saturation process and the HR recovery process. I think they are using individual signals measure in three circumstances: Paced, Exercise and Recovery, here. How can you characterise differences between such circumstances?

Views

Labview (most likely LabVIEW Biomedical Toolkit) or Matlab (which should be fine!)

  1. ECG,
  2. R-wave detection,
  3. IBI signal (Inter-Beat Interval),
  4. Expanded ECG,
  5. HRV spectrum.

    • I do not understand the reason which component is requiring to use Labview here and most likely its Biomedical Toolkit in the analysis like in 4. I sent a message to the developer about the thing but waiting for an answer. Why? I would like to use Matlab, but I need to know if there can be some electronics that limits you and is only suitable for Labview. I have built my own ECG boards and systems with mostly Analog Devices' electronics.
    • How is the R-wave detection done? I think this can describe the challenge better about the beginning of the action potential.
    • Which channel(s) is/are used precisely in the view ECG? How can the electrical activity view be created? Summation of all channels in steady intervals? I think we should not exclude things now but it can be later done if some some anatomical/physiological reason is found.
    • What is precisely the Expanded ECG?
    • How does the expanded ECG allow you to evaluate the mean electrical axis?

I think another problem with such views is that they are not fixing the mean electrical axis. However, I may be wrong, since I do not understand the definition of ECG view and expanded ECG view. How are you considering ECG channels here?

Joint time-frequency domain HRV

I am interested in how you associate frequencies (high, mid, low) with different intrinsic, autonomically-modulated periodic rhythms. I only see in slides the following link without an association

High Frequency = 0.25 Hz (15 cycles/min
Low Frequency = 0.1 Hz (6 cycles/min)
Very Low Frequency = 0.016 Hz 
(1 cycle/min)

Adapted from the presentation here and here but changed for t-f

N-N - normal-to-normal
To calculate a standard deviation of a series of numbers:
[0. missing step about location of action potential]
1. Find the average in R-R intervals [4]
2. Calculate the differences between each number and the average
3. Square each difference (so they don’t cancel out)
4. Sum
5. Divide by number of datapoints
6. Take square root
... 
n. no interpolation because FFT

How can you estimate the average beginning of the action potential in the joint t-f domain? I think you measure the distance between two peaks and count the variance.

Sources

  1. https://www.heartmath.org/research/, organisation about the field.
  2. Pruneti, C. A, and McCraty, R. Very interesting presentations about the topic.
  3. www2.unipr.it/~cprunet9/files/Heart-Rate-Variability.ppt, one example of HRV presentation.
  4. BME 333 Biomedical Signals and Systems, J. Schesser. https://web.njit.edu/~joelsd/signals/classwork/BME314signalscw12a.pdf About R-R intervals in time and frequency domains
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    $\begingroup$ The question is unclear; 1) ECGs don't show action potentials, but compound action potentials. 2) an image of a waveform would help 3) what is some analysis of channels' function? and 4) with sensitivity - sensitivity is dependent on the hardware, you might be talking about accuracy? And that is a subjective term, what is accurate? And for that matter, what is sensitive? Explain please. $\endgroup$ – AliceD Feb 17 '16 at 9:37
  • $\begingroup$ A start of something in the frequency domain is impossible. That's why it is called frequency domain. $\endgroup$ – AliceD Feb 18 '16 at 10:00
  • $\begingroup$ There is no time interval in the frequency domain. $\endgroup$ – AliceD Feb 18 '16 at 12:18
  • $\begingroup$ @Christiaan Yes, you are right. There is a time interval in the joint t-f. $\endgroup$ – Léo Léopold Hertz 준영 Feb 18 '16 at 12:33

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