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\begin{document}

\title{draft}

\author{C K}
\affiliation{Institute of Neuroscience, Trinity College, Dublin, Ireland}

\author{David López Pérez}
\affiliation{Institute of Neuroscience, Trinity College, Dublin, Ireland}




\selectlanguage{english}
\begin{abstract}
For many years, it has been speculated that consciousness and cognition
could be the based on~quantum information ~(Atmanspacher 2015) which
opposes the view~ that~ quantum coherence, the primary basis of quantum
computing~(Nielsen 2010), cannot survive in complex biological
systems~(Koch 2006, Tegmark 2000). However, recent findings in
photosynthesis~(Engel 2007, Collini 2010)~ have challenged this view
suggesting that only long-range quantum coherence between molecules can
account for its efficiency in light-harvesting.~Here, we investigated if
long-range quantum coherence may also play a decisive role in brain
function. We found~ surprisingly that the cardiac pressure pulse~
evoked~ zero-quantum coherence (iZQC)~(Warren 1998) which were by a
magnitude higher than theoretically expected.~ From this finding, we
concluded that underlying physiological process is~ - cautiously
speaking - of an unknown macroscopic non-classical kind. The process
reveals it importance by it temporal appearance; during consciousness it
is highly synchronized with the cardiac pulse,~ while during sleep,~ no
or only sporadic~ iZQC could be detected. This findings suggest that
this non-classical phenomenon is most likely~a necessity for
consciousness.~%
\end{abstract}%



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\section* {Introduction}
MRI provides a non-invasive  way to detect   long-range intermolecular multiple-quantum coherence (iMQC) via dedicated multiple spin echo (MSE) sequences  \cite{225062:5039968,225062:5040922,225062:5067325}.
In the quantum mechanical formalism by Warren \unskip~\cite{225062:5067241,225062:5042514},  all dipolar-couplings are taken into account explicitly but only those contributions dominate which  retain the  classical formalism that was initially introduced to describe MSE \cite{Jeener_2000}. MSEs are highly sensitive to spherical  symmetries \unskip~\cite{225062:5067412,225062:5041128,225062:5067413,225062:5067414} and dipole angulation. 
 Despite the dipole field angulation, MSEs have always a similar signal contrast in single-quantum coherence (SQC), mainly because  short-range iMQC influences also SQC  via T$_1$ and T$_2$ relaxation. Otherwise, specialized sequences are available like  diffusion MRI sequences which are able to detect  broken spherical symmetry (restricted diffusion).
For the measurement of long-range dipole-dipole interactions,  asymmetric magnetic field gradients ( asymmetric integrated over time) are applied in combination with at least two radio-frequency (RF) pulses \cite{225062:5039968,225062:5040922,225062:5067325}. This situation is similar to fast repeated single-slice gradient-echo echo planar imaging (GE-EPI) series, where  so-called  crusher gradients (to dephase any SQC signal that remains from the previous excitation) are added between two acquisitions (see figure \ref{548938}).
Therefore,  every second image could contain SQC and iZQC components whereby  the ratio of the iZQC to SQC  only reaches up to 0.02 at 4 T  \cite{Warren_1998,Rizi_2000} which fits the theoretical expectation well. At 3 T and without an optimized sequence this ratio should be substantively lower, which means that the iZQC signal is negligible in fast imaging series due to low signal-to-noise provided that there are no exotic quantum effects.
In our experiments, we used a conventional GE-EPI series with a short repetition time (TR) and two additional saturation pulses. The saturation pulses were introduce to increase long-range correlation via the additional gradients by a factor of around 6. 
\section*{Results}
 With this sequence, we found predominate alternations with the cardiac frequency in brain tissue.  In each cardiac cycle, we observed a period which varied in length between 150 and 420 ms showing an alternating signal of up to 15 \%  as plotted in Figure~\ref{125409} and \ref{499388}A  to which we will refer in the following as zigzags.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/1.5-Kipp1/voxels}
\caption{{A 4x4 voxel matrix randomly picked. On the left,~the red square shows
location in the brain slice. On the right, 16 corresponding signal time
courses of 24 s displaying the local tissue responses.~
{\label{125409}}%
}}
\end{center}
\end{figure}



   The zigzags as shown in Figure~\ref{499388}A were achieved using additional cushions inside the coil and by breath-holding (without taking a deep breath). Breath-holding showed an immediate increase in zigzags (up to 4-5 peaks) but no delayed response to the PCO$_2$ challenge as we found  in the blood vessels (not shown here).   Under normal condition, the zigzags usually only contain two or three peaks as shown in Figure~\ref{499388}B (during the first 10 s from 50 s to 60 s).  At 60 s, the volunteer was instructed to hyperventilate with the result that the zigzags immediately disappeared.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/voxels1/46f9e35b-d4e8-407a-a0d4-9eef099b60c0-ufirstdata1-0}
\caption{{\textbf{A}: Whole-slice averaged signal time course (selected by a mask)
during 8 heart cycles. Subject had extra head fixation and was
instructed to breath-hold during the period. In contrast to signals in
the veins (not shown here), zigzag signal showed no response to CO2
activity other than an immediate lengthening of the zigzag.~\textbf{B}:
Whole-slice averaged signal time course during normal breathing first.
At 60 s, the subject was instructed to hyperventilate. The inlet shows
the total time course with 3 hyperventilation periods and the selected
time interval in red.~
{\label{499388}}%
}}
\end{center}
\end{figure}

We used an finger pulse oximeter and MRI data of the superior sagittal sinus to find reference time frames for the zigzag pattern. We found that the zigzags always appeared during the arterial inflow phase. The abrupt end of the zigzags were coincident with the end-phase of the arterial pulse as shown in Figure~\ref{372115}A and the rise of venous outflow as demonstrated in Figure~\ref{372115}B. 

~\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/6667ba2b-0928-41af-a422-5575405ed5a6-uzeitidenti-0/6667ba2b-0928-41af-a422-5575405ed5a6-uzeitidenti-0}
\caption{{Signal time course (Blue) during 12 heart cycles compared
with~\textbf{A}: Simultaneous oximeter reading of a finger (Red) and
\textbf{B}: Signal time course (Red) of a vein.
{\label{372115}}%
}}
\end{center}
\end{figure}



We located the zigzags in tissue over the entire brain tissue except in areas which are known to be prone to motion like the periventricular area \unskip~\cite{225062:5067666} as shown in Figure~\ref{187392}.  Regions like skull, ventricle etc and in the attached test tubes showed no zigzags. Otherwise, we found that the zigzag, including the sudden end, could be restored while being averaged over the whole imaging slice Figure~\ref{499388}A.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Darkregion/Darkregion}
\caption{{Fourier-Transform of two representative voxel. Surrounded tissue (red
drawing) on the left shows signal dependency as shown in the bottom
plot.
{\label{187392}}%
}}
\end{center}
\end{figure}

For investigation of the underlying contrast mechanism, we varied the following sequence parameters using the averaged signal: (a) the slice angulation, (b) the off-resonance frequency of the saturation pulses, (c) the flip angle (FA) with saturation pulses, and (d) the flip angle (FA) without saturation pulses.\\ For (a), we found the angle dependency of the demagnetization field as shown in Figure~\ref{211018}A where $\varphi$ is the angle between the slice gradient and the main magnet field. The plot represents the fitted function $\vert(3\cdot cos^2\lbrack\varphi_{cor}\rbrack-1)\vert $ where $\varphi_{cor} $ takes additional gradients in read direction into account. Adjusted R$^2$ test of goodness-of-fit resulted in R$^2$=0.9958.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/1d67bef1-3625-44e0-9c6a-f6a9b4b5da53-u3together1copy-0/1d67bef1-3625-44e0-9c6a-f6a9b4b5da53-u3together1copy-0}
\caption{{Variation of sequence parameters. Data shows signal averaged over 5
subjects. \textbf{} Error bars represent the standard deviation from the
mean. \textbf{A}: Signal intensity plotted against the slice gradient
angulation \(\varphi\) in respect to the magnetic main field.
~\textbf{B}: Signal intensity plotted against the frequency offset of
the saturation slices of the averaged baseline signal (left) and
averaged signal of cardiac pattern (right).~\textbf{C}: Whole-slice
averaged signal time course plotted against flip angle variation with
saturation pulses (Blue) and without (Grey). IZQC prediction plotted in
Red.
{\label{211018}}%
}}
\end{center}
\end{figure}

For (b), we found a typical magnetization transfer contrast (MTC) change for the baseline signal which depended on the off-resonance frequency (Figure~\ref{211018}B, left-hand side). In contrast, the zigzag intensity showed no significant changes in the same frequency range (Figure~\ref{211018}B, right-hand side). \\For (c), we found a maximum peak intensity at 45$^\circ$ (Figure~\ref{211018}C). It followed the predicted signal course for intermolecular Zero Quantum Coherence (iZQC) \unskip~\cite{225062:5277829} in a range from 20$^\circ$ to 60$^\circ$ (R$^2$=0.9964).\\ For (d), we could extend our observation to 90$^\circ$ where we found a flat plateau following an initial signal increase.  In comparison, with (c) the signal was lower from 25$^\circ$ onward as shown in Figure~\ref{211018}C.
\section*{Discussion}
We found alternating signals (zigzags) which showed, when the saturation pulses were applied,  the remarkable immunity of  iZQC to MTC \unskip~\cite{225062:5277825} and the specific   flip angle dependency of iZQC with a maximum at 45$^\circ$ \unskip~\cite{225062:5277829}. Without the saturation pulses, we found a mixture of  quantum orders which explains the destructive coherences (signal plateau from 30$^\circ$ onward) \unskip~\cite{225062:5187628} dephasing the signal at higher flip angle.\\ 
The  angle dependency in Figure~\ref{211018}A  verified the MSE origin of the signal. From neglectable signal intensity at the magic angle, we could exclude SSEs as signal contrast. The missing SSE components rule out that the signal was generated by flow or movement, relaxation (including $T_2^*$-variation by blood oxygenation changes), field inhomogeneities or other multiple RF effects like stimulated echos.\\
Nevertheless, we investigated further if either flow or movement, the most reasonable signal sources due to the pulsative character, may have generated the signals. We could exclude  movement because on the one hand  increased  movement destroyed the zigzag as demonstrated in the hyperventilation challenge, while on the other hand  breath-holding, which reduced body movement, resulted in an immediate lengthening of the signal response. From the same experiment, we could exclude flow dependency because 
the zigzag did not respond to the CO$_{2}$ challenge, despite the fact, that we observed increased blood flow in major blood vessels (data not shown here). In a fMRI study \unskip~\cite{Kumar1994a}, we could confirm  further that local blood flow changes during visual activation left  the MSEs undisturbed.\\
%
Finally, we can underpin the above arguments by the spatial and temporal distribution.The remarkable high synchronization of symmetry breaking over the entire brain, which is reflected by the fact that the zigzag is recoverable in the averaged signal time courses, demonstrates that effective circulation is a global matter. As such, it is unlikely that a global sudden change (the spontaneous symmetry breaking evolves extremely fast in just few milliseconds) can be overlooked with SSE or other non-MRI methods, if detectable. To our knowledge, similar observations have not been made yet which single out symmetry breaking as contrast mechanism.\\
In respect of brain dynamics, the timing of the zigzags during the arterial pulsation  is consistent with the concept of the illusive brain wave \cite{Kerskens2018} where the key mechanism of the reverse energy flow, the spontaneous mirror-symmetry breaking, falls together with the arterial pulse.  Interestingly, we found that the zigzags decline in healthy aging and disappears completely with cognitive impairment\unskip~\cite{225062:5289252}.
%Indeed, from the temporal character of signal it follows that the broken symmetry had a physiological origin which we could only locate in  tissue.\\ 




    % Blood flow in healthy blood vessels is commonly considered to be laminar. Nevertheless, cerebral dynamics of the entire brain, where inter- and intracellular flows are included, may not meet the criteria for laminar flow.  In order to examine this further, let us use the following example; imagine water traveling as laminar flow inside an artery at high speed, the freely diffusible water molecules transiting randomly through the vessel wall into the tissue. As this occurs, it loses its layered flow pattern. In addition, the abrupt change of velocity during this transition enforces turbulent behavior. desired inverse cascades which are always accompanied by decaying cascades at larger scale (arterial pulsation). A reverse outflow must existsIn contrast to the vessel system, tissue in- and outflow share space and enviroment. because the return flow to venous system undergoes an inverse velocity change from slow to fast. In turbulent systems, this reverse mechanism must entail back- ward energy cascades to larger scales (inverse cascades). Separation in time explaininviscid \unskip~\cite{225062:5288437}.  What actually happens is that cerebral pulsation decays from large scales (arteries) to small scales (capillaries, tissue) (2, 3) in a heartbeat. The paradox reverse outflow which starts from small scales towards the veins (4) may then only be real- ized by backward energy cascades, so-called inverse cascades (5). The result  is cardiac pulse wave  which, after arrival in the brain, seems to travel effortlessly from the arterial into the venous system without any delay. despite the fact that arterial and venous system are not directly connected (3).
     
    
    


    
\section*
  {Methods}
40 subjects (between 18 and 46 years old) were scanned in a 3.0 T Philips whole-body MRI scanner (Philips, The Netherlands) operated with a 32-channel array receiver coil. Imaging protocols using standard single-shot GE EPI sequence were approved by the Trinity College School of Medicine Research Ethics Committee. \\
In our  consecutive EPI time series, only even-numbered readouts contained  MSEs (whereby counting begins one readout before the broken symmetry occurs). The asymmetric gradient field (Figure \ref{548938}), which are before the even-numbered slice-selection RF-pulses,  generated then zero quantum orders\unskip~\cite{225062:5289250}.\\
Initial experiments were carried out to establish a protocol that could deliver stable cardiac related signals over a range of subjects. Initially, test tubes with a water solution (1000 ml demineralized water contained 770 mg CuSO\ensuremath{_{4}}5H\ensuremath{_{2}}O, 1 ml Arquad (AkzoNobel), 0.15 ml H\ensuremath{_{2}}SO\ensuremath{_{4}}-(0.1 N)) were positioned close to the head for reference signals.  The finalized parameters of the GE-EPI sequence were as follows: FA = 45$^\circ$, TR = 45 ms and the TE = 5 ms with a voxel size was 3.5 x 3.5 x 3.5 mm, matrix size was 64x64, SENSE factor 3, bandwidth readout direction was 2148 Hz.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/0e84b25d-0979-4bf0-8dbf-1ca42c7da583-ugradientsimages2-0/0e84b25d-0979-4bf0-8dbf-1ca42c7da583-ugradientsimages2-0}
\caption{{Gradient scheme of the EPI sequence with two saturation pulse.
{\label{548938}}%
}}
\end{center}
\end{figure}



Figure~\ref{548938} shows the gradient scheme. Saturation gradients had a time integral (length x strength) of Gt$_{sat} = $ 5.1 ms x 6.25 mT/m, the crusher gradients in read and slice direction of  Gt$_{cru} = $ 1.3 ms x 25 mT/m, the slice rephase gradient of Gt$_{sr} = $ 0.65 ms x 25 mT/m, the slice termination gradient of Gt$_{st} = $ 0.65 ms x 15 mT/m, and the total read dephase after EPI readout gradient of Gt$_{rt} =$ 0.65 ms x 22.5 mT/m. The angle between magnet field and gradient field was then 
\begin{eqnarray*}\begin{array}{l}\varphi_{cor}=\varphi-\tan^{-1}\left[\frac{\textnormal{Gt}_{cru}-\textnormal{Gt}_{rt}}{2 \textnormal{Gt}_{sat}+\textnormal{Gt}_{cru}+\textnormal{Gt}_{st}}\right]=\varphi-\textnormal{9.6}^\circ\end{array}\end{eqnarray*}
where $\varphi $ is the slice angulation. The imaging slice was set coronal above the ventricle. In addition, two saturation slices of 5 mm (15mm above and 20mm below) in thickness were placed parallel to the imaged slice. The following alternation (each with 1000 repetitions in five participants) were carried out, (a) slice angulation starting from coronal 0$^\circ$ to axial 90$^\circ $in the steps as [0, 10, 20, 30, 40, 45, 50, 55, 60, 65, 70, 80, 90], (b) the distance of the REST slabs were varied between 0.8 mm and 50 mm to alter the off-resonance frequency. The off-resonance frequencies were [2.62, 3.49, 4.36, 5.23, 6.11, 6.98, 7.84, 8.73, 9.60, 10.47, 12.22, 13.96, 15.71, 17.45] kHz, (c) Flip angle was varied for the case with saturation pulses from 5$^\circ $ to 60$^\circ $ in steps of 5$^\circ $(60$^\circ $was the power limit by the specific absorption rate (SAR)) and without saturation pulses from 5$^\circ $to 90$^\circ$ in steps of 5$^\circ$, (d) 9 slices were acquired at different positions, with each slice matching from bottom to the top the position of those acquired in the anatomical scan. In four participants, we examined the motion sensitivity where we immobilized the head with multiple cushions. During indicated intervals the subjects were asked to stop breathing for 20 s or to hyperventilate for 40 s. Finally, anatomical MRI images in all studies included a high-resolution sagittal, T1-weighted MP-RAGE (TR = 2.1 s, TE = 3.93 ms, flip angle = 7).\mbox{}\protect\newline Data were processed with Matlab 2014a (http://www.mathworks.co.uk/). Rescaling was applied to all data sets before any analysis using the MR vendor's instructions. Average time series were visually inspected in 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 scans were removed to avoid signal saturation effects. The manual segmentation of the masks was eroded to avoid partial volume effects at the edges. The cardiac signal and baseline detection was based on the method proposed in Gomes and Pereira\unskip~\cite{225062:5042988}.  Final data presentation was carried with Mathematica (Wolfram Research, Champaign, Illinois). 
       
\section*
  {Authors' contributions}
D.L.P. and C.K. performed initial experiments, D.L.P. performed validation experiments and analyzed the data, C.K. designed the research and wrote the paper.
\section*{Acknowledgments}We would like to thank S. Joseph for carrying out the imaging protocols for our participants, R. Fallon for reading the manuscript, and Science Foundation Ireland for supporting D.L.P. from 2011-2015 (SFI-11/RFP.1/NES/3051).

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