Experimental indications of non-classical brain functions

Abstract

Recent proposals in quantum gravity have suggested that unknown systems can mediate entanglement between two known quantum systems, if the mediator itself is non-classical. This approach may be applicable to the brain, where speculations about quantum operations in consciousness and cognition have a long history. Proton spins of bulk water, which most likely interfere with any brain function, can act as the known quantum systems. If an unknown mediator exists, then NMR methods based on multiple quantum coherence (MQC) can act as an entanglement witness. However, there are doubts that today’s NMR signals can contain quantum correlations in general, and specifically in the brain environment. Here, we used a witness protocol based on zero quantum coherence (ZQC) where we minimized the classical signals to circumvent the NMR detection limits for quantum correlation. For short repetitive periods, we found evoked signals in most parts of the brain, whereby the temporal appearance resembled heartbeat-evoked potentials (HEPs). We found that those signals had no correlates with any classical NMR contrast. Similar to HEPs, the evoked signal depended on conscious awareness. Consciousness-related or electrophysiological signals are unknown in NMR. Remarkably, these signals only appeared if the local properties of the magnetization were reduced. Our findings suggest that we may have witnessed entanglement mediated by consciousness-related brain functions. Those brain functions must then operate non-classically, which would mean that consciousness is non-classical.

Full text

J. Phys. Commun. 6(2022)105001 https://doi.org/10.1088/2399-6528/ac94be
PAPER
Experimental indications of non-classical brain functions
Christian Matthias Kerskens and David López Pérez
1
Trinity College Institute of Neuroscience, Trinity College Dublin, The University of Dublin, Dublin, Ireland
1
Present address: Institute of Psychology, Polish Academy of Sciences; Jaracza 1, 00-378 Warsaw, Poland.
E-mail: kerskenc@tcd.ie
Keywords: entanglement witness, brain, non-classicality, MRI, zero quantum coherence
Abstract
Recent proposals in quantum gravity have suggested that unknown systems can mediate entanglement
between two known quantum systems, if the mediator itself is non-classical. This approach may be
applicable to the brain, where speculations about quantum operations in consciousness and cognition
have a long history. Proton spins of bulk water, which most likely interfere with any brain function,
can act as the known quantum systems. If an unknown mediator exists, then NMR methods based on
multiple quantum coherence (MQC)can act as an entanglement witness. However, there are doubts
that today’s NMR signals can contain quantum correlations in general, and specifically in the brain
environment. Here, we used a witness protocol based on zero quantum coherence (ZQC)where we
minimized the classical signals to circumvent the NMR detection limits for quantum correlation. For
short repetitive periods, we found evoked signals in most parts of the brain, whereby the temporal
appearance resembled heartbeat-evoked potentials (HEPs). We found that those signals had no
correlates with any classical NMR contrast. Similar to HEPs, the evoked signal depended on conscious
awareness. Consciousness-related or electrophysiological signals are unknown in NMR. Remarkably,
these signals only appeared if the local properties of the magnetization were reduced. Our findings
suggest that we may have witnessed entanglement mediated by consciousness-related brain functions.
Those brain functions must then operate non-classically, which would mean that consciousness is
non-classical.
1. Introduction
Quantum mechanisms are at work in sensory systems feeding the brain with information [1–3]. Foremost in
magneto-reception [4], there is no doubt that only quantum mechanical effects can explain its sensitivity [3].It
has been suggested that entangled radical electron pairs are involved.
Beyond those sensory inputs, more complex brain functionalities depend on the presence of specific nuclear
spins. For example, Lithium-6 isotopes with nuclear spin 1 increase activity of complex behaviour in contrast to
Lithium-7 isotopes with 3/2 spin where it decreases [5]. Similar, Xenon isotopes with 1/2 spin are effective
anaesthetizers in contrast to Xenon isotopes with spin 0 which have only little effects [6]. However, nuclear spins
can, like electron spins, influence chemical reactions [7], which then lead to macroscopic results as commonly
observed in physiology. Whether those, or other macroscopic systems in the brain can be non-classical, is still
unknown. Experimental methods, which could distinguish classical from quantum correlations in the living
brain, haven’t yet been established.
In this respect, recent proposals in quantum gravity [8,9]may help to overcome experimental restrictions in
living systems. Those proposals use auxiliary quantum systems, for which they showed that if a system can
mediate entanglement between auxiliary quantum systems, then the mediator itself is non-classical. If a cerebral
mediator of this kind exists, then it is likely that the entanglement plays an important role in the brain. Although,
quantum computing can be achieved without entanglement [10], it is commonly believed that entanglement is
essential to play out its full advantages [10]. Therefore, it is likely that entanglement, if mediated by any brain
function at all, may only occur during brain activity. Hence, the experimental demands on an auxiliary quantum
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system are that they can be measured non-invasively in the conscious-aware brain, and further that
entanglement can be witnessed.
NMR offers a non-invasive approach. The nuclear spins are quantum systems which could, in theory, be
entangled by a cerebral mediator. NMR sequences based on multiple quantum coherence (MQC)can also
witness entanglement [11]. The MQC entanglement witness relies on bounds which, for applications in biology,
may be based on the maxim um classical signal achievable. The maxim um classical MQC signal in fluids have
been estimated based on the intermolecular MQC (iMQC)approach [12]. The iMQC signal, despite the naming,
is an entirely classical signal because it can also be the classically derived [13], which is known as multiple spin
echo (MSE)[14,15]. Therefore, it can be used as the classical bound.
Further, an exclusion of classicality can also be argued on the following basis. A single quantum coherence
(SQC)which is weighted by
()
*
T
1,2
relaxation or diffusion contrast may respond similarly to physiological changes
as the iMQC contrast, which is caused by dipole-dipole interaction (like
()
*
T
1,2
)relaxation or rotational symmetry
breaking (similar to diffusion)[16–19]. Hence, a signal change in a MQC sequence with no corresponding
diffusion or
*
T
2
-weighted SQC signal is most likely non-classical. In contrast, classical SQC and classical MQC
signals should have a common subset.
With this knowledge at hand, we can now search for situations in which witnessing entanglement may be
possible. As mentioned before, brain activity, or more concretely brain computation, may play a crucial role in
the creation of cerebral entanglement. Hence, we can make additional observations specific to the brain. We
propose the following conditions:
(1)Sufficient condition for witness—It has been shown that direct mapping of brain activity, which is directly
related to electrophysiology, isn’t possible with SQC techniques [20,21]. Therefore, MQC signals
corresponding to electrophysiological events, which are not accompanied by secondary events causing a SQC
signal, have no common subsets with a SQC related component. Hence, those MQC signals are most likely
non-classical and therefore sufficient to witness entanglement.
(2)Necessary condition for witness—The brain can operate without any external magnetic fields, which means
that, without a brain function at work, all states are initially mixed. Hence, the assumed brain function
producing entanglement, must use a kind of quantum distillation process [22]on mixed states [23].
Therefore, we conclude that the NMR signal must initially be saturated. The following two arguments
underpin the importance of saturation for the detection further. The unusual omission of (pseudo-)pure
states on which the MR signal is normally constituted, circumnavigates the major problem that entanglement
of pure spins, which are in close proximity, is highly unlikely [24]. Further, the saturation of pure local states
may serve the existence of non-localities because local and non-local properties can be complimen-
tary [25,26].
Now, we are in the position to address the question whether the brain can mediate entanglement,
experimentally. Based on the above considerations, we explored if the conscious-aware brain may use
entanglement during computing. As indicators of brain computation, we focussed on electrophysiological brain
waves, which can be observed in the conscious-aware brain at rest. We acquired MRI time series which were
highly saturated and which were able to detect zero quantum coherence (ZQC ). Based on the maximal temporal
resolution of our method (<5Hz), we focussed on Heartbeat Evoked Potentials (HEPs)[27], which like other
electrophysiological signals are far below the detection threshold of conventional MRI sequences [20,21].
2. Results
We used the echo planar imaging (EPI)time series (as described in section 3)in human volunteers at rest. The
beginning of the sequential RF-pulses train of the EPI time series were used to saturate the magnetization of the
imaging slice. The desired reductions of the local NMR component were normally reached shortly before the
equilibrium magnetization. Then, we found regular, repeating signal bursts of predominant signal alternations
in single volumes of the brain slices as shown in figure 1, where the signal peaks of the bursts increased by up to
15%. In most cases, the alteration was sequential from one image acquisition to the next.
In the following, we will focus on the NMR contrast mechanism of the signal first, and then how it related to
physiology and mind.
2.1. NMR contrast
The burst signal alternated during burst, which confirmed that at least two RF pulses were necessary to generate
the signal. The two RF-pulses always enwrap an asymmetrical gradient interval G
a
T
a
(figure 2), which is the basic
pulse design to measure ZQC.
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J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

The consequential long-range ZQC contrast was verified further by altering sequence parameters.
For rotating the asymmetric gradients G
a
, we found the characteristic angulation dependency of the dipole-
dipole interaction as shown (figure 3(A)). The plot represents the fitted function
·∣( · [ ] )∣j-+
mc
3cos 1
2
(adjusted R
2
test of goodness-of-fit resulted in R
2
=0.9958)where jtakes the additional gradients in read and
phase direction into account, and m=3.51 is the signal magnitude. At the magic angle, the burst signals reach
the noise level at c=0.81.
For the flip angle variation, we found the predicted signal course for the ZQC flip angle dependency [28]
which was fitted to the data (R
2
=0.9964). Predicted maximum at 45°could be confirmed (figure 3(B)).In
contrast, the Ernst-angle [29]which is a good indication for the optimum angle for SQC is around 13°(for
T
1
=1.5 s).
For the alteration of the off-resonance frequency, we found a typical magnetization transfer contrast (MTC)
change for the baseline, which depended on the off-resonance frequency (figure 3(C)). In contrast, the signal
intensity showed the remarkable immunity to MTC as expected for ZQC [30]with no significant changes in the
same frequency range (figure 3(D)).
The effects of the competing effects, the build up of the ZQC on the one hand and de-phasing over time on
the other hand, were studied varying the TR. We found that from 38 ms onwards the signals showed no growth
of ZQC. The free induction dominated.
Finally, we varied the slice thickness to study Time-of-flight effects. We found no significant influence on the
relative signal.
Figure 1. MRI signal time course (Black)during 12 heart cycles compared with simultaneous oximeter reading of a finger (Grey).
Figure 2. Radio frequency (RF)and Gradient scheme of two consecutive EPI acquisition. The ‘asymmetry’field includes all
asymmetric gradients involved in the ZSE.
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J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

2.2. Physiology and mind
The periods of signal bursts repeated with the same rate as the heart-beat. We used three temporal reference
systems; (a)afinger pulse oximetry, (b)an electrocardiogram (ECG), and (c)the time-of-flight signal of a voxel
placed in the superior sagittal sinus. The signal bursts appeared with the pulse from the finger pulse oximetry
(figure 1). In relation to the ECG, we found using the Cross-Recurrence Quantification Analysis that the
maximum burst signal was delayed by 0.3s on average. With the start of the venous outflow, the bursts always
ended as shown in figure 4and figure A1.
Regarding the duration of the bursts under normal conditions, we mostly observed two sequential peaks
which equal led 4 TRs adding up to a period of 180 ms. We also saw longer periods building up to 10 TRs (see
figure 4(B)) extending the period to 450 ms.
We located the bursts in brain tissue of all slices except around the periventricular area (probably due to
movement induced by ventricular pulsation in those regions [31])as illustrated in figure A2.
The global aspect conformed with another interesting feature; the signal could be restored while being averaged over
the entire tissue component of the imaging slice (figure 1and figure 4B,singlevoxeltimecourseareshowninfigure A3).
We also found that the signal did not respond to the CO
2
challenge (figure 4(B)) in contrast to the SQC signal
from the voxel including the superior sagittal sinus (figure 4(A)) which indicated the blood flow response.
During our studies, we also realized that the signal depended on awareness and awakening. In seven participants,
from whom two had reported to have fallen asleep, we found that the signal pattern declined as shown in figure 5.For
the final data acquisition, all participants had been asked to stay awake during the imaging protocol. At this point, we
no longer detected a sleep pattern. In a case study, we observed the pattern change overa period of 20 minutes which
showed a gradual transition from awake to asleep as shown in the appendix at figure A4.
We used Recurrence Quantification Analysis and Multifractal Detrended Fluctuation Analysis to illustrate
the difference between wakefulness and the slow decline during the falling asleep period. The analysis shows that
periodicity, large and small fluctuations, repeating patterns and their predictability, and the stability of the
system were changing over the observation period (figure A5).
Figure 3. Variation of sequence parameters. Data shows signal averaged over 5 subjects. Error bars represent the standard deviation
from the mean. (A)Signal intensity plotted against the slice gradient angulation αin respect to the magnetic main field. Black line
shows the fitted prediction. (B)Signal plotted against flip angle variation. ZQC prediction plotted (Black line).(C)Signal intensity
plotted against the frequency offset of the saturation slices of the BS and (D)averaged signal of the AMP. (E)Relative signal change
plotted against slice thickness. (F)Signal plotted against repetition time.
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J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

3. Methods
We studied 40 subjects (between 18 and 46 years old)using a 3 Tesla whole-body MRI scanner (Philips, The
Netherlands)which was operated with a 32-channel array receiver coil. Imaging protocols were approved by
Figure 4. (A)Signal time course of an imaging voxel located next to the superior sagittal sinus demonstrates the blood flow increase in
response to the CO
2
challenge (breath-holding). In contrast to the vein signal, the corresponding ZQC signals (B)showed no response
to CO
2
activity. Breath-holding started at 140s. Volunteers were instructed to reduce any movement as long as possible (here until at
157s). From 157s, the signal breakdown was subject to movement.
Figure 5. Pattern observed in participant who had reported falling asleep. (A)Wake period. (B)Asleep, ZQC burst signals declined
coincident with an increase of the S/N level. At 34 s, the peak resulted from short head movement.
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J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

Trinity College Dublin School of Medicine Research Ethics Committee. All participants of final data acquisition
were asked to stay awake and stay still during the imaging protocol, or to report any failure to do so.
Fast gradient-echo EPI (GE-EPI)time series were carried out, which had been optimized over a wide range
of participants. The finalized parameters were as follows: FA =45°,TR=45 ms, TE =5, voxel
size =3.5 ×3.5 ×3.5 mm, matrix size =64 ×64, SENSE factor =3, bandwidth readout direction =2148 Hz,
saturation pulse thickness/distance =5/20 mm. Two saturation pulses placed parallel to the imaging slice
(figure 2)were added, which allowed us to vary long-range correlation of the ZSE and MTC. Saturation gradients
had a time integral (length ×strength)of GT
s
=5.1 ms ×6.25 mT m
−1
, the crusher gradients in read and slice
direction of GT
c
=1.3 ms ×25 mT m
−1
, the slice rephase gradient of GT
r
=0.65 ms ×25 mT m
−1
, and the
slice termination gradient of GT
t
=0.65 ms ×15 mT m
−1
. Gradients timing and arrangements are shown in
figure 2. Gradients relevant for ZSE are shown in the asymmetry field and are marked with indices t, c, r, and s for
identification. We rotated the asymmetric gradients in respect to the magnet field starting from coronal 0°to
axial 90°in twelve steps; slice angulation αrelated to the angulation from the spin-spin interaction as
([ ] [ · ])
j
aa=- - + + =-

-
tan GT GT 2 GT GT GT 9.6
cr sct
1. Further, we varied the correlation
distance via altering the amplitude and the duration of the saturation gradients.
We also altered the following sequence parameters in pseudo-randomised orders:
(a)variation of the flip angle from 5°to 60°in steps of 5°(60°was the power limit by the specific absorption
rate (SAR)).
(b)the off-resonance frequency was varied as [2.62, 3.49, 4.36, 5.23, 6.11, 6.98, 7.84, 8.73, 9.60, 10.47, 12.22,
13.96, 15.71, 17.45]kHz.
(c)slice thickness from 3 mm to 7 mm in steps of 0.5 mm.
(d)repetition time (TR)varied from 38 ms to 73 ms in steps of 5 ms.
Further, we explored the signal distribution over the entire brain. 9 slices (in 5 volunteers)were acquired at
different positions, with slices from the bottom to the top covering all anatomical regions.
In a breath-holding challenge, four participants were asked to stop breathing for 20 s without taking a deep
breath. Body movements were reduced through multiple cushions immobilizing the head.
For the time reference analysis, we used Cross-Recurrence Quantification Analysis [32]to calculate the delay
between the R-wave in electrocardiogram (ECG)and the MRI signal. For the calculation, we used the CRP
Toolbox [33,34]for Matlab [35].
For the NMR contrast analysis, we used the averaged maximum peak of the burst and the signals between
bursts as baselines. Calculations were performed using the routine by Gomes et al [36]which was implemented
in Matlab [35]. Preprocessing included the following; Rescaling, which was applied to all data sets before any
analysis using the MR vendor’s instructions. Visual inspection of average time series to search for irregularities,
which were manually removed from the analysis, leaving the rest of the time series unaltered. Manual
segmentation was used to create a mask to remove cerebral spinal fluid (CSF)contributions. The first 100 of
1000 scans were removed to avoid signal saturation effects. The manual segmentation of the masks was eroded to
avoid partial volume effects at the edges.
For the analysis of sleeping pattern, we used a Recurrence Quantification Analysis and a Multifractal
Detrended Fluctuation Analysis (for detailed description see Lopez-Perez et al [37]). All data graphics were
created with Mathematica [38]. Data and source code for analysis are available online [39].
4. Discussion
The aim of this study was to find evidence that brain functions can create entanglement in auxiliary quantum
systems. Thereby, we employed a hybrid MRI sequence which could contain SQC and ZQC, simultaneously. We
found that the heart pulsation evoked NMR signal burst with every heartbeat. We were able to show in
section 2.1 that the signal contrast originated from spin-spin interactions. Therefore, we might have witnessed
quantum entanglement. However, NMR signals can be altered by many physiological changes. Ultimately, we
had to prove that the signal bursts were not a ‘classical’ZQC.
As mentioned above, classical ZQC have corresponding contrasts in SQC, namely T2
*
relaxation and
diffusion. Both contrasts alter during the heart cycle. However, T2
*
changes have shown a different temporal
(shifted by more than half of the cycle time in respect to the ZQC signal)and spatial response (higher signal at
blood vessel)[40]. The tissue response at around 2% is much lower than during functional activation. In
contrast, functional activations showed no significant changes in the ZQC burst signal and only minimal signal
increases at the baseline [41]. Therefore, we can conclude that classical dipole-dipole interactions are ineligible
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J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

as a signal source. Further, ZQC depends on order [42]and rotational symmetries [16,17]which can be probed
with diffusion MRI. The order may correlate with the apparent diffusion coefficient (ADC), while the fractional
anisotropy (FA)indicates the rotational symmetry breaking. In praxis, MQC signals are higher at decreased ADC
and increased FA. Nakamura et al [43]have shown that the temporal changes of the ADC-values are in phase
with the intracranial volume change, while FA-values show a shift by 180°. Our ZQC signals coincided with the
transition phase from the highest to the lowest ADC (and vice versa for the FA). From those results, we can
deduce that the theoretical optimum (ADC minimal, FA maximal)for a classical ZQC is outside the time
window of the ZQC bursts. We conclude that our observation has no corresponding SQC contrast.
Furthermore, the signals surpassed the classical bound by far. For ‘classical fluids’, the S/N of ZQC
compared to the conventional MRI signal (SQC)only reaches up to 0.05 at 4 Tesla, experimentally [44,45]. Our
sequence was suboptimal because we replaced a 90°by a 45°RF-pulse (reduction by factor 2), used a 3 Tesla
field, and the evolution time was shorter. Therefore, we can infer that in combination with the EPI readout, that
classical ZQC signals weren’t detectable with our sequence. Even more, in the above argument, we discussed
baseline signals. Our observations showed fluctuations which, if translated to a classical ZQC, would then be
several magnitudes higher than the actual baseline ZQC signal.
Although, we found that the evoked bursts disappeared at the magic angle which means they have no SQC
component, cardiac pulsation can cause flow and motion effects which we further investigated. We varied slice
thickness and TR as possible sequence parameters, which are sensitive to time-of-flight effects. For the slice
thickness, the relative signal did not vary significantly (Figure 3(E)), for the repetition time, we found the free
induction decay dominating the decline (figure 3(F)). Furthermore, when we varied the blood flow with the help
of a CO
2
-challenge (figure 4), we found no significant response of the burst signal amplitude. From the fact that
signal bursts have no significant SQC component (figure 3(A)at the magic angle), we can also exclude all SQC
contrast mechanisms including changes in T
1
and T
2
relaxation, line narrowing, or magnetic field shifts.
Above, we have established that conventional MR sequences, be it SQC or MQC, are unable to detect the
observed signal bursts. Further, we found that the signal amplitude is above the bound which could be classically
reached.
By now, it is clear that the evoked signals can only be observed if the necessary condition, that the
magnetization is highly saturated, is met. We also considered what we called the sufficient condition above. We
found that the timing of the signal bursts coincided to the first cluster of the HEP [46]. Like the timing, the signal
intensity also showed a similar dependence on conscious awareness in this time window [27,47]. In another
study, López Pérez et al [37]have shown that the complexity of burst signals correlate with psychological test
results in short-term memory. This relation is also known in HEPs. To our knowledge, both, the direct
correlation to conscious awareness and short-term memory, are unreported in classical MRI experiments. It
underpins that our findings are from the same origin as HEPs and that there is no classical correlate in MRI.
5. Conclusion
The aim of this study was to show that the brain is non-classical. We assumed that unknown brain functions
exist which can mediate entanglement between auxiliary quantum systems. The experimental detection of such
an entanglement created by the brain would then be sufficient to prove cerebral non-classicality. We found
experimental evidence that such entanglement creation occurs as part of physiological and cognitive processes.
We argued that the ZQC signals were non-local because (a)ZQC signals were above the classical bound, and (b)
the signals had no SQC and MQC
2
correlates. Further, we could confirm that the signals were only detectable in
combination with reduced classical signals (necessary condition), and that they resembled HEPs which are
below verifiability in conventional MRI (sufficient condition). Our findings may disapprove the statement that
quantum entanglement or coherence can’t survive in the hot and wet environment of the brain [48]. Beyond the
fundamental question we tried to answer here, we found an undiscovered NMR contrast, which can detect brain
activity beyond conventional functional MRI. It may have interesting applications in psychology and medicine.
Data availability statement
The data that support the findings of this study are openly available at the following URL:https://www.github.
com/Mirandeitor/Entanglementwitnessed-in-the-human-brain.
2
using the conventional MQC sequence design
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J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

Declarations
•Funding:
This research project was funded by Science Foundation Ireland from 2011-15 (SFI-11/RFP.1/NES/
3051)and supported by Trinity College Institute of Neuroscience.
•Conflict of interest/Competing interests:
Not applicable
•Ethical statement:
Research was conducted in accordance with the principles embodied in the Declaration of Helsinki; local
statutory requirements were approved by the Trinity College Dublin School of Medicine Research Ethics
Committee (20.02.2013).
•Consent to participate:
Informed consent was obtained from all individual participants included in the study.
•Consent for publication:
The authors affirm that human research participants provided informed consent for publication of
the data.
•Authors’contributions:
Christian Kerskens: conceptualization, methodology (physics), writing (original draft), supervision,
funding acquisition.
David López Pérez: methodology (analysis), software, acquisition of data, data curation.
Appendix. Extended data
Figure A1. Whole-slice averaged signal time course (black line)which was selected by a mask over 12 heart cycles. The signal of the
Superior sagittal sinus (grey line)as reference time frame demonstrates the instant breakdown of quantum coherence with the
beginning outflow.
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J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

Figure A2. 9 Anatomical slices which correspond to the positioning of the EPI time series. Tissue surrounded by reddrawing showed
no ZQC bursts.
Figure A3. 4×4 voxel matrix randomly picked. On the left, the red square shows location in the brain slice.On the right, 16
corresponding signal time courses displaying the local tissue responses over a time period of 24s.
9
J. Phys. Commun. 6(2022)105001 C Kerskens and D López Pérez

ORCID iDs
Christian Matthias Kerskens https://orcid.org/0000-0003-0823-4648
David López Pérez https://orcid.org/0000-0002-1235-6376
Figure A4. Case study: ZQC burst pattern observed in participant who had reported falling asleep. Starting point of time series at (A)
16:26:29 (B)16:29:47 (C)16:30:54 (D)16:34:13 (E)16:37:32 (F)16:40:49 (awake, subject communicated with radiographer before
scan).
Figure A5. Case study: Results of a Recurrence Quantication Analysis and a Multifractal Detrended Fluctuation Analysis using 20 time
periods a 45s over a total time period of 21 minutes. (a)Entropy (Ent)is computed as the Shannon entropy of the distribution of the
repeating pattern of the system. If a signal has high entropy it exhibits diversity in short and long duration periodicities. (b)–(c)The
multifractal spectrum identifies the deviations in fractal structure within time periods with large and small
fluctuations. (d)Determinism (DET)represents a measure that quantifies repeating patterns in a system and it is a measure of its
predictability. Regular, periodic signals, such as sine waves, will have higher DET values, while uncorrelated time series will cause low
DET. (e)Trapping Time (TT)represents the average time the system remains in a given state and it is a measure of the stability of the
system. (f)Laminarity (Lam)determines the frequency of transitions from one state to another, without describing the length of these
transition phases. It indexes the general level of persistence in some particular state of one of the time-series.
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