Visual Memory Research
The Genesis of Mnemonic Visual Systems 
Recurrent Dynamics in Excitable Media

Topic D11: The Helmholtz Traveling Waves - HTW

These Global Waves Traverse the Visual Field in Four Seconds.

Eldridge Green 1920, 
paper  described  “currents seen in the dark…bluish violet circles  in the periphery…..  which ... advance to the center of vision ,  break and  brighten at the fovea..  and are .. . succeeded by  a second circle.    These  phenomena  were named  earlier by Helmholtz  as blue bands , which  he  noted to have  a rhythmic activity  linked  to respiratory cycles.

Ermentrout  and  Kleinfeld,  2001  remark that  traveling electrical waves in  (excised)  cortex: “ are typically present during  periods outside of   stimulation.” (presumably  applicable to exclusion  of  any environmental  inputs which might  engender  frequency variances )   

Steven  Strogatz  2002  calls  to attention Art Winfree’s  original  concept of  “ gigantic systems of weakly coupled oscillators with randomly distributed  frequencies  .. . as  the variance of frequencies is reduced the  oscillators remain incoherent until a critical  threshold is reached when the oscillators  synchronize spontaneously ”

An oscillatory  synchronization may be  witnessed  subjectively in the Helmholtz  Blue Band Effect , a visual  phenomenon  wherein   bi-chromic  traveling  bands are seen traversing the cognitive field   as  circular ,  elliptical or  hyperbolic  contours   Helmholtz Travelling Waves :   HTW.       
                                                                                                                                                               INDUCTION  METHODS of  HTW  and  PERSONAL  OBSERVATIONS: 
from 1962  to 2008

Induction: The Helmholtz  Blue  Bands    (global traveling waves ) These are most salient following activity  out-doors  in  sunshine;   then in a  dark-adaptive process  these waves  emerge to view for the  now  sedentary observer. After adaptation to bright  ambient light ,  retinal  stimulation by  diffuse or focal light (or by local pressure on a globe), an observer  who then  remains  at  rest  with eyes  closed  in the dark  may  shortly witness  the  Helmholtz Travelling Waves , HTW.  These luminous  annular  bands arise within a  minute and  can  iterate   for about  two minutes , each band  transits the visual  field  within four seconds   These  bands pass  across the full cognitive field appearing  as pairs of  bi –chromic;  luminous zones , only  two  such  opponent  pairs  are  present at any one time.   Each  blue-purple zone  is paired with  a dimmer green -yellow  zones. of  equal width .     Each  set  is  refreshed  at  ~ 2 second   intervals,  together  they  travel continuously at a steady pace , either  centrifugally  or  centripetally ,  and  with  either  circular ,  elliptical or  hyperbolic  contours ,  transiting the field within four seconds ,   this configuration may be   determined  by  retinal  stimulation by  diffuse or focal light ,  or by local pressure on a globe.,:
3.31.2007   When  arousing  from sleep while dark  adapted .  the   HTW  arise from   increasing synaptic activity  of  arousal , but  the  centripetal  bands are then  of  diminished   luminance  and  of  brief duration . 

Propagation Speed:  As if mapped onto a  retinal surface  the apparent  propagation speed of the retinal  Helmholtz  “traveling waves ”  is   5  to - 10  mm per second..   There is  no perception of  the acceleration  as seen in  evolution of  the migraine aura,   attributable  to retino-cortical magnification   Blake 2001  2001   writing on  the dynamics of  one dimensional  traveling waves in visual perception ,  notes that  “when mapped onto visual cortex, propagation speed  was computed at  24 mm /sec across VI   , and that  the  propagation speed of such  traveling  waves  is independent of  eccentricity                                                        

Cycling  Rate   The slow  rate of  HTW   intra-retinal cycling matches  that of  the  automatic  regulated respiration rate,    and is   comparable to the periodicity of  visual retinal rivalry seen  in  reversals of  ambiguous images ,  also  commonly   around  four seconds 

Hue and Kinetics.     A  purple /yellow green  bi- stability  is  reported elsewhere  E  13 , 14 . in illusory  phenomena ,  Welpe  1978   Schurcliff   1959. , identified as sourced in the retina             The  luminous  purple/blue  segment  of  the bi-chromic  HTW  band is usually un-textured,  waning   in intensity  from leading to trailing  edge.   At the rear  it  gives way to the darker  reticulated  and flickering  yellow-green  zone ,  this  green  zone then  is overtaken  by  the next  oncoming  blue/purple  wave- front .      

Each HTW  front  transits  “ from source to sink” in  about  3-  4  seconds,   each sinusoidal  band is generated anew at  rates  varying between  1- 3 seconds, and disappears  in a  “sink ” located  in the visual field  diametrically  opposite  its apparent  source of  its  origin.

.    .These  luminous bands  arise  from the “hot-spots” selected  for  priming  upon  either  retina .   With a panoramic light source,  the ensuing  annular bands  then converge  upon  the fovea  where they  disappear, as was described by Green in 1920 .    However ,  following  a focal macular irradiation the  bands are circular , expanding and  radiating away from  the  foveally  imprinted  “source ”    If  the stimulus was  restricted to one half or one quadrant of  a monocular field  the expanding  contours then appear in parallel  as elliptical ,  parabolic or arcuate  contours as they then traverse the full visual field ,   
By   imposing  asymmetric conditions   bi-retinal  neuro-convergence can be demonstrated                                                                           
1)    With  patching of  one eye (the right selected)  while  the left open eye  is engaged upon a normal reading  activity , the  patched R  eye  shortly  perceives  diffuse fine particulate  luminous agitation , an  “inter-ocular transfer”(Mackay )   This oscillatory  activity  is most salient  when a  low level of  diffuse light is then  permitted to enter  the “occluded” eye .   Now  steadily fixing the left  gaze upon some other  target or graphic ,  waves of  “perceptual blanking ” may  traverse the  cognitive field .   On then closing both eyes  this wavering  phenomenon  may  re-appear with the typical  tempo and topography of the  Helmholtz waves 

 2)  By  photic  priming  of  the retinas  asynchronously or  at  non-corresponding  points  
(focal macular versus  any  peripheral  site )  or  by applying  local  pressure to only one  globe ,  the consequently mis-matched  topologies  and  phases  of the  contralateral displays can  then easily identify each retinal contribution to the perceptually  discrepant displays         When  thus induced asymmetrically, both the   choreographies  and the  intensities of their  respective  bands can be distinguished,   either by  their being  mutually  out- of -phase and /or   topologically distinct.

Yet after  a few cycles these competing patterns  no longer resemble the  simply overlaid  conical sectors ( one,  the  circular ,  the second ,  the hyperbolic   pattern  as  described above ) .  Shortly the  wave- fronts combine to  follow an  apparently spiraling  vector ,  so that the display  now  resembles  a scimitar –shaped sector  which rotates around the central point, and may  so continue for several  cycles    

Wilson HR, Kim J.
  “ Perceived motion in the vector sum direction... the visual system combines  ..components  to produce perceived motion in the vector sum direction, even when this deviates by as much as 53 deg from the intersection of constraints direction.”
                                  Modulations of other phenomena by the HTW           

3)   The  HTW  bands contain opponent hues ,  these  zones  of equal widths  and these   modulate the  mandala  rosette  pattern, the  fixed  radial array*  over which these HTW  “currents ”  flow (See The Mandala,  Purkinje’s  Rosette  pattern , aka  Bresloff’s planform) 
The Blue / band,   in  the  more luminous phase,   appears to further  brighten and  intensify the  “already  bright- nodes  ” of  the  Rosette  pattern. But  the  succeeding  yellow/green, the   less luminous phase of   the HTW,   rather than appearing to darken the brighter figures of the array  brightens only  the  “darker - background” of an  already  established  overall  spatially  stable  Mandala  pattern. Thus , in addition to  a  hue-change effect  across the visual field ,  the  luminous  blue  band enhances   the  pattern’s  contrast ,  whereas the  yellow/green  activity  diminishes the  perceived contrast ,   and  together the two phases may create a  three-dimension  light/shadow aspect to the illusory  figures  

Smythies   J . 1958  - 2000  This sculptural effect is seen with closure of both eyes , and is sustainable for minutes.  

Shevelev IA   2000,  scanning of the visual cortex by a spreading wave process operating at the frequency of the alpha-rhythm, which reads information from the visual cortex...                                                                                                                

                    Modulations of the HTW by other phenomena                 

 4 ) HTW   Modulated  by  Respiration /  Brain Stem Activity ,   The system of bands transiting   from source to sink over  3 to  4  seconds,  are  synchronized  with  the respiratory rhythm rate,  as was noted by Helmholtz.   However,  when  respiration is voluntarily suspended  the phasic sweep rhythm continues unchanged for a few  cycles before the HTW cease .   This indicates  that  central neural  rather than  the peripheral mechanical  effects of respiration modulate  the perturbation  which is  imposed  locally  or monocularly   by  the  photo- adaptive  triggers    
 . Grossman P, 2007 Respiratory sinus arrhythmia plays a primary role in regulation of energy exchange by means of synchronizing respiratory and cardiovascular processes during metabolic and behavioral change…
McGuinness M, 2004.  Arnold tongues in human cardiorespiratory systems... While RSA can cause synchronization where inspiration modulates heart-rate)  the strongest mechanism for synchronization is CVC cardioventilatory coupling (CVC, where the heart is a pacemaker for respiration)

5)   HTW   Modulated   by Vestibular  Inputs       Smooth-pursuit of a selected up- rising  arcuate  wave –front  can be carried out--  or simulated -- by  smooth elevation  of the chin  over a  physically- convenient   120   degree  .angle  .   This  pursuit  succeeds  in tracking ...”.stabilizing .”.. a  selected  wavefront   for  some 5-seconds ,  thereafter  the perceived  motions of the oncoming wave-fronts resume across the cognitive field ,again traveling   upwards  relative to borders  of  the cognitive field . ( A similar  phenomenon  has been observed with smooth –pursuit  of illusory persistent motion   C  8 . )   
Nicola EM, 2002 Drifting pattern domains DPDs exist due to a locking of the interface velocities, which is imposed by the absence of space-time defects near these interfaces.          

 6)   Oculomotion  tends to disrupt  HTW .   Disruption of   retinotopically   based  TW  by oculomotion  was noted also  by Blake 


What -Neuro-Retinal  Mechanisms  may enable  Perception of the HTW? 

It appears that  concentric waves of  alternating  polarity  drive the  mechanism  initiating the  perturbations of the neuro-visual  system .  The  size  of these  cyclical  concentric  zones (some 45 degrees  subtense ) would preclude  their attribution to identifiable neuronal pools or networks in the retina. itself , for  these  are  not  of  comparable extent .                                      

In  the dark-adapted eye  the  pigment epithelium  participates  in  the  electric potential differences  in  ERG measurements, that  waves of  sequential firings of  opponent  elements in a second order network  might  coincide  with,  or  cause,  or  result from,  some  transient  electro-motive potential changes across this  p.e.  “ membrane.”   However, the cycling rate  of the HTW  is  much  slower,  so it  is  problematic to attribute the phenomenon to this  purely local mechanism , or  to account for the HTW  bi-chromaticity . .   See  E 15  bi-stable  opponencies   and flux .                                                                                                                         

However , depolarization of the photoreceptors  in the dark releases neuro-transmitter to horizontal cells and  to bipolar cells    The ganglion cells (Dacey  1996 )  do  exhibit spectral opponency ,  but  it is said  that the horizontal  cells . H 1 obtain  input from  L and  M  cones  only , and that  H 2  input is  mainly from S cones and  that  no opponent  transformation was  identified in either H cell type ..     Dacey DM  “Horizontal cells of the primate retina :  cone specificity without spectral opponency. ”  Science  1996  Dec 20 Feb 2 ;274(5295):656-9  and  1999Feb 2 ;2271(5249):616-7  .    Are we seeing differential firing sequences arising  from these two populations of Horizontal cells?      See  E 15  bi-stable opponencies  and  flux .                                                                                                   

Based on the  geometry  and  the kinetics of the  HTW  it seems  that  polarity reversals   are occurring  in the retina and cortex ,  with  wave- fronts   traveling at (a retinal ) 7 mm   per second  .  In a robust display the alternate  blue bands and yellow - green reticulum arise always in tandem, in a  week display . luminance but not chroma is distinguished    Triggered by  photic priming and dark-adaptive transients ,  HTW   are  manifested in  darkness , with  a  rhythmicity   imposed  by  brainstem activity… Dark adaptation  equates to deprivation of visual input, and  Ermentrout  and  Kleinfeld ,  2001  noted  that  traveling electrical waves in cortex  “ are typically present during periods outside of   stimulation.”                                                                                             
The subjectively  visible  bi-phasic  Helmholtz  blue  bands  are  most salient during physical  passivity  in  two-minute dark-adaptive conditions  imposed  following out-door  activity and solar  irradiation     During in-activity  in  the dark , the brain, this   gigantic system of weakly  coupled oscillators. has  had  the  variance  of  frequencies  reduced     After a  one minute  hiatus , some   critical  threshold is reached and   the  oscillators become synchronized   In the absence  of  external stimuli  and  motor events, oscillators  respond .to  the  internal  fundamental ,  the  cardio-respiratory  rhythms emitted  from the  brainstem ,  at  ~  0 .25   Hz. After a two-minute  interlude ,  the local  networks /systems apparently  reset to they idiosyncratic rhythms ,  and perception  of  the  HTW  global oscillations  ceases                                                                                                                                                                                                      It is  possible  that these  HTW are  merely  epi-phenomenal,  serving  as a  visual marker  of   the  brain-stem impulses  which  flow  throughout the CNS .   After a two-minute  interlude ,  the local  networks /systems reset to their  idiosyncratic rhythms ,  over-riding   the vital-center emissions ,   and the  HTW .phenomenon  abates    

McGuinness M, 2004.  Arnold tongues in human cardiorespiratory systems... while RSA can cause synchronization where inspiration modulates heart-rate)  the strongest mechanism for synchronization is CVC cardio-ventilatory coupling (CVC, where the heart is a pacemaker for respiration)                                                        

Supposedly   bi-stability  in opponent systems is  present  at all hierarchal levels  in all sensori-motor  modalities.   Possibly  retino-cerebral  dominances , sometimes  patchy affairs ,  are  compounded of  multiple  localized  bi-stable (  weakly-coupled  )  neural oscillating  mechanisms ;   Blake  considers those traveling  waves as   “dominance waves  which  may  provide a new tool for investigating fundamental cortical dynamics.”