Tutorial 25: Difference

[TUTORIAL UNDER DEVELOPMENT: NOT READY FOR PUBLIC USE]

Authors: Francois Tadel, Elizabeth Bock, Dimitrios Pantazis, Richard Leahy, Sylvain Baillet

In this auditory oddball experiment, we would like to test for the significant differences between the brain response to the deviant beeps and the standard beeps, time sample by time sample. Until now we have been computing measures of the brain activity in time or time-frequency domain. We were able to see clear effects or slight tendencies, but these observations were always dependent on an arbitrary amplitude threshold and the configuration of the colormap. With appropriate statistical tests, we can go beyond these empirical observations and assess what are the significant effects in a more formal way.

We are typically interested in comparing different groups of samples. We want to know what is significantly different in the brain responses between two experimental conditions or two groups of subjects. So we will be essentially computing differences, then testing if these differences are significantly different from zero.

This tutorial focuses only on the first part of this problem. Computing a difference between condition A and condition B sounds trivial, but it requires some reflexion when it comes to interpreting the sign of the subtraction of two signals oscillating around zero. Many options are available, we will try to give clear directions of the use cases for each option. The statistical significance will be discussed in the next tutorial.

Sign of the signals

First we need to define on which signals we want to compute the difference: sensor recordings, constrained sources (one signal per grid point) or unconstrained sources (three signals per grid point). For the first two we can compare directly the signals oscillating around zero or their absolute value, for unconstrained sources we have the additional option to compare the norm of the three orientations.

Using the rectified signals (absolute value) gives us an idea of the amount activity in one particular brain region, but alters the frequency information and therefore cannot be used for time-frequency or connectivity analysis. Additionally, the rectified signals may not be appropriate to detect effects between different experimental conditions, as illustrated in the next section.

In general, you should not apply an absolute value (or a norm) explicitely to your data. The only application cases for rectified signals are the display of the cortical maps and the comparison of magnitudes between conditions, and both can be done on the fly.

diff_signals.gif

Now let's consider the two conditions for each available option. The examples below show the difference (deviant-standard) for one signal only, corresponding to the auditory cortex. The operator |x| represents the absolue value of x.

MEG/EEG sensor

We observe some important differences between (A-B) and (|A|-|B|), in the absolute case the amplitude of the difference is not representative of the distance between the green and the red curves. In general, the sign of the signal recorded by and MEG or EEG sensor is meaningful and we need to keep it in the analysis to account for the differences between conditions.
Never use an absolute value on sensor data.

diff_sensors.gif

Constrained sources

We also observe important differences between (A-B) and (|A|-|B|). At 175ms, we have the highest distance between the red and green curves, but it corresponds to a zero in the rectified difference.

diff_constr.gif

(A-B)

|A|-|B|

Unconstrained sources

The exact same observations apply to the unconstrained sources, using the norm of the three orientations instead of the absolute values. Considering that X and Y are the source vectors with three components each (x,y,z) for conditions A and B.

Norm(X-Y): This statistic will detect vector differences between the two signals which can occur if the magnitude and/or orientation changes. It differs from (Norm(X)-Norm(Y)) in being sensitive to changes in apparent source orientation, but cannot differentiate increases from decreases in amplitude.

Norm(X)-Norm(Y): This is the unconstrained equivalent to |A|-|B|, i.e. it will produce a signed value that reflects increases or decreases in magnitude from A to B and should be interpreted similarly. Unlike Norm(X-Y) it is not sensitive to rotation of the source from A to B unless there is an accompanying amplitude change. But on the other hand, because the statistic is signed, we can differentiate between increases and decreases in amplitude.

diff_unconstr.gif

Source normalization

The examples above only show minimum norm current density maps that haven't been normalized. But the exact same conclusions can be applied to normalized source values, as long as you do not rectify the signals during the computation the normalization.

As a reminder, you should normalize the source maps if you are intending to compare different subjects, it will help bringing them to the same range of values. The list below shows the valid operations for the Zscore normalization, but the same is applicable for dSPM, sLORETA and MNp.

Constrained sources:

Unconstrained sources:

Always avoid using the following measures, for any reason (display, differences or statistics):

Difference deviant-standard

Before running complicated statistical tests that will take hours of computation, you can start by checking what the difference of the average responses looks like. If in this difference you observe obvious effects that are clearly not what you are expecting, it's not worth moving forward with finer analysis: either the data is not clean enough or your initial hypothesis is wrong.

Absolute difference: |A|-|B|

We are going to use the Process2 tab, at the bottom of the Brainstorm figure. It works exactly like the Process1 tab but with two lists of input files, referred to as FilesA (left) and FilesB (right).

Relative difference: (A-B)

Difference of means

Another process can compute the average and the difference at the same time. We are going to compute the difference of all the trials from both runs at the sensor level. This is usually not recommended because the subject might have moved between the runs. Averaging the recordings across runs is not accurate but can give a good first approximation, in order to make sure we are on the right tracks.

Time-frequency

In the case of time-frequency maps, there is no sign ambiguity.








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Tutorials/Difference (last edited 2015-11-04 22:22:36 by FrancoisTadel)