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invstats

Section: User Commands (1)
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NAME

invstats - Computes statistics of populations of diffusion tensors.

SYNOPSIS

invstats -inversion <index> -voxels <num voxels>

DESCRIPTION

Reads in the output of modelfit and computes statistics of the distribution of principal directions and shape properties in the results. Used mostly for simulations, performance analysis and calibration.

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:

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.

EXAMPLES

Here are some examples using synthetic data.

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

OPTIONS

Standard IO options, as listed in modelfit(1).
-voxels <number of voxels>: The number of voxels in the input data. Defaults to one, so must be specified.
-inversion <index>: Specify the index of the inversion used to generate the data. See modelfit(1) for a list of inversion indices.

AUTHORS

Daniel Alexander <camino@cs.ucl.ac.uk>

BUGS

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Time: 02:07:11 GMT, December 04, 2017

Invstats