How can I create an idealized cycle from quasiperiodic data?

I have data of blood velocity (attached) over several cardiac cycles. I'm trying to create a single idealized cycle that takes into account the natural variations in duration and velocity from cycle to cycle, while removing the noise. This is what the data looks like at the moment:

The standard way I've done it in the past is to manually pick points over a single cycle, then interpolate them. The blue interpolated line is roughly what I'm looking for as an output.

Is there any way I can create this kind of idealized cycle from the data I have?

Answer 1

[Star Strider]

This is called ‘ensemble averaging’. See for example Combining repetitive curves into one average curve and similar posts.

Try this —

LD = load('normalized_velocities.mat');
norm_values = LD.norm_values;
t = 1:numel(norm_values);

plocs = find(islocalmax(norm_values, 'MinProminence',0.1));
plocs = [plocs numel(t)];
vlocs = find(islocalmin(norm_values, 'MinProminence',0.005));
for k = 1:numel(plocs)-1
    ixm(k) = max(vlocs(vlocs<plocs(k)));                            % Min Before Peak
end

% for k = 1:numel(ixm)-1
%     ix{k} = ixm(k):ixm(k+1);
%     pulse{k} = norm_values(ix{k});
%     n(k) = numel(ix{k});
% end

for k = 1:numel(ixm)-1
    ix{k} = plocs(k)-11:ixm(k+1);
    pulse{k} = norm_values(ix{k});
    n(k) = numel(ix{k});
end

ens = zeros(1,max(n));                                              % Preallocate
for k = 1:numel(pulse)
    ens(k,1:n(k)) = pulse{k}(1:n(k));
end
ensavg = mean(ens,'omitnan');

figure
plot(t, norm_values,'.-')
hold on
plot(t(plocs), norm_values(plocs), '^r')
plot(t(vlocs), norm_values(vlocs), 'vg')
hold off
grid

figure
plot((0:max(n)-1), ens, '.-')
grid

figure
plot((0:max(n)-1), ensavg)
grid

producing:

Experiment to get the result you want.

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[Samuel Harvey]

Thank you! This is exactly what I was looking for.

[Star Strider]

As always, my pleasure!

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[Samuel Harvey]

Can you explain the difference between the commented section and the one directly beneath it? Are they two versions of the same function or do they have different purposes?

[Samuel Harvey]

Also, I spotted an issue in the preallocate section. There are zeros left in at the ends of the shorter cycles which are being averaged. I replaced

ens = zeros(1,max(n));  % original

with

ens = NaN(numel(n),max(n)); % new

which seems to fix it.

[Star Strider]

I chose zeros rather than NaN originally because NaN values can interfere with the calculations.

After running the code, I found that there were NaN values in the original data so the fix for that:

ensavg = mean(ens,'omitnan');

should work using NaN values for the preallocation.

My initial approach was just to use mean without the ‘nanflag’, so using zeros made sense in that context.

.

[Samuel Harvey]

Sorry, let me clarify. The issue with using zeros for placeholders is that at the tail end of the cycle those zeros are being treated as data points and affecting the average. Each curve is a slightly different length, so at the tail end it ends up averaging values from the longer curves with the zeros instead of only using existing data points. You can see in your figure that the idealized cycle drops off sharply at the very end, but that goes away when NaN values are used.

[Star Strider]

O.K.

The initial ‘ens’ vector is created to correspond to the maximum length of the discovered waveform segments, so it should be no longer than the longest one.

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