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macro:diffusion_analysis_time_ensemble_average
//Example macro that does a diffusion analysis on a results table of tracking
//data. The required format is as generated by the Manual Tracking plugin
//http://rsbweb.nih.gov/ij/plugins/track/track.html
//assuming Results table column headings: Track > Slice > X > Y
//It requires many tracks and many time points!
//The analysis uses the time ensemble average method described in Charsooghi, MA et al 2011
//http://www.sciencedirect.com/science/article/pii/S0010465510003620

//Get number of tracks (nTracks)
nTracks = 0;
for (a=0; a<nResults(); a++) {
if (getResult("Track",a)>nTracks)
{
nTracks = getResult("Track",a);
}
else{};
}

//Find the track length for each track - write track length to results table
//some variables
Track=1;
L_Track=0;

//work though tracks and determine length
for (i=0; i<nResults(); i++){
if (getResult("Track", i)==Track) {L_Track++;} else {

//Do this if its the first track
if(Track==1){		for (j=(i-L_Track); j<i; j++){
setResult("T_Length", j, L_Track);
}
L_Track=0;
Track++;

//Do this if its in the middle
L_Track=1;
} else {for (j=(i-L_Track); j<i; j++){
setResult("T_Length", j, L_Track);
}
L_Track=1;
Track++;
}
}
}
//Do this to get the last track
L_Track=0;
for (j=0; j<nResults; j++) {
if (getResult("Track", j)==nTracks) {L_Track++;}
}

for (k=0; k<nResults; k++) {
if (getResult("Track", k)==nTracks) {setResult("T_Length", k, L_Track);
}
}
updateResults();

//get last slice
maxslice = 0;
for (b=0; b<nResults(); b++) {
if (getResult("Slice",b)>maxslice)
{
maxslice = getResult("Slice",b);
}
else{};
}

//get first slice
minslice = maxslice;
for (c=0; c<nResults(); c++) {
if (getResult("Slice",c)<minslice)
{
minslice = getResult("Slice",c);
}
else{};
}

//The window sizes for analysis range from 1-step to - maxslice-1
//Calculate squared dispalcement from tracking data for all possible window sizes

MSD = newArray();
time = newArray();
divide=0;
r_total=0;
dis2 = 0;

for (u=1; u<(maxslice); u++) {

for (i=0; i<nResults(); i++){
if (getResult("Slice", i)<=u) {}

else{ if (getResult("Track", i)>getResult("Track", i-u)) {}

else { if (getResult("T_Length", i)>=u && getResult("Track", i-u)==getResult("Track", i)) {
B9 = getResult("X", i);
B8 = getResult("X", i-u);
C9 = getResult("Y", i);
C8 = getResult("Y", i-u);
disx2 = (B9-B8)*(B9-B8);
disy2 = (C9-C8)*(C9-C8);
dis2 = (disx2 + disy2);
r_total = r_total+dis2;
divide++;
}
}
}
}
time = Array.concat(time, u);
MSD = Array.concat(MSD, (r_total)/divide);
r_total=0;
divide=0;
}

Fit.doFit("Straight Line", time, MSD);
intercept = d2s(Fit.p(0),6);
slope = d2s(Fit.p(1),6);
r2 = d2s(Fit.rSquared,3);
print("slope = "+slope);
print("intercept = "+intercept);
print("R^2 = "+r2);
Fit.plot();

//Richard Mort 26/01/2013