NeuroImage 62 (2012) 693–698

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NeuroImage

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Review

Functional spectroscopy to no-gradient fMRI

Jürgen Hennig ⁎University Medical Center, Dept.of Radiology, Medical Physics, Breisacherst.60a, 79106 Freiburg, Germany

⁎ Fax: +49 761 27038310.E-mail address: juergen.hennig@uniklinik-freiburg.d

1053-8119/$ – see front matter © 2011 Elsevier Inc. Alldoi:10.1016/j.neuroimage.2011.09.060

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 23 September 2011Available online 1 October 2011

Keywords:Functional spectroscopyInitial dipMR-encephalography

The article embraces two periods in the history of fMRI starting with our early work on functional spectros-copy leading to the detection of the ominous initial dip and our recent development of gradient-less imagingbased on the principles of MR-encephalography (MREG). In addition to presenting examples from these twoperiods the article tries to convey the spirit and inspiration behind these developments.

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Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693Early days: functional spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693Now: MR-encephalography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698

Introduction

This article embraces the history of fMRI from the early days whenwe in our (then rather small) research group tried to elucidate the na-ture of the BOLD-effect by observing the free induction decay of thewater signal during activation to our recent work on ultrafast fMRIbased on the concepts of MR-encephalography. These developmentsare separated by more than 20 years, so not surprisingly there arehuge differences in terms of the equipment and performance be-tween then and now. A single voxel measurement based on a200 ms readout of a single FID and a full brain 3D-acquisition(64×64×64) at 10–20 Hz frame rate seem to be extremely farapart. Both developments were motivated by curiosity to figure out,what the MR-signal can tell about the physiological processes under-lying neuronal activity and what we can learn from reading the MR-signal about the ‘brain at work’.

Early days: functional spectroscopy

When fMRI came around and Ken Kwong et al. (1992) demon-strated, that EPI is the way to do it, I (well, my University) was inproud possession of a 2T scanner (Bruker MedSpec) with a non-shielded gradient system with 16 mT/m amplitude at 1 ms risetime,so EPI was beyond our capabilities. Intrigued by the early reportswe spontaneously formed a fMRI-team initially consisting of myselfand Thomas Ernst (now at University of Hawaii), later supplementedby Clemens Janz (who meanwhile became a teacher) and OliverSpeck (now at University Magdeburg). We implemented someFLASH-based fMRI to serve the interests of our neuroimaging part-ners, but our own interest was mainly piqued by our curiosity to elu-cidate the nature of the then rather elusive BOLD effect. The visionaryconcept developed by Seiji Ogawa et al. (1990) was based on theearly observation that cortical blood would become more oxygenatedduring functional activation by Fox and Raichle (1986). The exactmechanism and rationale behind the BOLD effect were not entirelyclear. In addition it became apparent pretty fast, that other effects ac-companying the measurement (Blood Flow Level Dependent (b-FOLD), CSF Oxygen Level Dependant (COLD), CSF Flow Level Depen-dant (c-FOLD) and especially motion Level Dependent (MOLD)(Hajnal J V, 1997)may confound the results and lead to erroneous (albeit

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interesting looking) results. The early results of the pioneers of BOLD-fMRI found an immediate and enthusiastic reception by the neurosci-ence community, part of which – due to lack of previous exposure toMRI –was rather naïvewith respect to the intricate signal characteristicsof BOLD-fMRI. Given the limited stability and sensitivity of the typicallyused 1.5T scanners, the limited understanding and correction for mo-tional effects as well as physiological noise, plus the fact, that readilyavailable software packages did not account for all intricacies of theBOLD-signal, the experimental basis of some of the more spectacular re-sults published at that time appeared to be somewhat shaky and itseemed a legitimate endeavor to look at the MR-signal at its roots(even at the risk of being regarded as spoil-sports).

The method we chose was a single-voxel PRESS-experiment,which allowed detailed observation of the effects of activation onthe water signal (Hennig et al., 1994). Spatial resolution (1–8 ml)and volume coverage (1 or 2 (Ernst and Hennig, 1991) voxels) werepoor, but this was compensated by the ability to directly distinguishthe signature of a T2*-related effect (like – but not only – the BOLD-effect) from other mechanisms. SNR of each measured FID was ex-tremely high (≫1000:1), so we chose a TR of 4–500 ms, whichleads to strong saturation effects due to the 180°-pulses used forvoxel selection, but leaves SNR still much higher than the temporalsignal fluctuations. With the ability for highly sensitive detection atvery high acquisition speed we hypothesized whether we would be

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Fig.1. Sample FIDs from a single voxel functional spectroscopy experiment performed withand 10,000 ms (c) after the onset of the stimulus, illustrating the different mechanisms of thFrom Hennig et al. (1995), Fig. 2.

able to observe some more immediate reaction to a stimulus preced-ing the rather slow BOLD-effect. This led to the observation of a tri-phasic response consisting of a small initial dip followed by theproper BOLD-response followed by a POST-BOLD undershoot(Fig. 1) (Ernst and Hennig, 1994). The latter was observed to persistfor about 1 min even after a very brief stimulus. It is worthwhile tokeep in mind, that any of the numerous fMRI-experiments performedso far is performed in a non-equilibrium, dynamic state at least withrespect to this undershoot. The notorious initial dip was observed asa very small and elusive early negative signal change occurring at~400–1200 ms preceding the BOLD-increase. The amplitude of the ef-fect was rather small (b0.2%) but significant (Fig. 1c). The effect wasalso reported by Menon et al. (1995) using standard EPI. In a furtherset of experiments we could demonstrate that this early responsedoes not show the typical signature of a BOLD-effect, but materializesas an apparent change in signal amplitude (Janz et al., 2001a, 2001b).In the discussion of this finding we suggested a number of possiblemechanisms related either to early changes in blood flow or othermechanisms like neuronal swelling (Janz et al., 2001a, 2001b) and/ora change in membrane associated water (Hennig et al., 1995), whichare known to occur upon depolarization of the cellular membraneand which have recently found new interest (Le Bihan et al., 2006).

The nature of the ‘initial dip’ still remains somewhat mysterious.In our experimental setup, a triphasic response was consistently

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TR of 400 ms. FIDs represent difference signals to baseline at 400 ms (a), 4400 ms (b),e observed effects. All signals are scaled to the FID immediately preceding the stimulus.

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observed even in experiments dedicated to other tasks, which givessome confidence that this is not just an artifact.

In EPI-based BOLD-imaging its observation seems to remain rathersporadic, so it appears that there must be differences related to theexperimental procedure used. Given the fact that ‘our’ early dipshows up as an amplitude change rather than a BOLD-effect theexpected signal change at typical echo times used for BOLD-fMRIhas decreased to ~0.1%, which would be very difficult to observe.On the other hand our measurements were performed on ratherlarge volume elements (8 ml). If the effect is caused only by a smallportion within the activated region, it should be amplified in the per-tinent voxels if observed at higher spatial resolution. The use of 180°pulses for voxel selection by formation of a dual echo induces varioussignal mechanisms (magnetization transfer, inversion/ saturation ofinflowing spins, flow attenuation, diffusion/ capillary flow in inhomo-geneous local fields…), which may contribute to the observed subtledifferences. With PRESS-preparation inflowing spins will have experi-enced at least one inversion pulse except for the ones coming inthrough the corners of the selected cube. Therefore early onset of per-fusion may explain an initial negative signal. Fast inflow will also leadto a rapid change CBV. Provided that PRESS is more sensitive to thetissue compartment due to flow dependent dephasing of the vascularsignal, this could also contribute to an early negative signal in addi-tion to the mechanisms discussed above.

The initial dip reported in EPI-based BOLD-fMRI has been mostlyattributed to a T2*-effect (Yacoub et al., 1999). It also differs from‘our’ effect with respect to timing and amplitude. Given the multipledifferences in signal formation it is hard to pinpoint the primarysource of the effect and the cause of the differences of measurementsbetween our experiments and EPI-measurements. It should also benoted that given the rather complex physiological events going onin the tissue, more than one signal mechanism is expected to contrib-ute to the observed effect.

Since the effect is very small and therefore not to be expected tobe of practical use, interest to further look into it has eventuallyfaded away.

We continued to use functional spectroscopy to investigate thelinearity/nonlinearity of the triphasic response as a function of theinterstimulus delay (Janz et al., 2000, 2001a, 2001b). With improvedscanner performance and the possibility to perform quantitativestudies at high spatial resolution using multi-echo EPI – work pio-neered by Oliver Speck – our interests were direct toward othergoals, but this is another story.

Now: MR-encephalography

The idea to perform fMRI without gradients evolved in the finalstages of preparing the Mansfield lecture for ISMRM in Miami in2005 (Hennig, 2005). The Mansfield lecture had been implementedin 2004 (with Bob Edelman as first lecturer), so I was more than abit nervous to live up to this prestigious honor. The topic of my talkwas ‘Fast Imaging Horizons in Rapid MR Imaging’. I had prepared anescalating presentation starting on more modest improvements forimaging speed (parallel imaging, view sharing), going through morehighly accelerated techniques like VIPR (Gu et al., 2005) and under-sampled elliptical 3D-SENSE (Hu et al., 2004) toward more exotic ap-proaches like MAMBA (Lee et al., 2002) and SEA (McDougall andWright, 2005) and I was looking for some eye-catcher to illustratethe ultimate speed limit to finish off the presentation. Conceptuallythe challenge appears to be hopeless: gradients are necessary to getspatial information. Gradients translate the localization probleminto a task of discriminating frequencies. Signal theory closely linksthe frequency domain and the time domain, so without even thinkingabout MR-sequences, there seem to be fundamental limitations toimaging performance which cannot be overcome. This fundamentallimitation can only be overcome if one negates its basis i.e. the use

of gradients for spatial encoding. Having gone so far the ‘solution’seemed to be straightforward: Leave out the gradients and produceimages based on the small sensitive volumes of multi-array coilsalone. This enables data acquisition at a temporal resolution only lim-ited by the speed of the ADC — ‘imaging’ at MHz frame rate becomesfeasible by sampling the FID directly. Using a periodic stream of RF-pulses a continuous steady state signal can be generated at still kHzframe rates.

At that time I had an 8-channel head coil for initial experiments.Given the large sensitive volumes of each coil element I expectedthe steady state-signal from each coil to consist of a flat line withoutmuch temporal structure. When performing a first test experiment ona volunteer I was quite surprised to see that even at that crude spatialresolution the signals clearly showed periodic variations attributed tobreathing and ECG-related pulsatility, so this seemed to be more in-teresting than just an intellectual exercise. By similarity of the mea-surement principle to electrophysiological techniques (EEG, MEG) Icoined the term MR-encephalography (MREG) for applications tothe brain or OVOC (=one voxel one coil)-imaging for more generalapplications (Hennig et al., 2007). Compared to EEG and MEG the lo-calization of the signal source detected by each coil is actually morestraightforward. A reference image can be acquired for each coil, theacquired signal is then known to come from exactly that region andthere is no nasty and undefined inverse problem to be solved. Thecombination of the reference coil images weighted by the signals ac-quired at high temporal resolution allows to reconstruct images withhigh spatial resolution with an SNR and spatial resolution solely de-pendent on the reference image and independent of the acquisitionspeed. This somewhat counterintuitive finding was first noted byChuck Mistretta, who adapted and further developed this concept toradial acquisition in his HYPR-technique (Mistretta et al., 2006). Healso coined the term ‘Hennig limit’ for the generation of an imagefrom reference data weighted by ultimately only 1 measurementpoint, but the discussion is still open, whether this refers to animage produced from a single data point or from no data at all.

It took us quite a while to get this going. Kai Zhong traveled to Bos-ton, where Larry Wald helped him built a coil array for more mean-ingful experiments. This still had only 8 coils, but these were smallcoils which fit nicely around the visual cortex. First results demon-strated the extremely high sensitivity of this approach. First experi-ments were performed using a slice selection gradient only and/oradding a readout gradient, which can be applied without compromisein acquisition time. Higher spatial resolution can be achieved by usinga highly undersampled radial acquisition with 3–4 projections withreconstruction based on an inverse imaging approach and Tikhonovregularization developed by Thimo Grotz (now Thimo Hugger), aPhD-student who joined my lab in 2006. In reference to Chuck Mis-tretta's VIPR-technique we called our approach COBRA (Grotz et al.,2009).

Looking at the signal variation along the temporal domain inMREG-acquisitions it becomes immediately apparent, that temporalnoise is dependent on the signal intensity (Fig. 2). This signal behav-ior has been reported first by Biswal et al. (1996) and further elabo-rated by Kruger and Glover (2001) and is known as ‘physiologicalnoise’. As a side remark, it should be noted that although ECG-andbreathing related signal variations are a major source of this variation,signal dependant noise is also observed in phantom experiments as aresult of fluctuations caused by eddy currents, limited reproducibilityof the gradient amplifiers and RF-receivers and others (Fig. 3b). Theterm ‘physiological noise’ therefore is actually a misnomer. This isno wonder, the sensitivity of the measurement is such that it detectschanges far beyond the specifications of any scanner hardware.

A plot of the signal variation as a function of intensity reveals a lin-ear relationship with respect to the total signal variations. Filteringthe signal at different frequency bands reveals frequency dependentvariations in the nature of the signal fluctuations (Fig. 3a). Whereas

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Fig. 2. FID acquired during a steady state MREG-experiment with TR=50 ms (left) over 2400 repetitions (=2 min). Signal traces on the right represent signal fluctuations at dif-ferent signal levels as indicated by the horizontal bars. The vertical scale of each trace is expanded by a factor of 10 for better visualization (for experimental details see (Hennig etal., 2007)).

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variability at the breathing frequency shows the same characteristicsas the total signal, variability at the ECG-frequency (and its higherharmonics) shows a more T2*-like behavior. This frequency depen-dent change clearly shows that there are different underlying sourcesbehind the observed signal variability. Due to the sharp peak of theECG-signal, the frequency spectrum of ECG-related signal fluctuationsreveals a long train of higher harmonics (see Fig. 2 in Hennig et al.,

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Fig. 3. a) Signal fluctuations dI (measured as the standard deviation) for FIDs after fre-quency filtering in the temporal domain illustrate difference noise sources at differentfrequency bands and b) Signal fluctuations of the FID of a water phantom. (experimen-tal details as in Fig. 2).

2007). Since the ECG-signal is not exactly periodic, these higher har-monics tend to become broadened.

Although the ECG-related pulsatility may be of interest for neuro-logical applications, for fMRI it constitutes a nuisance. At sufficientlyhigh acquisition rate, it can be removed from the measured signal.Given the harmonic spectrum of the ECG-signal, I decided early on,that a repetition time of 100 ms should not be exceeded in order tobe able to remove physiological noise. With the ability to removephysiological noise plus the improved statistical power afforded bythe increased number of sampling points MREG is considerablymore sensitive compared to conventional EPI-based fMRI (Grotz etal., 2009; Zahneisen et al., 2011a, 2011b) in addition to giving the op-portunity to investigate the dynamics of neuronal activity.

In parallel to our own efforts other groups worked on similar ap-proaches for gradient-less imaging and inverse reconstruction ofundersampled data. Indeed the principle to acquire images withoutgradients based on the sensitive volumes of small coils alone goesback to a purely theoretical paper by Hutchinson in 1988 (Hutchinsonand Raff, 1988). In parallel to our own work Fa-Hsuan Lin developedthe Inverse Imaging (InI)-technique and showed various approachesto make the best out of undersampled data by drawing on algorithmscoming from fields like EEG and radar (Lin et al., 2006; Lin et al.,2008a, 2008b; Lin et al., 2010; Liou et al., 2011). The train of thoughtleading to MREG was based on rather generic considerations of signaltheory. The resulting technique based on the use of multicoil arrayscan nevertheless be considered as just an extreme implementationof the then already well known principles of parallel imaging withthe PILS-technique (Griswold et al., 2000) as the closest relative. In-deed, without coil arrays developed for parallel imaging, our effortswould have been stuck early on. Furthermore, although the veryearly demonstration used nothing but sum-of-square combinationof reference signal weighted with the current measured value, all fur-ther developments were heavily based on the concepts of regularizedinverse image reconstruction of undersampled data.

This originates from non-MR applications in radar, EEG, and othersand has been introduced to MR in the original SENSE-paper by KlaasPruessmann et al. (1999). The concept to increase acquisition speedby making use of image sparsity really took off during ISMRM in Ber-lin, when a whole session was dedicated to accelerated imaging by it-erative inverse reconstruction using regularization. Numerousapproaches have been developed on various possibilities for imple-mentation. Tikhonov regularization using a L2-norm (favoringimage smoothness) and compressed sensing (Lustig et al., 2007) arethe most commonly used implementations, which is mainly due tothe fact, that these are computationally efficient and based on a wellestablished mathematical framework with a lot of code freely

T(visual) T(motor)

Fig. 4. Images acquired with a single shot concentric shells acquisition with 10 shells(acquisition time 60 ms, flipangle 15°, TE 15 ms) overlayed with activation maps fortwo simultaneous stimulation paradigms: a motor task consisting of randomizedblocks of 5 s finger-thumb opposition (blue) and a visual checkerboard stimulationwith 15 s activation/rest (red). The T-threshold was set to 10 for both tasks.From Zahneisen et al. (2011b).

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available through the internet. Especially compressed sensing hasgained enormous popularity due to the comparatively fast recon-struction times as a consequence of the fact, that it uses FFT andWavelet transform, for both of which fast implementations are easilyavailable.

Methods for undersampled imaging can be readily combined withparallel imaging techniques to yield very high acceleration factors.Based on our internal specifications (acquisition time b100 ms, iso-tropic volume coverage) we have gone through a series of implemen-tations using different k-space trajectories. Our first implementationwas based on a Rosette trajectory, which delivers a full brain64×64×64 volume in 23 ms acquisition time (Zahneisen et al.,2011a). Like other non-rectilinear trajectories this requires a correc-tion for local field inhomogeneity. The multiple crossings in this tra-jectory actually set rather high demands on the B0-field correction;therefore we more recently switched to concentric shells. In the im-plementation developed by Benjamin Zahneisen the number of shellsand the density of the spherical spiral on each shell can be freely var-ied (Zahneisen et al., 2011b). This high flexibility allows to generatetrajectories with optimized resolution and point spread function.

Using powerful but still standard multiprocessor computers withlarge onboard memory reconstruction times are now down to severalhours per timeseries. So although this is not yet ready for routine use,it is now ready for ‘real’ neuroscientifc applications beyond the feasi-bility studies on standard stimulation paradigms we used for our ini-tial studies. In addition the possibility to investigate the temporaldynamics of cortical activation i.e. in correlation to EEG (LeVan etal., 2011), one of the main current area of interest is the investigationof the dynamics of resting state networks (RSN) (Lee et al., 2011).Based on the observation by Hsu Lei Lee, that RSNs can be observednot only in the commonly used very low frequency range around0.01 Hz and lower, but also at higher frequencies, we have initiateda number of studies to investigate the dynamic action and interactionof RSN.

Conclusions

We started off with MREG by jumping over the barrier set by theNyquist theorem by omitting gradients altogether, which immediate-ly set us free from all (well most) constraints set by signal theory.Having done that we realized that we actually jumped too far and wedon't really need MHz-frame rates, so now we have worked our wayback by sacrificing some of the speed performance by using a little bitof gradient to improve spatial resolution within the voxels defined byour RF coil array. It is quite interesting to see that a comparable perfor-mance has meanwhile been achieved by groups, who have stayed onthe other side of the fence and who have worked their way up fromthere. An example is David Feinberg's multiplexed SIR-EPI, whichachieves a 100 ms temporal resolution based on multiband excita-tion of the whole multislice package in a single scan (Feinberg etal., 2010).

Challenges for future development will be to further improve spa-tial resolution. A lot of interesting neuroscientific problems can beaddressed at the current 3–4 mm voxel size. The main problem there-fore is not the low resolution per se, but the susceptibility dependantsignal loss across large voxels as shown in Fig. 4. Further improve-ments are on their way. A next-generation version of GraemeWiggins96-channel coil (Wiggins et al., 2009) – which actually has only 95coil elements – built by Thimo Hugger (aka Grotz) under the guid-ance of Larry Wald (Grotz et al., 2011) has the potential to acquirelarger matrices (80–963) at identical acquisition time. The use oflocal PatLoc-gradients (Hennig et al., 2008) may further improve gra-dient performance. RF-excitation with spatially variable excitationphase can be used to reduce susceptibility dependant signal loss. SoI am pretty confident, that the current status is only a fleeting glimpsein a rapid development which is far from reaching its end. One

problem, which will not be easily solved, is the tremendously in-creased computational effort necessary for image reconstruction.Larger matrices, faster acquisition, the use of non-linear gradientsand (to a minor degree) the use of 3D selective pulses for paralleltransmission lead to an increased computational demand, which inthe foreseeable future grows much faster than the increase in compu-tation performance. So just like in the olden days, when array proces-sors where necessary to get sufficient reconstruction times, we areback to using special hardware (GPUs) to make reconstructiontimes tolerable at least to a level acceptable for neuroscientific appli-cations. In the end we would like to get subcortical resolution at10 fps or better to really start looking at the brain at work. Ultrahighfield MR may help to pave the way a bit, but I am afraid (or ratherhope), that success cannot be bought by acquiring bigger and biggermachines alone and there will be still room and the necessity fornew ideas.

Comparing MREG with our early work on functional spectroscopyone may note some interesting correspondence in spite of the hugedifferences in technology. The generic MREG-experiment in whichsignal is acquired without any gradient encoding can be regarded asa functional spectroscopy experiment where the number of voxelsis given by the number of coil elements in the spirit of the OVOC-ap-proach. Interference with physiological noise has always been a majorconcern in measurements aimed at the detection of the elusive initialdip. With the opportunity of ultrafast fMRI measurements offered byMREG and other ultrafast techniques it may be possible to reconsiderthis issue and to resolve the debate.

Let me close with some personal remarks. As a MR-physicist it hasalways been my aim to use the magic of spin choreography for the in-vestigation of a broad range of applications. On the basis of technologi-cal and methodological developments – which inherently areindependent of one specific application – I have worked in neuro MR,cardiac MRI, MR in oncology and many other application fields. Neuro-scientific applications have always been fundamentally different. Neu-roscience means brains thinking about the brain, so neuroscience isinherently self-referential. Whereas in other fields of application it atleast appears to be possible to separate the scientist from his subjectmatter, in neuroscience this is in principle not possible. We may andhopefully do respect all proper procedures and quality measures ofgood scientific practice, the results of our research will nevertheless in-variably be self-referential: We only get answers to the questions weask. So although we may think, that we ‘objectively’ study the brain,in the end we are always looking into a mirror and we only see, whatwe dare to ask. Although this is true for science at large, a great dealof ‘zeitgeist’ can be noted in neuroscience in particular. As an example

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and looking back there seem to be quite an interesting fluctuation in thenumber and emphasis of reports on gender differences in fMRI studies,so even in its short history of fMRI, the ‘zeitgeist’ has varied.

The overwhelming current ‘zeitgeist’ topic is the genetic and mo-lecular definition of life leading to a proliferation of studies and pro-jects trying to link up genetics and molecular biology with fMRIfindings. This is a most exciting endeavor likely to generate newand relevant insight into the makings of the brain. I cannot help butfeel, however, that this will only reveal a part of the story. Trying toestablish a one-to-one correspondance from molecules to high-order traits to me is a bit like trying to understand a piece of art bya detailed chemical analysis of its constituents: One may undoubtedlylearn a lot this way, but one cannot help but feel, that something im-portant is missed. This doesn't mean that such research is irrelevant;to the contrary, learning about such correlations will add importantinsight into genetic predisposition. I am sure the journey will notend there. A better understanding about the limits and variability ofsuch predisposition will enable us to make the next step toward bet-ter and integrated understanding of the brain. I am sure fMRI willcontinue to play an important role in this never ending quest.

Acknowledgments

I wish to thank all the researchers I had the pleasure to work with inthis work. For the early work this especially includes Thomas Ernst,Clemens Janz, and Oliver Speck. The recent work is carried by ThimoHugger, Benjamin Zahneisen, Pierre Levan, Hsu Lei Lee, Jakob Assländer,Kuan Jin Lee, Marco Reisert, Maxim Zaitsev and Chris Cocosco. I wouldalso like to acknowledge grant support frommany sources, most notablythe INUMAC project supported by the German Federal Ministry of Educa-tion and Research grant 13N9208 and the ERC Advanced Grant ‘OVOC’#232908.

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