[FRIAM] Visual Migraines

[Stephen Guerin]

Frank,

Sorry you're experiencing migraines - no fun! On the upside, the
mathematician in you may appreciate the opportunity of direct observation
of potentially interesting feedback phenomena.

Jack Cowan, one of Stu's mentors, gave a nice talk at BioGroups back in
2001 on geometric patterns during hallucination due to instabilities
driving the feedback structures of the visual cortex. Jack had a couple
papers paper was with Paul Bressloff. Utah Math Department (
https://www.math.utah.edu/~bresslof/) Marty Golubitsky, co-author with Ian
Stewart of Fearful Symmetry
<https://www.amazon.com/Fearful-Symmetry-Geometer-Dover-Mathematics/dp/0486477584>,
and Peter Thomas <https://case.edu/math/thomas/>Case Western

paper here: https://www.math.uh.edu/~dynamics/reprints/papers/nc.pdf.
related paper here:
https://royalsocietypublishing.org/doi/abs/10.1098/rstb.2000.0769

What geometric visual hallucinations tell us about the visual cortex
Paul C. Bressloff, Jack D. Cowan*, Martin Golubitsky, Peter J. Thomas and
Matthew C. Wiener

ABSTRACT:
Geometric visual hallucinations are seen by many observers after taking
hal- lucinogens such as LSD, cannabis, mescaline or psilocybin, on viewing
bright flickering lights, on waking up or falling asleep, in “near death”
experiences, and in many other syndromes. Klu ̈ver organized the images
into four groups called “form constants”: (1) tunnels and funnels, (2)
spirals, (3) lattices, including honeycombs and triangles, and (4) cobwebs.
In general the images do not move with the eyes. We interpret this to mean
that they are generated in the brain. Here we present a theory of their
origin in visual cortex (area V1), based on the assumption that the form of
the retino-cortical map and the architecture of V1 determine their
geometry. We model V1 as the continuum limit of a lattice of interconnected
hypercolumns, each of which itself comprises a number of interconnected
iso-orientation columns. Based on anatomical evidence we assume that the
lateral connectivity between hypercolumns exhibits symmetries rendering it
invariant under the action of the Euclidean group E(2), composed of
reflections and translations in the plane, and a (novel) shift–twist
action. Using this symmetry, we show that the various patterns of activity
that spontaneously emerge when V1’s spatially uniform resting state becomes
unstable, correspond to the form constants when transformed to the visual
field using the retino–cortical map. The results are sensitive to the
detailed specification of the lateral connectivity and suggest that the
cortical mechanisms which generate geometric visual hallucinations are
closely related to those used to process edges, contours, textures and
surfaces.


_______________________________________________________________________
Stephen.Guerin at Simtable.com <stephen.guerin at simtable.com>
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On Mon, May 6, 2019 at 1:39 PM Frank Wimberly <wimberly3 at gmail.com> wrote:

> Also called optical migraines.  I experience them as perfect, complex,
> geometric patterns which scintillate and exhibit various colors.  How does
> that come about from the glop that is my brain or retina or whatever?  It's
> all glop.
>
> Frank
>
> -----------------------------------
> Frank Wimberly
>
> My memoir:
> https://www.amazon.com/author/frankwimberly
>
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> https://www.researchgate.net/profile/Frank_Wimberly2
>
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