A MATLAB class for Mean Square Displacement analysis.
With minuscule exceptions, all the code I make is about scientific image analysis and data analysis.
Mastodon (The scientific software for tracking cells and lineaging in large microscopy images, not the social network.)
Hello,
first of all great program!
When fitting trajectories of shorter length (both simulated and actual measurements), however, I noticed a lot of negative diffusion coefficients and r² values (which both afaik shouldn't be possible) and dug into the code of fitMSD.
If I interpret it correctly, the program determines how many time points correspond to 25% of the longest trajectory in the pool in terms of length, and than applies that to all other curves for their linear fit evaluation. This seems counter intuitive, as it includes very uncertain points from the shorter curves. The output even says "fitting the first 25% of EACH curve", but then the program doesn't take into account all the NaN points in the MSD data.
This also leads to the following problem: when I have 100 tracks of length 8 each, the program will not fit any because they are all shortened to 1 point prior to fitting. If I add just one track of e.g. length 16 , then suddenly all tracks are properly fitted from point 2 to 16*0.25=4. See the issue?
Edit: And yes, I realize that 25% of points of 8 is not 3, but this is beside the point here
Next, there is also another problem in regard to averaging the fits for a global diffusion coefficient. When I include ALL tracks, the estimate is about right (with a simulation of short tracks). However, when I include only the ones with r²>0.6 or so, a lot of the lower diffusion coefficients are discarded due to bad fit, causing an inflated estimate of total D. Maybe this will be solved with the problem above, when the fit can properly choose points and a correct r² is calculated for selection.
I think I came up with a coded solution for the point selection of each curve (not too hard) and can add it per request if you see the problem in the same way.
However, I have no idea yet on how to deal with the negative D's or averaging in regards to low r2 so that the global mean is accurate, and what math says about the negative r2.
Thank you for reading.
Hi, I have been trying to do MSD analysis, following parts of this manual and this tutorial. However, I am hitting a wall with NaN values:
Error using fit>iFit (line 232)
X, Y and WEIGHTS cannot have NaN values.
Error in fit (line 116)
[fitobj, goodness, output, convmsg] = iFit( xdatain, ydatain, fittypeobj, ...
Error in msdanalyzer/fitMeanMSD (line 44)
[fo, gof] = fit(t, y, ft, 'Weights', w);
Error in MSD_a (line 63)
[fo, gof] = ma.fitMeanMSD;
My whole Matlab script (the error comes from the very last section % calculate diffusion coefficiency):
% housekeeping
addpath('C:\Users\...\MSD-a\Fiji.app\scripts' )
% import track
file_path_tracks = 'PEI_chan00_Tracks.xml';
tracks = importTrackMateTracks(file_path_tracks);
n_tracks = numel( tracks );
fprintf('Found %d tracks in the file.\n', n_tracks)
% remove Z set time scale
clipZ = true; % Remove Z coordinates, if you know you can.
scaleT = true; % Use physical time for T.
tracks = importTrackMateTracks(file_path_tracks, clipZ, scaleT);
tracks{1}(5, :)
[ tracks, md ] = importTrackMateTracks(file_path_tracks, ...
clipZ, scaleT);
md
% plot figure
figure
hold on
c = jet(n_tracks);
for s = 1 : n_tracks
x = tracks{s}(:, 2);
y = tracks{s}(:, 3);
plot(x, y, '.-', 'Color', c(s, :))
end
axis equal
xlabel( [ 'X (' md.spaceUnits ')' ] )
ylabel( [ 'Y (' md.spaceUnits ')' ] )
% MSD calculation
SPACE_UNITS = 'µm';
TIME_UNITS = 's';
ma = msdanalyzer(2, SPACE_UNITS, TIME_UNITS);
ma = ma.addAll(tracks);
disp(ma)
ma = ma.computeMSD;
ma.msd
% Plot MSD
figure
ma.plotMSD;
% weighted average
cla
ma.plotMeanMSD(gca, true)
mmsd = ma.getMeanMSD;
t = mmsd(:,1);
x = mmsd(:,2);
dx = mmsd(:,3) ./ sqrt(mmsd(:,4));
errorbar(t, x, dx, 'k')
% calculate diffusion coefficiency
[fo, gof] = ma.fitMeanMSD;
plot(fo)
ma.labelPlotMSD;
legend off
And my PEI_chan00_Tracks.xml as outputted from TrackMate on FIJI (sorry about the mess, GitHub doesn't allow attaching this format):
<?xml version="1.0" encoding="UTF-8"?>
<Tracks nTracks="1" spaceUnits="pixel" frameInterval="1.0" timeUnits="frame" generationDateTime="Fri, 31 Dec 2021 00:44:16" from="TrackMate v7.4.0">
<particle nSpots="423">
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<detection t="409" x="243.7338581741474" y="342.6558379785023" z="0.0" />
<detection t="410" x="243.0183864691459" y="344.26253253042063" z="0.0" />
<detection t="411" x="244.16996138307113" y="342.57292842666914" z="0.0" />
<detection t="412" x="244.13527769590496" y="342.0666091951257" z="0.0" />
<detection t="413" x="243.026431280147" y="342.424675183517" z="0.0" />
<detection t="414" x="244.17478407619075" y="341.53275460008894" z="0.0" />
<detection t="415" x="243.8382276918444" y="342.7102356575479" z="0.0" />
<detection t="416" x="244.13947269149944" y="342.0957901406573" z="0.0" />
<detection t="417" x="244.05220740421703" y="341.31859106947417" z="0.0" />
<detection t="418" x="243.85793638400204" y="340.8446018674191" z="0.0" />
<detection t="419" x="244.09058094003132" y="341.76507450664" z="0.0" />
<detection t="420" x="244.73533480541968" y="341.2792053882503" z="0.0" />
<detection t="421" x="243.58544871761143" y="342.9334984777053" z="0.0" />
<detection t="422" x="243.431320056101" y="343.2301651661782" z="0.0" />
<detection t="423" x="244.10975559275707" y="340.14118211428126" z="0.0" />
</particle>
</Tracks>
Apologies in advance because this sounds like a rather trivial problem on the surface, but I am quite new to Matlab, and I have no clue how to even begin looking for these NaN values.
Hello,
Thank you for the great problem.
Can I make a suggestion? Currently, missing points must be removed by the user from the track list before loading it into msdanalyzer.
The data set I am working on has a NaN position for missing frames. At first I didn't realise this and it loads fine in msdanalyser and I can fit the mean msd curve but when I try to fit the individual curves, it fails due to individual curves having lots of NaNs (propagated from a single missing point by addition).
As another user may not realise the problem, I suggest adding
track=track(~isnan(track(:,2)),:);
after line 51 in computeMSD.m
Best,
Sean
Hi,
I have this real movie with particles that I tracked with Trackmate. Some of the particles bleach or move in 3D so I have unequal track lengths. When I import the .csv into MATLAB to extract the tracks in the format ([ Ti Xi Yi ...]) as per your tutorial, I don't always have the same measurements per particles. Would the msdanalyzer still work or do I have to pad the data?
Hi @tinevez
Thanks for sharing the code. I have 3D data coordinates (x,y,z) for freely diffusing colloidal microspheres. How can I incorporate the 3rd dimension in the example code? (https://tinevez.github.io/msdanalyzer/tutorial/MSDTuto_brownian.html).
I can see the cell tracks in the workspace contains x,y,z coordinates along with the time steps when I define N_DIM=3 .
I believe it has something to do with the ma.plotTracks
Thanks
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