Start point of R wave

Through several posts, I introduced how to find the QRS start point and end point using boundary conditions in phase space. In this post, I introduce how to use the boundary condition to determine the starting point of the R wave.

1.    Method A, use a general electrocardiogram

Fig. 1 and 2 show cases where multiple R waves appear. There are 2 to 3 R waves, and the peaks between the R wave and R’ wave vary somewhat significantly. First of all, the problem is that the R’ peak can be mistaken for a P wave. Anyone with some knowledge of electrocardiography will have no difficulty finding P peak. However, in the case of Figures 1 and 2, it is not an easy task to make a computer, rather than a person, recognize the difference between P wave and R’ wave.

I tried to distinguish P peak and R’ peak by the slope of the straight line from the peak circled in red in Figures 1-2 to the R’ peak.

In Figures 2 to 4, the first R peak has two R’ peaks. In this case, the slopes should be obtained for the two R’ peaks from Peak A shown in Figure 4, and the one with the smaller absolute slope value should be selected. The reason for selecting the one with the smaller absolute value of the slope is because the one with the smaller slope is likely to be a P wave.

The absolute value of the slope of the blue line of the first R’ peak of the first R peak in Figure 4 is close to 1.

Looking at Figures 3 and 4, the absolute slope value of P peak is 1 or less, and the absolute slope value of R’ peak is 1 or more. The coding up to this point is quite complex and quite extensive. The complexity and voluminous nature of the coding means that debugging is quite difficult. When trying to find something wrong, I sometimes think that if it was something I worked on a long time ago, it would be faster to try to understand my coding and work on it again.

Figure 6 shows a case where a PR segment does not exist. In this case, the distance between P peak and R peak becomes closer, and the absolute slope of the line connecting Q peak and P peak exceeds 1. This shows that method A has an error.

I was confused when something I had spent quite a long time working on turned out to be the wrong method.

Now I decided to try again using Phase space.

2.    Method B, use a Phase space

I looked at how the red circles A and B shown in Figure 7 appear in phase space and looked into possibilities.

Figure 8 shows a case with two R’ peaks. The slope of the line(red line) from the downward peak of the first R' peak to the Imaginary peak of the first R' peak was compared with the slope of the line(blue line) heading to the negative Imaginary peak of the P peak.

Fig. 8 and 9 show two slopes as in Method A in phase space for the two cases in Figure 7. The red line has a negative slope, and the blue line has a positive slope.

There is a clear difference between these two slopes.

Fig. 10 compares the slope in phase space of Fig. 6, which caused problems in Method A. As in the two cases in Fig. 7, the two lines have opposite slopes. This simple and intuitive coding finds the start point of the R wave without any errors.

#ECG #patent