Tag Archives: Tensor vs. vector

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.

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Here’s just how poor the research on Autism Spectrum Disorder has been

A stroke 50 years ago would be a stroke today. Cancer is still cancer. Not so with Autism, Autism Spectrum Disorder (ASD), Asperger’s syndrome. The Diagnostic and Statistical Manual of the American Psychiatric Association (DSM to you) has gone through 6 editions (DSM-I through DSM-V, including DSM-IV-TR). The terms are defined differently in all (or not even defined). For the gory details see:

http://www.autismconsortium.org/symposium-files/WalterKaufmannAC2012Symposium.pdf

Here’s a summary.

DSM-I (1952) & DSM-II (1968)
No term Autism or Pervasive Developmental Disorder Closest term: Schizophrenic Reaction (Childhood Type)
1980 DSM-III
Pervasive Developmental Disorders (PDD):
Childhood Onset PDD, Infantile Autism, Atypical Autism
1987 DSM-III-R
Pervasive Developmental Disorders (PDD):
PDD-NOS, Autistic Disorder
1994 DSM-IV
Pervasive Developmental Disorders (PDD):
PDD-NOS, Autistic Disorder, Asperger Disorder, Childhood Disintegrative Disorder, Rett syndrome
2000 DSM-IV-TR
Same diagnoses, text correction for PDD-NOS

Needless to say, DSM-V (out since May 2013) has it differently.

The following paper [ Proc. Natl. Acad. Sci. vol. 111 pp. 1981 – 1986 ’14 ] should have neuroscientific researchers on Autism Spectrum Disorder (ASD) of the DSM-IV hanging their heads in shame.

The criteria for ASD are obviously a wastebasket. Here they are from the DSM-IV-TR

Autistic disorder (classic autism)
Asperger’s disorder (Asperger syndrome)
Pervasive developmental disorder not otherwise specified (PDD-NOS)
Rett’s disorder (Rett syndrome)
Childhood disintegrative disorder (CDD).

Just about any kid not doing well cognitively fits in to #3. Hopefully the DSM-V makes things better — it’s too early to tell. The link has the details and a lot of the reasoning behind yet another change.

All the work cited in the PNAS paper concerns ASD as diagnosed by DSM-IV-TR. DSM-V is too new to have papers out using its criteria.

If you take 100 kids developing normally, do various types of magnetic resonance imaging (MRI) on their brains, and compare then with 100 kids not doing well, you are certain to find more structural abnormalities of the brain in the second group, regardless of how they were diagnosed, or what they were diagnosed with.

Dozens of papers were written on MRIs in ASD kids. 40% had fewer than 15 subjects. The most replicated finding (up to the PNAS paper) was poor connections between various parts of the brain, manifest as abnormalities of the white matter. Exactly what they were measuring, and how the measurement requires a tensor and not a vector is really quite interesting and can teach you some math. I’ll save this for the end.

Only 2 of the dozens of papers controlled for data quality. MRIs have been around long enough, that most know that to get a decent study the subject has to be quite still, something very difficult for kids, and even harder for autistic kids.

When head motion was controlled for in this large (52 ASDs 73 normals to start) all the abnormalities disappeared (save one, and they looked at 18 different white matter tracts in the brain). They had to throw out the studies on 12/52 of the autistics and 2/73 normals because of motion– showing how suspect the previous data really was. The head motion was producing the abnormalities.

Is this terrible research or what (PNAS paper excepted)?

Perhaps the new criteria in DSM-V will result in a more homogenous group.

What does diffusion tensor imaging actually measure? Imagine the nerve fibers (axons) of the brain in the deep white matter as a bundle of wires, most of them going in the same direction in any small volume. Assume they are bathed in water. Now add some colored water at one end, and see how quickly the color diffuses in various directions in the bundle. The color will diffuse faster along the bundle, than in the two directions perpendicular to it. This is what the diffusion tensor measures — diffusion of tissue water in a variety of directions. If the bundle is loose, or disorganized, or some wires are missing, than the diffusion in the various directions won’t differ as much — this is called lack of anisotropy. Take out the wires and the diffusion is the same in all directions (no anisotropy at all). This was the finding in ASD — less white matter anisotropy in diffusion tensor imaging — implying that there is something wrong with it.

Why wouldn’t an overall vector summing up the diffusion in the major direction be enough. One can add vectors together after all. Because you’d lose all the information about anisotropy. The tensor preserves it. It’s why tensors are used to measure the stress in a given material. Slick. Now you understand (something) about tensors. However it should be noted that vectors are tensors too. There’s a lot more too it (particularly indices).