How to calculate area-under-the-curve with crossing zeros

Hello I am really bad at matlab and I am trying to create a script to calculate the area under the curve for my ERG data.

Here is my problem. I have time (x) and the response (y). The data goes to <0 and up >0, to form the b-wave. My idea is to collect after pass the zero point to the next zero, and calculate the area.

The problem is a have more then 1000 curves to analyzed and I can find a good solution to make a script.

Here is one example.

time (is always the same)

0.00E+00
7.83E-04
1.57E-03
2.35E-03
3.13E-03
3.91E-03
4.70E-03
5.48E-03
6.26E-03
7.05E-03
7.83E-03
8.61E-03
9.39E-03
1.02E-02
1.10E-02
1.17E-02
1.25E-02
1.33E-02
1.41E-02
1.49E-02
1.57E-02
1.64E-02
1.72E-02
1.80E-02
1.88E-02
1.96E-02
2.04E-02
2.11E-02
2.19E-02
2.27E-02
2.35E-02
2.43E-02
2.51E-02
2.58E-02
2.66E-02
2.74E-02
2.82E-02
2.90E-02
2.98E-02
3.05E-02
3.13E-02
3.21E-02
3.29E-02
3.37E-02
3.44E-02
3.52E-02
3.60E-02
3.68E-02
3.76E-02
3.84E-02
3.91E-02
3.99E-02
4.07E-02
4.15E-02
4.23E-02
4.31E-02
4.38E-02
4.46E-02
4.54E-02
4.62E-02
4.70E-02
4.78E-02
4.85E-02
4.93E-02
5.01E-02
5.09E-02
5.17E-02
5.25E-02
5.32E-02
5.40E-02
5.48E-02
5.56E-02
5.64E-02
5.71E-02
5.79E-02
5.87E-02
5.95E-02
6.03E-02
6.11E-02
6.18E-02
6.26E-02
6.34E-02
6.42E-02
6.50E-02
6.58E-02
6.65E-02
6.73E-02
6.81E-02
6.89E-02
6.97E-02
7.05E-02
7.12E-02
7.20E-02
7.28E-02
7.36E-02
7.44E-02
7.52E-02
7.59E-02
7.67E-02
7.75E-02
7.83E-02
7.91E-02
7.98E-02
8.06E-02
8.14E-02
8.22E-02
8.30E-02
8.38E-02
8.45E-02
8.53E-02
8.61E-02
8.69E-02
8.77E-02
8.85E-02
8.92E-02
9.00E-02
9.08E-02
9.16E-02
9.24E-02
9.32E-02
9.39E-02
9.47E-02
9.55E-02
9.63E-02
9.71E-02
9.79E-02
9.86E-02
9.94E-02
1.00E-01
1.01E-01
1.02E-01
1.03E-01
1.03E-01
1.04E-01
1.05E-01
1.06E-01
1.07E-01
1.07E-01
1.08E-01
1.09E-01
1.10E-01
1.10E-01
1.11E-01
1.12E-01
1.13E-01
1.14E-01
1.14E-01
1.15E-01
1.16E-01
1.17E-01
1.17E-01
1.18E-01
1.19E-01
1.20E-01
1.21E-01
1.21E-01
1.22E-01
1.23E-01
1.24E-01
1.25E-01
1.25E-01
1.26E-01
1.27E-01
1.28E-01
1.28E-01
1.29E-01
1.30E-01
1.31E-01
1.32E-01
1.32E-01
1.33E-01
1.34E-01
1.35E-01
1.35E-01
1.36E-01
1.37E-01
1.38E-01
1.39E-01
1.39E-01
1.40E-01
1.41E-01
1.42E-01
1.43E-01
1.43E-01
1.44E-01
1.45E-01
1.46E-01
1.46E-01
1.47E-01
1.48E-01
1.49E-01
1.50E-01
1.50E-01
1.51E-01
1.52E-01
1.53E-01
1.53E-01
1.54E-01
1.55E-01
1.56E-01
1.57E-01
1.57E-01
1.58E-01
1.59E-01
1.60E-01
1.61E-01
1.61E-01
1.62E-01
1.63E-01
1.64E-01
1.64E-01
1.65E-01
1.66E-01
1.67E-01
1.68E-01
1.68E-01
1.69E-01
1.70E-01
1.71E-01
1.71E-01
1.72E-01
1.73E-01
1.74E-01
1.75E-01
1.75E-01
1.76E-01
1.77E-01
1.78E-01
1.79E-01
1.79E-01
1.80E-01
1.81E-01
1.82E-01
1.82E-01
1.83E-01
1.84E-01
1.85E-01
1.86E-01
1.86E-01
1.87E-01
1.88E-01
1.89E-01
1.89E-01
1.90E-01
1.91E-01
1.92E-01
1.93E-01
1.93E-01
1.94E-01
1.95E-01
1.96E-01
1.97E-01
1.97E-01
1.98E-01
1.99E-01
2.00E-01
2.00E-01
2.01E-01
2.02E-01
2.03E-01
2.04E-01
2.04E-01
2.05E-01
2.06E-01
2.07E-01
2.07E-01
2.08E-01
2.09E-01
2.10E-01
2.11E-01
2.11E-01
2.12E-01
2.13E-01
2.14E-01
2.15E-01
2.15E-01
2.16E-01
2.17E-01
2.18E-01
2.18E-01
2.19E-01
2.20E-01
2.21E-01
2.22E-01
2.22E-01
2.23E-01
2.24E-01
2.25E-01
2.25E-01
2.26E-01
2.27E-01
2.28E-01
2.29E-01
2.29E-01
2.30E-01
2.31E-01
2.32E-01
2.33E-01
2.33E-01
2.34E-01
2.35E-01
2.36E-01
2.36E-01
2.37E-01
2.38E-01
2.39E-01
2.40E-01
2.40E-01
2.41E-01
2.42E-01
2.43E-01
2.43E-01
2.44E-01
2.45E-01
2.46E-01
2.47E-01
2.47E-01
2.48E-01
2.49E-01
2.50E-01
2.51E-01
2.51E-01
2.52E-01
2.53E-01
2.54E-01
2.54E-01
2.55E-01
2.56E-01
2.57E-01
2.58E-01
2.58E-01
2.59E-01
2.60E-01
2.61E-01
2.61E-01
2.62E-01
2.63E-01
2.64E-01
2.65E-01
2.65E-01
2.66E-01
2.67E-01
2.68E-01
2.69E-01
2.69E-01
2.70E-01
2.71E-01
2.72E-01
2.72E-01
2.73E-01
2.74E-01
2.75E-01
2.76E-01
2.76E-01
2.77E-01
2.78E-01
2.79E-01
2.80E-01
2.80E-01
2.81E-01
2.82E-01
2.83E-01
2.83E-01
2.84E-01
2.85E-01
2.86E-01
2.87E-01
2.87E-01
2.88E-01
2.89E-01
2.90E-01
2.90E-01
2.91E-01
2.92E-01
2.93E-01
2.94E-01
2.94E-01
2.95E-01
2.96E-01
2.97E-01
2.98E-01
2.98E-01
2.99E-01
3.00E-01
3.01E-01
3.01E-01
3.02E-01
3.03E-01
3.04E-01
3.05E-01
3.05E-01
3.06E-01
3.07E-01
3.08E-01
3.08E-01
3.09E-01
3.10E-01
3.11E-01
3.12E-01
3.12E-01
3.13E-01
3.14E-01
3.15E-01
3.16E-01
3.16E-01
3.17E-01
3.18E-01
3.19E-01
3.19E-01
3.20E-01
3.21E-01
3.22E-01
3.23E-01
3.23E-01
3.24E-01
3.25E-01
3.26E-01
3.26E-01
3.27E-01
3.28E-01
3.29E-01
3.30E-01
3.30E-01
3.31E-01
3.32E-01
3.33E-01
3.34E-01
3.34E-01
3.35E-01
3.36E-01
3.37E-01
3.37E-01
3.38E-01
3.39E-01
3.40E-01
3.41E-01
3.41E-01
3.42E-01
3.43E-01
3.44E-01
3.44E-01
3.45E-01
3.46E-01
3.47E-01
3.48E-01
3.48E-01
3.49E-01
3.50E-01
3.51E-01
3.52E-01
3.52E-01
3.53E-01
3.54E-01
3.55E-01
3.55E-01
3.56E-01
3.57E-01
3.58E-01
3.59E-01
3.59E-01
3.60E-01
3.61E-01
3.62E-01
3.62E-01
3.63E-01
3.64E-01
3.65E-01
3.66E-01
3.66E-01
3.67E-01
3.68E-01
3.69E-01
3.70E-01
3.70E-01
3.71E-01
3.72E-01
3.73E-01
3.73E-01
3.74E-01
3.75E-01
3.76E-01
3.77E-01
3.77E-01
3.78E-01
3.79E-01
3.80E-01
3.80E-01
3.81E-01
3.82E-01
3.83E-01
3.84E-01
3.84E-01
3.85E-01
3.86E-01
3.87E-01
3.88E-01
3.88E-01
3.89E-01
3.90E-01
3.91E-01
3.91E-01
3.92E-01
3.93E-01
3.94E-01
3.95E-01
3.95E-01
3.96E-01
3.97E-01
3.98E-01
3.98E-01
3.99E-01
4.00E-01

The response (y)

3.47E-06
2.30E-06
2.35E-06
5.96E-06
8.94E-06
9.14E-06
6.70E-06
-4.82E-07
-1.28E-05
-2.90E-05
-4.83E-05
-6.59E-05
-7.92E-05
-8.95E-05
-9.23E-05
-8.62E-05
-7.88E-05
-7.03E-05
-5.98E-05
-5.21E-05
-4.74E-05
-4.54E-05
-3.68E-05
-1.04E-05
3.65E-05
8.04E-05
9.46E-05
8.05E-05
4.84E-05
1.13E-06
-4.52E-05
-4.64E-05
2.76E-05
1.21E-04
1.65E-04
1.56E-04
1.21E-04
7.61E-05
2.42E-05
-2.26E-05
-3.85E-05
-1.65E-05
3.12E-05
7.58E-05
8.97E-05
8.06E-05
6.43E-05
4.48E-05
2.67E-05
1.60E-05
1.47E-05
2.31E-05
3.84E-05
5.41E-05
6.26E-05
6.54E-05
6.13E-05
5.37E-05
4.67E-05
4.20E-05
3.90E-05
3.79E-05
3.83E-05
4.13E-05
4.44E-05
4.72E-05
4.84E-05
4.83E-05
4.70E-05
4.57E-05
4.38E-05
4.23E-05
4.13E-05
4.02E-05
3.97E-05
3.90E-05
3.76E-05
3.68E-05
3.62E-05
3.56E-05
3.57E-05
3.53E-05
3.39E-05
3.19E-05
2.98E-05
2.86E-05
2.72E-05
2.65E-05
2.63E-05
2.62E-05
2.57E-05
2.43E-05
2.20E-05
1.91E-05
1.74E-05
1.65E-05
1.55E-05
1.57E-05
1.84E-05
2.03E-05
2.08E-05
2.10E-05
2.00E-05
1.75E-05
1.55E-05
1.42E-05
1.43E-05
1.35E-05
1.18E-05
1.05E-05
9.43E-06
8.60E-06
8.06E-06
7.87E-06
8.31E-06
7.92E-06
7.43E-06
6.50E-06
4.74E-06
3.38E-06
2.69E-06
2.25E-06
2.40E-06
1.76E-06
2.35E-06
2.20E-06
1.52E-06
-7.26E-07
-2.63E-06
-4.73E-06
-6.88E-06
-7.81E-06
-8.78E-06
-1.05E-05
-1.09E-05
-9.42E-06
-8.05E-06
-7.71E-06
-6.88E-06
-6.44E-06
-6.68E-06
-7.03E-06
-8.29E-06
-9.32E-06
-1.14E-05
-1.34E-05
-1.48E-05
-1.62E-05
-1.70E-05
-1.82E-05
-1.76E-05
-1.45E-05
-1.33E-05
-1.32E-05
-1.28E-05
-1.38E-05
-1.54E-05
-1.61E-05
-1.60E-05
-1.66E-05
-1.74E-05
-1.77E-05
-1.82E-05
-1.83E-05
-1.81E-05
-1.72E-05
-1.71E-05
-1.74E-05
-1.87E-05
-1.99E-05
-2.08E-05
-2.08E-05
-2.08E-05
-2.07E-05
-2.11E-05
-2.12E-05
-2.20E-05
-2.26E-05
-2.35E-05
-2.36E-05
-2.36E-05
-2.35E-05
-2.36E-05
-2.35E-05
-2.37E-05
-2.37E-05
-2.43E-05
-2.44E-05
-2.49E-05
-2.49E-05
-2.44E-05
-2.41E-05
-2.35E-05
-2.36E-05
-2.35E-05
-2.45E-05
-2.50E-05
-2.46E-05
-2.44E-05
-2.39E-05
-2.33E-05
-2.31E-05
-2.26E-05
-2.34E-05
-2.49E-05
-2.56E-05
-2.49E-05
-2.45E-05
-2.27E-05
-2.19E-05
-2.14E-05
-2.10E-05
-2.08E-05
-2.12E-05
-2.19E-05
-2.21E-05
-2.10E-05
-1.99E-05
-1.81E-05
-1.71E-05
-1.75E-05
-1.94E-05
-2.03E-05
-2.10E-05
-2.02E-05
-1.89E-05
-1.74E-05
-1.66E-05
-1.67E-05
-1.69E-05
-1.72E-05
-1.74E-05
-1.80E-05
-1.82E-05
-1.75E-05
-1.72E-05
-1.74E-05
-1.77E-05
-1.80E-05
-1.86E-05
-1.97E-05
-1.98E-05
-1.93E-05
-1.87E-05
-1.88E-05
-1.86E-05
-1.67E-05
-1.54E-05
-1.40E-05
-1.33E-05
-1.28E-05
-1.39E-05
-1.52E-05
-1.56E-05
-1.60E-05
-1.49E-05
-1.18E-05
-9.47E-06
-8.59E-06
-7.46E-06
-8.29E-06
-9.56E-06
-1.02E-05
-1.11E-05
-1.16E-05
-1.20E-05
-1.19E-05
-1.10E-05
-7.76E-06
-3.27E-06
-3.35E-07
1.67E-06
1.33E-06
-8.72E-07
-3.75E-06
-5.76E-06
-6.83E-06
-6.88E-06
-6.44E-06
-3.41E-06
-6.28E-07
1.67E-06
3.08E-06
3.03E-06
1.03E-06
-1.41E-06
-3.41E-06
-5.46E-06
-5.76E-06
-3.36E-06
-2.53E-06
-1.17E-06
2.64E-06
3.96E-06
4.16E-06
4.11E-06
3.33E-06
3.57E-06
4.60E-06
6.31E-06
8.16E-06
9.14E-06
8.36E-06
8.45E-06
8.50E-06
8.41E-06
8.31E-06
8.65E-06
9.14E-06
8.94E-06
9.43E-06
9.38E-06
9.33E-06
9.68E-06
9.38E-06
9.63E-06
9.38E-06
9.19E-06
9.87E-06
1.06E-05
1.10E-05
1.10E-05
1.03E-05
9.14E-06
8.36E-06
8.26E-06
8.75E-06
9.43E-06
1.02E-05
1.08E-05
1.04E-05
9.14E-06
8.06E-06
7.72E-06
7.72E-06
8.16E-06
9.33E-06
1.01E-05
1.04E-05
9.09E-06
7.72E-06
6.26E-06
5.04E-06
4.30E-06
4.35E-06
3.57E-06
3.13E-06
2.30E-06
1.08E-06
2.94E-06
5.38E-06
6.99E-06
9.04E-06
9.33E-06
8.89E-06
7.58E-06
6.89E-06
5.96E-06
5.09E-06
4.65E-06
4.11E-06
4.74E-06
5.23E-06
5.18E-06
4.60E-06
3.82E-06
3.28E-06
1.91E-06
1.67E-06
2.20E-06
3.77E-06
4.89E-06
4.99E-06
4.69E-06
3.82E-06
3.47E-06
2.79E-06
3.03E-06
3.08E-06
3.23E-06
3.72E-06
3.23E-06
1.52E-06
-1.07E-06
-3.22E-06
-4.88E-06
-5.12E-06
-1.85E-06
1.08E-06
2.74E-06
3.18E-06
1.96E-06
-1.56E-06
-4.93E-06
-7.12E-06
-6.39E-06
-3.07E-06
1.04E-07
2.35E-06
3.43E-06
3.23E-06
2.20E-06
6.90E-07
6.90E-07
5.44E-07
4.46E-07
3.00E-07
-3.35E-07
-1.41E-06
-1.80E-06
-2.19E-06
-2.39E-06
-2.24E-06
-2.19E-06
-2.68E-06
-2.92E-06
-3.46E-06
-3.36E-06
-3.66E-06
-3.36E-06
-2.92E-06
-1.85E-06
-1.61E-06
-1.75E-06
-2.19E-06
-3.17E-06
-3.31E-06
-3.46E-06
-2.87E-06
-1.65E-06
-9.21E-07
5.55E-08
-1.40E-07
-1.17E-06
-2.48E-06
-3.46E-06
-3.75E-06
-3.90E-06
-3.61E-06
-2.78E-06
-2.14E-06
-2.83E-06
-3.41E-06
-4.29E-06
-4.44E-06
-4.78E-06
-3.66E-06
-2.83E-06
-2.48E-06
-1.95E-06
-1.95E-06
-2.73E-06
-2.97E-06
-3.02E-06
-2.63E-06
-2.92E-06
-2.53E-06
-3.17E-06
-3.75E-06
-4.68E-06
-5.46E-06
-5.27E-06
-5.22E-06
-4.29E-06
-3.85E-06
-3.95E-06
-3.95E-06
-4.39E-06
-4.83E-06
-5.46E-06
-5.56E-06
-4.93E-06
-4.63E-06
-4.24E-06
-4.19E-06
-4.53E-06
-5.90E-06
-6.29E-06
-6.15E-06
-6.10E-06
-5.71E-06
-5.51E-06
-5.41E-06
-5.76E-06
-5.95E-06
-6.19E-06
-7.07E-06
-7.71E-06
-8.39E-06
-8.00E-06
-8.05E-06
-8.54E-06
-9.27E-06
-1.07E-05
-1.14E-05
-1.29E-05
-1.16E-05
-8.93E-06
-7.12E-06
-5.71E-06
-5.41E-06
-6.34E-06
-9.27E-06
-1.12E-05
-1.22E-05
-1.34E-05
-1.47E-05
-1.53E-05
-1.66E-05
-1.65E-05
-1.53E-05
-1.42E-05

Lets says I just want to calculate the area under the curve only between time point 0 to 0.1511. So selecting the first time it crosses zero and then finishing in the second time it crosses. then calculate the area.

I tried different combinations I found in the forum but i don´t get the results correctly.

One thing I tried was :

zeros = find( (y(1:end-1) ./ y(2:end)) <= 0 );
startingIndex = find(x==0);
endingIndex = find(x== 0.1511);

desiredx = x(startingIndex:endingIndex);
desiredy = y(startingIndex:endingIndex);

area = trapz(desiredx,desiredx);
plot(desiredx,desiredx,'b', x(zeros), 0, 'ro');
grid on;

I have the original data in excel files... Is really difficult for me to get the area correctly

also tried

area = trapz(find( (y(1:end-1) ./ y(2:end)) <= 0 ));

please if anybody knows how to help me I´ll really appreciate it

[Walter Roberson]

find() returns indices; you do not want to trapz() the indices.

[Star Strider]

I plotted your data, and looked up the electroretinogram (ERG) ‘b’ wave in NCBI PubMed The Electroretinogram: ERG in order to understand what you’re doing. (I’m an Internal Medicine Physician, not an Ophthalmologist). Your ‘b’ wave is corrupted by initial high-frequency oscillations, and your sampling times are not uniform, with a mean sampling interval of 0.783 milliseconds and standard deviation of 0.358 milliseconds. That is a significant variation.

You can resample your signal to get constant sampling intervals in order to use a discrete filter on it. That is not a problem.

What do you want to do about the high-frequency oscillations? I have no idea myself, and with no experience in elecroretinography, I have no idea if you want to eliminate them or integrate your signal as it exists (with the oscillations) from the onset of the ‘b’ wave to the end. What do you define as the beginning and what do you define as the end? Plot your signal, annotate it as necessary, save the annotated plot as a .png file, and upload it here. Use the brown-framed green ‘picture’ icon for that.

Please don’t assume we know what you want to do or how you want to process your signal. We have no idea. You have to tell us in some detail.

Also, it would help if you saved your time and data vectors to a .mat file and attached it, rather than listing long columns of data. Use the ‘paperclip’ icon to attach it.

[Milagros ARIETTI]

In general you only measured a and b amplitude and latency in this experiments but what I am seeing is a difference in the raw trace. after the highest pick the decay of the b wave is different, but I want to show it in numbers, so I thought to use the area under the curve, just when b starts. the example I upload is just one, for one eye. I have more then 1000, (2000 if you count the other eye).

[Milagros ARIETTI]

I thought, selecting the crossing zero, so I narrow the trace, eliminate a part and maybe the long ending part, and just trying to calculate the area under the curve of that. since i don´t handle matlab well I wanted to know if someone could help

Answer 1

[Walter Roberson]

trapz( max(0, y), x)

[Milagros ARIETTI]

I tried that and it gives me a number, but I think is the area under the curve of all the response. I would like only to select the area where the line is on the graph. From the first time it crosses zero from the negative to the end of the line. If it is not too much trouble to help me with that.

Thank you for the previous one. I´ll work on it to see if I can use it and do it more automatically.

thank you again

[Walter Roberson]

Your data starts greater than 0. It is not clear why that initial bit is not being included?

Your data has a single 5.55E-08 (positive) towards the right; it is not clear why that is not the point at which you stop the integration.

In the stretch that you marked out with a black line, there are portions that are negative; is the negative to count against the area? Or do you want to only know the area of the seconds that are purely positive? Do you want it broken up into segments, the areas of each of the positive stretches individually?

[Milagros ARIETTI]

the area I´m interested is that, I was thinking in using cumtrapz to solve that problem with the negative, but I still have some problems to get only the area in the black line.

[Milagros ARIETTI]

maybe to be more clear, I want the (Y) values in that black line so then I can try to calculate the area under the curve that those values form. for each trace I have and then do statistical analysis

[Walter Roberson]

ypos = y > 0;
begin_pos = strfind(ypos, [0 1]);  %goes from below 0 to above 0
begin_pos = begin_pos(1);          %first such

end_pos = stfind(ypos, [1 0 0]);   %goes negative and stays negative
end_pos = end_pos(end);            %last such

cumulative_area = cumtrapz(y(begin_pos:end_pos), t(begin_pos:end_pos));

[Milagros ARIETTI]

Error using strfind Input strings must have one row.

Error in area (line 2061) begin_pos = strfind(ypos, [0 1]); %goes from below 0 to above 0

[Walter Roberson]

ypos = (y > 0).';