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. 