Axiomatize This !

“Analyze This”, is a very funny 1999 sendup of the Mafia and psychiatry with Robert DeNiro and Billy Crystal.  For some reason the diagram on p. 7 of Barrett O’Neill’s book “Elementary Differential Geometry” revised 2nd edition 2006 made me think of it.

O’Neill’s  book was highly recommended by the wonderful “Visual Differential Geometry and Forms” by Tristan Needham — as “the single most clear-eyed, elegant and (ironically) modern treatment of the subject available — present company excpted !”

So O’Neill starts by defining a point  as an ordered triple of real numbers.  Then he defines R^3 as a set of such points along with the ability to add them and multiply them by another real number.

O’Neill then defines tangent vector (written v_p) as two points (p and v) in R^3 where p is the point of application (aka the tail of the tangent vector) and v as its vector part (the tip of the tangent vector).

All terribly abstract but at least clear and unambiguous until he says — “We shall always picture v_p as the arrow from point p t0 the point p + v”.

The picture is a huge leap and impossible to axiomatize (e.g. “Axiomatize This”).   Actually the (mental) picture came first and gave rise to all these definitions and axioms.

The picture is figure 1.1 on p. 7 — it’s a stick figure of a box shaped like an orange crate sitting in a drawing of R^3 with 3 orthogonal axes (none of which is or can be axiomatized).  p sits at one vertex of the box, and p + v at another.  An arrow is drawn from p to p + v (with a barb at p + v) which is then labeled v_p.  Notice also, that point v appears nowhere in the diagram.

What the definitions and axioms are trying to capture is our intuition of what a (tangent) vector really is.

So on p. 7 what are we actually doing?  We’re looking at a plane in visual R^3 with a bunch of ‘straight’ lines on it.  Photons from that plane go to our (nearly) spherical eye which clearly is no longer a plane.  My late good friend Peter Dodwell, psychology professor at Queen’s University in Ontario, told me that the retinal image actually preserves angles of the image (e.g. it’s conformal). 1,000,000 nerve fibers from each eye go back to our brain (don’t try to axiomatize them).   The information each fiber carries is far more processed than that of a single pixel (retinal photoreceptor) but that’s another story, and perhaps one that could be axiomatized with a lot of work.

100 years ago Wilder Penfield noted that blood flowing through a part of the brain which was active looked red rather than blue (because it contained more oxygen).  That’s the way the brain appears to work.  Any part of the brain doing something gets more blood flow than it needs, so it can’t possibly suck out all the oxygen the blood carries.  Decades of work and zillions researchers have studied the mechanisms by which this happens.  We know a lot more, but still not enough.

Today we don’t have to open the skull as Penfield did, but just do a special type of Magnetic Resonance Imaging (MRI) called functional MRI (fMRI) to watch changes in vessel oxygenation (or lack of it) as conscious people perform various tasks.

When we look at that simple stick figure on p. 7, roughly half of our brain lights up on fMRI, to give us the perception that that stick figure really is something in 3 dimensional space (even though it isn’t).  Axiomatizing that would require us to know what consciousness is (which we don’t) and trace it down to the activity of billions of neurons and trillions of synapses between them.

So what O’Neill is trying to do, is tie down the magnificent Gulliver which is our perception of space with Lilliputian strands of logic.

You’ve got to admire mathematicians for trying.

Visual Differential Geometry and Forms — Take 3

Visual Differential Geometry and Forms is a terrific math book about which I’ve written

here — https://luysii.wordpress.com/2021/07/12/a-premature-book-review-and-a-60-year-history-with-complex-variables-in-4-acts/

and

here — https://luysii.wordpress.com/2021/12/04/a-book-worth-buying-for-the-preface-alone-or-how-to-review-a-book-you-havent-read/

but first some neurology.

In the old days we neurologists figured out what the brain was doing by studying what was lost when parts of the brain were destroyed (usually by strokes, but sometimes by tumors or trauma).  Not terribly logical, as pulling the plug on a lamp plunges you in darkness, but the plug has nothing to do with how the lightbulb or LED produces light.  It was clear that the occipital lobe was important — destroy it on both sides and you are blind — https://en.wikipedia.org/wiki/Occipital_lobe but it’s only 10% of the gray matter of the cerebral cortex.

The information flowing into your brain from your eyes is enormous.  The optic nerve connecting the eyeball to the brain has a million fibers, and they can fire ‘up to 500 times a second.  If each firing (nerve impulse) is a bit, then that’s an information flow into your brain of a gigaBit/second.   This information is highly processed by the neurons and receptors in the 10 layers of the retina.  There are many different cell types — cells responding to color, to movement in one direction, to a light stimulus turning on, to a light stimulus turning off, etc. etc.   Over 30 cell types have been described, each responding to a different aspect of the visual stimulus.

So how does the relatively small occipital lobe deal with this? It doesn’t.At least half of your the brain responds to visual stimuli.  How do we know?   It’s complicated, but something called functional Magnetic Resonance Imaging (fMRI) picks up increased neuronal activity (primarily by the increase in blood flow it causes).

Given that half your brain is processing what you see, it makes sense to use it to ‘see’ what’s going on in Mathematics.  This is where Tristan Needham’s books come in.

If you’ve studied math at the college level with some calculus you shouldn’t have much trouble.  But you definitely need to look at Euclid as it’s used heavily throughout. Much use is made of similar triangles to derive relationships.

I’ll assume you’ve read the first two posts mentioned above.  Needham’s description of curvature and torsion of curves in 3 dimensional space is terrific.  They play a huge role in relativity, and I was able to mouth the formulas for them but they remained incomprehensible to me, as they are just symbols on the page.  Hopefully the discussion further on in the book will let me ‘see’ what they are when it comes to tensors.

He does skip about a bit passing Euclid when he tell how people living t on a 2 dimensional surface could tell it wasn’t flat (p. 19).  It involves numerically measuring the circumference of a circle.  But this involves a metric and putting numbers on lines, something Euclid never did.

Things really get interesting when he started talking about how Newton found the center of curvature of an arbitrary curve.  Typically Needham doesn’t really define curve, something obvious to a geometer, but it’s clear the curve is continuous.  Later he lets it slip that the curve is differentiable (without saying so).

So what did Newton do?   Start with a point p and find its normal line.  Then find point q near p on the curve and find its normal line and see where they intersect.  The center of curvature at p is the point of intersection of the normals as the points get closer and closer to p.

This made wonder how Newton could find the normal to an arbitrary continuous curve.  It would be easy if he knew the tangents, because Euclid very early on (Proposition 11 Book 1) tells you how to construct the perpendicular to a straight line.  It is easy for Euclid to find the tangent to a circle at point p — it’s just the perpendicular to the line formed between the center of the circle (where you put one point of the compass used by Newton) and the circle itself (the other point of the compass.

But how does Newton find the tangent to an arbitrary continuous curve?  I couldn’t find any place that he did it, but calc. 101 says that you just find the limit of secants ending at p as the other point gets closer and closer.  Clearly this is a derivative of sorts.

Finally Needham tells you that his curves in 3 dimensions are differentiable in the following oblique way.  On p. 106 he says that “each infinitesimal segment (of a curve) nevertheless lies in a plane.”  This tells you that the curve has a tangent, and a normal to it at 90 degrees (but not necessarily in the plane).  So it must be differentiable (oblique no?).   On p. 107 he differentiates the tangent in the infinitesimal plane to get the principal normal (which DOES  lie in the plane).  Shades of Bishop Berkeley (form Berkeley California is named) — differentiating the ghost of a departed object.

Addendum: 28 March ’22:  It’s was impossible for me to find a definition of surface even reading the first 164 pages.  Needham highly recommends a book I own “Elementary Differential Geometry (revised 2nd edition) by Barrett O’Neill calling it “the single most clear-eyed elegant, and (ironically) modern treatment of the subject  . . .  at the undergraduate level”.  The first edition was 1966.   In the preface to his book O’Neill says “One weakness of classical differential geometry is its lack of any adequate definition of surface”.    No wonder I had trouble.

So it’s great fun going through the book, get to “Einstein’s Curved Spacetime” Chapter 30 p. 307, “The Einstein FIeld Equation (with Matter) in Geometrical Form” complete with picture p. 326.

More Later.

The pericyte controls local cerebral blood flow

Actively firing neurons get all the blood flow they need. More in fact. And this is the entire basis of functional magnetic resonance imaging (fMRI). At long, long last we may be close to understanding exactly how this happens.

Almost 100 years ago Wilder Penfield operating on unanesthetized patients with epilepsy to find the epileptic focus and remove it, noted that when a patient had a seizure on the table, veins became red, because so much blood flowed to the active area that it couldn’t absorb all the oxygen contained in the hemoglobin of the red cells, so they stayed red. Penfield was not a sadist, the brain contains no pain fibers, and so the skull could be opened using just local anesthetics. 

Exactly the same thing happens locally when neurons become active firing lots of action potentials. The functional MRI signal is due to the difference in magnetic susceptibility of the iron atom in hemoglobin when it is binding oxygen and when it isn’t.

So how does a firing neuron tell blood vessels it needs more flow?  A superb paper [ Proc. Natl. Acad. Sci. vol. 117 pp. 27022 – 27033 ’20 ]–https://www.pnas.org/content/pnas/117/43/27022.full.pdf probably explains exactly how this happens.  

The pericyte is a cell which is found outside cerebral capillaries and very small arteries.  It isn’t like a rubber band around the vessel (that’s for smooth muscle).  It’s like our bony spine with ribs coming from it, so the spine lies on the long axis of the vessel with the ribs coming down and wrapping (partially) around the vessel.

Pericytes in the brain and the retina are found primarily where two capillaries join each other according to the paper (which provides a convincing picture).

Neurons firing impulses release potassium into the extracellular space.  The endothelial cells of brain capillaries sense this and open up the inwardly rectifying potassium channel KIR2.1, exposing the outside to the resting potential of potassium which is quite negative (e. g the endothelial cell hyperpolarizes in response to neuronal activity.  The signal propagates upstream THROUGH the endothelial cells (because they are coupled together by gap junctions). 

Enter the pericytes which are electrically coupled to the underlying capillary endothelium by gap junctions, so they can receive the endothelial hyperpolarizing signal directly.  This causes the pericyte process receiving the signal to relax opening up the capillary or small artery increasing blood flow.  The authors followed this by watching intracellular calcium changes in pericytes, and noted that individual processes (ribs in the analogy above) could respond individually.  This is how a pericyte straddling the junction of two capillaries will open just the one which is hyperpolarized by neural activity.  

An incredibly elegant mechanism.  Of course with something so dramatic the work needs to be repeated. 

It is a pleasure to write something not involving the pandemic virus and our response to it. 

Functional MRI research is a scientific sewer — take 2

You’ve heard of P-hacking, slicing and dicing your data until you get a statistically significant result.  I wrote a post about null-hacking –https://luysii.wordpress.com/2019/12/22/null-hacking-reproducibility-and-its-discontents-take-ii/.  Welcome to the world of pipeline hacking.  Here is a brief explanation of the highly technical field of functional magnetic resonance imaging (fMRI).   Skip to the **** if you know this already.

Chemists use MRI all the time, but they call it Nuclear Magnetic Resonance. Docs and researchers quickly changed the name to MRI because no one would put their head in something with Nuclear in the name.

There are now noninvasive methods to study brain activity in man. The most prominent one is called BOLD (Blood Oxygen Level Dependent), and is based on the fact that blood flow increases way past what is needed with increased brain activity. This was actually noted by Wilder Penfield operating on the brain for epilepsy in the 1930s. When a patient had a seizure on the operating table (they could keep things under control by partially paralyzing the patient with curare) the veins in the area producing the seizure turned red. Recall that oxygenated blood is red while the deoxygenated blood in veins is darker and somewhat blue. This implied that more blood was getting to the convulsing area than it could use.

BOLD depends on slight differences in the way oxygenated hemoglobin and deoxygenated hemoglobin interact with the magnetic field used in magnetic resonance imaging (MRI). The technique has had a rather checkered history, because very small differences must be measured, and there is lots of manipulation of the raw data (never seen in papers) to be done. 10 years ago functional magnetic imaging (fMRI) was called pseudocolor phrenology.

Some sort of task or sensory stimulus is given and the parts of the brain showing increased hemoglobin + oxygen are mapped out. As a neurologist as far back as the 90s, I was naturally interested in this work. Very quickly, I smelled a rat. The authors of all the papers always seemed to confirm their initial hunch about which areas of the brain were involved in whatever they were studying.

****

Well now we know why.  The data produced by and MRI is so extensive and complex that computer programs (pipelines) must be used to make those pretty pictures.  The brain has a volume of 1,200 cubic centimeters (or 1,200,000 cubic millimeters).  Each voxel of an MRI (like the pixels on your screen is about 1 cubic millimeter) and basically gives you a number of how much energy is absorbed by the voxel.  Computer programs (called pipelines) must be used to process it and make those pretty pictures you see.

Enter Nature vol. 582 pp. 36 – 37, 84 – 88 ’20 and the Neuroimaging Analysis Replication and Prediction Study (NARPS).  70 different teams were given the raw data from 108 people, each of whom was performing one or the other of two versions of a task through to study decision making under risk.  The groups were asked to analyze the data to test 9 different hypotheses about what part of the brain should light up in relation to  specific feature of the task.

Now when a doc orders a hemoglobin from the lab he’s pretty should that they’ll all give the same result because they determine hemoglobin by the same method.  Not so for functional MRI.  All 70 teams analyzed the data using different pipelines and workflows.

Was there agreement.  20% of the teams reported a result different from most teams.  Random is 50%.  Remember they all got the same raw data.

From the News and Views commentary  on the the paper.

“It is unfortunately common for researchers to explore various pipelines to find the ver­sion that yields the ‘best’ results, ultimately reporting only that pipeline and ignoring the others.”

This explains why I smelled a rat 30 years ago.  I call this pipeline hacking.

Further infelicities in the field can be found in the following posts

l. it was shown in 2014 that 70% of people having functional MRIs (fMRIs) were asleep during the test, and that until then fMRI researchers hadn’t checked for it. For details please see
https://luysii.wordpress.com/2014/05/18/how-badly-are-thy-researchers-o-default-mode-network/. You don’t have to go to med school, to know that the brain functions quite differently in wake and sleep.

2. A devastating report in [ Proc. Natl. Acad. Sci. vol. 113 pp. 7699 – 7600, 7900 – 7905 ’16 ] showed that certain common settings in 3 software pacakages (SPM, FSL, AFNI) used to analyze fMRI data gave false positive results ‘up to’ 70% of the time. Some 3,500 of the 40,000 fMRI studies in the literature over the past 20 years used these settings. The paper also notes that a bug (now corrected after being used for 15 years) in one of them also led to false positive results.  For details see — https://luysii.wordpress.com/2016/07/17/functional-mri-research-is-a-scientific-sewer/

In fairness to the field, the new work and #1 and #2 represent attempts by workers in fMRI to clean it up.   They’ve got a lot of work to do.

Measuring what the brain thinks it is perceiving rather than the stimulus itelf

It’s usually not hard to do neuropsychology experiments.  The hard part is being smart enough to think of a good one.  I found a recent one absolutely brilliant, as the authors were able to measure a signal which had to be coming from the conscious perception of motion in a particular direction [ Proc. Natl. Acad. Sci. vol. 116 pp. 5096 – 5101 ’19 ].

Throw any stimulus at a living human and you’ll get some sort of measurable electrical response or a measurable change in blood flow in a particular brain area (you can use functional MRI — fMRI to measure the latter).  But how do you know whether the response has anything to do with conscious perception.  You don’t.

Here’s where the cleverness of the authors comes in.  Probably most people reading this post know about Cartesian coordinates, but to not leave the nonMathematically inclined behind, I’ll use baseball to describe the experimental set up.

We talk about a baseball diamond, and that’s the way it looks to people sitting in the stands behind home plate.  But actually the 4 bases form a perfect square 90 feet on a side.

So turn the ‘diamond’ on its side so the path between home plate and first base is horizontal, as is the path between 2nd and third while the paths between first and second and between third base and home are vertical.

Now that you’re oriented, imagine this on a computer screen. What the authors did was to light up first and third for .15 seconds, turn things off for .067 seconds and then light up home plate and second base for .15 seconds.  So the dot pairs alternate about 4 times a second.

But what does this look like to a human being?  For about 10 seconds the dots actually appear to actually be moving horizontally, then they appear to be moving vertically.  Remember the dots themselves  aren’t moving at all, just blinking.

The brilliance of the setup is that with exactly the same stimulus (alternately lit pairs of dots) the same person will have two different perceptions of the way the dots are moving at different times.

What do you think they did next?

They put the same people in an MRI machine and then showed the dots actually moving across the screen horizontally and then vertically.  Different parts of the brain responded to vertical motion than responded to horizontal motion.  The response was increased blood flow to that area, which is what fMRI actually measures.

So then back to the original set up with alternate pairs of dots on and off about 4 times a second.  Then they asked people which way the dots appeared to be moving, and the area of the brain which lit up (showed increased flow) was the same one which lit up to actual motion in that direction.

So they were actually measuring conscious perception of motion, rather than some nonspecific response to the visual stimulus, because the stimulus didn’t change regardless of the way it was perceived.

One of things this means is that the brain is producing the same neural response when it perceives motion in one direction (even though none is present) that real motion produces.

I think this is just brilliant.  Bravo. Something for the philosophers among you to chew on.

Functional MRI research is a scientific sewer

First a primer about the science underlying functional Magnetic Resonance Imaging (fMRI). Chemists use MRI all the time, but they call it Nuclear Magnetic Resonance. Docs and researchers quickly changed the name to MRI because no one would put their head in something with Nuclear in the name.

There are now noninvasive methods to study brain activity in man. The most prominent one is called BOLD (Blood Oxygen Level Dependent), and is based on the fact that blood flow increases way past what is needed with increased brain activity. This was actually noted by Wilder Penfield operating on the brain for epilepsy in the 1930s. When a patient had a seizure on the operating table (they could keep things under control by partially paralyzing the patient with curare) the veins in the area producing the seizure turned red. Recall that oxygenated blood is red while the deoxygenated blood in veins is darker and somewhat blue. This implied that more blood was getting to the convulsing area than it could use.

BOLD depends on slight differences in the way oxygenated hemoglobin and deoxygenated hemoglobin interact with the magnetic field used in magnetic resonance imaging (MRI). The technique has had a rather checkered history, because very small differences must be measured, and there is lots of manipulation of the raw data (never seen in papers) to be done. 10 years ago functional magnetic imaging (fMRI) was called pseudocolor phrenology.

Some sort of task or sensory stimulus is given and the parts of the brain showing increased hemoglobin + oxygen are mapped out. As a neurologist as far back as the 90s, I was naturally interested in this work. Very quickly, I smelled a rat. The authors of all the papers always seemed to confirm their initial hunch about which areas of the brain were involved in whatever they were studying. Science just isn’t like that. Look at any issue of Nature or Science and see how many results were unexpected. Results were largely unreproducible. It got so bad that an article in Science 2 August ’02 p. 749 stated that neuroimaging (e.g. functional MRI) has a reputation for producing “pretty pictures” but not replicable data. It has been characterized as pseudocolor phrenology (or words to that effect). Keep reading you’re about to find out just why this was.

What was going on? The data was never actually shown, just the authors’ manipulation of it. Acquiring the data is quite tricky — the slightest head movement alters the MRI pattern. Also the difference in NMR signal between hemoglobin without oxygen and hemoglobin with oxygen is small (only 1 – 2%). Since the technique involves subtracting two data sets for the same brain region, this doubles the error.

Under two years ago, it was shown that 70% of people having functional MRIs (fMRIs) were asleep during the test, and that until then fMRI researchers hadn’t checked for it. For details please see
https://luysii.wordpress.com/2014/05/18/how-badly-are-thy-researchers-o-default-mode-network/. You don’t have to go to med school, to know that the brain functions quite differently in wake and sleep.

Recent work shows that functional MRI work is even worse. A devastating report in [ Proc. Natl. Acad. Sci. vol. 113 pp. 7699 – 7600, 7900 – 7905 ’16 ] showed that certain common settings in 3 software pacakages (SPM, FSL, AFNI) used to analyze fMRI data gave false positive results ‘up to’ 70% of the time. Some 3,500 of the 40,000 fMRI studies in the literature over the past 20 years used these settings. The paper also notes that a bug (now corrected after being used for 15 years) in one of them also led to false positive results.

Here’s a bit more detail on what they did. It turns out that analyzing one voxel (essentially a single MRI pixel) at a time produces valid results. The problem comes when multiple voxels (clusters) are analyzed together. Clusterwise inference considers both the strength of activity at spots throughout the brain as well as the size of the spots. When a parameter called the cluster defining threshold (CDT) is set too low, the analysis is more likely to be false positive. This was true for all 3 packages tested. Parametric statistical methods produce the problem (not for voxels but for clusters). It relies on Gaussian Random Field Theory (RFT) for clusters , which depends on two other assumptions (1) the spatial autocorrelation function has a squared exponential shape — e.g. Gaussian (2) the spatial smoothness of the fMRI signal is constant over the brain. Neither of these assumptions is correct. Those of you who’ve read Nassim Nicholas Taleb about the stock market know about ‘fat tails’. It turns out that the spatial correlation function has them. Here’s what a fat tail is all about. Human height goes fall quite nicely into a Gaussian distribution. There are 7 and 8 footers about but they are rare. If the human height distribution wasn’t Gaussian but had a fat tail, we’d see 12 and 15 footers.

If that wasn’t bad enough,the following is even worse (in my opinion). 40% of 241 recent fMRI studies didn’t report using well known methods for correcting for multiple testing. They may have done so, but every biomedical paper, and drug study says so explicitly. Not only that but drug studies are required to explicitly state the hypothesis (or hypotheses) they are testing.

This is probably why in the early days, fMRI researchers always confirmed their original hypothesis. They could test the massive fMRI for statistical rarity, and since the data was so large, find it and post hoc propter hoc publish it. Possibly they did so out of ignorance, but even so this is inexcusable

Spot the flaw

Mathematical talent varies widely. It was a humbling thing a few years ago to sit in an upper level college math class on Abstract Algebra with a 16 year old high school student taking the course, listening with one ear while he did his German homework. He was later a double summa in both math and physics at Yale. So do mathematicians think differently? A fascinating paper implies that they use different parts of their brain doing math than when not doing it. The paper has one methodological flaw — see if you can find it.

[ Proc. Natl. Acad. Sci. vol. 113 pp. 4887 – 4889, 4909 – 4917 ’16 ] 15 expert mathematicians and 15 nonMathematicians with comparable academic qualifications were studied (3 literature, 3 history 1 philosophy 2 linguistics, 1 antiquity, 3 graphic arts and theater 1 communcation, 1 heritage conservation — fortunately no feminist studies). They had to listen to mathematical and nonMathematical statements and decide true false or meaningless. The nonMathematical statements referred to general knowledge of nature and history. All this while they were embedded in a Magnetic Resonance Imager, so that functional MRI (fMRI) could be performed.

In mathematicians there was no overlap of the math responsive network (e.g. the areas of the brain activated by doing math) with the areas activated by sentence comprehension and general semantic knowledge.

The same brain networks were activated by all types of mathematical statement (geometry, analysis, algebra and topology) as opposed to nonMathematical statement. The areas activated were the dorsal parietal, ventrolateral temporal and bilateral frontal. This was only present in the expert mathematicians (and only to mathematical statements) These areas are outside those associated with language (inferior frontal gyrus of the left hemisphere). The activated areas are also involved in visual processing of arabic numbers and simple calculation. The activated areas in mathematicians were NOT those related to language or general knowledge.

So what’s wrong with the conclusion? The editorialist (pp. 4887 – 4889) pointed this out but I thought of it independently.

All you can say is that experts working in their field of expertise use different parts of their brain than they use for general knowledge. The nonMathematicians should have been tested in their field of expertise. Shouldn’t be hard to do.

Why some of us gamble

If you are one of the hapless schlubs who bought a Powerball ticket or two and didn’t win (like me), modern neuroscience can tell you why (but not without a bit of pompous terminology). They call a small chance of winning large amounts — e.g. Powerball along with a large chance of losing a little a positively skewed gamble. Impressed? I’m not.

Nonetheless [ Neuron vol. 89 pp. 63 – 69 ’16 ] is a very interesting paper. Functional Magnetic Resonance Imaging (fMRI – https://en.wikipedia.org/wiki/Functional_magnetic_resonance_imaging) has shown that increased blood flow in one area of the brain (the nucleus accumbent sept) predicts risk seeking choices, while increased blood flow in another (the anterior insula) predicts aversion to risk. The unproven assumption behind fMRI is that increased blood flow is due to increased neural activity.

The neurochemistry of the two regions is quite different. The accumbens gets dopamine input while the insula gets norepinephrine projections.

BTW the insula is unique to man. Our cortex has grown so much (particularly in the frontal region) that it folds over on itself burying the insular cortex — https://en.wikipedia.org/wiki/Insular_cortex.

We are now actually able to measure axon bundles (white matter fiber tracts) in the living brain, using something called diffusion weighted MRI. By and large, fiber tracts tend to have the fibers parallel and running in the same direction. It is far easier for water to flow along parallel fibers than across them, and this is what the technique measures. For the mathematically inclined, what is actually measured is a tensor field, because at any given point in the brain it varies in direction, unlike a vector field which points just one way at a given point (the mathematically inclined know that this is a simplification because vectors are actually a type of tensor).

At any rate, the work used diffusion wieghted MRI to study the white matter tracts connecting the two areas. The larger the tract between insula and accumbens was the more risk averse an individual was. The implication being that a larger tract is a better connection between the two. So your nucleus is your impulsive child and the anterior insula is your mother telling you not to do anything crazy.

Fascinating, but like all this stuff it needs to be replicated, as it probably confirms the original idea for the study.

The Silence is Deafening

A while back I wrote a post concerning a devastating paper which said that papers concerning the default mode of brain activity (as seen by functional magnetic resonance imaging { fMRI } ) had failed to make sure that the subjects were actually awake during the study (and most of them weren’t). The post is copied here after the ****

Here’s a paper from July ’14 [ Proc. Natl. Acad. Sci. vol. 111 pp. 10341 – 10346 ’14 ] Functional brain networks are typically mapped in a time averaged sense, based on the assumption that functional connections remain stationary in the resting brain. Typically resting state fMRI (default network == rsfMRI) is sampled at a resolution of 2 seconds or slower.

However the human connectome project (HCP) has high-quality rsfMRI data at subsecond resolution (using multiband accelerated echo planar imaging. This work used a sliding window approach mapping the evolution of functional brain networks over a continuous 15 minute interval at subsecond resolution in 10 people. I wrote the lead author 21 July ’14 to ask how he knew the subjects weren’t asleep during this time.

No response. The silence is deafening.

Another more recent paper [ Proc. Natl. Acad. Sci. vol. 111 pp. 14259–14264 ’14 ] had interesting things to say about brain maturation in attention deficit disorder/ hyperactivity — here’s the summary

It was proposed that individuals with attention-deficit/hyperactivity disorder (ADHD) exhibit delays in brain maturation. In the last decade, resting state functional imaging has enabled detailed investigation of neural connectivity patterns and has revealed that the human brain is functionally organized into large-scale connectivity networks. In this study, we demonstrate that the developing relationships between default mode network (DMN) and task positive networks (TPNs) exhibit significant and specific maturational lag in ADHD. Previous research has found that individuals with ADHD exhibit abnormalities in DMN–TPN relationships. Our results provide strong initial evidence that these alterations arise from delays in typical maturational patterns. Our results invite further investigation into the neurobiological mechanisms in ADHD that produce delays in development of large-scale networks.

I wrote the lead author a few days ago to ask how he knew the subjects weren’t asleep during this time.

No response. The silence is deafening.

***

Addendum 22 Nov ’14 — In a huge review of resting state MRI (Neuron vol. 84 pp. 681 – 696 ’14) The following appeared —
“The issue of inadvertent sleep has only recently gained prominence, and the field has not yet developed consensus on how to deal with this issue.” Well, silence is no longer an option.

If you Google “default mode network” you get 32 million hits in under a second. This is what the brain is doing when we’re sitting quietly not carrying out some task. If you don’t know how we measure it using functional mMRI skip to the #### and then come back. I’m not a fan of functional MRI (fMRI), the pictures it produces are beautiful and seductive, and unfortunately not terribly repeatable.

If [ Neuron vol. 82 pp. 695 – 705 ’14 ] is true than all the work on the default network should be repeated.

Why?

Because they found that less than half of 71 subjects studied were stably awake after 5 minutes in the scanner. E.g. they were actually asleep part of the time.

How can they say this?

They used Polysomnography — which simultaneously measures tons of things — eye movements, oxygen saturation, EEG, muscle tone, respiration pulse; the gold standard for sleep studies on the patients while in the MRI scanner.

You don’t have to be a neuroscientist to know that cognition is rather different in wake and sleep.

Pathetic.

####

There are now noninvasive methods to study brain activity in man. The most prominent one is called BOLD, and is based on the fact that blood flow increases way past what is needed with increased brain activity. This was actually noted by Wilder Penfield operating on the brain for epilepsy in the 30s. When the patient had a seizure on the operating table (they could keep things under control by partially paralyzing the patient with curare) the veins in the area producing the seizure turned red. Recall that oxygenated blood is red while the deoxygenated blood in veins is darker and somewhat blue. This implied that more blood was getting to the convulsing area than it could use.

BOLD depends on slight differences in the way oxygenated hemoglobin and deoxygenated hemoglobin interact with the magnetic field used in magnetic resonance imaging (MRI). The technique has had a rather checkered history, because very small differences must be measured, and there is lots of manipulation of the raw data (never seen in papers) to be done. 10 years ago functional magnetic imaging (fMRI) was called pseudocolor phrenology.

Some sort of task or sensory stimulus is given and the parts of the brain showing increased hemoglobin + oxygen are mapped out. As a neurologist, I was naturally interested in this work. Very quickly, I smelled a rat. The authors of all the papers always seemed to confirm their initial hunch about which areas of the brain were involved in whatever they were studying. Science just isn’t like that. Look at any issue of Nature or Science and see how many results were unexpected. Results were largely unreproducible. It got so bad that an article in Science 2 August ’02 p. 749 stated that neuroimaging (e.g. functional MRI) has a reputation for producing “pretty pictures” but not replicable data. It has been characterized as pseudocolor phrenology (or words to that effect).

What was going on? The data was never actually shown, just the authors’ manipulation of it. Acquiring the data is quite tricky — the slightest head movement alters the MRI pattern. Also the difference in NMR signal between hemoglobin without oxygen and hemoglobin with oxygen is small (only 1 – 2%). Since the technique involves subtracting two data sets for the same brain region, this doubles the error.

A huge amount of work will need to be redone

The previous post is reprinted below the —- if you haven’t read it, you should do so now before proceeding.

Briefly, no one had ever bothered to check if subjects were asleep while studying the default mode of brain activity. The paper discussed in the previous post appeared in the 7 May ’14 issue of Neuron.

In the 13 May ’14 issue of PNAS [ Proc. Natl. Acad. Sci. vol. 111 pp. E2066 – E2075 ’14 ] a paper appeared on genetic links to default mode abnormalities in schizophrenia and bipolar disorder.

From the abstract “Study subjects (n = 1,305) underwent a resting-state functional MRI scan and were analyzed by a two-stage approach. The initial analysis used independent component analysis (ICA) in 324 healthy controls, 296 Schizophrenic probands, 300 psychotic bipolar disorder probands, 179 unaffected first-degree relatives of schizophrenic pro bans, and 206 unaffected first-degree relatives of psychotic bipolar disorder probands to identify default mode networks and to test their biomarker and/or endophenotype status. A subset of controls and probands (n = 549) then was subjected to a parallel ICA (para-ICA) to identify imaging–genetic relationships. ICA identified three default mode networks.” The paper represents a tremendous amount of work (and expense).

No psychiatric disorder known to man has normal sleep. The abnormalities found in the PNAS study may not be of the default mode network, but in the way these people are sleeping. So this huge amount of work needs to be repeated. An tghis is just one paper. As mentioned a Google search on Default Networks garnered 32,000,000 hits.

Very sad.

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How badly are thy researchers, O default mode network

If you Google “default mode network” you get 32 million hits in under a second. This is what the brain is doing when we’re sitting quietly not carrying out some task. If you don’t know how we measure it using functional mMRI skip to the **** and then come back. I’m not a fan of functional MRI (fMRI), the pictures it produces are beautiful and seductive, and unfortunately not terribly repeatable.

If [ Neuron vol. 82 pp. 695 – 705 ’14 ] is true than all the work on the default network should be repeated.

Why?

Because they found that less than half of 71 subjects studied were stably awake after 5 minutes in the scanner. E.g. they were actually asleep part of the time.

How can they say this?

They used Polysomnography — which simultaneously measures tons of things — eye movements, oxygen saturation, EEG, muscle tone, respiration pulse; the gold standard for sleep studies on the patients while in the MRI scanner.

You don’t have to be a neuroscientist to know that cognition is rather different in wake and sleep.

Pathetic.

****

There are now noninvasive methods to study brain activity in man. The most prominent one is called BOLD, and is based on the fact that blood flow increases way past what is needed with increased brain activity. This was actually noted by Wilder Penfield operating on the brain for epilepsy in the 30s. When the patient had a seizure on the operating table (they could keep things under control by partially paralyzing the patient with curare) the veins in the area producing the seizure turned red. Recall that oxygenated blood is red while the deoxygenated blood in veins is darker and somewhat blue. This implied that more blood was getting to the convulsing area than it could use.

BOLD depends on slight differences in the way oxygenated hemoglobin and deoxygenated hemoglobin interact with the magnetic field used in magnetic resonance imaging (MRI). The technique has had a rather checkered history, because very small differences must be measured, and there is lots of manipulation of the raw data (never seen in papers) to be done. 10 years ago functional magnetic imaging (fMRI) was called pseudocolor phrenology.

Some sort of task or sensory stimulus is given and the parts of the brain showing increased hemoglobin + oxygen are mapped out. As a neurologist, I was naturally interested in this work. Very quickly, I smelled a rat. The authors of all the papers always seemed to confirm their initial hunch about which areas of the brain were involved in whatever they were studying. Science just isn’t like that. Look at any issue of Nature or Science and see how many results were unexpected. Results were largely unreproducible. It got so bad that an article in Science 2 August ’02 p. 749 stated that neuroimaging (e.g. functional MRI) has a reputation for producing “pretty pictures” but not replicable data. It has been characterized as pseudocolor phrenology (or words to that effect).

What was going on? The data was never actually shown, just the authors’ manipulation of it. Acquiring the data is quite tricky — the slightest head movement alters the MRI pattern. Also the difference in NMR signal between hemoglobin without oxygen and hemoglobin with oxygen is small (only 1 – 2%). Since the technique involves subtracting two data sets for the same brain region, this doubles the error.