Content-type: text/html
For a single tensor inversion, the output is:
- number of trials over which statistics computed,
- fraction of successful trials,
- mean direction (x, y, z),
- mean dyadic eigenvalues (l1, l2, l3),
- mean trace,
- std trace,
- mean FA,
- std FA.
For two tensor inversions:
- number of trials over which statistics computed,
- fraction of successful trials,
- mean direction 1 (x, y, z),
- mean dyadic eigenvalues 1 (l1, l2, l3),
- mean trace 1,
- std trace 1,
- mean FA 1,
- std FA 1,
- mean direction 2 (x, y, z),
- mean dyadic eigenvalues 2 (l1, l2, l3),
- mean trace 2,
- std trace 2,
- mean FA 2,
- std FA 2,
- mean prop,
- std prop.
For three tensor inversions:
- number of trials over which statistics computed,
- fraction of successful trials,
- mean direction 1 (x, y, z),
- mean dyadic eigenvalues 1 (l1, l2, l3),
- mean trace 1,
- std trace 1,
- mean FA 1,
- std FA 1,
- mean direction 2 (x, y, z),
- mean dyadic eigenvalues 2 (l1, l2, l3),
- mean trace 2,
- std trace 2,
- mean FA 2,
- std FA 2,
- mean direction 3 (x, y, z),
- mean dyadic eigenvalues 3 (l1, l2, l3),
- mean trace 3,
- std trace 3,
- mean FA 3,
- std FA 3,
- mean prop1,
- std prop1,
- mean prop2,
- std prop2 .
The dyadic of a direction n is the 3x3 matrix n n^T. The mean dyadic is the average the the dyadics for corresponding directions over all trials. The first eigenvalue kappa_1 of the mean dyadic indicates the concentration of the population of directions; the closer kappa_1 is to one the greater the concentration. Another common concentration statistic, used for example in Alexander and Barker, NeuroImage 27 2005, is gamma = -log(1-kappa_1).
Note that the order in which the inversions output multiple fitted tensors is arbitrary, so we need to cluster the directions into those which correspond. This program uses the simple iterative algorithm described in Alexander and Barker, NeuroImage 27 2005 to associate corresponding directions from each trial.
datasynth -voxels 20 -testfunc 1 -schemefile test/bmx7.scheme -snr 16 | bin/modelfit -schemefile test/bmx7.scheme -inversion 1 | invstats -inversion 1 -voxels 20 | double2txt
Outputs the following:
2.000000E01 Number of trials
1.000000E00 Fraction of successful trials (always 1 for single tensor)
9.999622E-01 |
-5.471425E-03 | The mean principal direction. Close to x, as expected
6.760559E-03 | for this synthetic data.
9.977014E-01 :
1.622163E-03 : Three mean dyadic eigenvalues; kappa_1 = 0.977014
6.764810E-04 :
2.091067E-09 Mean Trace(D)
7.214781E-11 Std Trace(D)
8.638374E-01 Mean FA
2.936898E-02 Std FA
The following is a simple investigation of how the concentration of principal directions
varies with noise level. Note how shredder pulls out the sixth number from each output,
which is the first eigenvalue of the mean dyadic.
for snr in 4 8 12 16 20 24 28 32; do echo SNR is $snr kappa1 is; datasynth -voxels 20 -testfunc 1 -schemefile test/bmx7.scheme -snr $snr | modelfit -schemefile test/bmx7.scheme -inversion 1 | invstats -inversion 1 -voxels 20 | shredder $((8*5)) 8 $((8*6)) | double2txt; done
Using a two-tensor inversion:
datasynth -voxels 20 -testfunc 3 -schemefile test/bmx7.scheme -snr 16 | bin/modelfit -schemefile test/bmx7.scheme -inversion 31 | invstats -inversion 31 -voxels 20 | double2txt
Outputs:
2.000000E01 Number of trials
1.000000E00 Fraction of successful trials (always 1 for single tensor)
9.998340E-01 |
-1.476980E-02 | The mean first principal direction. Close to x.
-1.066846E-02 |
9.932763E-01 :
3.698652E-03 : Mean dyadic for first direction.
3.025043E-03 :
2.259456E-09 Mean Trace(D_1)
8.076961E-10 Std Trace(D_1)
8.338131E-01 Mean FA_1
6.817987E-02 Std FA_1
-7.727805E-04 |
9.999895E-01 | The mean second principal direction. Close to y.
-4.518970E-03 |
9.888926E-01 :
6.457407E-03 : Mean dyadic for second direction.
4.649951E-03 :
2.798081E-09 Mean Trace(D_2)
1.646975E-09 Std Trace(D_2)
8.875209E-01 Mean FA_2
5.012714E-02 Std FA_2
5.519017E-01 Mean mixing parameter of D_1
9.971714E-02 Std mixing parameter D_1
Using a three-tensor inversion:
datasynth -voxels 20 -testfunc 4 -schemefile test/bmx7.scheme -snr 16 | bin/modelfit -schemefile test/bmx7.scheme -inversion 231 | invstats -inversion 231 -voxels 20 | double2txt
Outputs:
2.000000E01 Number of trials
1.000000E00 Fraction of successful trials (always 1 for single tensor)
2.976950E-02 |
9.990879E-01 | The mean first principal direction. Close to y.
-3.061276E-02 |
9.244842E-01 :
5.971932E-02 : Mean dyadic for first direction.
1.579646E-02 :
6.190711E-09 Mean Trace(D_1)
1.210998E-08 Std Trace(D_1)
8.763614E-01 Mean FA_1
1.152649E-01 Std FA_1
1.789741E-03 |
3.642901E-02 | The mean second principal direction. Close to z.
9.993346E-01 |
9.344133E-01 :
5.812832E-02 : Mean dyadic for second direction.
7.458347E-03 :
5.776993E-09 Mean Trace(D_2)
6.946526E-09 Std Trace(D_2)
9.013713E-01 Mean FA_2
5.259647E-02 Std FA_2
9.984848E-01 |
-5.117159E-02 | The mean third principal direction. Close to x.
2.023680E-02 |
9.119526E-01 :
7.157123E-02 : Mean dyadic for third direction.
1.647618E-02 :
2.085125E-09 Mean Trace(D_3)
1.143271E-09 Std Trace(D_3)
8.020855E-01 Mean FA_3
1.291003E-01 Std FA_3
3.172367E-01 Mean mixing parameter of D_1
8.778177E-02 Std mixing parameter D_1
2.996109E-01 Mean mixing parameter of D_2
5.259398E-02 Std mixing parameter D_2