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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.
`

`The raw signal is formed by the RR intervals (ie the time between two
``spikes R on the electrocardiogram) or tachogram.
`

`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.
`

`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.
`
To compute SD1 and SD2 I write the following function :
function [SD1,SD2,ratio] = casado_poincare(x,lag)
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.
`
Thanks in advance,
Samir Sharshar MD
EA 2689-Inserm, Lille France
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**Poincaré plot quantification**,
*Samir Sharshar* **<=**