Topological analysis of differential effects of ketamine and propofol anaesthesia on brain dynamics

Research has found that the vividness of conscious experience is related to brain dynamics. Despite both being anaesthetics, propofol and ketamine produce different subjective states: we explore the different effects of these two anaesthetics on the structure of dynamic attractors reconstructed from electrophysiological activity recorded from cerebral cortex of two macaques. We used two methods: the first embeds the recordings in a continuous high-dimensional manifold on which we use topological data analysis to infer the presence of higher-order dynamics. The second reconstruction, an ordinal partition network embedding, allows us to create a discrete state-transition network, which is amenable to information-theoretic analysis and contains rich information about state-transition dynamics. We find that the awake condition generally had the ‘richest’ structure, visiting the most states, the presence of pronounced higher-order structures, and the least deterministic dynamics. By contrast, the propofol condition had the most dissimilar dynamics, transitioning to a more impoverished, constrained, low-structure regime. The ketamine condition, interestingly, seemed to combine aspects of both: while it was generally less complex than the awake condition, it remained well above propofol in almost all measures. These results provide deeper and more comprehensive insights than what is typically gained by using point-measures of complexity.

1. Consideration of "nonconscious neural activity" vs. high dimensional space of neural activity While you mention the issue of conscious vs. nonconscious neural activity in some places, I would suggest that you discuss this issue in Discussion as this is a serious issue in consciousness research.
The paper reviews an adequate amount of the literature on the "level" of consciousness, however, it doesn't cover "contents" of consciousness. This is fine in itself. However, the latter literature has generated a huge amount of empirical evidence to suggest that not all neural activities are relevant for consciousness (See for example, Koch 2016Nat Rev Neuro, Mashour et al 2020. Given this, including all the available channels (>120) for the analysis can possibly reflect neural activities that are irrelevant for supporting consciousness but more directly related to nonconscious processing. This needs to be acknowledged and you may want to discuss how to resolve this issue in the future.
One possible approach is the identification of "complex" as suggested by the integrated information theory (IIT) by Tononi.

Structural measures/characterizations of consciousness
Page 3. L15 -"these point-summary measures, while informative, collapse multi-scale dynamics into a single number and thus have difficulty capturing its specific shape or form." I totally agree with this statement. And I would say that this is pretty much in line with the philosophy of the integrated information theory (IIT). This aspect has become more explicit since IIT3.0. Recently, we have published a paper directly addressing this structural and topological consideration on the level of consciousness based on the empirical neural data (Leung et al 2021 PLoS Comp), which you might want to look at.
Also, as you refer to epsilon machines several times in the manuscript as an alternative way to characterize the topology/shape of information structure, it may be worth looking at our recent paper where we applied the epsilon machine on the loss of consciousness (Munos et al 2020 Physical Review Research).

Limits of OPN
With respect to the limit of OPN, I think it is better to mention other approaches that have also taken multivariate approaches. IIT can be considered as one of them, where it explicitly deals with the integration among channels, which your OPN approach explicitly ignores. To the extent that integration is critical to understand consciousness, this may be a potential oversight / limitation of your approach.
Along with this line, I also think you should acknowledge a couple of papers that have already analyzed the same NeuroTycho data with different ways (e.g., Tajima et al 2015 PLoS Comp).

Lack of principles and theories.
Your approach is data-driven and highly descriptive. It may make more sense to explicitly admit this in Discussion and discuss its limitations. Alternatively, you may want to try to link your findings with predictions from some theories. I would imagine some of the findings can be linked with the other theories of consciousness other than the Entropy hypothesis or IIT, but I will leave this to you.

Minor issues
Page 2, line 30-Lots of double negatives make this paragraph difficult to read for those who are not familiar with these concepts. Line 34: "light central nervous system stimulation". Probably, you meant that weak stimulation of the nervous system? Better if you can revise here. Line 41: result it -> result in? P3 L5: Ref 51&53 didn't really measure entropy. The sentence needs to be revised. P4 L34: Description of Chibi doesn't make sense. Probably typo for George? P8: Figure 2 mentions "temporal principal component" but this is not explained anywhere else in the manuscript. (By the way, I was not able to access to the Supplementary Material for this paper) P8: No significant differences on the lag parameter is mentioned but the data is not shown. Please show it on Supplementary Material. P8: "a directed network X with N" -> "a directed network X with N nodes/states"? P9: the equations for determinism and degeneracy are identical. I think the one for degeneracy should use W_in? P10: The right side of Table 1 is not visible (if something is there?) P13: Determinism ( Fig 5C) is lowest for awake, which is inconsistent with Table 3. I guess the figure is correct?
There are several typos throughout. (e.g., "spacial" "repetoire" "asses") Decision letter (RSOS-201971.R0) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

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Reviewer comments to Author:
Reviewer: 1 Comments to the Author(s) This paper presents two analyses on the previously collected open data (NeuroTycho). Their first analysis uses EPC with TDA and the second uses OPNs. I have some comments to improve the paper, but I think this paper can be accepted with minor revision.
Signed review by Naotsugu Tsuchiya.
Major issues.
1. Consideration of "nonconscious neural activity" vs. high dimensional space of neural activity While you mention the issue of conscious vs. nonconscious neural activity in some places, I would suggest that you discuss this issue in Discussion as this is a serious issue in consciousness research.
The paper reviews an adequate amount of the literature on the "level" of consciousness, however, it doesn't cover "contents" of consciousness. This is fine in itself. However, the latter literature has generated a huge amount of empirical evidence to suggest that not all neural activities are relevant for consciousness (See for example, Koch 2016 Nat Rev Neuro, Mashour et al 2020 Neuron). Given this, including all the available channels (>120) for the analysis can possibly reflect neural activities that are irrelevant for supporting consciousness but more directly related to nonconscious processing. This needs to be acknowledged and you may want to discuss how to resolve this issue in the future.
One possible approach is the identification of "complex" as suggested by the integrated information theory (IIT) by Tononi.

Structural measures/characterizations of consciousness
Page 3. L15 -"these point-summary measures, while informative, collapse multi-scale dynamics into a single number and thus have difficulty capturing its specific shape or form." I totally agree with this statement. And I would say that this is pretty much in line with the philosophy of the integrated information theory (IIT). This aspect has become more explicit since IIT3.0. Recently, we have published a paper directly addressing this structural and topological consideration on the level of consciousness based on the empirical neural data (Leung et al 2021 PLoS Comp), which you might want to look at.
Also, as you refer to epsilon machines several times in the manuscript as an alternative way to characterize the topology/shape of information structure, it may be worth looking at our recent paper where we applied the epsilon machine on the loss of consciousness (Munos et al 2020 Physical Review Research).

Limits of OPN
With respect to the limit of OPN, I think it is better to mention other approaches that have also taken multivariate approaches. IIT can be considered as one of them, where it explicitly deals with the integration among channels, which your OPN approach explicitly ignores. To the extent that integration is critical to understand consciousness, this may be a potential oversight / limitation of your approach.
Along with this line, I also think you should acknowledge a couple of papers that have already analyzed the same NeuroTycho data with different ways (e.g., Tajima et al 2015 PLoS Comp).

Lack of principles and theories.
Your approach is data-driven and highly descriptive. It may make more sense to explicitly admit this in Discussion and discuss its limitations. Alternatively, you may want to try to link your findings with predictions from some theories. I would imagine some of the findings can be linked with the other theories of consciousness other than the Entropy hypothesis or IIT, but I will leave this to you.

Minor issues
Page 2, line 30-Lots of double negatives make this paragraph difficult to read for those who are not familiar with these concepts. Line 34: "light central nervous system stimulation". Probably, you meant that weak stimulation of the nervous system? Better if you can revise here. Line 41: result it -> result in? P3 L5: Ref 51&53 didn't really measure entropy. The sentence needs to be revised. P4 L34: Description of Chibi doesn't make sense. Probably typo for George? P8: Figure 2 mentions "temporal principal component" but this is not explained anywhere else in the manuscript. (By the way, I was not able to access to the Supplementary Material for this paper) P8: No significant differences on the lag parameter is mentioned but the data is not shown. Please show it on Supplementary Material. P8: "a directed network X with N" -> "a directed network X with N nodes/states"? P9: the equations for determinism and degeneracy are identical. I think the one for degeneracy should use W_in? P10: The right side of Table 1 is not visible (if something is there?) P13: Determinism ( Fig 5C) is lowest for awake, which is inconsistent with Table 3. I guess the figure is correct?
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Decision letter (RSOS-201971.R1)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Mr Varley,
It is a pleasure to accept your manuscript entitled "Topological Analysis of Differential Effects of Ketamine and Propofol Anesthesia on Brain Dynamics" in its current form for publication in Royal Society Open Science.
Please ensure that you send to the editorial office an editable version of your accepted manuscript, and individual files for each figure and table included in your manuscript. You can send these in a zip folder if more convenient. Failure to provide these files may delay the processing of your proof. You may disregard this request if you have already provided these files to the editorial office.
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6
Signed review by Naotsugu Tsuchiya. 7 We would like do that Dr. Tsuchiya for his thoughtful and insightful comments on this paper. 8 We have responded to them below and hope that they are satisfactory. Our responses are noted in 9 blue font. Where we are quoting from the main manuscript, we use italicized font. suggest that you discuss this issue in Discussion as this is a serious issue in consciousness research.

15
The paper reviews an adequate amount of the literature on the "level" of consciousness, however, 16 it doesn't cover "contents" of consciousness. This is fine in itself. However, the latter literature has 17 generated a huge amount of empirical evidence to suggest that not all neural activities are relevant this, including all the available channels (¿120) for the analysis can possibly reflect neural activities 20 that are irrelevant for supporting consciousness but more directly related to nonconscious processing.

21
This needs to be acknowledged and you may want to discuss how to resolve this issue in the future.

22
One possible approach is the identification of "complex" as suggested by the integrated informa-23 tion theory (IIT) by Tononi.

24
The distinction between conscious and non-conscious complex activity is a good one -we agree 25 that it is worth discussing. We were, however, limited in our ability to make any inferences about 26 the content of consciousness at all since 1. anaesthesia is typically light on content and 2. the animal 27 models cannot report their experience. We have added the following to the Introduction to make 28 the distinction between level and content of consciousness clear: 29 We should note that in this project we have focused primarily on the issue of level of consciousness 30 rather than the content of consciousness. This is a subtle distinction that has been discussed in 31 detail (for review, see Koch, 2016) but briefly, the level of consciousness quantifies the "amount" This notion was recently given empirical support by the finding that, when attempting to dis-50 criminate between conscious and anesthetized states, high-dimensional information structures did a 51 significantly better job than standard scalar measures (Leung et al., 2021). This strongly suggests 52 that when attempting to characterize a system as complex as a conscious (or even unconscious) 53 brain, which can vary along many different axes, a more comprehensive picture is necessary 54 Also, as you refer to epsilon machines several times in the manuscript as an alternative way to 55 characterize the topology/shape of information structure, it may be worth looking at our recent

64
With respect to the limit of OPN, I think it is better to mention other approaches that have also 65 taken multivariate approaches. IIT can be considered as one of them, where it explicitly deals with 66 the integration among channels, which your OPN approach explicitly ignores. To the extent that 67 integration is critical to understand consciousness, this may be a potential oversight / limitation of 68 your approach. 69 We have expanded the discussion to include references to several different frameworks that explic-70 itly explore integration between many elements, including the recent work in integrated information 71 decomposition, historical work on functional connectivity network approaches, IIT, and work on 72 criticality and consciousness. We stress that the methods developed here may be useful additions to 73 existing frameworks, rather than replacements.

74
The OPN and EPC framework may be complemented by other research frameworks that explic-75 itly aim to understand "integration" in the form of statistical dependencies between many interacting 76 elements of the brain, for example the recent work on consciousness an integrated information decom-

85
We have added the following to the discussion:

86
Within the time-delay and state-space reconstruction framework, work on cross-embeddings using 87 the same NeuroTycho data has found that multivariate state-space reconstruction can yield insights 88 into how anaesthesia changes the interactions between brain regions (Tajima et al., 2015). This 89 approach could be unified with approaches for constructing cross-and joint-OPNs (Guo et al., 2018) 90 to enable the applications of our methods to multivariate datasets.  Your approach is data-driven and highly descriptive. It may make more sense to explicitly admit 93 this in Discussion and discuss its limitations. Alternatively, you may want to try to link your findings 94 with predictions from some theories. I would imagine some of the findings can be linked with the 95 other theories of consciousness other than the Entropy hypothesis or IIT, but I will leave this to 96 you.

97
Done -we make it explicit that we are doing a data-driven analysis and deliberate choose not to 98 adjudicate between various theories of consciousness. 99 he work presented here is explicitly data driven, rather than theory-driven. There are a large   Table 1 is not visible (if something is there?)

133
The right side is a tad cut off due to the LaTeX formatting, but there are no missing columns.

134
This will presumably be fixed when the paper is formatted for the journal.