Deriving an average loop waveform from multiple loops
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Hi team,
I am plotting pressure-volume loops that have been generated across multiple cycles. I was wondering how to obtain an average loop waveform based on multiple loops as seen below.
Alternatively, I did come across a plausible method as shown below but am not sure how to get there.
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Mathieu NOE
2021-6-3
So finally after some attempts and headaches , a positive result emerged
this is it
and the code that generated it - there is for sure a bit of work to clean it and add a few comments (was too tired this evening)
clc
clearvars
[MCLdata,MCLdataStructure,dataOut,hWaitBar] =NewMCLDataRead_Begin3('fileName','SVHMCL78.mat ','timePrompt',0)
P_LV = MCLdata.P_LV;
LVVol = MCLdata.LVVol;
x = LVVol;
y = P_LV;
s = 1:length(x);
centroid_x = mean(x);
centroid_y = mean(y);
[theta,r] = cart2pol(x-centroid_x,y-centroid_y);
threshold = 0;
[t0_pos,s0_pos,t0_neg,s0_neg]= crossing_V7(theta,s,threshold,'linear'); % positive (pos) and negative (neg) slope crossing points
% ind => time index (samples)
% t0 => corresponding time (x) values
% s0 => corresponding function (y) values , obviously they must be equal to "threshold"
figure(1)
subplot(211),plot(s,theta,t0_pos,s0_pos,'+r',t0_neg,s0_neg,'+g','linewidth',2,'markersize',12);grid on
legend('signal','positive slope crossing points','negative slope crossing points');
subplot(212),plot(s,r,'linewidth',2,'markersize',12);grid on
xlabel('Time (s)');
nb_of_loops = length(t0_pos) -1;
r2all = [];
theta2all = [];
for ci = 1:nb_of_loops
ind_start(ci) = floor(t0_pos(ci));
ind_stop(ci) = ceil(t0_pos(ci+1));
a(ci) = ind_stop(ci) - ind_start(ci);
end
maxx = min(a);
for ci = 1:nb_of_loops
theta2 = unwrap(theta(ind_start(ci):ind_stop(ci)));
r2 = r(ind_start(ci):ind_stop(ci));
% now we can average r2interp data on the n loops
r2all = [r2all; r2(1:maxx)];
theta2all = [theta2all; theta2(1:maxx)];
end
theta2 = theta2(1:maxx);
r2_mean = mean(r2all,1);
theta2_mean = mean(theta2all,1);
[u,v] = pol2cart(theta2_mean,r2_mean);
u = mean(u,1);
v = mean(v,1);
u = u + centroid_x;
v = v + centroid_y;
% to close the loop, append the first u, v values at the end
u = [u u(1)];
v = [v v(1)];
figure(2),plot(LVVol,P_LV,u,v);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t0_pos,s0_pos,t0_neg,s0_neg] = crossing_V7(S,t,level,imeth)
% [ind,t0,s0,t0close,s0close] = crossing_V6(S,t,level,imeth,slope_sign) % older format
% CROSSING find the crossings of a given level of a signal
% ind = CROSSING(S) returns an index vector ind, the signal
% S crosses zero at ind or at between ind and ind+1
% [ind,t0] = CROSSING(S,t) additionally returns a time
% vector t0 of the zero crossings of the signal S. The crossing
% times are linearly interpolated between the given times t
% [ind,t0] = CROSSING(S,t,level) returns the crossings of the
% given level instead of the zero crossings
% ind = CROSSING(S,[],level) as above but without time interpolation
% [ind,t0] = CROSSING(S,t,level,par) allows additional parameters
% par = {'none'|'linear'}.
% With interpolation turned off (par = 'none') this function always
% returns the value left of the zero (the data point thats nearest
% to the zero AND smaller than the zero crossing).
%
% [ind,t0,s0] = ... also returns the data vector corresponding to
% the t0 values.
%
% [ind,t0,s0,t0close,s0close] additionally returns the data points
% closest to a zero crossing in the arrays t0close and s0close.
%
% This version has been revised incorporating the good and valuable
% bugfixes given by users on Matlabcentral. Special thanks to
% Howard Fishman, Christian Rothleitner, Jonathan Kellogg, and
% Zach Lewis for their input.
% Steffen Brueckner, 2002-09-25
% Steffen Brueckner, 2007-08-27 revised version
% Copyright (c) Steffen Brueckner, 2002-2007
% brueckner@sbrs.net
% M Noe
% added positive or negative slope condition
% check the number of input arguments
error(nargchk(1,4,nargin));
% check the time vector input for consistency
if nargin < 2 | isempty(t)
% if no time vector is given, use the index vector as time
t = 1:length(S);
elseif length(t) ~= length(S)
% if S and t are not of the same length, throw an error
error('t and S must be of identical length!');
end
% check the level input
if nargin < 3
% set standard value 0, if level is not given
level = 0;
end
% check interpolation method input
if nargin < 4
imeth = 'linear';
end
% make row vectors
t = t(:)';
S = S(:)';
% always search for zeros. So if we want the crossing of
% any other threshold value "level", we subtract it from
% the values and search for zeros.
S = S - level;
% first look for exact zeros
ind0 = find( S == 0 );
% then look for zero crossings between data points
S1 = S(1:end-1) .* S(2:end);
ind1 = find( S1 < 0 );
% bring exact zeros and "in-between" zeros together
ind = sort([ind0 ind1]);
% and pick the associated time values
t0 = t(ind);
s0 = S(ind);
if ~isempty(ind)
if strcmp(imeth,'linear')
% linear interpolation of crossing
for ii=1:length(t0)
%if abs(S(ind(ii))) > eps(S(ind(ii))) % MATLAB V7 et +
if abs(S(ind(ii))) > eps*abs(S(ind(ii))) % MATLAB V6 et - EPS * ABS(X)
% interpolate only when data point is not already zero
NUM = (t(ind(ii)+1) - t(ind(ii)));
DEN = (S(ind(ii)+1) - S(ind(ii)));
slope = NUM / DEN;
slope_sign(ii) = sign(slope);
t0(ii) = t0(ii) - S(ind(ii)) * slope;
s0(ii) = level;
end
end
end
% extract the positive slope crossing points
ind_pos = find(sign(slope_sign)>0);
t0_pos = t0(ind_pos);
s0_pos = s0(ind_pos);
% extract the negative slope crossing points
ind_neg = find(sign(slope_sign)<0);
t0_neg = t0(ind_neg);
s0_neg = s0(ind_neg);
else
% empty output
ind_pos = [];
t0_pos = [];
s0_pos = [];
% extract the negative slope crossing points
ind_neg = [];
t0_neg = [];
s0_neg = [];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Addition:
% % Some people like to get the data points closest to the zero crossing,
% % so we return these as well
% [CC,II] = min(abs([S(ind-1) ; S(ind) ; S(ind+1)]),[],1);
% ind2 = ind + (II-2); %update indices
%
% t0close = t(ind2);
% s0close = S(ind2);
end
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