Request for Comments on Abstract

[ingber at umiacs.umd.edu]

Below is the Abstract and Conclusion of a 100+ page paper submitted to
Physical Review.  Comments are welcome, and I will fulfill reprint requests
after publication of this paper.

==============================================================================

                 Statistical mechanics of neocortical interactions:
                A scaling paradigm applied to electroencephalography


                                    Lester Ingber
            Science Transfer Corporation, P.O. Box 857, McLean, VA 22101


               A series of papers has developed a statistical mechanics  of
          neocortical  interactions  (SMNI), deriving aggregate behavior of
          experimentally  observed  columns  of  neurons  from  statistical
          electrical-chemical  properties  of synaptic interactions.  While
          not useful to yield insights at the single neuron level, SMNI has
          demonstrated  its capability in describing large-scale properties
          of short-term memory and electroencephalographic (EEG)  systemat-
          ics.   The necessity of including nonlinear and stochastic struc-
          tures in this development has been stressed.  In  this  paper,  a
          more  stringent test is placed on SMNI: The algebraic and numeri-
          cal algorithms previously developed in this and  similar  systems
          are  brought  to  bear  to fit large sets of EEG/evoked potential
          data being collected to investigate  genetic  predispositions  to
          alcoholism  and  to  extract  brain  "signatures"  of  short-term
          memory.  It is demonstrated that SMNI can indeed  fit  this  data
          within   experimentally   observed   ranges   of  its  underlying
          neuronal-synaptic parameters, and use the  quantitative  modeling
          results  to  examine  physical neocortical mechanisms to discrim-
          inate between  high-risk  and  low-risk  populations  genetically
          predisposed  to  alcoholism.  Since this first study is a control
          to include  relatively  long  time  epochs,  similar  to  earlier
          attempts  to  establish such correlations, this discrimination is
          inconclusive.  However, the model is shown to be consistent  with
          EEG  data  and  with  neocortical mechanisms previously published
          using this approach.  This paper  explicitly  identifies  similar
          nonlinear   stochastic   mechanisms   of   interaction   at   the
          microscopic-neuronal,   mesoscopic-columnar   and    macroscopic-
          regional  scales of neocortical interactions.  These results give
          strong quantitative support for an  accurate  intuitive  picture,
          portraying    neocortical    interactions    as   having   common
          algebraic/physics mechanisms that scale  across  quite  disparate
          spatial   scales   and   functional/behavioral  phenomena,  i.e.,
          describing interactions among neurons, columns  of  neurons,  and
          regional masses of neurons.


          PACS Nos.: 87.10.+e, 05.40.+j, 02.50.+s, 02.70.+d

                                   VI. CONCLUSION

               We have outlined in some detail  a  reasonable  approach  to
          extract  more  ``signal''  out  of  the ``noise'' in EEG data, in
          terms of physical dynamical variables, than by merely  performing
          regression  statistical  analyses  on  collateral  variables.  To
          learn more about complex systems, we inevitably must  form  func-
          tional  models  to represent huge sets of data.  Indeed, modeling
          phenomena is as much a cornerstone of 20th century science as  is
          collection of empirical data.

               We have been able to fit  these  sets  of  EEG  data,  using
          parameters either set to experimentally observed values, or being
          fitted within experimentally  observed  values.   The  ranges  of
          columnar  firings  are  consistent  with  a  centering  mechanism
          derived in earlier papers.

               The ability to fit data to these particular SMNI  functional
          forms  goes  beyond  nonlinear statistical modeling of data.  The
          plausibility of the SMNI model, as emphasized in this and  previ-
          ous  SMNI  papers,  as spanning several important neuroscientific
          phenomena, suggests that the fitted functional forms may yet help
          to  explicate  some underlying biophysical mechanisms responsible
          for the normal and abnormal behavioral states being investigated,
          e.g.,  excitatory  and/or inhibitory influences, background elec-
          tromagnetic influences from nearby firing states (by  using  SMNI
          synaptic conductivity parameter in the fits).

               There is much more  work  to  be  done.   We  have  not  yet
          addressed  the  "renormalization"  issues  raised,  based  on the
          nature of EEG data collection, and which  are  amenable  to  this
          framework.   While  the  fitting of these distributions certainly
          compacts the experimental data onto a reasonable algebraic model,
          a  prime  task  of most physical theory, in order to be useful to
          clinicians (and therefore to give more feedback to  theory)  more
          data  reduction  must  be  performed.   We are experimenting with
          path-integral calculations and some methods of "scientific  visu-
          alization"  to  determine what minimal, or at least small, set of
          "signatures" might suffice to be faithful to the data yet  useful
          to  clinicians.   We  also  are examining the gains that might be
          made by putting these codes  onto  a  parallel  processor,  which
          might  enable  real-time  diagnoses  based  on  non-invasive  EEG
          recordings.

               In order to detail such a model of EEG phenomena we found it
          useful  to seek guidance from ``top-down'' models, e.g., the non-
          linear string model representing nonlinear  dipoles  of  neuronal
          columnar  activity.   In  order  to  construct  a  more  detailed
          ``bottom-up'' model that could give us reasonable algebraic func-
          tions  with physical parameters to be fit by data, we then needed
          to bring together a wealth of empirical  data  and  modern  tech-
          niques of mathematical physics across multiple scales of neocort-
          ical activity.  At each of these scales, we  had  to  derive  and
          establish  reasonable procedures and sub-models for climbing from
          scale to scale.  Each of these sub-models could  then  be  tested
          against  some  experimental  data  to see if we were on the right
          track.  For example, at the  mesoscopic  scale  we  checked  con-
          sistency  of  SMNI  with  known  aspects  of  visual and auditory
          short-term memory; at  the  macroscopic  scale  we  checked  con-
          sistency with known aspects of EEG and propagation of information
          across neocortex.  Here, we have demonstrated that the  currently
          accepted  dipole  EEG  model can be derived as the Euler-Lagrange
          equations of an electric-potential Lagrangian.

               The theoretical  and  experimental  importance  of  specific
          scaling  of  interactions  in  neocortex  has been quantitatively
          demonstrated: We have shown that the explicit algebraic  form  of
          the probability distribution for mesoscopic columnar interactions
          is driven by a nonlinear threshold factor of the same form  taken
          to  describe  microscopic  neuronal  interactions,  in  terms  of
          electrical-chemical synaptic and neuronal  parameters  all  lying
          within their experimentally observed ranges; these threshold fac-
          tors largely determine the nature of the drifts and diffusions of
          the  system.   This  mesoscopic probability distribution has suc-
          cessfully described STM phenomena and, when used as  a  basis  to
          derive  most  likely trajectories using the Euler-Lagrange varia-
          tional equations, it also has described the  systematics  of  EEG
          phenomena.   In  this paper, we have taken the mesoscopic form of
          the full probability distribution more seriously for  macroscopic
          interactions, deriving macroscopic drifts and diffusions linearly
          related to sums of  their  (nonlinear)  mesoscopic  counterparts,
          scaling  its  variables  to  describe interactions among regional
          interactions correlated with observed electrical activities meas-
          ured by electrode recordings of scalp EEG, with apparent success.
          These results give strong quantitative support  for  an  accurate
          intuitive  picture, portraying neocortical interactions as having
          common  algebraic/physics  mechanisms  that  scale  across  quite
          disparate  spatial  scales  and  functional/behavioral phenomena,
          i.e., describing interactions among neurons, columns of  neurons,
          and regional masses of neurons.

               It seems reasonable to speculate on the evolutionary des