Whole brain modelling for simulating pharmacological interventions on patients with disorders of consciousness

Abstract

Disorders of consciousness (DoC) represent a challenging and complex group of neurological conditions characterised by profound disturbances in consciousness. The current range of treatments for DoC is limited. This has sparked growing interest in developing new treatments, including the use of psychedelic drugs. Nevertheless, clinical investigations and the mechanisms behind them are methodologically and ethically constrained. To tackle these limitations, we combined biologically plausible whole-brain models with deep learning techniques to characterise the low-dimensional space of DoC patients. We investigated the effects of model pharmacological interventions by including the whole-brain dynamical consequences of the enhanced neuromodulatory level of different neurotransmitters, and providing geometrical interpretation in the low-dimensional space. Our findings show that serotonergic and opioid receptors effectively shifted the DoC models towards a dynamical behaviour associated with a healthier state, and that these improvements correlated with the mean density of the activated receptors throughout the brain. These findings mark an important step towards the development of treatments not only for DoC but also for a broader spectrum of brain diseases. Our method offers a promising avenue for exploring the therapeutic potential of pharmacological interventions within the ethical and methodological confines of clinical research.

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communications biology Article
https://doi.org/10.1038/s42003-024-06852-9
Whole brain modelling for simulating
pharmacological interventions on patients
with disorders of consciousness
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I. Mindlin 1,R.Herzog 1, L. Belloli1,2, D. Manasova1,3, M. Monge-Asensio4,J.Vohryzek
4,
A. Escrichs 4, N. Alnagger5,6,P.Núñez
5,6, O. Gosseries 5,6,M.L.Kringelbach 7,8,9, G. Deco 4,10,
E. Tagliazucchi2,11,12, L. Naccache 1,B.Rohaut
1,13,J.D.Sitt 1,14 &Y.SanzPerl 1,2,4,14
Disorders of consciousness (DoC) represent a challenging and complex group of neurological
conditions characterised by profound disturbances in consciousness. The curr ent range of treatments
for DoC is limited. This has sparked growing interest in developing new treatments, including the use of
psychedelic drugs. Nevertheless, clinical investigations and the mechanisms behind them are
methodologically and ethically constrained. To tackle these limitations, we combined biologically
plausible whole-brain models with deep learning techniques to characterise the low-dimensional
space of DoC patients. We investigated the effects of model pharmacological interventions by
including the whole-brain dynamical consequences of the enhanced neuromodulatory level of
different neurotransmitters, and providing geometrical interpretation in the low-dimensional space.
Our findings show that serotonergic and opioid receptors effectively shifted the DoC models towards a
dynamical behaviour associated with a healthier state, and that these improvements correlated with
the mean density of the activated receptors throughout the brain. These findings mark an important
step towards the development of treatments not only for DoC but also for a broader spectrum of brain
diseases. Our method offers a promising avenue for exploring the therapeutic potential of
pharmacological interventions within the ethical and methodological confines of clinical research.
Despite the lack of broad definitions of consciousness as a global brain state,
it is accepted that it can be lost or diminished when we fall asleep, or as the
effect of drugs, such as those employed to induce general anaesthesia.
Consciousness is also impaired in pathological conditions, such as during
coma or in post-comatose disorders of consciousness (DoC). The two
primary categories within the spectrum of DoC are unresponsive wake-
fulness syndrome (UWS) which is also coined vegetative state (VS), and
minimally conscious state (MCS). UWS is characterised by preserved
arousal without any behavioural evidence of consciousness, while MCS
represents a condition with richer cognitive processes that are not limited to
reflexive processes. Observation of MCS patients demonstrates that—in
contrast with UWS/VS patients—cortical networks still play a role in their
overt behaviour1,2. DoC are complex neurological diseases with hetero-
geneous etiologies and presentations, often resulting in a substantial mis-
diagnosis rate with potentially devastating implications3.
In the last two decades, the incorporation of neuroimaging techniques
resulted in significant improvements regarding the diagnosis and prognosis
of DoC patients4. Data-driven machine learning approaches are capable of
identifying brain activity patterns that predict different levels of impaired
consciousness, with an accuracy comparable to that of expert
1Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Sorbonne Université, Paris, 75013, France. 2Consejo Nacional de Investigaciones Científicas y
Técnicas (CONICET), Ministry of Science, Technology and Innovation, Buenos Aires, Argentina. 3Université Paris Cité, Paris, France. 4Center for Brain and
Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain. 5Coma Science Group, GIGA Consciousness, University of Liège,
Liège, Belgium. 6Centre du cerveau, CHU of Liège, Liège, Belgium. 7Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford,
Oxford, UK. 8Department of Psychiatry, University of Oxford, Oxford, UK. 9Center for Music in the Brain, Department of Clinical Medicine, Aarhus University,
Aarhus, Denmark. 10Institució Catalana de la Recerca i Estudis Avançats (ICREA), Barcelona, Spain. 11Latin American Brain Health Institute (BrainLat), Universidad
Adolfo Ibáñez, Santiago, Chile. 12Cognitive Neuroscience Center, Universidad de San Andrés, Buenos Aires, Argentina. 13APHP, Hôpital de la Pitié Salpêtrière,
DMU Neurosciences, Neuro ICU, Sorbonne Université, Paris, France.
14
These authors jointly supervised this work: J. D. Sitt, Y. Sanz Perl.
e-mail: ivan.mindlin@icm-institute.org;jacobo.sitt@icm-institute.org;yonatan.sanz@upf.edu
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neurologists5–7. One downside of these approaches is that they are not based
on generative models, therefore they cannot be used to test causal
mechanisms underlying the observed differences between groups8. In turn,
the insufficient understanding of how consciousness is lost in brain-injured
patients hinders the development of novel therapeutic interventions9.
Currently, the range of treatments for DoC includes Zolpidem and
Amantadine as pharmacological options10,aswellasinvasive
11 and non-
invasive electrical magnetic stimulation methods, such as transcranial
magnetic stimulation (TMS)12. The pharmacodynamics of the pharmaco-
logical interventions are heterogeneous. Zolpidem is a sedative-hypnotic
that interestingly has a selective agonism to the GABA receptor subtype ω1
which is strongly present in basal ganglia and striatum provoking an inhi-
bition of these inhibitory areas. It restores consciousness in chronic patients
due to this paradoxical effect13,anditseffectwearsoffalongwiththedrug
14.
In contrast, Amantadine is a N-methyl-D-aspartate receptor antagonist and
indirect dopamine agonist capable of inducing both short (5-10 days) and
long-term (4-6 weeks) improvements15, and it was incorporated in DoC
practical guidelines for clinicians16.Unfortunately,availabledrugshave
modest therapeutic efficacy and act via unknown specific mechanisms, thus
hindering the development of new options, while clinical trials are difficult
to organise due to a low number of participants and other limitations
intrinsic to patients with conscious impairments9.
In recent years, serotonergic psychedelics have been proposed as a
potential new treatment to accelerate the recovery of DoC patients17.
This proposal was not based on pharmacological considerations, but on
the measured effects of psychedelics on brain activity, and the inter-
pretation assigned to these changes by theories of consciousness18.
Psychedelic drugs are suggestive to increase brain complexity measured
using either Shannon Entropy or Lempel-Ziv complexity19, both metrics
known to decrease du ring episodes of diminished awarenes s (deep sleep,
general anaesthes ia, and DoC)20. At the same time, over the past year s the
use of psychedelics for treating mental health disorders has shown
promising results in conditions such as depression21–24 and obsessive-
compulsive disorder25. It is speculated that psychedelics can result in
functional rearrangements mediated by serotonin 2 A (5-HT2A)
receptor agonism, which modulates the emergent whole-brain dynam-
ics, generating principal psychoactive effects of these drugs26 . Impor-
tantly, the density of this receptor is maximal in key sub-cortical and
high-level cortical association areas implicated with conscious infor-
mation processing27 . Taken as a whole, these findings support the pro-
posal by Scott and Carhart-Harris of exploring classic psychedelics as
new avenues for the treatment of DoC.
The current consensus is that psychedelic drugs are very safe sub-
stances when consumed by healthy individuals under adequate conditions28.
However, a deeper analysis reveals distinct ethical concerns for the use of
psychedelics in non-communicative patients29. Computational modelling
offers an alternative to evaluate the therapeutic action of serotonergic psy-
chedelics without facing the ethical challenges of human in vivo experi-
mentation. While this research cannot replace proper clinical trials, it can be
used to support the feasibility of this intervention, adding to evidence from
other sources, such as animal experimentation.
Here we proposed a framework combining deep learning and com-
putational whole-brain modelling to provide mechanistic understanding of
possible pharmacological treatments for DoC, including serotonergic
treatments, in a controlled and ethical manner. We used a biophysically-
grounded model based oncoupled meanfields representing the dynamics of
brain regions at the macroscale, composed by excitatory and inhibitory
neural populations30. The strength of connection between nodes is informed
through anatomical structural connectome informed by diffusion MRI
(dMRI). Using this Dynamic Mean Field (DMF) model, we simulated
agonism at multiple receptors by altering the nonlinear response of neu-
ronal populations to synaptic input, weighted by the local density of nor-
malised receptors informed by Positron Emission Tomography (PET) data.
This integrative multimodal approach in computational modelling has
already demonstrated its effectiveness in capturing the intricate interplay
between coupled whole-brain networks and neurotransmitter systems31.To
assess the effects of simulated interventions, we used a variational auto-
encoder (VAE) trained on the output of the DMF model fitted to the
pathological and healthy control states. The VAE learns the defining attri-
butes of the data in an unsupervised manner and projects it into a low-
dimensional latent space, where different brain states are clustered in a
continuous and organised way32–34. The perturbations can then be inter-
preted as trajectories within this space, which we characterise using well-
established metrics sensitive to the level of conscious awareness.
Results
Methodological overview
The procedure followed in this work is represented in Fig. 1.First,we
implemented a biologically realistic DMF model30 fitted to fMRI data from
DoC patients and healthy controls. The DMF models brain dynamics as the
emergent activity of local recurrent excitatory/inhibitory connections, with
long-range excitatory connections between cortical regions, scaled by the
global connectivity parameter (G) and the structural connectivity. The
structural connectivity (SC) is determined by the amount of white fibre
passing through each pair of regions and was obtained from aninde pendent
cohort of healthy subjects with high-quality DTI data from the H CP dataset.
TheSCusedinthisworkisobtainedby averaging the individual SC from
this dataset. Local inhibition is controlled by the Feedback Inhibitory
Current (FIC), which offsets inter-areal excitation and clamps the average
excitatory firing rate around 3 Hz. The G parameter, and thus indirectly the
FIC, are tuned to maximise the similarity to the empirical brain functional
connectivity (FC), as computed from the fMRI Blood-Oxygen-Level-
Dependent (BOLD) signals. Finally, the expression of neurotransmitter
receptors on each region is obtained from PET maps, and the susceptibility
of each region to the activation of these receptors is controlled via a global
scaling parameter. Since every region has its own level of receptor expres-
sion, this global scaling parameter will introduce regionally heterogeneous
neuromodulation. In past studies, this procedure was successfully used to
simulate different states of consciousness, such as propofol-induced
anaesthesia35 and the psychedelic state elicited by LSD36.
After tuning the model, we used the inferred parameters for each
condition (Gand FIC) to generate surrogate FC matrices as a data synthesis
procedure37 to train a variational autoencoder (VAE), resulting in a two-
dimensional encoding of each FC matrix. We then characterised this low-
dimensional space in terms of different metrics sensitive to changes in
consciousness and explored the effects of pharmacological interventions. As
a result, changes in receptor scalings yield the potential to reflect global shifts
in neurotransmission signalling and can explain whole-brain dynamics in
response to a drug intervention.
We implemented this procedure with 8 different receptors (ser-
otonergic 5HT2A, 5HT1A, 5HT6; dopaminergic D1, D2; dopamine
transporter (DAT); opiate μ, Histamine H3). We selected serotonergic
receptors to test the effect of psychedelic drugs, whose main target is the
5HT2A receptor28, while the choice of dopaminergic receptors stemmed
from their relevance to current treatments for DoC (e.g., Amantadine).
Including opiate and histamine receptors completed the spectrum of
potential stimulation targets, resulting in a comprehensive array of diverse
receptors for analysis. These receptors were normalised (see Supplementary
Fig. 1) to account for their overall presence in the brain, independent of the
absolute PET values.
As a final step, we encoded the pharmacological intervention in the
two-dimensional latent space, parametrised by the scaling that modulates
the receptor density maps. This combined framework allowed us to
represent the interventions as trajectories in the latent space and compute
geometrical properties that characterised the intervention, such as distance
to the healthy controls, the distance from the original non-perturbed model,
as well as changes in brain complexity, network integration, and correlation
with the anatomical connectivity.
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Baseline model fitting
To explore the effect of perturbing via different receptors, we first created a
baseline model for healthy controls (CNT) and each patient group, namely
UWS and MCS. For each value of G, we conducted repeated simulations for
the number of subjects in each group and then also repeated the training
process 20 times to optimise the SSIM between simulation and our target
data at group level. The SSIM is a similarity measure that balances corre-
lation and euclidean distance between the inputs38,inthiscasethesimulated
and the empirical FC. The range of G values were defined such that the
model always remained in a biologically plausible regime, below hyper-
excited and hyper-correlated activity. In Fig. 2A, the plots demonstrate the
fitting performances for each group. In all three groups, a point of instability is
reached, resulting in the breakdown of the goodness of fit. Prior to this
instance, all the models attain their best fit. We repeated this exploration of G
values 15 times. Then, we calculated the optimal value of G for each condition
by taking the mean optimal G obtained across iterations (mean +-std:
G
UWS
=1.59+−0.04; G
MCS
=1.75+−0.07 ; G
CNT
=2.1+−0.06). The low
variability in the results across iterations highlights the robustness of our
models. These G values determine how we model each condition with the
DMF at the baseline.
As a next step, we assessed if these models were distinguishable between
levels of consciousness. To this end, we generated 3000 simulations and
calculated the SSIM between their FC and the empirical FC of each condition.
We compared the SSIM values obtained between simulations and empirical
FCs for each condition and measured the effect size using Cohen’sd.The
models simulations were significantly different across states (Empirical
UWS/Simulations CNTvsMCS Cohen’s d = 23.45 MCSvsUWS Cohen’s
d = 8.75 CNTvsUWS Cohen’s d = 31.96 Empirical MCS/CNTvsMCS
Cohen’s d = 17.24 CNTvsUWS Cohen’s d = 22.60 MCSvsUWS Cohen’s
d=−5.39 Empirical CNT/MCSvsUWS Cohen’sd=−0.68 CNTvsMCS
Cohen’sd=7.20CNTvsUWSCohen’s d = 6.87). Additionally, each model
had the highest similarity with the condition they were fitted to
(SSIM
uws
= 0.38, SSIM
MCS
=0.34,SSIM
CNT
=0.27),as showninFig.2B. As
the Gparameter was decreased, regions did not interact between themselves,
Fig. 1 | Overview of the whole brain model, variational autoencoder and per-
turbation pipeline. A biophysical model simulates the local dynamics of a 90 region
parcellation, with structural connectivity provided by DTI data of healthy subjects.
Model parameters are adjusted to fit FC matrices derived from fMRI data of each
condition. Pharmacological perturbations are simulated by changing the synaptic
scaling of each region weighted by PET receptor maps, which provide a measure of
local receptor density. Subsequently, a variational autoencoder (VAE) is trained to
reconstruct the input data, resulting in a low-dimensional latent space which
facilitates the visualisation of the perturbations, while also providing a geometric
interpretation of their effect.
Fig. 2 | Model fitting and validation of the baseline
models. A Model fit curves where the parameter G is
optimised to maximise the SSIM to the empirical FC.
The optimal values of G for each condition
(mean +-std: GUWS = 1.59 +−0.04; GMCS =
1.75 +−0.07; GCNT = 2.1 +−0.06) align with
existing literature, where lower Gis associated with
reduced consciousness. Error bars show standard
error for each G value. BThe optimal model for each
condition exhibits significantly better SSIM values to
its corresponding empirical dataset compared to the
rest, as shown in the dashed line for each condition.
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reducing integration of the network and stabilising the overall dynamics to
those determined by the anatomical structure. This situation was seen for
unconscious brain states, whereas the opposite could be seen for conscious
controls. Therefore the resulting optimal values of G found for each condition
are consistent with this observation (G
UWS
<G
MCS
<G
CNT
).
Latent space embedding of baseline models
After fitting the baseline models, we employed 3000 simulations from each
condition to train a variational autoencoder (VAE) for reconstructing the
input data, following previous work33. The VAE is a type of generative model
that combines the strengths of traditional autoencoders with the probabil-
istic framework of variational inference. The variational component allows
the model to learn the statistical distribution of the data in the latent space
rather than just mapping the data to a fixed point. By learning the statistical
distribution of the input data, the VAE constructs a continuous and smooth
latent space32, called manifold, that captures the underlying structure of the
simulated FC. This results in a meaningful representation of the data, where
similar inputs are mapped closer together and dissimilar inputs are mapped
farther apart in the latent space. The use of the 2-dimensional latent space
allowed us to visualise a perturbational landscape, summarising the impact
of all possible pharmacological perturbations applied to the DoC models.
Once the VAE was trained, we encoded a test set to observe how the
different conditions organised in the latent space, as depicted in Fig. 3A. The
different conditions formed separate clusters with very small overlap, which
means that conditions were distinguishable within the latent space
embedding. We quantified this by training a Support Vector Machine that
successfully classified the projected clusters (See Supplementary Table 1).
Additionally, there appeared an ordering along an axis starting from lower
consciousness (UWS), passing through an intermediate stage (MCS), and
finally to the fully conscious state (CNT). Fig. 3C–E. The highlighted area
shows the value at the centroid of each condition. As seen in Fig. 3C, the
embedded FC matrices from the control group appear in regions that exhibit
higher Shannon Entropy (H) than the corresponding DoC regions (Median,
IQR HUWS = 4.04, 0.1, HMCS = 4.17,0.07, HCNT = 4.32, 0.04
UWSvsMCS Cohen’sd=−1.99 MCSvsCNT Cohen’sd=−2.80
UWSvsCNT Cohen’sd=−4.13). We calculated the H value on the node
strength vector of the FC matrix, following the methodology established in
previous studies39. The mean value of FC (mFC) matrices has been related to
the depthness of unconsciousness33 due to the hierarchical decline of this
value as awareness is lost (Median, IQR mFC
UWS
= 0.21, 0.03,
mFC
MCS
= 0.25, 0.03, mFC
CNT
= 0.32, 0.03 UWSvsMCS Cohen’sd=−1.81
MCSvsCNT Cohen’sd=−2.82 UWSvsCNT Cohen’sd=−4.76). As
shown by previous research, loss of consciousness abolishes functional
interactions that are not directly mediated by structural links, thus making FC
patterns of DoC patients more similar to the underlying structural con-
nectivity (SC) pattern40,41.Fig.3E shows these values for our three conditions
(Median, IQR SC-CORR
UWS
= 0.70, 0.02, SC-CORR
MCS
= 0.67, 0.01, SC-
CORR
CNT
= 0.64,0.015 UWSvsMCS Cohen’s d = 2.08 MCSvsCNT Cohen’s
d = 3.47 UWSvsCNT Cohen’sd=5.25).
Pharmacological perturbations produce transitions away from
baseline dynamics
Once we obtained an interpretable latent space of our baseline simulations,
we simulated pharmacological perturbations of the DoC models using the
normalised PET density maps of different receptors. As mentioned before,
these maps give a density value for each node that is then scaled by the
scaling parameter (see Methods). The perturbation consists of increasing
this value in a range between 0 (no receptor intervention) to 1 with a step of
0.01. Embeddings of the perturbations applied to MCS and UWS groups are
showninFig.4A, B, respectively. Fore achre ceptormap we embedded in the
latent space the simulated FC after applying the scaling value in a given step.
The resulting trajectory comes from encoding the simulated FC ma trices for
all steps in the scaling range. Different receptor trajectories reach different
distances and the proximity to the control centroid is limited by its starting
point (Fig. 4C, D). Another interesting observation is that all t he trajectories
seem to move approximately in the same direction, i.e., in parallel to the line
that unites the three groups from states of more diminished consciousness
towards the group of wakeful conscious controls. Despite lacking data on
subjects undergoing pharmacological interventions, we simulated 5HT2A
activation in healthy individuals, observing a slight deviation from the
“wakeful”axis (Supplementary Fig. 2) when introducing this perturbation.
This suggests that psychedelics may exacerbate some of the defining char-
acteristics of the conscious wakeful state.
These results show that despite exhibiting different anatomical het-
erogeneities, the perturbed dynamics exist only in certain regions in latent
space, while others are forbidden, thus narrowing the repertoire of possible
transitions. The main difference between the trajectories is the distance from
the end point to the starting point (Longest and shortest distance achieved
for each condition: Max-MCS
5HT1A
=3.49, Max-UWS
5HT2A
= 4.61, Min-
MCS
D2
=1.62,Min-UWS
D2
=0.74).
Relationship between distribution of receptors and perturbation
trajectories
We investigated the relationship between the final distance reached by the
trajectory and two attributes of the receptor maps: the mean density of the
normalised map and a structural divergence (SD) metric (see Methods).
Briefly, the SD is the euclidean distance between the density map and the
node strength, which represents the average structural connection strength
from each node to the rest. Since we are summing the overall difference
between density and connectivity in each region, a low SD will imply that the
density map and the node strength are similar (small differences), sug-
gesting that the receptor has high density values in strongly connected
nodes, or hubs, and vice versa.
We found a strong correlation between the mean density of the nor-
malised map and the final distance of the trajectory (Fig. 5A, B, MCS
Pearson correlation: 0.89, p= 0.003; UWS Pearson correlation: 0.96,
p= 0.0001). The difference in correlation values can be attributed to the
curvature of the trajectory after crossing the CNT region in MCS pertur-
bations, which leads to changes in linear distance from the starting point.
Furthermore, Fig. 5C, D demonstrates that SD is not correlated with the
length of the trajectory. To reaffirm this result, we generated a randomised
version of a receptor map that preserved spatial autocorrelation42 and the
mean density. We then perturbed our patient models with this null version
of the map. In Supplementary Fig. 3 we can see that the distances from the
starting point are indistinguishable. The combination of these results sug-
gests that the neuromodulation of a given receptor displaces the dynamics of
a baseline DoC model independently of the topology of the stimulated
nodes. Instead, it primarily depends on the receptor presence throughout
the brain.
Additionally, we assessed how intensely each receptor should be sti-
mulated to shift brain dynamics. Different drugs may require different
relative dosages to alter brain dynamics depending on their pharmacoki-
netic and pharmacodynamic properties. Ideally, good candidates for
treatments should exert their action with small doses to avoid u ndesired side
effects due to the stimulation of off-target receptors. For this purpose, we
estimated how quickly the perturbation could displace the model towards
CNT-like dynamics. Trajectories may reach similar distances, yet this can
occur at different speeds. In mathematical terms we are interested in
quantifying the non-linearity of the increase in travelled distance. We cal-
culated the dot product between each projected simulation and an axis
drawn between the starting point of the models and the CNT centroid
(Fig. 5E, F). To quantify the non-linearity we applied a quadratic regression
fittothecumulativedistancealongthisaxisasthescalingincreases.Ifthe
quadratic coefficient is null, the change is constant. If it is negative the
change will be large at first but then decrease as the scaling increases, sug-
gesting a larger effect for a small scaling value. We label “perturbational
efficiency”(PE) the negative quadratic coefficient of the best fit, which
represents the aforementioned rate. We observe that 5HT2A has the highest
PE, even though it has a similar perturbational distance than the other
serotonin receptor subtype, 5HT1A.
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Fig. 3 | Groups are distinguished and characterised by their latent space
embedding in an ordered manner. A Scatter plot of FC matrices obtained from the
three baseline models for the three groups of participants. The groups are clearly
separated within the embedded regions. Embedded FC matrices from Disorders of
Consciousness (DoC) conditions are distinguished by (B) their distance from the
centroid of the FC matrices from the healthy control (CNT) condition, which is the
largest for unresponsive wakefulness syndrome (UWS) and smallest for minimally
conscious state (MCS). We sampled FC matrices from a grid to calculate different
metrics over the latent space: (C) Entropy, (D) mean FC value and (E) correlation to
structural connectivity. Each square corresponds to a point from that grid and has
therefore an associated value. Highlighted squares indicate the position of the
centroids of each group in this space. The values of these metrics in the regions
corresponding to each condition are consistent with their interpretation concerning
consciousness. F–HDistribution of the previous measures when sampling the
embedded points from (A).
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Discussion
DoC encompasses a set of devastating conditions, affecting not only the lives
of the patients themselves but also causing emotional distress among their
families and caretakers. The diagnosis of DoC patients is very challenging,
also resulting in a difficult evaluation of potential treatment options. This
and other issues, such as heterogeneous etiologies and small available
populations, hinder the systematic exploration of new pharmacological
alternatives. Currently used drugs became available as a consequence of
indirect assumptions, instead of being optimised specifically for the treat-
ment of DoC patients. The purpose of this study is to demonstrate the
feasibility of using biophysically-grounded whole-brain models to inform
the effect of targeted receptor stimulation in the clinical status of DoC
patients. We were able to map different pharmacological interventions into
two-dimensional space trajectories, from which we derived features indi-
cative of treatment feasibility and efficacy. Moreover, successful perturba-
tions not only recovered conscious-like dynamics, but also restored to
baseline levels of the three metrics previously introduced: Shannon Entropy,
correlation to structural connectivity and mean FC value as a proxy for
integration.
Our results highlight that stimulation of two serotonin receptor sub-
types (2A and 1A) restores dynamics indicative of conscious wakefulness.
Interpreted within the context of previous proposals to investigate psy-
chedelicsastreatmentoptionsinDoC
17,thisresultcanbetakenasan
additional suggestive element favouring further steps, such as the explora-
tion of animal models. Interestingly,eventhoughthe5HT2Areceptoristhe
main target of psychedelic drugs (i.e., all psychedelics are full or partial
agonists at this receptor), we also found comparable results for the 5HT1A
receptor. Psychedelic compounds are divided into two main families
depending on their chemical structure: substituted tryptamines (including
N,N-Dimethyltryptamine and psilocybin) and substituted phenethyla-
mines (such as mescaline). Of these families, tryptamines present significant
agonism at serotonin 5HT2A/1A receptors28. This raises the possibility
that the potential therapeutic effect of psychedelics on DoC patients is
not universal for all psychedelics, but can change from compound to
Fig. 4 | Hierarchy of target neurotransmitter
receptors based on how their simulated activation
displaces whole-brain dynamics towards con-
scious wakefulness. Panels (A) and (B) display
embedded trajectories for perturbing the MCS and
UWS baseline models, respectively, at the different
receptors. All perturbations displace the embedded
FC matrices along the same axis in latent space,
indicating significant variations in the final distance
covered across the entire perturbation range. This is
presented in panels (C) and (D), where the covered
distances are similar, with differences in the max-
imum distance reached. Specifically, for UWS, the
perturbations did not deviate as far from their
starting point, as was observed for the MCS models.
Simulated perturbations at the serotonergic recep-
tors and the MU receptor presented the most sig-
nificant impact on the models.
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compound. It is also important to note that not all 5HT2A receptor agonists
induce psychedelic effects43, thus it could be possible that a non-psychedelic
serotonergic agonist is eventually capable of improving the clinical status of
DoC patients.
Our model also predicted that stimulation of opioid μreceptors should
have a positive impact on DoC patients. This result is consistent with a
recent publication demonstrating that use of opioid drugs during surgery
correlates with consciousness improvement44.Asimilarroleofμreceptor
stimulation is suggested by the study of neurorehabilitation and recovery of
brain-injured patients after severe COVID-19 infections, since for MCS
patients the amount of oxycodone (an opioid analgesic drug) received
during treatment correlated with their recovery indices after the infection45.
It has been speculated that opioid compounds could have neuroprotective
properties, which could be beneficial for brain-injured patients46.These
studies should be taken with care, however, as they report observational
findings instead of the results of clinical trials designed to evaluate the safety
and efficacy of opioids in DoC patients.
The validity of the perturbational analysis depends on the capacity of
the baseline biophysical models to capture the relevant features of whole-
brain dynamics. The results of the model fitting are consistent with previous
studies, such as the work of Lopez-Gonzales and colleagues, showing that a
less biophysically-realistic whole-brain model optimises the reproduction of
fMRI DoC patient dynamics with low coupling (G) values47.Thesame
behaviour was demonstrated using the same model fitted to statistical
observables derived from the turbulent brain dynamics regime48.Inourcase,
the optimal G values correlated with the expected level of consciousness per
group (i.e., UWS < < MCS < CNT), in accordance with previous work using
this model49. Interestingly, this behaviour seems to be invariant with respect
to the choice of model and its optimisation targets, thus being indicative of a
neurobiological principle.
Another key point of our analysis is the data-driven synthesis of
training samples for the VAE. The use of data synthesis or augmentation
techniques is a standard procedure when training deep learning algorithms;
in this case, data synthesis was obtained as the output of a generative
dynamical system trained to capture the whole-brain FC of participants37,50.
In addition, using the output of the whole-brain model to train the VAE
provided a dataset with fixed underlying parameters and controlled initial
conditions, which is difficult to obtain from empirical recordings. While the
VAE was not strictly necessary to fit the data and simulate the perturbations,
it provided a framework to interpret and visualise the results. Instead of
reducing our study to evaluate if a given perturbation can induce a healthy-
like state, observing them as trajectories in a continuous space opens more
Fig. 5 | Geometric properties show that pertur-
bation trajectories are related to the density dis-
tribution of stimulated receptors. Panels (A) and
(B) show that the maximum distance reached from
the starting point exhibits a strong linear correlation
with the mean receptor density. In panels (C) and
(D), in contrast, we show that there is no significant
correlation between the maximum distance reached
and the “structural divergence”(representing the
spatial relationship between receptor maps and the
weight vector of connections). This finding high-
lights the extent to which the model dynamics can be
shifted independently of the spatial arrangement of
receptors. E,FDotted lines show the perturbational
distance accumulated as the scaling increases. Solid
lines indicate the quadratic regression fitted to the
cumulative distances. The inset shows the “pertur-
bational efficiency”(PE) for each receptor. The
5HT2A receptor has the highest PE despite reaching
a similar overall perturbational distance than
the 5HT1A.
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possibilities for analysis. Additionally it facilitates interpretations con-
sidering the high-dimensional nature of fMRI data34, endowing each point
in latent space with the value of relevant metrics, namely entropy, mean FC
value, and correlation to structure40,41,51. Thus, the construction of the latent
space allowed us to demonstrate that the three groups (UWS, MCS and
CNT) appeared organised within a one-dimensional direction representing
the extent of consciousness impairment, which is aligned with previous
results obtained using phenomenological models33. As expected, this
direction was also characterised by a decrease in whole-brain entropy and
mean FC, as well as an increase in correlation to anatomical connectivity, of
the sampled FC matrices, affirming that the chosen metrics are sensitive to
the level of impaired consciousness of the patients.
Previous research investigated the capacity of simulated external per-
turbations (e.g., TMS and tDCS) to transition towards states of increased
consciousness33,52. Here, we adopted biophysical models capable of repre-
senting the effects of pharmacological perturbations, resulting in a first
exploration of simulated drug treatment in DoC patients. In combination
with receptor density PET maps of different neuromodulatory systems53,we
introduced heterogeneities in the model by changing the slope of the
synaptic scaling function, weighted by local receptor density estimates36,54.It
is important to note that the scaling allows us to understand large-scale
neurotransmission in terms of the regional heterogeneity of susceptibility to
endogenous and exogenous modulatory signals. Consequently, changes in
the scaling yield the potential to reflect global shifts in neurotransmission
signalling and explain whole-brain dynamics in response to a drug inter-
vention, but these changes are not directly modelling the dosage of a drug.
For each value of scaling we projected the generated FC into our latent space.
As the scaling increased, the projected simulations moved from the lower
consciousness regions to that corresponding to the healthy controls in a
continuous manner. Leveraging the VAE latent space representation, these
trajectories could be quantified using simple geometrical properties, as well
as by the features previously assigned to each point of the space. We found
that perturbing some receptors induced a significant shift in the dynamics of
the DoC model as determined by the travelled distance as the scaling
parameter increased. A key aspect of this work is that although global
coupling and neuromodulation account for different mechanisms, when we
perturb pharmacologically in our model we can see an effect relatable to
global coupling. Even more, although we cannot biologically increase global
coupling in a patient, we can modulate responsiveness through receptor
stimulation. Of note, the least effective in terms of reaching a maximum
change in the dynamics, were the dopaminergic receptors, which are cur-
rently used as treatment options10,15. This discrepancy could arise due to
downstream effects of dopaminergic stimulation not included in our model,
or due to the fact that dopaminergic drugs used to treat DoC are non-specific
with regards to the targeted dopamine receptor subtype. Future work should
attempt to characterise the effect of multi-target stimulation in DoC
patients.
Our results show that the mean density of the normalised receptor is
highly correlated with the maximum distance reached after the perturbation
suggesting an effect driven by the widespread presence of the receptor in the
brain; however, this result was not found for the local node strength, sug-
gesting that the underlying topological structure has a limited effect on the
outcome of the perturbation. PET measurements may generate different
magnitudes of values depending on the chosen region of reference, therefore
our result is not linked with an absolute density between receptors, but
rather the relative normalised density distribution. Additionally, we mea-
sured the impact of different receptors by determining how much scaling
was required to shift brain dynamics towards a healthy state. Even though
some receptors eventually reached the same overall perturbational distance,
they did so at different speeds. Notably, the 5HT2A receptor, the main target
of serotonergic psychedelics, presented the highest efficiency in this regard.
The present work contributes to demonstrating the usefulness of in
silico experimentation to investigate perturbations to transition between
different brain states. It has been recently stated that this type of modelling
approach can be a crucial step towards personalised treatments31,55.
Leveraging the concept of digital twins56 and the idea of phase 0 clinical
trials55,57, these computational models offer unique opportunities to explore
and predict the effects of therapeutic interventions. Through virtual simu-
lations of patient-specific brain dynamics, “digital twins”provide a testing
ground for different treatment strategies, opening doors for personalised
and targeted approaches to manage DoC. Additionally, phase 0 clinical trials
present a platform for early exploratory studies, allowing researchers to
assess the safety and efficacy of potential treatments in a limited patient
cohort before scaling up to larger trials.
A main limitation of our work is the lack of interaction between
neuromodulatory systems in the model. Future work should address this
with a more sophisticated modelling of the neuromodulation, for example
by perturbing multiple receptors from the same neuromodulatory system.
For instance, in the case of LSD, despite its main action being exerted via the
serotonergic system, it also exhibits agonism for dopaminergic receptors58.
Other large scale data-driven works have shown that most mind-altering
drugs can be understood in terms of contributions from multi-
neurotransmitter systems59,60. In the same direction, the impact of the het-
erogeneities in the model should be explored via different parameters
depending on the drug that is modelled. For instance, sedative compounds
such as ketamine and memantine are postulated to exert their effects by
modulating the balance between excitatory and inhibitory mechanisms.
This hypothesis can be experimentally evaluated by manipulating the FIC
parameter. It is important to note that absolute density of a PET map is not
biologically meaningful due to PET measurements (binding potential)being
a relative measure. We addressed this issue by normalising each map and
then scaling the modulation of each map within the models which allow us
to interpret the results, nevertheless the interpretation of the absolute value
of each map in each region is not possible.
Additionally, there are interesting directions to take with respect to
non-pharmacological perturbations such as central thalamic Deep Brain
Stimulation, which requires implanting electrodes, or non-invasive repeti-
tive transcranial magnetic stimulation. This would also require using a
whole-brain parcellation with higher subcortical resolution, such as the
Melbourn Subcortex Atlas61. Although there are theoretical benefits for
subcortical stimulation, the clinical results are not conclusive or still in early
stages62, which could be benefited from in silico experimentation.
Another limitation of our work is the lack of structural connectivity
included in the DoC patient model construction. The aberrant function
presented by the brains of DoC patients is ultimately underwritten by
structural damage. As the model fitted to patient data estimates the struc-
tural connectivity from a set of healthy controls, this assumption may omit
key aspects of simulating patient brain function of individual patients and
assessing the result of introducing pharmacological perturbations. The use
of the average SC for modelling the three conditions is justified by the
objective of demonstrating that modulations of serotonergic receptors
induce transition from DoC patients towards healthy states across partici-
pants, without shifting our focus to individual participants. The latter
possibility is undermined by the current lack of data at the level of individual
subjects. Note that the receptor maps are measured at the group level in an
independent cohort, moreover, the same is valid for the SC matrix. Faced
with this limitation, we decided to train a model to represent on average each
condition. The use of high quality SC was justified by this objective, fol-
lowing multiple previous works by our group and others adopting the same
approach. In Supplementary Fig. 4 we show that individually fitted models
using the group averaged SC yield an inferior fit. Nevertheless, we consider
that investigating how the modulation of dynamics via neurotransmitter
receptor activation at the individual level is crucial for a personalised
approach. As stated in by Luppi and colleagues55, given the heterogeneity of
DoCitisimperativetocreatemodelsthatarefitted individually. Future
publications should aim to improve the accuracy of such models via
incorporating patient structural connectivity in their generation. Another
unexplored avenue of research is the parametrization of the hemodynamic
response model to take into consideration the variations in DoC brain
vasculature that would affect BOLD signals. Beyond the particular case of
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our work, we believe it would be an interesting step to create a multi-modal
biophysical model to profit from abundant EEG data acquired from DoC
patients. This type of data has been proven useful to diagnose DoC patients6,7
and could contribute improved temporal resolution which is lacking from
fMRI data.
Our study is based on the hypothesis that manipulating brain activity to
reflect a state of heightened complexity and entropy will be reflected in (at
least a partial) recovery of consciousness in DoC patients, since brain activity
of conscious healthy individuals shows these signatures. However, there is
no clear causal relationship between complexity-based neuroimaging
markers and levels of consciousness, and such a relationship cannot be
demonstrated solely by modelling studies. Instead, our work should be taken
as a proof of plausibility in the context of future empirical studies aimed to
investigate the causal link between complexity markers and consciousness
in DoC patients.
We provided in silico support for the use of serotonergic compounds in
the treatment of DoC patients, while also introducing a computational
framework to investigate the effect of pharmacological stimulation in
neuropsychiatric conditions. Drug development is a lengthy and expensive
process, and only a small percentage of the assayed compounds are even-
tually adopted in clinical practice. The drugs that are currently used to treat
DoC patients were not developed for this objective, instead, they were
repurposed after their efficacy was discovered. It must be emphasised that
our method cannot replace the evidence generated by clinical trials. How-
ever, adding whole-brain biophysical models to the arsenal of methods
available for the discovery of novel pharmacological treatments could
facilitate the concentration of efforts on promising leads, even in cases where
the ethical implications could outweigh the unknown benefits to the
patients.
Methods
Patients
Our study encompassed a total of 11 patients in MCS (with 5 females; mean
age ± s.d., 47.25 ± 20.76 years), 10 patients in UWS (with 4 females; mean
age ± s.d., 39.25 ± 16.30 years), and 13 healthy controls (including seven
females; mean age ± s.d., 42.54 ± 13.64 years), as detailed in ref. 48.The
clinical evaluation and Coma Recovery Scale-Revised (CRS-R) scoring63
were conducted by trained medical professionals to ascertain the partici-
pants’levels of consciousness. A diagnosis of MCS was assigned to patients
displaying behaviours potentially indicative of awareness, such as visual
tracking, localisation of noxious stimulation, or consistent response to
commands. Conversely, patients were categorised as UWS if they exhibited
arousal (eye-opening) without any indications of awareness, never dis-
playing purposeful voluntary movements. This study received approval
from the local ethics committee Comité de Protection des Personnes Ile de
France 1 (Paris, France) under the designation ‘Recherche en soins courants’
(NEURODOC protocol, no. 2013-A01385-40). Informed consent was
obtained from the relatives of the patients, and all investigations adhered to
the principles of the Declaration of Helsinki and the regulations of France.
Anatomical connectivity
We employed diffusion MRI (dMRI) data from a cohort of 16 healthy right-
handed participants (5 women, mean age: 24.8 ± 2.5) gathered at Aarhus
University, Denmark. The research protocol was approved by the internal
research board at CFIN, Aarhus University, and received ethical clearance
from the Research Ethics Committee of the Central Denmark Region (De
Videnskabsetiske Komiteer for Region Midtjylland). All participants pro-
vided written informed consent before participating in the study.
Anatomical connectivity acquisition
The imaging data was acquired during a single session using a 3T Siemens
Skyra scanner at CFIN, Aarhus University. The structural MRI T1 scan
employed the following parameters: voxel size of 1 mm³; reconstructed
matrix size of 256 ×256; echo time (TE) of 3.8 ms, and repetition time (TR)
of 2300 ms.
For the dMRI data collection, a TR of 9000 ms, TE of 84 ms, flip angle of
90 degrees, reconstructed matrix size of 106 ×106, voxel size of 1.98 ×1.98 mm
with a slice thickness of 2 mm, and a bandwidth of 1745 Hz/Px were used.
The dataset was recorded with 62 optimal nonlinear diffusion gradient
directions at b= 1500 s/mm². Additionally, one non-diffusion weighted
image (b= 0) was acquired per every 10 diffusion-weighted images. The
acquisition of dMRI images employed both anterior-to-posterior phase
encoding direction: one in anterior to posterior and the opposite in the rest.
Resting-state fMRI acquisition
MRI images of both patients and healthy subjects were acquired using a 3T
General Electric Signa System. T2*-weighted whole-brain resting-state
images were obtained through a gradient-echo EPI sequence with axial
orientation (200 volumes, 48 slices, slice thickness: 3 mm, TR/TE: 2400
ms/30 ms, voxel size: 3.4375 × 3.4375 × 3.4375 mm, flip angle: 90°,
FOV: 220 mm²).
Probabilistic tractography analysis for anatomical data
In this study, we utilised previously obtained structural connectivity data of
healthy subjects from ref. 64.Briefly, the averaged whole-brain structural
connectivity matrix involved a three-step process: first, defining regions
based on the AAL template used in functional MRI data; second, estimating
connections (edges) between nodes using probabilistic tractography within
the whole-brain network; third, averaging data across participants. In brief,
the FSL toolbox’s linear registration tool (www.fmrib.ox.ac.uk/fsl,FMRIB,
Oxford)65 was used to co-register the EPI image with the T1-weighted
structural image. The T1-weighted image was co-registered to the T1
template of ICBM152 in MNI space. Combining and reversing these
transformations, we applied them to map the AAL template66 from MNI
space to the EPI native space, preserving labelling values through nearest-
neighbourinterpolationforaccuratebrainparcellationsinindividualnative
space. For further details please refer to the original work64.
Resting state pre-processing and FC estimation
Resting state data preprocessing was conducted using FSL, following the
methodology outlined48. In summary, resting state fMRI data were pro-
cessed using MELODIC (multivariate exploratory linear optimised
decomposition into independent components)67. The process involved
discarding the initial five volumes, motion correction using MCFLIRT65,
brain extraction using the brain extraction tool (BET)68,applicationof
spatial smoothing with a 5 mm FWHM Gaussian kernel, rigid-body
registration, high pass filtering with a cutoff of 0.01 Hz, and application of
single-session independent component analysis (ICA) with automatic
dimensionality estimation. Subsequently, for patients, lesion-driven arte-
facts were identified and regressed out, along with noise components,
independently for each subject, utilising FIX (FMRIB’sICA-basedX-
noiseifier)69. Lastly, FSL tools were employed to co-register the images and
extract the time series from the AAL atlas66 for each subject in MNI space,
encompassing 90 cortical brain regions. Subsequently, the mean time series
for each parcellated region were extracted, followed by the calculation of
Pearson correlations between the time series of each pair of regional areas to
derive the interregional FC matrices.
Parcellation
Drawing from our earlier comprehensive whole-brain investigations, we
adopted the AAL atlas, specifically focusing on the 90 cortical and sub-
cortical non-cerebellar brain regions66. This atlas served as the foundation
for integrating all structural, functional, and neuromodulation data.
Leveraging FSL tools, we harnessed the publicly accessible receptor density
maps in MNI space to derive the mean receptor density for each distinct
AAL region in every individual.
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Whole brain modelling
In this study, we employed a network model to simulate spontaneous brain
activity at the whole-brain level, where individual brain areas were repre-
sented as nodes, and the white matter connections between them were
depicted as links. The dynamic mean field (DMF) model, as proposed in
ref. 30, was utilised to describe the activity in each brain area. This DMF
model offers a reductionist approach, summarising the activity of inter-
connected excitatory (E) and inhibitory (I) spiking neurons into a simplified
set of dynamical equations. Within the DMF framework, excitatory synaptic
currents IðEÞ
iare mediated by NMDA receptors, while inhibitory currents
IðIÞ
iare mediated by GABA receptors.
Each brain area iin the DMF model consists of mutually inter-
connected E and I neuronal pools. Additionally, inter-area coupling
between two areas nand pis exclusively established at the E-to-E level and is
adjusted based on the structural connectivity Cij (for details, refer to
Methods - Anatomical Connectivity). This configuration enables the
simulation of brain activity and interactions between different regions,
providing insights into the dynamics of large-scale neural networks.
More specifically, the DMF model at the whole-brain level is expressed
by the following system of coupled differential equations:
IðEÞ
i¼Iext
iþWEI0þwþJNMDASðEÞ
iþGJNMDA XjCij SðEÞ
jJiSðIÞ
ið1Þ
IðIÞ
i¼WII0þJNMDASðEÞ
iSðIÞ
ið2Þ
rðEÞ
i¼HðEÞðIðEÞ
iÞ¼ MiðaEIðEÞ
ibEÞ
1expðdEMiðaEIðEÞ
ibEÞÞ ð3Þ
rðIÞ
i¼HðIÞðIðIÞ
iÞ¼ MiaIIðIÞ
ibI
1expðdIðaIIðIÞ
ibIÞÞ ð4Þ
Mi¼sDiþ1ð5Þ
dSðEÞ
iðtÞ
dt¼dSðEÞ
i
τE
þð1SðEÞ
iÞγrðEÞ
iþσviðtÞð6Þ
dSðIÞ
iðtÞ
dt ¼dSðIÞ
i
τI
þrðIÞ
iþσviðtÞð7Þ
In our computational model, each brain area n was characterised by exci-
tatory (E) and inhibitory (I) pools of neurons, where IðE;IÞ
i(in nA) represents
the total input current, and rðE;IÞ
i(in Hz) represents the firing rate. Addi-
tionally, SðE;IÞ
idenotes the synaptic gating variable. The neuronal nonlinear
response functions, HðE;IÞ, were applied to convert the total input currents
received by the E and I pools into firing rates, rðE;IÞ
i,basedontheinput-
output function proposed by Abbott and Chance70. The model employed
specific gain factors, threshold currents, and constants to determine the
shape of the curvature of Haround the threshold.
In this study we used receptor density maps from healthy subjects
estimated using PET tracer studies obtained by Hansen et al.53.AllPET
images were registered to the MNI-ICBM 152 nonlinear 2009 (version c,
asymmetric) template and subsequently parcellated to the 90 region AAL
atlas66. More details on the acquisitions and limitations of this dataset can be
found in ref. 53. This processed dataset provided us with a quantitative
measure of receptor densities in each AAL region denoted as Di.These
density values were normalised using min-max normalisation:
D0¼D=ðmaxðDÞminðDÞÞ
Dnorm ¼D0maxðDÞþ1
.Leveraging Dnormi,wemodulatedthefiring rates rðE;IÞ
iof the excita-
tory and inhibitory neuronal pools in each brain region, drawing i nspiration
from70. Receptors were thus used to modulate the gain of the neuronal
response function HðE;IÞin each brain area.
The parameters of the DMF model were calibrated to mimic resting-
state conditions, ensuring that each isolated node exhibite dthe typical noisy
spontaneous activity with a low firing rate (r<3Hz)observedinelectro-
physiology experiments. Additionally, the inhibition weight, Ji, was adjuste d
for each node ito achieve Feedback Inhibition Control (FIC). This reg-
ulation, described in ref. 32, ensured that the average firing rate of the
excitatory pools rðEÞ
iremained clamped at 3 Hz even when receiving exci-
tatory input from connected areas. The FIC was shown to lead to a better
prediction of resting-state functional connectivity (FC) and more realistic
evoked activity.
The synaptic gating variable for excitatory pools, SðEÞ
i, was governed by
NMDA receptors, with specific decay time constant tNMDA = 0.1 s and a
constant g = 0.641. On the other hand, the average synaptic gating in
inhibitory pools depended on GABA receptors with a decay time constant
tGABA = 0.01 s. The overall effective external input was represented by
I0= 0.382 nA, with specificweightsWE=1andWI=0.7forexcitatoryand
inhibitory pools, respectively. The model further considered recurrent
excitation with a weight of wþ= 1.4 and excitatory synaptic coupling with
weight JNMDA =0.15nA. Gaussian noise, vi,withanamplitudeof
σ= 0.01 nA was introduced in the system.
In our whole-brain network model, we considered N = 90 brain areas
after parcellation of the structural and functional MRI data. Each area n
received excitatory input from all structurally connected areas p into its
excitatory pool, weighted by the connectivity matrix Cnp derived from
dMRI data. All inter-area E-to-E connections were equally scaled by a global
coupling factor G. This global scaling factor was adjusted to optimise the
system’s working point, where the simulated activity best matched the
empirical resting-state activity of participants under placebo conditions. To
explore different scenarios, simulations were run for a range of G values
between 0 and 2.5 with an increment of 0.025 and a time step of 1 ms. Each G
value underwent 20 simulations of 192 s duration, mirroring the empirical
resting-state scans of 10,11 and 13 participants for the UWS, MCS and CNT
conditions respectively.
Generated BOLD signal
To map the simulated mean field activity to a BOLD signal, we adopted the
generalised hemodynamic model proposed by Stephan et al.71.TheBOLD
signal in each brain area iwas computed based on the firing rate of the
excitatory pools rðEÞ
i.Inthismodel,anincreaseinthefiring rate led to an
increase in a vasodilatory signal, si, which was further subject to auto-
regulatory feedback. The changes in blood inflow, fi, were proportionally
influenced by this signal, resulting in alterations in blood volume viand
deoxyhemoglobin content qi. The relationships between these biophysical
variables were governed by the following equations:
dsiðtÞ
dt ¼0:5rðEÞ
iþ3sikiγiðfi1Þð8Þ
df iðtÞ
dt¼sið9Þ
τi
dviðtÞ
dt¼fiv1=α
ið10Þ
τi
dqiðtÞ
dt ¼fið1ð1ρiÞ1=fiÞ
ρi
qiv1=α
i
vi
ð11Þ
where ρis the resting oxygen extraction fraction, τis a time constant and α
that represents the resistance of the veins. Finally, the BOLD signal in each
area i,Bi, is a static nonlinear function of volume, vi, and deoxyhemoglobin
content, qi, that comprises a volume-weighted sum of extra- and
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intravascular signals:
Bn¼V0½ðk1ð1qiÞþk2ð1qi=viÞþk3ð1viÞ ð12Þ
All biophysical parameters were taken as in71. To concentrate on the
frequency range where resting-state activity appears the most functionally
relevant, both empirical and simulated BOLD signals were band pass filtered
between 0.01 and 0.1 Hz. As with the empirical data we derived the inter-
regional FC matrices between each pair of nodes by calculating the Pearson
correlations of their time series.
Randomised receptor map
To confirm that the shift towards healthy-like dynamics was not driven by
structure we created a randomised variation of the 5HT2A receptor map
while preserving spatial autocorrelation. For this we used the Neuromaps
library72 which implements various null models. Concretely we used the
‘moran‘function which uses Moran spectral randomisation42 to create the
null variations of the receptor map. We used min-max normalisation
rescaled accordingly to obtain the same mean as the original receptor map.
Metrics
Shannon Entropy: To calculate the Shannon entropy of the functional
connectivity (FC) matrix, we divided the connectivity values into 30 equal-
width bins, with each bin representing a range of connectivity values. The
frequency of FC values falling into each bin was counted to create a histo-
gram, which was subsequently normalised by dividing each bin’scountby
the total number of FC values, yielding a probability distribution. Shannon
entropy H was then calculated using the formula
H¼
Xn
i
1
nPðiÞlogðPðiÞÞ
where PðiÞis the probability of the FC values falling into the i-th bin and nis
the total number of bins (30). Only non-zero probabilities were included in
the summation to avoid undefined values from the logarithm of zero. This
procedure quantified the entropy of the FC matrix, providing a measure of
the complexity and variability of the functional connectivity pattern.
Mean FC: It’s been shown that the decrease in this value is related to the
level of unconsciousness33. Particularly, the nodes that exert the biggest
changes are the ones that have inter modular connections suggesting a
change in the integrative capacity of the network. This value was calculated
by taking the overall mean of the FC matrix.
Variational Autoencoders
We employed a Variational Autoencoder (VAE)32 to encode the functional
connectivity matrices Cij into a low-dimensional representation. VAEs are
neural networks that map inputs to probability distributions in a latent
space, allowing for regularisation during training to generate meaningful
outputs after decoding the latent space coordinates. The VAE architecture
(depicted in Fig. 1) comprises three components: the encoder network, the
middle variational layer, and the decoder network.
The encoder network is a deep neural network utilising rectified linear
units (ReLU) as activation functions and includes two dense layers. This part
of the network bottlenecks into the two-dimensional variational layer,
represented by units z
1
and z
2
, which span the latent space. The encoder
applies a nonlinear transformation to map the functional connectivity
matrices (Cij) into Gaussian probability distributions in the latent space.
Conversely, the decoder network mirrors the encoder architecture and
reconstructs matrices Cij from samples of these distributions.
The VAE is trained using error backpropagation via gradient descent to
minimise a loss function consisting of two terms. The first term is a standard
reconstruction error computed from the units in the output layer of the
decoder. The second term is a regularisation term measured as the Kullback-
Leibler divergence between the distribution in latent space and a standard
Gaussian distribution. This regularisation term ensures continuity and
completeness in the latent space, ensuring that similar values are decoded
into similar outputs and that these outputs represent meaningful combi-
nations of the encoded inputs.
For training the VAE model, we generated 9000 correlation matrices
(Cij) corresponding to healthy control, UWS and MCS conditions. The
model’s hyperparameters were optimised using a training set, which was
created by randomly splitting the dataset into 80% training and 20% test sets.
The training procedure involved using batches with 256 samples and 50
training epochs, with the Adam optimiser and the loss function described in
the previous paragraph.
Statistics and reproducibility
Effect size to compare model simulations were calculated using Cohen’sd.
Perturbational effects in the latent space were evaluated using Pearson
correlation, quantifying the linear relationship between variables. A Wil-
coxon signed rank test was used in Supplementary Fig. 3.
Data availability
Source data to reproduce figures is available on Figshare (https://doi.org/10.
6084/m9.figshare.26728804)73 along with the code (See Code availability).
The disorder of consciousness datasets contain information from a clinical
population and are not publicly available due to constraints imposed by the
approved ethics protocol. Data can be shared upon request to the authors.
Code availability
All code is publicly available in https://doi.org/10.5281/zenodo.1333034974.
Received: 31 January 2024; Accepted: 5 September 2024;
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Acknowledgements
The authors express gratitude to all the individuals who participated in the
studies. Additionally, we extend our thanks to the dedication and support
provided by the clinicians at the Neuro ICU, DMU Neurosciences, APHP
SorbonneUniversité, Hôpitalde la Pitié Salpêtrière,Paris, France. Moreover,
we acknowledge the invaluable contributions of patient families whose
consent and understanding significantly contribute to the advancement of
the field. We finally thank the financial support of the FLAG-ERA research
funding organisation (project ModelDXConsciousness). Y.S.P.is supported
by European Union’s Horizon 2020 research and innovation programme
under the Marie Sklodowska-Curie grant 896354, and ‘ERDF A way of
making Europe’, ERDF, EU,Project NEurological MEchanismSof Injury, and
Sleep-like cellular dynamics (NEMESIS; ref. 101071900) funded by the EU
ERC SynergyHorizon Europe.M.L.K. is supported bythe Center for Music in
the Brain, funded by the Danish National Research Foundation (DNRF117),
and Centre for Eudaimonia and Human Flourishing at Linacre College fun-
ded by the Pettit and Carlsberg Foundations. ET is supported by grants
FONCYT-PICT (2019-02294), CONICET-PIP (11220210100800CO), and
ANID/FONDECYT Regular(1220995). O.G. is researchassociate and N.A. is
research fellow at FNRS. G.D. is supported by grant no. PID2022-
136216NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by
‘ERDF A way of making Europe’, ERDF, EU, Project NEurological
MEchanismS of Injury, and Sleep-like cellular dynamics (NEMESIS; ref.
101071900) funded by the EU ERC Synergy Horizon Europe, and AGAUR
research support grant (ref. 2021 SGR 00917) funded by the Department of
Research and Universities of the Generalitat of Catalunya.
Author contributions
Mindlin I: Conceptualisation, Methodology, Software, Formal analysis,
Investigation, Writing—Original Draft, Visualisation. Herzog R: Software,
Conceptualisation, Writing—Review & Editing. Belloli L: Conceptualisation,
Writing—Review & Editing. Manasova D Software, Conceptualisation,
Writing—Review & Editing, Monge-Asensio M: Software, Resources, Writ-
ing - Review & Editing, Vohryzek J: Resources, Writing - Review & Editing.
Anira Escrichs: Resources, Writing—Review & Editing. Alnagger N: Writing
—Review& Editing. Núñez NovoP: Writing—Review & Editing. GosseriesO:
Writing—Review & Editing, Morten L. Kringelbach: Writing—Review &
Editing. Deco G: Conceptualisation, Writing—Review & Editing. Taglia-
zucchi E: Conceptualisation, Writing—Review & Editing, Naccache L:
Resources, Writing—Review & Editing. Rohaut B: Resources, Writing—
Review & Editing. Sitt*JD: Supervision, Conceptualisation, Project Admin-
istration, Funding Acquisition, Writing—Review & Editing. Sanz Perl*Y
Supervision, Methodology, Software, Conceptualisation, Project Adminis-
tration, Writing—Review & Editing.
Competing interests
The authors declare to have no conflict of interest. E.T. is an Editorial Board
Member for Communications Biology, but was not involved in the editorial
review of, nor the decision to publish this article.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s42003-024-06852-9.
Correspondence and requests for materials should be addressed to
I. Mindlin, J. D. Sitt or Y. Sanz Perl.
Peer review information Communications Biology thanks Amy Kuceyeski
and the other, anonymous, reviewer(s) for their contribution to the peer
review of this work. Primary Handling Editor: Manuel Breuer. A peer review
file is available.
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