What psychedelic research can, and cannot, tell us about consciousness


The short piece below first appeared in Scientific American (Observations) on October 26, 2018.  It is a coauthored piece, led by me with contributions from Michael Schartner, Enzo Tagliazucchi, Suresh Muthukumaraswamy, Robin Carhart-Harris, and Adam Barrett.  Since its appearance, both Dr. Kastrup and Prof. Kelly have responded. I attach links to their replies after our article, offering a few comments in further response (entirely my own point of view). These comments just offer additional clarifications – I stand fully by everything said in our Sci Am piece.

It’s not easy to strike the right balance when taking new scientific findings to a wider audience. In a recent opinion piece, Bernardo Kastrup and Edward F. Kelly point out that media reporting can fuel misleading interpretations through oversimplification, sometimes abetted by the scientists themselves. Media misinterpretations can be particularly contagious for research areas likely to pique public interest—such as the exciting new investigations of the brain basis of altered conscious experience induced by psychedelic drugs.

Unfortunately, Kastrup and Kelly fall foul of their own critique by misconstruing and oversimplifying the details of the studies they discuss. This leads them towards an anti-materialistic view of consciousness that has nothing to do with the details of the experimental studies—ours or others.

Take, for example, their discussion of our recent study reporting increased neuronal “signal diversity” in the psychedelic state. In this study, we used “Lempel-Ziv” complexity—a standard algorithm used to compress data files—to measure the diversity of brain signals recorded using magnetoencephalography (MEG). Diversity in this sense is related to, though not entirely equivalent to, “randomness.” The data showed widespread increased neuronal signal diversity for three different psychedelics (LSD, psilocybin and ketamine), when compared to a placebo baseline. This was a striking result since previous studies using this measure had only reported reductions in signal diversity, in global states generally thought to mark “decreases” in consciousness, such as (non-REM) sleep and anesthesia.

Media reporting of this finding led to headlines such as “First evidence found that LSD produces ‘higher’ levels of consciousness” (The Independent, April 19, 2017)—playing on an ambiguity between cultural and scientific interpretations of “higher”—and generating just the kind of confusion that Kastrup and Kelly rightly identify as unhelpful.

Unfortunately, Kastrup and Kelly then depart from the details in misleading ways. They suggest that the changes in signal diversity we found are “small,” when it is not magnitude but statistical significance and effect size that matters. Moreover, even small changes to brain dynamics can have large effects on consciousness. And when they compare the changes reported in psychedelic states with those found in sleep and anesthesia, they neglect the important fact that these analyses were conducted on different data types (intracranial data and scalp-level EEG respectively—compared to source-localized MEG for the psychedelic data)—making quantitative comparisons very difficult.

Having set up the notion that the changes we observed were “small,” they then say, “To suggest that brain activity randomness explains psychedelic experiences seems inconsistent with the fact that these experiences can be highly structured and meaningful.” However, neither we nor others claim that “brain activity randomness” explains psychedelic experiences. Our finding of increased signal diversity is part of a larger mission to account for aspects of conscious experience in terms of physiological processes. In our view, higher signal diversity indicates a larger repertoire of physical brain states that very plausibly underpin specific aspects of psychedelic experience, such as a blending of the senses, dissolution of the “ego,” and hyper-animated imagination. As standard functional networks dissolve and reorganize, so too might our perceptual structuring of the world and self.

“In short, a formidable chasm still yawns between the extraordinary richness of psychedelic experiences and the modest alterations in brain activity patterns so far observed.” Here, their misrepresentations are again exposed. To call the alterations modest is to misread the statistics. To claim a “formidable chasm” is to misunderstand the incremental nature of consciousness research (and experimental research generally), to sideline the constraints and subtleties of the relevant analyses and to ignore the insights into psychedelic experience that such analyses provide.

Kastrup and Kelly’s final move is to take this presumed chasm as motivation for questioning “materialist” views, held by most neuroscientists, according to which conscious experiences —and mental states in general—are underpinned by brain states. Our study, like all other studies that explore relations between experiential states and brain states (whether about psychedelics or not), is entirely irrelevant to this metaphysical question.

These are not the only inaccuracies in the piece that deserve redress. For example, their suggestion that decreased “brain activity” is one of the more reliable findings of psychedelic research is incorrect. Aside from the well-known stimulatory effects of psychedelics on the excitatory glutamate system, early reports of decreased brain blood flow under psilocybin have not been well replicated: a subsequent study by the same team using a different protocol and drug kinetics (intravenous LSD) found only modest increases in brain blood flow confined to the visual cortex. In contrast, more informative dynamic measures have revealed more consistent findings, with network disintegration, increases in global connectivity and increased signal diversity/entropy appearing to be particularly reliable outcomes, replicated across studies and study teams.

Consciousness science remains a fragile business, poised precariously between grand ambition, conflicting philosophical worldviews, immediate personal relevance and the messy reality of empirical research. Psychedelic research in particular has its own awkward cultural and historical baggage. Against this background, it’s important to take empirical advances for what they are: yardsticks of iterative, self-correcting progress.

This research is providing a unique window onto mappings between mechanism and phenomenology, but we are just beginning to scratch the surface. At the same time—and perhaps more importantly—psychedelic research is demonstrating an exciting potential for clinical use, for example in alleviating depression, though larger and more rigorous studies are needed to confirm and contextualize the promising early findings.

Kastrup and Kelly are right to guard against overplaying empirical findings by the media. But by misrepresenting the explanatory reach of our findings in order to motivate metaphysical discussions irrelevant to our study, they risk undermining the hard-won legitimacy of a neuroscience of consciousness. Empirical consciousness science, based firmly on materialistic assumptions, is doing just fine. And unlike alternative perspectives that place themselves “beyond physicalism,” it will continue to shed light on one of our deepest mysteries through rigorous application of the scientific method.

You can read Dr. Kastrup’s response here, and Prof. Kelly’s here. In the spirit of constructive clarification I will offer a few additional comments on the parts of the work I was involved in: the signal diversity study and the general interpretation of how empirical work on the brain basis of psychedelic research speaks to metaphysical debates about the nature of consciousness. These comments relate mainly to Prof. Kelly’s critique.

(With respect to Dr. Kastrup’s comments I will simply offer, as he no doubt knows, that relating fMRI BOLD to neural activity, in terms of global baseline and regionally differentiated metabolics, functional neuronal connectivity, and so on – remains an area of extremely active research and rapid methodological innovation.)

1. Prof Kelly notes that we do not provide ‘exact N’s for the data segments we used to compute measures of signal diversity.  This is because they varied substantially between drug condition, participant, and analysis method. We do however clearly state that “[a]nalyses were performed using non-overlapping segments of length 2 sec for a total length between 2 min and 10 min of MEG recording per participant and state” (Schartner et al 2017, p.5)” These numbers indeed lead to a total number of segments ranging from ~3,500 to ~27,000 per participant and per state (since we have 90 channels/sources per segment). These large numbers provide stable statistical inference (e.g., by the central limit theorem). Also, as we mentioned (above) the absolute scores on the diversity scale are not as meaningful as effect size and statistical significance. I’d also like to add that in our paper we go to great lengths to establish that our reported diversity changes do not trivially follow from well-known spectral changes in the drug conditions – this is part of the unavoidable computational sophistication of the method, when done properly.

2. When Prof. Kelly says that “relatively simple neuroimaging methods can easily distinguish between wakeful and drowsy states and other commonplace conditions” I do not disagree at all. Our paper was specifically interested in signal diversity as a metric of brain dynamics (and as mentioned above we take care to de-confound our diversity results from spectral changes). Also, we do not claim these diversity changes fully explain the extraordinary phenomenology of psychedelic states. However, I do believe that they contribute helpfully to the incremental empirical project of mapping, in explanatorily satisfying ways, between mechanism and phenomenology.  I defend the general approach in this 2016 Aeon article: ‘the “real” problem of consciousness’.

3.  I also agree the measures of signal diversity we apply are only part of the story when mapping between experiential richness and brain dynamics. My lab (and others too) have have worked hard on developing empirically adequate measures of ‘neural complexity’, ‘causal density’, and ‘integrated information’ which are theoretically richer – but unfortunately, at least so far, not very robust when applied to actual data – and are substantially more computationally sophisticated. See here for a recent preprint.  We have to do what we can with the measures we have, while always striving to generate and validate better measures.

4. I do not buy the claim that near-death-experiences provide an empirical challenge to physicalist neuroscience (as argued by Prof. Kelly). See my previous blog post on this issue (‘the brain’s last hurrah‘).

5. No need to impute me with a bias towards physicalism! I explicitly and happily adopt physicalism as a pragmatic metaphysics for pursuing a (neuro)science of consciousness.  I can do this while remaining agnostic about the actual ontological status of consciousness. The problem with many alternative metaphysics – in my view – is that they do not lead to testable propositions.  Dr Kastrup and Prof Kelly are of course entirely entitled to their own metaphysics. I was merely objecting to their usage of our psychedelic research in support of their metaphysics, because I think it is entirely irrelevant. I simply do not accept that there are any “evident tensions between physicalist expectations and the experimental results [from psychedelic neuroimaging]”.

6. Finally, we can hopefully all agree on the importance of forestalling, as far as possible, media misinterpretations.  This is true whatever one’s metaphysics.  And it’s why, when our diversity paper first appeared, I felt compelled to pen an immediate corrective right here in this blog (‘Evidence for a higher state of consciousness? Sort of‘).

After posting, I realized I had not specifically responded to Bernardo’s initial reaction to our Sci Am piece. There is some overlap with the above points, but please anyway allow me to correct this oversight here.

1. Clearing the semantic fog.  I hope I have made clear my intended distinction between ‘fully explain’ and ‘incrementally account for.’ Again my Aeon piece elaborates the strategy of refining explanatory mappings between mechanism and phenomenology.

2. Metaphysical claims. Our work is consistent with materialism and is motivated by it, but empirical studies like this are not suited to arbitrate between competing metaphysical positions (unless such positions state that there are no relations at all between brains and conscious experiences). Empirical studies like ours try to account for phenomenological properties in terms of mechanisms – but in doing so there is no need to make claims that one is addressing the (metaphysical) ‘hard problem’ of consciousness.  Kastrup and Kelly have written that “the psychedelic brain imaging research discussed here has brought us to a major theoretical decision point as to which framework best fits with all the available data” – where ‘physicalism’ is one among several (metaphysical) ‘frameworks’. I continue to think the research discussed here is irrelevant to this ‘decision point’, unless one is deciding to reject frameworks that postulate no relation between consciousness and the brain. The fact that the research is about psychedelics rather than (for example) psychophysics is neither here nor there.

3. What the researchers fail to address. I do not agree with the premise that there is an inconsistency between the dream state and the psychedelic state in terms of neural evidence. As noted above, measures of brain dynamics and activation are being continuously refined and innovated and it is overly simplistic to characterise the relevant dimensions in terms of gross ‘level of activity’.  Also, dreams and psychedelia are different. The point about ‘randomness’ I have  addressed already (diversity is not presented as an exhaustive explanation of psychedelic phenomenology).

4. A surprising claim. I respectfully refrain from addressing these points about the MRI/MEG studies since I was not involved with them. This does not mean I condone Bernardo’s comments. I will only repeat that brute measures of increased/decreased brain activity are less informative than more sophisticated measures of neural dynamics and connectivity, and studies are accumulating to more precisely map brain changes in psychedelic states.

5. The issue of statistics. It is not meaningful to compare, quantitatively, ‘magnitudes’ in changes in subjective experience with magnitudes of statistical effect size as applied to (for example) our diversity measures.  We made this point already in our Sci Am piece.  I find it quite natural to suppose that a massively meaningful change in subjective experience might have a subtle neuronal signature in the brain (and as I have said, diversity/randomness is only a small part of any full ‘explanation’ anyway).

6. A non-sequitur.  I do think its misleading to speak of a “formidable chasm” between “the magnitude of the subjective effects of a psychedelic trance and the accompanying physiological changes” for the reasons given in point 5 above.

7. Final thoughts. I indeed hope we can all agree that psychedelic research is interesting, exciting, valuable, evolving, clinically important, and generally highly worthwhile.  I hope we can also agree, as mentioned above, that forestalling media misrepresentations is important.  On other matters I doubt there will be full agreement between my views (and those of my colleagues) and Bernardo’s and Edward’s.  They are certainly entitled to their metaphysics. I simply wish to point out (i) our studies do help build explanatory bridges between neural mechanism and psychedelic phenomenology, and (ii) they do not provide any additional reasons to entertain non-physicalist metaphysics.

And with that, I’m afraid I’ll have to draw a line under this interesting discussion – at least for my involvement. I hope it generates some light amid the heat.


Evidence for a higher state of consciousness? Sort of.


Bicycle Day Celebration Blotter.  By YttriumOx CC BY-SA 3.0

On April 19 1943, seventy-four years ago to the day, Albert Hoffman conducted his now famous self-experimentation on the psychological effects of LSD, a compound he had been the first to synthesize some years earlier. Now called ‘bicycle day’ in honour of how Hoffman made his way home, it led to some remarkable descriptions:

“… Little by little I could begin to enjoy the unprecedented colors and plays of shapes that persisted behind my closed eyes. Kaleidoscopic, fantastic images surged in on me, alternating, variegated, opening and then closing themselves in circles and spirals, exploding in colored fountains, rearranging and hybridizing themselves in constant flux …”

In the decades that followed, academic research into LSD and other psychedelics was cast into the wilderness as worries about their recreational use held sway. Recently, however, the tide has started to turn. There is now gathering momentum for studies showing a remarkable clinical potential for psychedelics in treating recalcitrant psychiatric disorders, as well as experiments trying to understand how psychedelics exert their distinctive effects on conscious experience.

In a new paper published in Scientific Reports on this bicycle day anniversary, we describe a distinctive neuronal signature of the psychedelic state: a global increase in neuronal signal diversity. So – is this evidence for a ‘higher state’ of consciousness? And could it account for the nature of psychedelic experience? Let me answer these questions by summarizing what we did.

Our study analyzed data previously collected by Dr. Robin Carhart-Harris (Imperial College London) and Dr. Suresh Muthukumaraswamy (then Cardiff, now at Auckland). These were magnetoencephalographic (MEG) brain-imaging data from healthy volunteers either in a normal waking state, or after having taken LSD, psylocibin (the active ingredient in magic mushrooms) or ketamine (which in low doses acts as a psychedelic – in high doses it has an anaesethetic effect). MEG data combine a very high temporal resolution, with a much better spatial resolution than EEG (electroencephalography), allowing us to compute some relatively sophisticated mathematical measures of signal diversity. The participants in our study had passed strict ethical criteria, and were asked simply to rest quietly in the scanner during the experiment. Afterwards, they were asked various questions about what they had experienced.

With Carhart-Harris and Muthukumaraswamy, and with Dr. Adam Barrett and first-author Michael Schartner of the Sackler Centre for Consciousness Science here at Sussex, we chopped up the MEG data into small segments and for each segment calculated a range of different mathematical measures. The most interesting is called ‘Lempel Ziv (LZ) complexity,’ which measures the diversity of the data by figuring out how ‘compressible’ it is. A completely random data sequence would be maximally diverse since it is not compressible at all. A completely uniform data sequence would be minimally diverse since it is easy to compress. In fact, because of these properties the algorithm for computing LZ complexity is widely used to compress digital photos into smaller files, in an optimal way.


Changes in LZ complexity under LSD, as compared to the waking state.  Data are source localized MEG.  Image from Suresh Muthukumaraswamy and appears in Figure 3 in the paper.

We found that MEG signals had a reliably higher level of LZ – and hence signal diversity – for all three psychedelic compounds, with perhaps the strongest effects for LSD. The fact that we found the same pattern of results across all three psychedelic compounds is both striking and reassuring – it means our results are not likely to have arisen by chance.

Intuitively, these findings mean that the brain-on-psychedelics is less predictable, more random – and more diverse than in the normal waking state.

Our data can be thought of as evidence for a ‘higher’ state of consciousness only in this very specific way, and only in the context provided by other studies where a loss of consciousness has been associated with a reduction of neuronal diversity. For example, studies in our lab have shown reduced LZ complexity (reduced diversity) for both anaesthesia and for (non-dreaming) sleep. (Interestingly, levels of LZ returned to ‘normal’ during REM sleep when dreams are likely.) What’s striking about our results, in this context, is that increases in quantitative measures of conscious level, compared to the waking state, have never been found before.

Interpreting our data in terms of conscious level also make sense since measures of signal diversity, like LZ, can be thought of as approximations to related quantities like the ‘perturbation complexity index’ (PCI). This measure captures the diversity of the brain’s response to an electromagnetic stimulus: think banging on the brain (but using transcranial magnetic stimulation which applies a sharp electromagnetic ‘bang’), and listening to the echo. Studies using PCI, pioneered by Prof. Marcello Massimini at the University of Milan, have found a remarkable sensitivity to changes in conscious level, and even an ability to predict residual consciousness in devastating neurological conditions like coma and the vegetative state. The differences between LZ and PCI are subtle, having mainly to do with whether they measure simple diversity or a mixture of diversity and ‘integration’ in brain dynamics.

More generally, measures of diversity are related to influential theories which associate consciousness with ‘integrated information’ or ‘causal density’ in the dynamics of the brain. While these theories specify even more complicated mathematical measures of conscious level, the fact that we see measurable increases in diversity so reliably across conscious states gives some support to these theories.  Our results are also consistent with Robin Carhart-Harris’ ‘entropic brain‘ theory, which proposes that the psychedelic state is associated with greater entropy or uncertainty in neural dyamics.

In this broader theoretical context, what’s interesting about our results is that they show that a measure of conscious level – previously applied to sleep and anesthesia – is also sensitive to differences in conscious content, as in the contrast between the psychedelic state and normal wakefulness. This helps shed some new light on an old debate in the science of consciousness – the relationship between conscious level (how conscious you are) and conscious content (what you’re conscious of, when you’re conscious).

Taking this research forward, we plan to understand more about how specific properties of neural dynamics relate to specific properties of psychedelic experiences. In the present study, we found some tentative correlations between changes in signal diversity and the degree to which people reported experiences like ‘ego dissolution’ and ‘vividness of imagination’. However, these correlations were not strong. One possible reason is that the subjective reports were taken outside the scanner, likely some time after the peak effect of the drug. Another possibility – which we are currently looking into – is that more fine-grained measures of information flow in the brain, like Granger causality, might be needed in order to closely map properties of psychedelic experience to changes in the brain.

Overall, our study adds to a growing body of work – much of which has been led by Carhart-Harris and colleagues –  that is now revealing the brain-basis of the psychedelic state. Our data show that a simple measure of neuronal signal diversity places the psychedelic state ‘above’ the normal waking state, in comparison to the lower diversity found in sleep and anesthesia. Taking this work forward stands to do much more than enhance our understanding of psychedelics. It may help expose how, why – and for whom – psychedelics may help alleviate the appalling suffering of psychiatric disorders like depression. And in the end, it may help us figure out how our normal everyday conscious experiences of the world, and the self, come to be.

After all, everything we experience – even when stone cold sober – is just a kind of ‘controlled hallucination.’ Our perceptions are just the brain’s “best guess” of what’s going on, reined in by sensory signals. It’s just that most of the time we agree with each other about our hallucinations, and call them reality.

‘Increased spontaneous MEG signal diversity for psychoactive doses of ketamine, LSD and psilocybin’ by Michael Schartner, Robin Carhart-Harris, Adam Barrett, Anil Seth and Suresh Muthukumaraswamy is published in Scientific Reports (7): 46421, 2017. It is freely available here as an open-access publication. I am the corresponding author.

The study has been extensively covered in the media. Particularly good pieces are in The Guardian in the New Scientist and in Wired. There is also a highly active Reddit thread, which on the day of publication was consistently on the Reddit homepage. 

I would like to specifically acknowledge Michael Schartner and Adam Barrett in this post.  Michael’s Ph.D. – awarded just a few months ago – was all about measuring signal diversity in various different conscious states (sleep, anesthesia, psychedelia. Michael was primarily supervised by Dr. Barrett who devoted his considerable mathematical expertise to the project. Very many thanks are also due to Robin Carhart-Harris and Suresh Muthukumaraswamy for generously engaging with this collaboration.

Carhart-Harris, Muthukumaraswamy and colleagues have published a number of other important studies on the neural basis of the psychedelic state.  See here and here – or just look on PubMed.

Can we figure out the brain’s wiring diagram?


The human brain, it is often said, is the most complex object in the known universe. Counting all the connections among its roughly 90 billion neurons, at the rate of one each second, would take about 3 million years – and just counting these connections says nothing about their intricate patterns of connectivity. A new study, published this week in Proceedings of the National Academy of Sciences USA, shows that mapping out these patterns is likely to be much more difficult than previously thought — but also shows what we need to do, to succeed.

Characterizing the detailed point-to-point connectivity of the brain is increasingly recognized as a key objective for neuroscience. Many even think that without knowing the ‘connectome’ – the brain’s wiring diagram – we will never understand how its electrochemical alchemy gives rise to our thoughts, actions, perceptions, beliefs, and ultimately to our consciousness. There is a good precedent for thinking along these lines. Biology has been galvanized by sequencing of the genome (of humans and of other species), and genetic medicine is gathering pace as whole-genome sequencing becomes fast and cheap enough to be available to the many, not just the few. Big-science big-money projects like the Human Genome Project were critical to these developments. Similar efforts in brain science – like the Human Connectome Project in the US and the Human Brain Project in Europe – are now receiving vast amounts of funding (though not without criticism, especially in the European case) (see also here). The hope is that the genetic revolution can be replicated in neuroscience, delivering step changes in our understanding of the brain and in our ability to treat neurological and psychiatric disorders.

Mapping the networks of the human brain relies on non-invasive neuroimaging methods that can be applied without risk to living people. These methods almost exclusively depend on ‘diffusion magnetic resonance imaging (dMRI) tractography’. This technology measures, for each location (or ‘voxel’) in the brain, the direction in which water is best able to diffuse. Taking advantage of the fact that water diffuses more easily along the fibre bundles connecting different brain regions, than across them, dMRI tractography has been able to generate accurate, informative, and surprisingly beautiful pictures of the major superhighways in the brain.

Diffusion MRI of the human brain.  Source: Human Connectome Project.

Diffusion MRI of the human brain. Source: Human Connectome Project.

But identifying these neuronal superhighways is only a step towards the connectome. Think of a road atlas: knowing only about motorways may tell you how cities are connected, but its not going to tell you how to get from one particular house to another. The assumption in neuroscience has been that as brain scanning improves in resolution and as tracking algorithms gain sophistication, dMRI tractography will be able to reveal the point-to-point long-range anatomical connectivity needed to construct the full connectome.

In a study published this week we challenge this assumption, showing that basic features of brain anatomy pose severe obstacles to measuring cortical connectivity using dMRI. The study, a collaboration between the University of Sussex in the UK and the National Institutes of Health (NIH) in the US, applied dMRI tractography to ultra-high resolution dMRI data obtained from extensive scanning of the macaque monkey brain – data of much higher quality than can be presently obtained from human studies. Our analysis, led by Profs. Frank Ye and David Leopold of NIH and Ph.D student Colin Reveley of Sussex, took a large number of starting points (‘seed voxels’) in the brain, and investigated which other parts of the brain could be reached using dMRI tractography.

The result: roughly half of the brain could not be reached, meaning that even our best methods for mapping the connectome aren’t up to the job. What’s more, by looking carefully at the actual brain tissue where tractography failed, we were able to figure out why. Lying just beneath many of the deep valleys in the brain (the ‘sulci’ – but in some other places too), are dense weaves of neuronal fibres (‘white matter’) running largely parallel to the cortical surface. The existence of these ‘superficial white matter fibre systems’, as we call them, prevents the tractography algorithms from detecting where small tributaries leave the main neuronal superhighways, cross into the cortical grey matter, and reach their destinations. Back to the roads: imagine that small minor roads occasionally leave the main motorways, which are flanked by other major roads busy with heavy traffic. If we tried to construct a detailed road atlas by measuring the flow of vehicles, we might well miss these small but critical branching points.

This image shows, on a colour scale, the 'reachability' of different parts of the brain by diffusion tractography.

This image shows, on a colour scale, the ‘reachability’ of different parts of the brain by diffusion tractography.

Identifying the connectome remains a central objective for neuroscience, and non-invasive brain imaging – especially dMRI – is a powerful technology that is improving all the time. But a comprehensive and accurate map of brain connectivity is going to require more than simply ramping up scanning resolution and computational oomph, a message that mega-budget neuroscience might usefully heed. This is not bad news for brain research. Solving a problem always requires fully understanding what the problem is, and our findings open new opportunities and objectives for studies of brain connectivity. Still, it goes to show that the most complex object in the universe is not quite ready to give up all its secrets.

Colin Reveley, Anil K. Seth, Carlo Pierpaoli, Afonso C. Silva, David Yu, Richard C. Saunders, David A. Leopold*, and Frank Q. Ye. (2015) Superficial white-matter fiber systems impede detection of long-range cortical connections in diffusion MR tractography. Proc. Nat. Acad. Sci USA (2015). doi/10.1073/pnas.1418198112

*David A. Leopold is the corresponding author.