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## Poincaré plot quantification

 From: Samir Sharshar Subject: Poincaré plot quantification Date: Fri, 15 Oct 2004 21:49:17 +0200

```Hello,

```
I know that the subject is not really relevant in this mailing list, but I hope someone who's working on biomedical signals helps me.
```
```
I'm currently analyzing Heart Rate Variability (HRV). Study of HRV is lot of interest because it may leads to early diagnosis of myocardical infarction or sudden death. Methods of analysis call both to linear and non linear tools.
```
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The raw signal is formed by the RR intervals (ie the time between two spikes R on the electrocardiogram) or tachogram.
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```
Poincaré plot is drawn by plotting the RR at time i vs RR at time i-lag (lag usually between 1 and 4). Typically a Poincare plot draw an ellipse. Two indices are calculated from the graph.
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The first (called in the medical litterature SD2) seems to take into account the differences between the markings and the transversal axe. The second (called SD1) idem with the longitudinal axe.
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To compute SD1 and SD2 I write the following function :

if(size(x,1)<size(x,2))
x = x';
end

if(isempty(lag))
lag=1;
else
if(lag>4)
error('lag must be >= 1 and <= 4');
end
end

S1 = x(1+lag:size(x,1),1);
S2 = x(1:size(x,1)-lag,1);

# Longitudinal axis

p2 = polyfit(S1, S2, 1); # get the equation of a least square line
y2 = polyval(p2,[1:1:size(S1,1)]);
SD2 = std(y2'-S2); # compute the SD

# Transversal axis

p1 = polyfit(S1,flipud(S2),1);
y1 = polyval(p1,[1:1:size(S1,1)]);
SD1 = std(y1'-flipud(S2));

ratio = SD1/SD2;

```
I'm not sure that I'm computing SD1 and SD2 in the right way. I do not found in papers the detailed algorith to do so.
```

Samir Sharshar MD
EA 2689-Inserm, Lille France

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