View source for Talk:EEG microstates

== Reviewer A:  ==

As will be obvious to my old friend Dietrich, this review is written by Paul Nunez. Greetings to my friends in Switzerland. I will use the word “you” to refer to this group.  

For quite some time, I have felt that Dietrich's research group has obtained very interesting and important results with the “microstates,” but communication of these results is hampered by inadequate integration with other work as well as the language barriers that often separate medical and physical scientists. This article starts with a very nice introductory paragraph, but goes down hill rather quickly. I start with some general comments.

1. The microstates label. I understand “micro” from the viewpoint of conscious experience, but from a brain dynamical perspective, something that lasts for 100 milliseconds is better described as a “macro (dynamic) state.” I’m not suggesting that the label be changed, only that this little inconsistency be acknowledged, especially for readers seeing this material for the first time. 

2. I will brazenly present some self-serving references to my own work, especially on the reference electrode issue in 

Nunez and Srinivasan, Electric Fields of the Brain: the Neurophysics of EEG, 2nd ed,  Oxford U Press, 2006 (ref 1). 

and the relationship of neocortical dynamics to scalp potentials in both Ref 1 and 

Nunez PL and Srinivasan R, A theoretical basis for standing and traveling brain waves measured with human EEG with implications for an integrated consciousness, Clinical Neurophysiology 117: 2424-2435, 2006 (ref 2). 

3. Section 1 titled “Brain electric fields.” Two mistakes in one title! You are not directly recording electric fields (if you were, there would be no reference electrode issue). You are not recording “brain” potentials, only scalp potentials. The latter is a critical point, not just a minor language issue. All spatial patterns (say waves on the ocean surface) can be represented as a sum over spatial frequencies (by Fourier analysis). Why is it important to look at “brain waves” in this way--because the head volume conductor acts as a spatial filter. Scalp potentials represent only the very long wavelength cortical dynamics.

4. The follow up on #3: Years ago Grey Walter found multiple alpha rhythms with ECoG. Pfurtscheller’s group studied multiple alphas using the NN Laplacian. In ref 1, we use the spline Laplacian to distinguish the long and shorter contributions to the alpha band, which may have somewhat different oscillation frequencies. We describe the dynamic process as cell assemblies embedded in global fields of synaptic action. There are, of course, several complementary ways to picture any complex process. The more of these complementary pictures you can identify and site, the better the communication.

5. Section 1. I think the hill metaphor is fine, but overworked to the point of confusion. Yes, in one sense, the reference does not matter, yet the locations of the maxima and minima shown in figs 2 and 9 clearly do depend on the reference. To see this imagine that the reference were placed on the right occipital scalp (say 0.5 cm from the “18” in fig 2), in which case the “18” would become close to zero. We know this because the reference is defined as zero potential and a very large tangential scalp electric field would be required for the site “18” to be anything but close to zero. 

6. To follow up on #5. In ref 1, Ramesh and I have provided unambiguous interpretations of various references, including the average reference (others may have done this a long time ago, I just haven’t found it). The (common) average reference provides an estimate of the nominal scalp potential with respect to infinity. By “nominal” I mean the potential due to all sources within the head. Unfortunately, with only 30-35 electrodes, the average reference probably provides a very poor estimate; you probably need 100 or so. Obviously, if a certain spatial pattern of scalp potentials is obtained using (any) reference and (using the same reference) the spatial pattern changes, this indicates that the underlying cortical source distribution has changed. This is the main point and this is why I think this research is important. But, in presenting the results, you mix this central issue with reference-depended plots like figs 2 and 9.   

7. Map hilliness of some other measure of potential gradients are truly reference independent. I would think that figs 2 and 9 should represent some reference independent measure, but this is not what the caption to fig. 2 says; it says “potential.” On the other hand, the fig. 9 caption says “field,” but since the article tends to mix such words indiscriminately I am not sure what is rally meant. 

8. There are probably many ways to represent hilliness. For example, Roberto could fit instantaneous potential maps to spline functions and use the splines to estimate the electric field components Ex and Ey at each electrode site. Although these would be only very crude estimates, they would provide genuine reference-free maps of local hilliness. Furthermore, these maps would probably provide much better connections to the underlying cortical source distributions.

9. Parsing the series…I like fig. 1, especially since it looks like standing waves, composed of spherical harmonics Ylm (spatial frequencies on a sphere). The different microstates can then be expressed a different linear combinations of the Ylm’s. Others, including myself, have found that alpha rhythm appears as traveling waves over the scalp for very short periods; one may speculate that these periods correspond to transition times between microstates, which appear to be standing waves. 

10. I realize that I may have misinterpreted some of this article. If so, I accept a little blame, but I think it would indicate places where a much clearer presentation is needed. Be precise with physical terminology, and as much as possible show the overlap with other studies.

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==Authors' reply to Reviewer A==
In the following, we copy reviewer A's points and follow them with our replies. However, some points will be parsed into sub-points so as to make our comments more specific.

'''Reviewer A''': As will be obvious to my old friend Dietrich, this review is written by Paul Nunez. Greetings to my friends in Switzerland. I will use the word “you” to refer to this group.
For quite some time, I have felt that Dietrich's research group has obtained very interesting and important results with the “microstates,” but communication of these results is hampered by inadequate integration with other work as well as the language barriers that often separate medical and physical scientists. This article starts with a very nice introductory paragraph, but goes down hill rather quickly. I start with some general comments.

'''Our reply''': Introduction to our replies to Paul Nunez

Hi Paul, greetings from Switzerland!
We appreciate your comments and proposals. Before we reply to the 10 individual points, of which some include sub-points, we note that there appear to be three fundamental themes that are reappearing basic tenets in the 10 paragraphs:

(1) There is basic disagreement between you and us whether a change of the reference location in a momentary electric potential field changes the landscape of this field. You imply that it does, we state that it does not.

(2) The microstate analysis concept is based on the topographic assessment of momentay maps of electric fields, of landscapes of potential distributions. It assesses changes over time recognizing changes in map landscape. It does not use assessments of the data in terms of (spatial or temporal) waves, and accordingly does not use transformations of the data into the (spatial or temporal) frequency domain.

(3) There are terminology issues, which we will take up where they appear in your comments.

Having named these basic themes, we address now your 10 individual points:

'''Reviewer A: 1.''' The microstates label. I understand “micro” from the viewpoint of conscious experience, but from a brain dynamical perspective, something that lasts for 100 milliseconds is better described as a “macro (dynamic) state.” I’m not suggesting that the label be changed, only that this little inconsistency be acknowledged, especially for readers seeing this material for the first time.

'''Our reply: A1.''' "Micro" is in general use a relative term. For example, "microscope" refers to devices that pick up structures whose higher resolution configuration is far smaller than what the microscope sees.

We use the term "macrostate" [e.g. Lehmann, D. and Koenig, T. Spatio-temporal dynamics of alpha brain electric fields, and cognitive modes. Int. J. Psychophysiol. 26:99-112, 1997] in reference to the longer-lasting temporal chunks of EEG recordings that are recognized by adaptive segmentation techniques of the channel-wise recorded EEG waveforms (autoregressive segmentation cf. Bodenstein, G. & Praetorius, H.M. Feature extraction from the electroencephalogram by adaptive segmentation. Proceed. of the IEEE, 1977,65[5]:642-652); the duration of such macrostates is in the range of seconds. A hierarchical analysis would first parse the data into waveshape-based macrostates, then into landscape-based microstates.

'''Reviewer A: 2.''' I will brazenly present some self-serving references to my own work, especially on the reference electrode issue in

Nunez and Srinivasan, Electric Fields of the Brain: the Neurophysics of EEG, 2nd ed, Oxford U Press, 2006 (ref 1). 

'''Our reply: A2-a.''' Obviously, we have some basic disagreements on the reference electrode question. See below, our reply to your point #5.

'''Reviewer A: 2 continued''': and the relationship of neocortical dynamics to scalp potentials in both Ref 1 and

Nunez PL and Srinivasan R, A theoretical basis for standing and traveling brain waves measured with human EEG with implications for an integrated consciousness, Clinical Neurophysiology 117: 2424-2435, 2006 (ref 2).

'''Our reply: A2-b.''' Your paper concerns temporal frequencies and spatial waves. However, these topics are not in the microstate concept as stated above in our introduction to our replies. No doubt, brain dynamics has been assessed by many different approaches that fit the data as well as the microstate approach, including implications for consciousness.

Possible relations between, on one hand, microstate assessment and, on the other hand, frequency spectra and wavenumber maps, or other measures of dynamics such as e.g. dimensionality measures, or connectivity is not the topic of the present microstate article.

'''Reviewer A: 3.''' Section 1 titled “Brain electric fields.” Two mistakes in one title! You are not directly recording electric fields (if you were, there would be no reference electrode issue). You are not recording “brain” potentials, only scalp potentials. The latter is a critical point, not just a minor language issue.

'''Our reply: A3-a.''' Rigorously, this is true. “Electric field” has a precise definition in physics, being the gradient of the scalar electric potential field. We admit to having used the term rather vernacularly. However, we do not find this misleading, since – as you so aptly describe it in your book entitled “Electric Fields of the Brain” – one can only measure potential differences.

The use of the term “brain” is due to the origin of the measurements as in the term “electroencephalogram” that corresponds to “encephalon” and not to the skin on the head surface (scalp). Of course we all know that the recorded EEG/ERP data contain many electric signals whose sources are not the brain such as muscle, eyeball, tongue, heart, etc ("artifacts" for brain studies).

Taken literally, the expression “scalp potential” might imply skin sources, such as due to sweat glands. “Scalp potential” might be a time-honored term commonly used in the community but it is potentially misleading. (Other conventions likewise refer to the target of the recording, not to the location of the recording electrodes: one does not speak of "hand and foot skin potential" when referring to Einthoven’s electrocardiogram data).

In conclusion, we feel justified to keep the term “Brain” related to the measurements, and we will use the expression “brain potentials recorded on the head surface” where it might clarify the issue. The use of the term “field” is not restricted to “electric field”; the electric potential field on the scalp is a legitimate use of “field” as well (functional analysis terminology, which is partly the language of physics).

'''Reviewer A: 3. continued''': All spatial patterns (say waves on the ocean surface) can be represented as a sum over spatial frequencies (by Fourier analysis). Why is it important to look at “brain waves” in this way--because the head volume conductor acts as a spatial filter. Scalp potentials represent only the very long wavelength cortical dynamics.

'''Our reply: A3-b.''' The suggestion is to make a high-pass spatial filter for the “brain potentials recorded on the head surface”, because these are closer to true “brain waves”. This seems to imply that the low spatial frequencies are irrelevant to brain function. We do not agree with this approach. We prefer to keep the measurements in their entirety (low and high spatial frequency components). We do not partial out different spatial or temporal frequencies in microstate analysis.

In addition, the microstate theory/ hypothesis / phenomenon does not deal with nor makes use of “brain waves”. The reason is purely phenomenological: we observe jumps between sequential maps, no waves.

'''Reviewer A: 4.''' The follow up on #3: Years ago Grey Walter found multiple alpha rhythms with ECoG. Pfurtscheller’s group studied multiple alphas using the NN Laplacian. In ref 1, we use the spline Laplacian to distinguish the long and shorter contributions to the alpha band, which may have somewhat different oscillation frequencies. We describe the dynamic process as cell assemblies embedded in global fields of synaptic action. There are, of course, several complementary ways to picture any complex process. The more of these complementary pictures you can identify and site, the better the communication.

'''Our reply: A4.''' We wish to clarify that the microstate approach does not contradict that different types of alpha rhythm might exist.

As for the use of the Laplacian, i.e. high-pass spatial filtering, we refer here to our arguments in our reply “A3-b” above.

'''Reviewer A: 5.''' Section 1. I think the hill metaphor is fine, but overworked to the point of confusion. Yes, in one sense, the reference does not matter, yet the locations of the maxima and minima shown in figs 2 and 9 clearly do depend on the reference. To see this imagine that the reference were placed on the right occipital scalp (say 0.5 cm from the “18” in fig 2), in which case the “18” would become close to zero.

'''Our reply: A5-a.''' We view the reference electrode effect on momentary potential maps as follows (see footnote below): For an instantaneous scalp map, the choice of reference will add, to all electrodes, a certain constant value (the same for all electrodes, as can also be found in your book, see also our Geselowitz 1998 reference). Therefore, the scalp positions of the maximum value and the minimum value do not change. In other words, important features of a given field such as the position of maximum and minimum are invariant to the choice of the reference position.

A comment: The legend to Fig 2 explains that this is a map that summarizes the incidence of occurrence of extreme potentials (% of time) at the 19 electrode positions of the maps shown in the movie (Fig. 1). What you refer to as Fig 9 is Fig 3 ("Fig 9" is part of the copied page of the 1971 paper which includes the copy of the legend that correctly says “Fig 9”) - and this figure displays the same message as Fig 2. We will mend the legend to Fig 3 so that it becomes clearer.

However, presume Fig. 2 does display momentary potential values at 19 electrodes. Thus if one takes the electrode with the value 18 in Fig. 2 as reference, its new value becomes zero, and all others must have 18 subtracted from their original value. Thus, the electrode with the new value of zero will continue to show the maximum of all measured potential values.

As you can see, we are dealing with the values at hand, no interpolation method at all in Fig 2, and a linear interpolation method in Fig 3, which is incapable of placing extreme values outside the measurement set.

With respect to the last sentence in your point 5 "…imagine that the reference were placed on the right occipital scalp (say 0.5 cm from the “18” in fig 2), in which case the “18” would become close to zero. ", please clarify, because it seems that you are giving a special meaning to a potential value of zero, that in our view signifies nothing special since this numeric label depends on the chosen reference point.

(footnote): Of course, the choice of a reference will change the EEG temporal waveshapes recorded from the different electrodes (single channel time series), thereby changing power spectra (and their maps), phase angles, coherences, dimensionalty, etc of these traces.

'''Reviewer A: 5 continued''': We know this because the reference is defined as zero potential and a very large tangential scalp electric field would be required for the site “18” to be anything but close to zero.

'''Our reply: A5-b.''' We do not understand the term "tangential scalp electric field". Please explain.

'''Reviewer A: 6.''' To follow up on #5. In ref 1, Ramesh and I have provided unambiguous interpretations of various references, including the average reference (others may have done this a long time ago, I just haven’t found it). The (common) average reference provides an estimate of the nominal scalp potential with respect to infinity. By “nominal” I mean the potential due to all sources within the head. Unfortunately, with only 30-35 electrodes, the average reference probably provides a very poor estimate; you probably need 100 or so. Obviously, if a certain spatial pattern of scalp potentials is obtained using (any) reference and (using the same reference) the spatial pattern changes, this indicates that the underlying cortical source distribution has changed. This is the main point and this is why I think this research is important.

'''Our reply: A6-a.''' The reference issue was covered in our reply “A5-a”.

'''Reviewer A: 6 continued''': But, in presenting the results, you mix this central issue with reference-depended plots like figs 2 and 9.

'''Our reply: A6-b.''' This point concerning the actual reference independence of Fig 2 and Fig 3 (read as "Fig 9") was covered in our reply “A5-a”.

'''Reviewer A: 7.''' Map hilliness of some other measure of potential gradients are truly reference independent.

'''Our reply: A7-a.''' To clarify: "Map Hilliness" as defined in the text (following our definition of 1971 and thereafter) refers to the global hilliness of a map (the sum of all absolute momentary potential values referred to average reference, devided by number of electrodes); it results in a single-number assessment of a property of the entire potential field. It is not related in any way to curvature (nor first nor second spatial derivatives of the field).

'''Reviewer A: 7 continued''': I would think that figs 2 and 9 should represent some reference independent measure, but this is not what the caption to fig. 2 says; it says “potential.” On the other hand, the fig. 9 caption says “field,” but since the article tends to mix such words indiscriminately I am not sure what is rally meant.

'''Our reply: A7-b.''' As to reference-independence see our reply A5-a.

As to the terminology issue, the term “EEG field on the scalp” is quite clearly referring to spatial potential distribution. Please see also the paragraph “A comment” in our reply A5-a.

'''Reviewer A: 8.''' There are probably many ways to represent hilliness. For example, Roberto could fit instantaneous potential maps to spline functions and use the splines to estimate the electric field components Ex and Ey at each electrode site. Although these would be only very crude estimates, they would provide genuine reference-free maps of local hilliness. Furthermore, these maps would probably provide much better connections to the underlying cortical source distributions.

'''Our reply: A8.''' We do not refer to curvature in the article. We use reference-independent hilliness as unambiguously defined in the article and repeated above (see also our reply “A7-a”).

By the way, Roberto has published on curvature, see for example Equation 3 in [Pascual-Marqui, R.D., S.L. Gonzalez-Andino, P.A. Valdes-Sosa, and R. Biscay-Lirio, Current source density estimation and interpolation based on the spherical harmonic Fourier expansion. International Journal of Neuroscience, 1988. 43(3-4): p. 237-249], and Dietrich published a map of local gradients of a 45-channel EEG: Figure 11 in [Lehmann, D.: Principles of spatial analysis. In: A. Gevins and A. Remond (eds): Handbook of Electroencephalography and Clinical Neurophysiology, Vol. 1: Methods of Analysis of Brain Electrical and Magnetic Signals. Elsevier, Amsterdam. [ISBN 0-444-80804-3]. pp. 309-354 (1987)].

'''Reviewer A: 9.''' Parsing the series…I like fig. 1, especially since it looks like standing waves, composed of spherical harmonics Ylm (spatial frequencies on a sphere). The different microstates can then be expressed a different linear combinations of the Ylm’s. Others, including myself, have found that alpha rhythm appears as traveling waves over the scalp for very short periods;

'''Our reply: A9-a.''' You are proposing a “wave” interpretation of the microstates. At this moment, we see no deeper insight possibly emerging from the application of wave theory.

As to the application of wave-oriented analyses to microstates, please see our replies “A2-b” and “A3-b”.

'''Reviewer A: 9 continued''': one may speculate that these periods correspond to transition times between microstates, which appear to be standing waves.

'''Our reply: A9-b.''' The dynamics of the microstates certainly is a most interesting aspect. For example, we observed aberrant transition rules between microstate classes in schizophrenia [Lehmann et al. Psychiatry Res.: Neuroimaging 138: 141-156, 2005]. In our view, the dynamics of the microstates can be modeled as a Markov process [Wackermann et al., Int. J. Psychophysiol. 14: 269-283, 1993], especially since the transitions between states (i.e. microstates) are very brief, and occur when the signal power (i.e. the hilliness or global field power) is at a minimum. Anyway, this topic is extremely interesting and worth a possible future collaboration.

'''Reviewer A: 10.''' I realize that I may have misinterpreted some of this article. If so, I accept a little blame, but I think it would indicate places where a much clearer presentation is needed. Be precise with physical terminology, and as much as possible show the overlap with other studies.

'''Our reply: A10.''' We appreciate being made aware of our, at times, misunderstandable wording, which certainly will help us improve the web page. With respect to “overlap with other studies”, we feel that the quoted references already cover quite enough of the microstate-related literature.

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A final comment: We have made no changes yet to the text, awaiting the reviews.
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== Reviewer A (second round):  ==

Re: reference electrode and landscape arguments.

Yes, the highest mountain peak will still be the highest peak regardless of whether the reference is a lower peak or sea level. Unfortunately, this metaphor breaks down when the mountain moves up and down (above and below sea level) with time. Thus, if the reference is the mountain peak, the reference moves such that it stays, by definition, at zero height. 

Obviously, when scalp potentials are recorded with respect to a reference electrode, the potential at any location very close to this electrode is near zero (and exactly zero at the reference). Current density in the scalp is proportional to the gradient of potential (tangential electric field), limited by volume conduction (and to a lesser degree nonzero electrode size) to a maximum magnitude of something like 5 microvolts/cm, meaning any "recording" electrode placed within a cm or so from its reference cannot record potentials larger than about 5 microvolts. 

The potential at any scalp location (including the reference) can always be represented as a sum over frequency components, each having an amplitude and phase. To keep my example simple, I will assume a single frequency (1/2pi) over the entire scalp, but allow differences in amplitude and phase (the latter in argeement with all EEG data). The following example shows that the locations of maxima and minima generally depend on the reference location as there is nothing special about the numbers chosen here.    

Cheers,
Paul Nunez


Reference electrode potentials with respect to any fixed location X:

VR1 = 10 Sin[t + pi/4]

VR2 = 10 Sin[t + 5pi/4]

Actual potentials at scalp locations 1 and 2 with respect to location X:

V1 = 20 Sin[t]

V2 = 20 Sin[t + pi/6]

Measured potentials using references R1 or R2 are shown in the following table along with the maximum recorded potential. When reference 1 is used, the maximum measured potential is 14.74, which occurs at electrode 1. When reference 2 is used, the maximum recorded potential is 29.78, which occurs at electrode 2. In general, the location of maxima and minima recorded potentials depend on the location of the reference electrode.  

Measured Potential Difference---(Maximum Potential Difference)
Ref 1	(V1 − VR1)	                   (14.74)
Ref 1	(V2 − VR1)	                   (10.66)
		
Ref 2	(V1 − VR2)	                   (27.98)
Ref 2	(V2 − VR2)	                   (29.78)

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== Authors' reply to Reviewer A (second round) ==

Hi Paul,

Having read your equations we now understand your approach. 

Your approach examines, at each electrode location, time series ("waveshapes") of potential differences relative to a reference. Since the potential at the reference also varies with time, any waveshape feature is reference-dependent (e.g., maximum potential value and its time of occurrence, as shown in your example). 

The microstate approach examines, at each time point, spatial distributions ("momentary landscapes") of potential differences relative to a reference. 
Momentary, reference-independent features are extracted from each landscape (among others, e.g., momentary location of the maximum and minimum potential value; for an explicit description of this, see below). 

Thus, to state it shortly, we have been using the term "maximum" in a completely different way.

In view of this, we cannot accept your statement "In general, the location of maxima and minima recorded potentials depend on the location of the reference electrode." Your reference-dependent definitions are not general. 
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In the following, we give a non-ambiguous algorithmic description of our procedure for the construction of Figures 2 and 3:

Step A. Take the first recorded momentary (instantaneous) scalp map (electric potential field over the scalp). At this moment in time, select the locations of the maximum and the minimum potential values over the scalp. Note that the spatial features we are interested in are “locations”, not "values". In this instantaneous map, these “locations” are invariant to addition of an arbitrary constant value to the scalp field (any reference change). Referring to the metaphor, the location of the instantaneous highest mountain or lowest valley is unique, regardless of the reference.

Step B. Repeat Step A, separately, to each of the following time instants. At each time instant, the location of the instantaneous highest mountain is unique, regardless of the reference.

Step C: Take an electrode, and count the total number of times a maximum occurred at this location.

Step D: Repeat Step C to each electrode separately.

Step E: This is how our reference-independent Figures 2 and 3 where constructed, based on spatial features that are, by definition, reference-independent.
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With all this documentation, we hope that our divergent views are clarified. Each can exist in its own place. We are simply dealing with different models.

Best,

Dietrich, Roberto and Christoph.

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== Reviewer B ==
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Reviewer B inserted his comments at several places directly into the article. Below follows the text of the article (in regular font) with '''reviewer B's comments (in bold font)''' as of March 4, 2009, at 11:14, when reviewer B entered his last comments before acceptance.
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EEG microstates
                                                        
A complex system such as the brain that comprises many local functional states can be said to be in one particular global functional state at each moment in time (Ashby, 1960). Brain states change in a non-continuous manner: brain functional state over time shows extended periods during which there is small variance of state; these periods of quasi-stability are concatenated by rapid and major changes of state. An example is wakeful consciousness and its sudden disappearance with sleep onset. Such state changes are associated with major changes in brain electric activity as recorded from the scalp of the intact human head as electroencephalogram ("EEG"). In the sub-second time range which is relevant for human conscious mentation and for useful interaction with the environment, brain electric activity can be parsed into brief split second microstates characterized by quasi-stable spatial distributions (landscapes) of electric potential that are connected by quick changes in landscapes. As different electric potential landscapes must have been generated by different distributions of neuronal electric activity in the brain, it is reasonable to assume that different microstates embody different functions of the brain. The experimental results suggest that the seemingly continual stream of consciousness is incorporated by successive steps of brain operations, reminiscent of the flight-perch-sequences of subjective experience (James, 1890). Microstate analysis has begun to develop a dictionary of functions of these sub-second brain microstates and to explore their syntax.

'''Reviewer B: To the editor: If I understood the idea of scholarpedia correctly, I should target my comments and suggestions mainly towards readability of this article for an audience that is more or less (mainly less?) informed about cognitive neuroscience and ERPs in general.'''

'''Reviewer B: To the authors: Dear Dr. Lemmann and coauthors, We were introduced several years ago by Marianne Regard (well, more than a decade age). I had just finished my studies in Konstanz and wanted eagerly to work together with you and Marianne. Unfortunately this did not work out. I still think that this would have been a great opportunity for me. I hope that my comments and suggestions are helpful to improve the article. Best regards from Münster, Christian Dobel'''

'''Reviewer B: With regard to the abstract: This is a very readable abstract for the informed reader, but I have some doubts that readers with no ERP background will understand it. From your very first sentences you seem to imply that you are mostly interested in brain states. But from the following I gather that you are in fact after mental states and their relationship to brain states (or is that the same (identical) for you?). As an example you introduce "consciousness" which is probably for many readers a state that may last for hours. In contrast, you discuss brain states in terms of subseconds. This sounds puzzling, because one starts immediately to doubt a strong relationship. Do you mean the "contents of consciousness"? Here, readers might recognize from the start that these are often fleeting and changing quickly.'''


Brain electric fields

Brain electric field data (EEG and event-related potentials [ERP]) recorded simultaneously from many electrodes (locations) on the human head surface can be viewed as series of maps of the momentary spatial distributions of electric potential, as 'potential landscapes' (Lehmann, 1971, 1972). Typically, 128 to 512 maps per second are used.

'''Reviewer B: Comment: It might be helpful if you provide a short overview about what is going to come. Could you provide information about your estimation of a minimum number of sensors required for this type of analysis. Could you explain why you use typically 128 or 512 Hz? I assume that with less than 128 you don't have the sensitivity to measure microstates anymore whereas higher sampling rates are not necessary. Working in an MEG lab, I wonder why microstates analyses should not be applied to MEG.'''

The historical and unfortunate discussions in the EEG community about the choice of a presumable 'inactive' electric reference location are not an issue here, because a given landscape cannot be changed by the location of the point from which it is measured; this choice merely determines the value labels of the isopotential lines - quite like the rising or receding water level of a lake in a mountainous area changes the location of the zero water level mark, but not the landscape (Lehmann, 1987; Geselowitz, 1998). 

'''Reviewer B: Comment: this sounded to me like the start to list the advantages of microstate analysis in contrast to other methods, but then it stopped. Maybe this paragraph is better place elsewhere. Otherwise you could also emphasize other strengths of this method. In contrast to other methods, I value the completely data driven approach which does not make it necessary to make a lot of assumptions before starting the analysis.'''

Over time, the potential landscapes vary in electric strength. Map Hilliness (Lehmann, 1971) assesses map strength; it is defined as the sum of the absolute microvolt values measured at all electrodes divided by the number of electrodes; the assessment must be done after the values in each map have been expressed as deviations from the mean of all momentary values (spatial DC offset removal, 'average reference'). Global Field Power is a related, parametric assessment of map strength, computed as standard deviation of the momentary potential values (Lehmann and Skrandies, 1980).

'''Reviewer B: Comment: as above: this is an excellent data driven method to define time intervals of interest...'''

Over time, the potential landscapes vary also in configuration. For numerical comparisons of map landscapes, Global Map Dissimilarity is computed (Lehmann and Skrandies, 1980): The two maps to be compared are average-referenced and scaled to unity Global Field Power; then, one map is subtracted form 

'''Reviewer B: comment: typo: from'''

the other one. The value of Global Field Power of the resulting difference map is the magnitude of Global Map Dissimilarity.

Statistical comparison of potential landscapes between experimental conditions or between different groups of subjects uses as dependent measure Global Map Dissimilarity, or extracted parameters such as the location of the two centroid locations of the map's positive and negative potential areas (Wackermann et al., 1993) or the electric gravity center (the mean of the two centroid locations); all are strength-independent measures. Such analyses determine whether different neuronal generators have been involved in the different conditions or groups at a given time. Typically, non-parametric randomization tests are used (Karniski et al. 1994; Kondakor et al., 1995; Strik et al., 1998; see Murray et al., 2008). Statistical assessment of the specificity of the microstates for different experimental conditions has been achieved by spatial fitting procedures using Global Map Dissimilarity as metric (Brandeis et al., 1992; Pegna et al., 1997; Michel et al., 1999; Michel et al., 2001; Murray et al., 2008). 

'''Reviewer B: Comment: if there is enough figure space, could you provide examples for centroid locations and gravity center etc.'''


Parsing the series of momentary potential maps into microstates

In continually recorded human EEG, series of momentary maps of electric potential landscapes during task-free resting show discontinuous changes of landscapes (Lehmann, 1971, 1972). The movie (Fig. 1) visualizes this: it shows the sequence of EEG landscapes recorded from 19 electrodes during a 2 second epoch from a healthy young man who was asked to relax with closed eyes (128 maps per second; the head is seen from above, nose up; red are positive, blue are negative potential regions referenced to the mean of all momentary potentials).

Figure 1: Scalp field potential distribution maps during 2 seconds (time-stretched into about 25 sec, endless loop). Head seen from above, nose up; red positive, blue negative potential areas.

'''Reviewer B: Comment: I assume that many readers might think of alpha rhythm right away. Can you refer to this? I find the movie hard to "understand" without start and end and time line information.'''

Map strength in general is irrelevant for landscape comparisons: only the spatial configuration of the potential distribution is considered when assessing map similarity. In the case of EEG where there is oscillatory activity of the generator processes, polarity also is irrelevant. In the case of event-related potential (ERP) maps, map polarity is important; polarity was used to label the conventional 'components', the peaks and troughs of ERP waveshapes.
In EEG as well as ERP map series, for brief, sub-second time periods, map landscapes typically remain quasi-stable, then change very quickly into different landscapes. A sequential microstate analysis approach first showed the feature of non-continuity of landscape changes in spontaneous EEG, using plots of the electrode locations of extreme (maximum or minimum) potential values over time. Fig. 2 shows such plots for the movie sequence of Fig. 1; Fig. 3 illustrates mean results from 5 subjects.

Figure 2: Plots of the % time that a maximum (left) or minimum (right) potential value was observed at the 19 electrode positions in the movie sequence of Fig. 1. On brown: >4% time.

Figure 3: after Fig. 9 in Lehmann, 1971.

These plots demonstrated that extreme potentials occur in restricted scalp regions, residing in a given region for several successive maps, then jumping to another region. Thus typically, step-wise changes and not continual 'travelling' of the extreme locations are observed (Lehmann, 1971). Using the entire information in the maps, curves of Global Map Dissimilarity for pairs of successive maps over time determined microstate changes that are represented by peaks in the curve of ERP data (Lehmann and Skrandies 1980, 1984; Brandeis and Lehmann, 1986; Michel et al., 1992; Michel and Lehmann, 1993) and EEG data (Lehmann et al., 1987). Post-hoc, microstates can be clustered into a limited number of landscape classes (Wackermann et al., 1993; Strik and Lehmann, 1993). The global microstate analysis approach clusters all maps that are to be analyzed into a preselected or self-determined (via cross-validation), finite number of landscape classes applying Global Map Dissimilarity (Pascual-Marqui et al., 1995; Koenig et al., 1999; Michel et al., 1999) as illustrated in Fig. 4 for spontaneous EEG and Fig. 5 for ERP data.

Figure 4: Microstate Segmentation of 4 seconds of spontaneous EEG using a cluster analysis. The waveshapes represent eyes-closed EEG recorded from 42 electrodes. For each time point, the potential distribution map was calculated and all maps of the 4 seconds were subjected to a k-means cluster analysis. A cross-validation criterion identified four dominant maps. Fitting these maps back to the original data revealed that each map appeared repeatedly and dominated during certain time segments, the 'microstates'. These microstates are color-coded in the curve of Global Field Power at the bottom, and marked by numbers under this curve; they were then classified (illustrated in the 3rd row) according to the standard microstate classes of Fig. 6.

Figure 5: Microstate analysis of event-related potentials (ERP). Subjects were listening to series of tones of two different frequencies presented in random sequence, one frequently (75%), the other rarely (25%). Subjects were instructed to count the rare tones. ERP were calculated separately for rare and frequent tones. 

'''Reviewer B: Comment: it might be helpful if you explain briefly that this is an oddball paradigm which evokes a P300 and what standard interpretations of this component are. '''

The overlaid traces of all 128 recording channels are shown in the middle, with black traces for rare tones and red traces for frequent tones. Both ERP were conjointly subjected to a cluster analysis that identified 9 maps best representing the whole dataset. Fitting these maps to the ERP revealed that each map was present during a certain time period (a microstate). These periods are illustrated under the Global Field Power curve of the two conditions. Same color indicates same maps. The initial microstates and the final microstates were the same in the two conditions, but three microstates during 150-650 ms differed. One of them represents the "P300 component". Thus, microstate segmentation of ERP defines components as periods of time with stable map topography that only increase and decrease in strength.


Functional significance of EEG microstates

In spontaneous EEG, four standard classes of microstate landscapes were distinguished (Fig. 6), whose parameters (e.g. duration, occurrences per second, covered percentage of analysis time) change as function of age (Koenig et al., 2002). 

'''Reviewer B: Comment: how was this measured? relaxed, eyes open etc.'''

Figure 6: The four microstate classes (standard classes) as identified in the spontaneous EEG of 496 healthy people (6 to 80 year-olds). The mean duration of the microstates is around 80-100 ms and varies with age. Head seen from above, nose up; red positive, blue negative potentail areas (after Koenig et al., 2002).

EEG microstates in medication-naïve, first-episode, productive schizophrenics (Koenig et al., 1999; Lehmann et al., 2005; Irisawa et al., 2006) were shortened in two of the four standard classes, and showed aberrant sequencing of the microstate classes (abnormal microstate 'syntax') compared to healthy controls (Lehmann et al., 2005).

'''Reviewer B: Comment: what is the interpretation of this finding? Or is it the same as below for the chronic schizophrenics?'''

Chronic schizophrenics with positive symptomatology also exhibited shortened microstate duration (Strelets et al., 2003). The shortening of microstates of certain classes was interpreted as abortive termination of specific steps of information processing that result in the schizophrenic symptomatology of loosened associations. Neuroleptic medication increased microstate duration in schizophrenics (Yoshimura et al 2007). Shortening of microstate duration has also been observed in depressive patients along with increased topographical variance (Strik et al., 1995). In healthy people, microstate durations were found to depend on wakefulness and sleep stage (Cantero et al., 1999, 2002), to decrease in deep hypnosis (Katayama et al., 2007), and to increase in meditation (Faber et al., 2005).

'''Reviewer B: Comment: i.e. as a rule of thumb long microstates are beneficial?'''

Cognition-enhancing medication affected microstate topography in a dose-dependent way (Lehmann et al., 1993). Spontaneous thoughts which are high or low on a visual imagery scale are associated with two different EEG microstate classes immediately before the prompted reports (Lehmann et al., 1998); these spontaneous microstates and event-related microstates 286-354 ms post-stimulus while reading abstract or imagery words (Koenig et al., 1998) when analyzed with tomographic imaging ('LORETA', Pascual-Marqui et al., (1994) showed common activated intracerebral brain areas: left anterior brain areas for abstract, right posterior for imagery (Lehmann et al., 2004).

'''Reviewer B: Comment: some concluding sentences of all these findings might be helpful; right now it sounds like an unconnected list of results'''

Microstates as atoms of thought and consciousness

Durations of microstates during spontaneous task-free resting EEG on average are in the range of 70 to 125 milliseconds (Lehmann et al., 1987, 1998, 2005; Koenig et al., 2002). The type of momentary thought (e.g. visual versus abstract thinking) is incorporated in different microstates (Lehmann et al., 1998, 2004). The observations on microstates in spontaneous brain electric activity suggest that the apparent continual "stream of consciousness" consists of concatenated identifiable brief packets in the time range of fractions of seconds, in a time range postulated for ‘elementary deliberations’ (Newell, 1992), for visual and auditory perceptions (Efron, 1970), and as needed or available for changing or bridging perceptual input organization or attention (Michaels and Turvey, 1979; DiLollo, 1980; Reeves and Sperling, 1986; Posner et al., 1987; Motter, 1994). Entry of content chunks into consciousness (e.g., Baars' Global Workspace, Baars, 2007) apparently requires such minimum durations. In sum, the evidence suggests that brain electric microstates qualify for basic building blocks of mentation, as candidates for conscious or non-conscious 'atoms of thought and emotion' (Lehmann 1990; Lehmann et al., 1998, 2004, 2005; Changeux and Michel, 2004).

'''Reviewer B: Comment: I find it puzzling that you start with a spontaneous and task-free mental state and make conclusions about thought and emotion. Wouldn't your argument be stronger in the situation where participants actually have tasks and emotions are evoked?'''


Event-related microstates

Numerous studies on ERP microstates contribute to a microstate dictionary of different brain functions. For example, subjective contour perception and attention were incorporated in specific ERP microstates (Brandeis and Lehmann, 1989). Specific microstates distinguish visual depth from contour perception (Michel et al., 1992) and perception of color in motion as compared to achromatic moving stimuli (Morand et al., 2000). A microstate has been identified that systematically increased in duration with the angle of rotation of a letter that had to be rotated mentally (Pegna et al., 1997). Similar mental rotation microstates were found for body parts (Overnay et al., 2005; Petit et al., 2006; Arzy et al., 2006). In schizotypy, perceptual aberration of body image correlated with increased duration of the microstate 310-390 ms after task onset that asked to report the orientation of the displayed body image (Arzy et al., 2007). Reading abstract and visual imaginable (concrete) words evoked two different microstate classes around 300 ms after word onset (Koenig et al., 1998; Sysoeva et al., 2007) and during a 40–100 ms microstate (Sysoeva et al., 2007). Priming differently affected ERP microstates to abstract and concrete words (Wirth et al., 2008). An early distinct microstate also was identified for emotional words (Ortigue et al., 2004). When reading emotional words, their emotional valence is represented in an earlier microstate than their arousing strength (Gianotti et al., 2008). Correct rejection of irrelevant visual information is reflected in a specific microstate very early after stimulus presentation (Schnider et al., 2002). Unique microstates have been described for auditory and somatosensory what and where perception (Ducommun et al., 2002; Spierer et al., 2007) as well as for multisensory information processing (Murray et al., 2004). Also reported were pharmacological effects on specific ERP microstates (e.g., Michel et al., 1993).

'''Reviewer B: Comment: if I understand this paragraph correctly, the message is that each of these tasks (or conditions) evokes different microstates. Taken together they build the "dictionary". It would be helpful to take as an example similar tasks/experiments/conditions to demonstrate how microstates help us to understand the underlying mechanisms of cognition/emotion.'''


Microstate-dependent information processing

The general rule that information processing by the brain depends on the brain's momentary funtional state

'''Reviewer B: Comment: typo: functional'''

also holds at the microstate level: The microstate just before stimulus onset determines how the stimulus is going to be processed. When evoked potentials are separately averaged for different pre-stimulus microstate classes, they drastically differ, despite physically identical stimuli (Kondakor et al., 1997; Lehmann et al., 1994). 

'''Reviewer B: Comment: I don't understand this paragraph. I thought it is about pre-stimulus periods, i.e. there are not stimuli present yet...''

Different pre-stimulus microstates also change the perception of physically identical stimuli: Specific microstates precede the change of illusory motion perception (Müller et al., 2005) as well as the switch in perception of a Necker-cube (Britz et al., 2008). Perception of emoitional 

'''Reviewer B: Comment: typo: emotional'''

words presented to the left visual field (right hemisphere) is facilitated when a specific microstate is present just before word presentation (Mohr et al., 2005). Together these studies demonstrate the state-dependency of brain information processing in the subsecond time range.

'''Reviewer B: Comment: is this the final conclusion for the whole article or only this section? My interpretation of this paragraph was that microstate analysis allows to predict from microstates in the baseline period what a participant is going to perceive. This is a very important finding and should be stressed more.'''

'''Reviewer B: In general, I think that this is not a satisfying end for an article. It just stops. There should be a summary, a wrap-up, a conclusion or an outlook, whatever...'''

'''Reviewer B: I enjoyed reading this short overview and it attracted definitely my attention to microstate analysis. As a user I would be grateful to get information about software packages, computational requirements and other background information (required operating system etc. etc.). Again, I hope that my comments and suggestions helped to improve the manuscript.'''

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== Authors' reply to Reviewer B March 9, 2009 ==
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Dear Christian,
Firstly, many thanks for your careful reading of our manuscript, and for your thoughtful and very useful comments. At this moment, because we received a warning from the Scholarpedia Editors that if we delay accepting the paper, we run into the problem that unauthorized changes may be made by other people, we decided to accept it. We accepted it in the version without your comments in the text. Note that your commented version appears under "revisions". We will place your commented version into the "REVIEW" section, and we will as soon as possible revise our manuscript taking up the various points you and the other two Reviewers had raised. We really enjoyed reading your review, and we thank you again for your helpful and constructive criticism.

With best regards,
Dietrich, Roberto, and Christoph


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== Reviewer C:  ==

Microstates have been an influential concept in EEG and ERP analysis. There are two main issues here: 1) The usefulness of microstates as a tool for objective data reduction or descriptive statistics, 2) the idea of microstates as a general concept for the interpretation of electrophysiological data. 
There can be no doubt that microstates are of great value with respect to point 1. In many ERP studies, one still finds time windows defined “by eye”, or with magical numbers such as “300-500ms”. For spontaneous EEG responses, defining time ranges of interest is even more complicated. Microstates methodology has done a great service to the EEG community by providing objective measures to address these problems. My criticism mainly refer to point 2, as I will outline below.

1) Only relatively simple measures such as “centroids”, “hilliness” and “Global Map Dissimilarity” are described in more detail in this article. I was surprised not to read more about more sophisticated multivariate methods, such as the k-cluster analysis approach introduced by Pascqual-Marqui. Even if the simple measures are valid measures for microstates, one still faces the problem of objectively defining boundaries between them. The “Global Map Dissimilarity” appears to serve the purpose of a conventional correlation coefficient, which to me would be the most obvious measure to compare the global similarity of two distributions, and would be more familiar to most researchers.

2) The article starts with the statement “As different electric potential landscapes must have been generated by different distributions of neuronal electric activity in the brain, it is reasonable to assume that different microstates embody different functions of the brain”. I agree, although one might quibble about the definition of “functions of the brain”. The reverse, however, is not true: If the topography does not change abruptly, this does not imply that the brain is continuing the same process. Studies on word and object recognition, for example, have provided evidence for cascaded, i.e. partly overlapping, processing stages. The “microstates theory” as presented in this article assumes strict seriality of cognitive process, which clearly cannot be a general principle to explain electrophysiological data of cognitive processes. 

3) As Einstein said: “A good theory should be as simple as possible – but not simpler”. Following my first two points, one could turn things around: Starting from the assumption that brain processes of cognition and consciousness must be complex, continuous and overlapping, the finding that EEG+microstates reduces them to only a few stable patterns, characterised by only a few parameters, and occurring at few distinct points in time, must mean that this approach is missing a lot. 

4) When interpreting EEG/MEG signals one must always keep in mind that these methods don’t see everything – some sources and source distribution do not produce any measurable signals at the surface. Making inferences from the surface signal on “brain states” only on the basis of observations at the surface level, i.e. without a clear model that links the specific process with the specific signal, can be misleading.

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==Authors' reply to Reviewer C==
In the following, we copy reviewer C's points and follow them with our replies. However, some points will be parsed into sub-points so as to make our comments more specific.

'''Reviewer C0:'''
Microstates have been an influential concept in EEG and ERP analysis. There are two main issues here: 1) The usefulness of microstates as a tool for objective data reduction or descriptive statistics, 2) the idea of microstates as a general concept for the interpretation of electrophysiological data. There can be no doubt that microstates are of great value with respect to point 1. In many ERP studies, one still finds time windows defined “by eye”, or with magical numbers such as “300-500ms”. For spontaneous EEG responses, defining time ranges of interest is even more complicated. Microstates methodology has done a great service to the EEG community by providing objective measures to address these problems. My criticism mainly refer to point 2, as I will outline below.

'''Our reply C0:'''
We appreciate the reviewer’s thoughtful comments. Completely satisfying answers are not available for all points, but his comments invited more considerations as sketched out in our replies. 

'''Reviewer C1:'''
Only relatively simple measures such as “centroids”, “hilliness” and “Global Map Dissimilarity” are described in more detail in this article. I was surprised not to read more about more sophisticated multivariate methods, such as the k-cluster analysis approach introduced by Pascqual-Marqui. Even if the simple measures are valid measures for microstates, one still faces the problem of objectively defining boundaries between them. The “Global Map Dissimilarity” appears to serve the purpose of a conventional correlation coefficient, which to me would be the most obvious measure to compare the global similarity of two distributions, and would be more familiar to most researchers.

'''Our reply C1:'''
We had very briefly described two basic approaches of microstate analysis, (a) sequential analysis (comparing successive pairs of maps) and (b) global analysis (modified k-means clustering of all maps). In the case of sequential methods, time points of maximum global dissimilarity were used as microstate boundaries (Reference#1; Reference#2). Other criteria were developed for identifying unique microstate boundaries (Reference#3; Reference#4). In the case of the global clustering approach, once the number of microstate prototypes is determined (using, e.g. cross-validation error), the bondaries are again unique. In general, various metrics can be employed to assess dissimilarity between maps, one of them is “Global Map Dissimilarity” that the reviewer correctly recognizes as a measure related to the correlation coefficient (if map polarity is taken into account: Reference#5). One can also define metrics based on e.g. the map gravity center, the two centroid locations of the positive and negative polarity area, the orientation of the field.

*Reference#1: Lehmann, D. and Skrandies, W.: Reference-free identification of components of checkerboard-evoked multichannel potential fields. Electroenceph. Clin. Neurophysiol. 48: 609-621 (1980).
*Reference#2: Lehmann, D., Ozaki, H. and Pal, I.: EEG alpha map series: brain micro-states by space-oriented adaptive segmentation. Electroenceph. Clin. Neurophysiol. 67: 271-288 (1987).
*Reference#3: Strik, W.K. and Lehmann, D. Data-determined window size and space-oriented segmentation of spontaneous EEG map series. Electroenceph. Clin. Neurophysiol. 87: 169-174 (1993).
*Reference#4: Koenig, T., Kochi, K. and Lehmann, D. Event-related electric microstates of the brain differ between words with visual and abstract meaning. Electroenceph. Clin. Neurophysiol. 106: 535-546 (1998).
*Reference#5: Brandeis D, Naylor H, Halliday R, Callaway E, Yano L. Scopolamine effects on visual information processing, attention, and event-related potential map latencies. Psychophysiol. 29: 315-336 (1992).


'''Reviewer C2.1:'''
The article starts with the statement “As different electric potential landscapes must have been generated by different distributions of neuronal electric activity in the brain, it is reasonable to assume that different microstates embody different functions of the brain”. I agree, although one might quibble about the definition of “functions of the brain”. 

The reverse, however, is not true: If the topography does not change abruptly, this does not imply that the brain is continuing the same process. 

'''Our reply C2.1:'''
This is true; two identical topographies of potential distributions on the head could have arisen from different current density distributions in the brain. This applies to EEG/ERP in general, not only to microstate analysis. But the microstate model, rather than capitalizing on non-changes (i.e. similarity), it capitalizes on dissimilarity (i.e. significant differences): once a change of topography is established, a different brain state has occurred. These are the only assertions one can prove.

'''Reviewer C2.2:'''
Studies on word and object recognition, for example, have provided evidence for cascaded, i.e. partly overlapping, processing stages. The “microstates theory” as presented in this article assumes strict seriality of cognitive process, which clearly cannot be a general principle to explain electrophysiological data of cognitive processes.

'''Our reply C2.2:'''
Yes, microstate analysis is strictly serial, but it assumes - as we said in the first sentence of the article - "A complex system such as the brain that comprises many local functional states can be said to be in one particular global functional state at each moment in time (Ashby, 1960)". With this quotation we meant to say that we agree with the common notion that always, there certainly are many parallel brain processes active at each moment in time. As to microstate analysis, processes partly overlapping in time are expected to result in additional microstates - if the change is detectable in the head surface-recorded brain electric fields. Presume there is a continuing Process #1 whose head surface potential landscape is labeled as microstate A. After some time, Process #2 kicks in and adds - in parallel - changes to the potential landscape. As a consequence there is a landscape called microstate B. If now Process #1 terminates, there will be a microstate C landscape. In conclusion, partly overlapping processes are compatible with the microstate model, that describes them as a sequence of unique states, each consisting of possible substates.

'''Reviewer C3:'''
As Einstein said: “A good theory should be as simple as possible – but not simpler”. Following my first two points, one could turn things around: Starting from the assumption that brain processes of cognition and consciousness must be complex, continuous and overlapping, the finding that EEG+microstates reduces them to only a few stable patterns, characterised by only a few parameters, and occurring at few distinct points in time, must mean that this approach is missing a lot.

'''Our reply C3:'''
Conceptually, the number of possible classes of microstates is unlimited. Super-demanding identity criteria would practically result in as many microstates as there were momentary maps (time points) in the analyzed data. The sequential analysis approach produces as a first-level result a series of microstates whose number simply increases with time. Thus, theoretically, very little information is lost. In practice, post-hoc clustering to a small number of microstate classes provides a data reduction that allows manageable statistical analyses between subjects or conditions.

The number of available parameters to characterize a potential distribution potentially is very large – in its most direct form it is only the number and location of the measurement points, but there are numerous other possible derived measures besides the few we mentioned in the website (the mentioned ones we feel are reality-close, i.e. imageable).

As to overlapping processes, see our reply to C2)2.

As to continuous processes: our results indicate that brain electric processes are discontinuous. 

'''Reviewer C4.1:'''
When interpreting EEG/MEG signals one must always keep in mind that these methods don’t see everything – some sources and source distribution do not produce any measurable signals at the surface. Making inferences from the surface signal on “brain states” only on the basis of observations at the surface level, 

'''Our reply C4.1:'''
True, we can only see that brain electric activity that is detectable on the head surface - and that likely is precious little relative to the complete information. There are only the head surface-recorded signals to classify brain states, see our reply "C2) 1".

'''Reviewer C4.2:'''
i.e. without a clear model that links the specific process with the specific signal, can be misleading

'''Our reply C4.2:'''
The linkages between behavioral or subjective states and brain electric states are descriptive; it is all about establishing taxonomies and building dictionaries.

But perhaps you thought about something else when you mentioned the model issue?