Induced activity

Michael Wibral michael.wibral at WEB.DE
Wed Apr 7 09:49:01 CEST 2010

```Hi Thomas,

"...
Maybe I wasn't clear. The trick is to maintain the
complex components (real and imag) after the wavelet transform, then to
separate induced and evoked and then to calculate power in the end.
..."

>>From what I understand you suggest to:

(a) take the FFT of a trial :

FFT(trial i)

(b) then to take the average of those FFTs and stay in the complex domain:

1/n [sum(FFT(trial i))]

(c) to subtract this complex quantity from each trial:

FFT(trial i) - 1/n [sum(FFT(trial i))]

(d) and to take the power and then the average , finally:

1/n sum {(FFT(trial i) - 1/n [sum(FFT(trial i))])^2}

If you transform this, taking the linearity of the FFT into account where appropriate you get:

1/n sum {(FFT(trial i) - 1/n [sum(FFT(trial i))])^2} =

1/n sum {(FFT(trial i - 1/n [sum(trial i)])^2}=

1/n sum {(FFT(trial i - ERF))^2 }

In the end you seem to subtract the ERF from each trial, then take the FFT compute power and then compute the average. I am  a bit confused here: To me this seems to be the same approach as simply subtracting the ERF in the time domain before computing power, i.e. a simple version of the old regression approach. In my opinion this must be the case. This is because keeping the numbers complex, means keeping phase information and computing the average over trials in the Fourier domain should then be the same as computing the (trivially phase-sensitive) average in the time domain, then taking the Fourier transform.

On the other hand, if you really take power as the very last operation:

{1/n sum (FFT(trial i) - 1/n [sum(FFT(trial i))])}^2 =

{1/n sum (FFT(trial i - ERF)) }^2 =

{1/n sum (FFT(trial i)) - FFT(ERF)) }^2 =

{1/n sum (FFT(trial i)) - 1/n n FFT(ERF) }^2 =

{FFT(1/n sum (trial i)) - FFT(ERF)}^2 =

{FFT(ERF) - FFT(ERF)}^2 = 0

Could you let me know where I misunderstand that approach?

With regards to something like the ERF being present in every single trial, I was thinking of other mechanisms like phase-reset or asymetric modulations of oscillation amplitude that may or may not be detected by looking at power increases.

Michael

-----Ursprüngliche Nachricht-----
Von: Thomas Witzel <twitzel at NMR.MGH.HARVARD.EDU>
Gesendet: Apr 6, 2010 5:56:53 PM
An: FIELDTRIP at NIC.SURFNET.NL
Betreff: Re: [FIELDTRIP] Induced activity

>
>Maybe I wasn't clear. The trick is to maintain the
>complex components (real and imag) after the wavelet transform, then to
>separate induced and evoked and then to calculate power in the end.
>This can be done with entire TFRs that way. I'm not sure whether this is
>possible in the regular fieldtrip workflow which might cause confusion with
>terminology here.
>As for the ERF not reflecting activity that might not be present in this
>form in the trials, I guess we have a bit of a philosophical question
>here. The entire premise of an ERF is that the brain response is identical
>in every trial + some noise. Since EEG/MEG is extremely noisy you can't
>tell from single trials whats really going on, so averaging all trials
>could be the best estimation of what the signal in every trial looks like.
>Now, of course we know that this is not entirely true, because in many
>experiments we know of systematic trial to trial variation, in which
>case the whole ERF or for that matter most common analysis methods are
>inappropriate.
>Also, even if there is random trial to trial variation, some of it might
>not be noise, as already described by Schimmel back in 1967 in a nice
>Science article. This is where the induced signal comes in. For me its
>signal that can be detected by its respective increase or decrease in
>power, but its not coherent across trials so it cancels mostly in ERFs.
>Now subtracting the ERF from every trial brings the assumption back in
>that the evoked signal is the same in every trial which it might be or
>might not be. In most of the experiments I have analyzed subaverages
>(separate even and odd trials, or early and late ones) were very similar,
>so the assumption that the evoked response is the same in every trial was
>fair.
>Practically I found that subtracting the ERF or not, has very little
>impact on the final outcome, but I didn't test every case, so I'm
>subtracting where its deemed appropriate....
>
>Thomas
>
>
>  On Tue, 6 Apr
>2010, Michael Wibral wrote:
>
>> Dear Thomas,
>>
>> you write  "...as long no non-linear operations have been applied...". Computing power is exactly such a non linear operation. Hence the approach you proposed may fail. Also see the discussion on the list. Moreover the average (ERF) may not reflect actvity that is really present in this form in the trials.
>>
>> Michael
>>
>>
>> -----Ursprüngliche Nachricht-----
>> Von: Thomas Witzel <twitzel at NMR.MGH.HARVARD.EDU>
>> Gesendet: Mar 30, 2010 7:24:16 PM
>> An: FIELDTRIP at NIC.SURFNET.NL
>> Betreff: Re: [FIELDTRIP] Induced activity
>>
>>> Hello all,
>>>
>>> just my two cents late in this discussion, and I hope I'm not repeating
>>> what someone else has just said. The way I and my code calculate induced
>>> activity was that I would first average all trials to get an ERF, then
>>> subtract the ERF from each individual trial, and then calculate the the
>>> power. This can be done in complex domain (i.e. after some frequency
>>> analysis as well) as long no non-linear operations have been applied.
>>> I never really had any problems with this approach.
>>> As for the point made by Bobby about the frequency band being strong
>>> troughout the trial (even baseline), this makes sense as there is
>>> presumably some variation during the baseline as well. To get the "nice"
>>> picture, you need to represent the result relative to the baseline to show
>>> change of power/magnitude relative to the baseline with whatever flavour
>>> normalization you like....
>>>
>>> Thomas
>>>
>>>  On
>>> Tue, 30 Mar 2010, Oakman, Erin wrote:
>>>
>>>> Hello Bobby,
>>>>
>>>> Thanks for raising a very relevant question about the difference between induced and evoked activity !
>>>>
>>>> A good discussion of this can be found here, or attached as text
>>>> https://listserv.surfnet.nl/scripts/wa.cgi?A3=ind0704&L=FIELDTRIP&E=quoted-printable&P=234745&B=--Apple-Mail-1--1050075873&T=text%2Fhtml;%20charset=WINDOWS-1252&XSS=3
>>>>
>>>> There is not a definite way to separate the induced and evoked activity.  The reason is that the sum of the squares is not the same as the square of the sum.
>>>>
>>>> In my very limited experience, I have noticed that researchers sometimes use the term "induced" or "event-related spectral perturbation" to refer to the average of the single-trials power, which has been base-line corrected .  At least that is the case in the "induced power" in this paper:   Krishnan, G. P., W.P. Hetrick, C.A. Brenner, A. Shekhar, A.N. Steffen and B.F. O'Donnell 2009. Steady state and induced auditory gamma deficits in schizophrenia. Neuroimage.
>>>>
>>>>
>>>> Erin
>>>>
>>>>
>>>>
>>>> Hi
>>>>>     A late follow-up to this topic. I have recentrly been musing over how to
>>>>> get a "clean" measure of the non-phase locked activity. I have tried
>>>>> subtracting the ERF out prior to time-frequency computation but this
>>>>> produces quite a bit of artifact...presumably since the single trial data
>>>>> will have considerable ;atency "jitter"
>>>>
>>>> The ERF collapses two sources of "jitter"; in the latency of the transient activity (if it exists) and the phase of ongoing oscillatory activity.
>>>>
>>>>>    The comments from Christian below make sense ( I think) why simply
>>>>> subtracting the two time-frequency power representaions is not valid. But I
>>>>> wonder would this subtractive approach be valid if one worked with the
>>>>> magnitude of the signal rather than power..omitting all the squaring operations?
>>>>
>>>> Computing the magnitude is still a non-linear operation (square root of a sum of squares, rectification, whatever ... ). The problem for why this won't work either resides in averaging part: in the evoked case you have a linear average followed by a non-linear operation, and in the induced case you have an average of the non-linearly transformed quantity. The "catch phrase" here is: the sum of the squares is not the same as the square of the sum! (or the sum of the rectified data is not the same as the rectified sum)
>>>>
>>>> Hope this helps,
>>>> Christian
>>>>
>>>>
>>>>>   If this right theoretically, how to achieve this in Fieldtrip?. Would
>>>>> setting cfg.output = 'fourier then abs'ing the output work. My suspicion is
>>>>> no since the summing is being done first here. Alternatively, does one need
>>>>> to hack the code to return the magnitude.
>>>>>
>>>>> Thanks for your help on this and sorry for waking old threads :)
>>>>>
>>>>>    - Suresh
>>>>>
>>>>> On Fri, 23 Feb 2007 01:44:59 +0100, Christian Hesse
>>>>> <c.hesse at FCDONDERS.RU.NL> wrote:
>>>>>
>>>>>> One further comment (please see below):
>>>>>>
>>>>>>> Hi Thomas,
>>>>>>>> Following up on this conversation. It seems that the ?induced
>>>>>>>> activity? contains both phase-locked and non-phase-locked
>>>>>>>> activity, whereby the ?evoked? activity contains only phase-locked
>>>>>>>> activity. Is it then kosher to separate these components by linear
>>>>>>>> subtraction? For example, if we first compute the ?induced?
>>>>>>>> activity by averaging power over individual trials, and from that
>>>>>>>> subtract the ?evoked activity? (calculated based on average
>>>>>>>> response) to get the induced activity without any phase-locked
>>>>>>>> activity?
>>>>>>>
>>>>>>> It is not correct to subtract because computing the induced and
>>>>>>> evoked power spectra involves squaring signal amplitudes (a non-
>>>>>>> linear operation), and hence, taking your terminology to refer to
>>>>>>> the instantaneous amplitudes of the signal components (this applies
>>>>>>> to any time-frequency tile)
>>>>>>>> Induced = Phase + Non-Phase
>>>>>>>>
>>>>>>>> And
>>>>>>>>
>>>>>>>> Evoked = Phase
>>>>>>>>
>>>>>>>> Then
>>>>>>>>
>>>>>>>> Non-Phase = Induced ? Evoked
>>>>>>>>
>>>>>>>>
>>>>>>> what you actually get from spectral or time-frequency analysis is
>>>>>>> the power of your MEASURED signal
>>>>>>>
>>>>>>> Induced^2 = (Phase + Non-Phase)^2 = Phase^2 + 2*Phase*Non-Phase +
>>>>>>> Non-Phase^2
>>>>>>>
>>>>>>> Evoked^2 = Phase^2
>>>>>>>
>>>>>>> Then
>>>>>>>
>>>>>>> Induced^2 - Evoked^2 = 2*Phase*Non-Phase + Non-Phase^2  AND NOT Non-
>>>>>>> Phase^2
>>>>>>>
>>>>>> Note that the other crucial thing to consider here is that you are in
>>>>>> one case averaging power over trials over trials:
>>>>>>
>>>>>> E[ (Induced^2)  ] =  E[ (Phase + Non-Phase)^2 ] = E[ (Phase^2 +
>>>>>> 2*Phase*Non-Phase + Non-Phase^2) ] = E[ (Phase^2) ] E[ (Non-
>>>>>> Phase^2) ] + E[ 2*Phase*Non-Phase ]
>>>>>>
>>>>>> this is why taking the square root of sqrt(Induced^2) does not give
>>>>>> (Phase + Non-Phase) but sqrt(E[ (Phase+Non-Phase)^2 ]).
>>>>>>
>>>>>> in the evoked case you are taking the power of the average amplitude
>>>>>>
>>>>>> Evoked^2 = E[ Phase ]^2  (---> note the ^2 on the outside of the sum)
>>>>>>
>>>>>> so in subtracting you are actually assuming that E[Phase]^2 = E
>>>>>> [(Phase)^2] which is unlikely to be accurate the case in finite samples.
>>>>>>
>>>>>> Hope I have not confused others (or myself) here.
>>>>>> Christian
>>>>>>
>>>>>>
>>>>
>>>>
>>>>>
>>>>> This is indeed the approach that I have followed succesfully a couple of
>>>>> times (e.g. Bastiaansen et al., JOCN 2006), although the terminology that
>>>>> you are using is somewhat confusing. I (and I guess most people) would refer
>>>>> to induced activity as that part of the EEG that is non-phase-locked, so I
>>>>> would restate your equation to:
>>>>> induced = EEG - evoked.
>>>>>
>>>>> However, there is a drawback to this approach, since it assumes that the ERP
>>>>> is absolutely stationary over trials. This is not the case in reality (e.g.
>>>>> subjects' attentional level or other states may change from trial to trial,
>>>>> giving rise to variability in the single-trial ERPs). This means that by
>>>>> subtracting the average ERP, one may introduce frequency components in the
>>>>> residual EEG that were not present before. Klimesch, and Kalcher and
>>>>> Pfurtscheller, have come up with ways of scaling the average ERP so as to
>>>>> yield a best fit of the average with each single-trial ERP, but also that
>>>>> approach may be sub-optimal.
>>>>> My latest way around the problem is to run a TF analysis on the untreated
>>>>> EEG (containing both evoked and induced activity), and comparing this to a
>>>>> TF analysis of the subject-averaged ERPs (the evoked activity alone).
>>>>> Qualitative differences between the two analyses can now only be attributed
>>>>> to induced activity.
>>>>>
>>>>> Marcel
>>>>>
>>>>> Thomas Thesen wrote:
>>>>>>
>>>>>> Hi FieldTrippers,
>>>>>>
>>>>>>
>>>>>>
>>>>>> Following up on this conversation. It seems that the ?induced activity?
>>>>> contains both phase-locked and non-phase-locked activity, whereby the
>>>>> ?evoked? activity contains only phase-locked activity. Is it then kosher to
>>>>> separate these components by linear subtraction? For example, if we first
>>>>> compute the ?induced? activity by averaging power over individual trials,
>>>>> and from that subtract the ?evoked activity? (calculated based on average
>>>>> response) to get the induced activity without any phase-locked activity?
>>>>>>
>>>>>>
>>>>>>
>>>>>> So if
>>>>>>
>>>>>> Induced = Phase + Non-Phase
>>>>>>
>>>>>> And
>>>>>>
>>>>>> Evoked = Phase
>>>>>>
>>>>>> Then
>>>>>>
>>>>>> Non-Phase = Induced ? Evoked
>>>>>>
>>>>>>
>>>>>>
>>>>>> Or does the fact that this is a linear operations on data that have been
>>>>> constructed through a non-linear process render this somehow invalid? It has
>>>>
>>>>
>>>>
>>>>
>>>> ________________________________________
>>>> From: FieldTrip discussion list [FIELDTRIP at NIC.SURFNET.NL] On Behalf Of Bobby Stojanoski [stojanoski at UTSC.UTORONTO.CA]
>>>> Sent: Thursday, March 25, 2010 1:33 PM
>>>> To: FIELDTRIP at NIC.SURFNET.NL
>>>> Subject: [FIELDTRIP] Induced activity
>>>>
>>>> Dear Fieldtrippers,
>>>>
>>>> I am a relatively new user of fieldtrip and am very impressed!
>>>>
>>>> I am interested in comparing differences at certain frequencies ? induced 40-100 Hz ? between 2 experimental conditions.  My understanding was that I can calculate induced activity in the gamma range by calculating the power for each trial (subject average -- freqanalysis) and then averaging across subjects (grand average -- freqdescriptives/freqgrandaverage).
>>>>
>>>> To my dismay, when I plotted the results of my grandaverage I found a band of power at 55 - 65 Hz for the entire duration of my epoch. I should add this was not the case when I plotted power across trials for each participant.
>>>>
>>>> Earlier discussions mention computing induced+evoked (using freqanalysis and freqgrandaverage) and subtracting that from evoked (using timelockanalysis+freqanalysis) to get extract induced only activity. However, later posts suggest that this is not a valid approach.
>>>>
>>>> 1. Where have I made my mistake?
>>>>
>>>> 2. If ((induced+evoked)-evoked)) is not valid, what is the correct approach to calculating induced activity at 40 - 100 Hz?
>>>>
>>>> Any help would be greatly appreciated!
>>>>
>>>> Thank you
>>>> Bobby Stojanoski
>>>>
>>>>
>>>>
>>>>
>>>> ----------------------------------
>>>>
>>>> The aim of this list is to facilitate the discussion between users of the FieldTrip toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis.
>>>>
>>>> http://listserv.surfnet.nl/archives/fieldtrip.html
>>>>
>>>> http://www.ru.nl/fcdonders/fieldtrip/
>>>>
>>>>
>>>>
>>>>
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>>>> =================================
>>>> </body>
>>>>
>>>>
>>>>
>>>> ----------------------------------
>>>> The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.
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>>
>> ----------------------------------
>> The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.
>
>----------------------------------
>The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.

----------------------------------
The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.
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