Detecting patterns in waves

Question

I'm trying to read a image from a electrocardiography and detect each one of the main waves in it (P wave, QRS complex and T wave). Now I can read the image and get a vector like (4.2; 4.4; 4.9; 4.7; ...) representative of the values in the electrocardiography, what is half of the problem. I need a algorithm that can walk through this vector and detect when each of this waves start and end.

Here is a example of one of its graphs:

Would be easy if they always had the same size, but it's not like it works, or if I knew how many waves the ecg would have, but it can vary too. Does anyone have some ideas?

Thanks!

Updating

Example of what I'm trying to achieve:

Given the wave

I can extract the vector

[0; 0; 20; 20; 20; 19; 18; 17; 17; 17; 17; 17; 16; 16; 16; 16; 16; 16; 16; 17; 17; 18; 19; 20; 21; 22; 23; 23; 23; 25; 25; 23; 22; 20; 19; 17; 16; 16; 14; 13; 14; 13; 13; 12; 12; 12; 12; 12; 11; 11; 10; 12; 16; 22; 31; 38; 45; 51; 47; 41; 33; 26; 21; 17; 17; 16; 16; 15; 16; 17; 17; 18; 18; 17; 18; 18; 18; 18; 18; 18; 18; 17; 17; 18; 19; 18; 18; 19; 19; 19; 19; 20; 20; 19; 20; 22; 24; 24; 25; 26; 27; 28; 29; 30; 31; 31; 31; 32; 32; 32; 31; 29; 28; 26; 24; 22; 20; 20; 19; 18; 18; 17; 17; 16; 16; 15; 15; 16; 15; 15; 15; 15; 15; 15; 15; 15; 15; 14; 15; 16; 16; 16; 16; 16; 16; 16; 16; 16; 15; 16; 15; 15; 15; 16; 16; 16; 16; 16; 16; 16; 16; 15; 16; 16; 16; 16; 16; 15; 15; 15; 15; 15; 16; 16; 17; 18; 18; 19; 19; 19; 20; 21; 22; 22; 22; 22; 21; 20; 18; 17; 17; 15; 15; 14; 14; 13; 13; 14; 13; 13; 13; 12; 12; 12; 12; 13; 18; 23; 30; 38; 47; 51; 44; 39; 31; 24; 18; 16; 15; 15; 15; 15; 15; 15; 16; 16; 16; 17; 16; 16; 17; 17; 16; 17; 17; 17; 17; 18; 18; 18; 18; 19; 19; 20; 20; 20; 20; 21; 22; 22; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 32; 33; 33; 33; 32; 30; 28; 26; 24; 23; 23; 22; 20; 19; 19; 18; 17; 17; 18; 17; 18; 18; 17; 18; 17; 18; 18; 17; 17; 17; 17; 16; 17; 17; 17; 18; 18; 17; 17; 18; 18; 18; 19; 18; 18; 17; 18; 18; 17; 17; 17; 17; 17; 18; 17; 17; 18; 17; 17; 17; 17; 17; 17; 17; 18; 17; 17; 18; 18; 18; 20; 20; 21; 21; 22; 23; 24; 23; 23; 21; 21; 20; 18; 18; 17; 16; 14; 13; 13; 13; 13; 13; 13; 13; 13; 13; 12; 12; 12; 16; 19; 28; 36; 47; 51; 46; 40; 32; 24; 20; 18; 16; 16; 16; 16; 15; 16; 16; 16; 17; 17; 17; 18; 17; 17; 18; 18; 18; 18; 19; 18; 18; 19; 20; 20; 20; 20; 20; 21; 21; 22; 22; 23; 25; 26; 27; 29; 29; 30; 31; 32; 33; 33; 33; 34; 35; 35; 35; 0; 0; 0; 0;]

I would like to detect, for example

P wave in [19 - 37]

QRS complex in [51 - 64]

etc...

Answer 1

using BioSPPY

it is not presently possibly to implement T-wave analysis, as at present it only contains R-wave analysis. eg Tstart Tpeak Tend

are not automatically implimented

one would have to use your own analysis.

my suggestion would be to try and implement the below method

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3201026/

which is one that I have recently discovered and found to be very interesting

The other t-wave analysis method worth looking at is that by ECGlib team

http://ieeexplore.ieee.org/document/6713536/

hope this helps

Answer 2

This is a wonderful question! I have a few thoughts:

Dynamic Time Warping could be an interesting tool here. You would establish "templates" for your three classes, and then using DTW could see the correlation between your template and "chunks" of the signal (break the signal up into, say, .5 second bits, ie. 0-.5 .1-.6 .2-.7...). I've worked with something similar for gait analysis with accelerometer data, it worked reasonably well.

Another option is a combined signal processing/ machine learning algorithm. Break your signal into "chunks" again. Make "templates" again (you'll want a dozen or so for each class) take the FFT of each chunk/template and then use a Naïve Bayes Classifier (or another ML classifier, but NB should cut it) to classify for each of your three classes. I've also tried this on gait data, and was able to get upwards of 98% precision and recall with relatively complicated signals. Let me know how this works, it's a very exciting problem.

Answer 3

One approach that will very likely yield good results is curve fitting:

• Divide the continuous wave into intervals (probably it's best to have the interval borders about half way between the sharp peaks of the qrs complexes). Only consider a single interval at a time.

• Define a model function that can be used to approximate all possible variations of electrocardiographic curves. This is not as difficult as it seems first. The model function can be constructed as a sum of three functions with parameters for the origin (t_), amplitude (a_) and width (w_) of each wave.

     f_model(t) = a_p   *  f_p  ((t-t_p  )/w_p) + 
                  a_qrs *  f_qrs((t-t_qrs)/w_qrs) +
                  a_t   *  f_t  ((t-t_t  )/w_t)
  

  The functions f_p(t), f_qrs(t), f_t(t) are some simple function that can be uses to model each of the three waves.

• Use a fitting algorithm (e.g. the Levenberg-Marquardt-Algorithm http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm) to determine the fitting parameters a_p, t_p, w_p, a_qrs, t_qrs, w_qrs, a_t, t_t, w_t for the dataset of each intervall.

  The parameters t_p, t_qrs and t_p are the ones you are interested in.

Answer 4

The first thing that I would do is see what is already out there. Indeed, this specific problem has already been heavily researched. Here is a brief overview of some really simple methods: link.

I must respond to another answer, as well. I do research in signal processing and music information retrieval. On the surface, this problem does appear similar to onset detection, but the problem context is not the same. This type of biological signal processing, i.e., detection of the P, QRS, and T phases, can exploit knowledge of specific time-domain characteristics of each of these waveforms. Onset detection in MIR doesn't, really. (Not reliably, at least.)

One approach that would work well for QRS detection (but not necessarily for note onset detection) is dynamic time warping. When time-domain characteristics remain invariant, DTW can work remarkably well. Here is a short IEEE paper that uses DTW for this problem: link.

This is a nice IEEE magazine article that compares many methods: link. You'll see that many common signal processing models have been tried. Skim the paper, and try one that you understand at a basic level.

EDIT: After browsing these articles, a wavelet-based approach seems most intuitive to me. DTW will work well, too, and there exist DTW modules out there, but the wavelet approach seems best to me. Someone else answered by exploiting derivatives of the signal. My first link examines methods from before 1990 that do that, but I suspect that they are not as robust as more modern methods.

EDIT: I'll try to give a simple solution when I get the chance, but the reason why I think wavelets are suited here are because they are useful at parameterizing a wide variety of shapes regardless of time or amplitude scaling. In other words, if you have a signal with the same repeated temporal shape but at varying time scales and amplitudes, wavelet analysis can still recognize these shapes as being similar (roughly speaking). Also note that I am sort of lumping filter banks into this category. Similar things.

Answer 5

I'm no expert in this specific problem, but just off the top of my head from more general knowledge: Let's say you know the QRS complex (or one of the other features, but I'll use the QRS complex for this example) takes place in roughly some fixed time period of length L. I wonder if you could treat this as a classification problem as follows:

1. Split your signal into overlapping windows of length L. Each window either does or doesn't have the full QRS complex in it.
2. Fourier transform each window. Your features are the signal strength at each frequency.
3. Train a decision tree, support vector machine, etc. on some hand-annotated data.

Answer 6

Are those other two sharp peaks and valleys also qrs complexes?

Off the top of my head, I think what you need to do is calculate the slope of this graph at each point. Then you also need to see how quickly the slope changes (2nd derivative???). If you have an abrupt change then you know you've hit some kind of sharp peak. Of course, you want to limit the detection of the change, so you might want to do something like "if the slope changes by X over time interval T", so that you don't pick up the tiny bumps in the graph.

It's been a while since I did any math... and this seems like a math question ;) Oh, and I haven't done any sort of signal analysis either :).

Just adding another point. You can also try signal-averaging I think. For example, averaging the last 3 or 4 data points. I think you can detect abrupt changes that way too.