[FieldTrip] High norm and correlation between columns of some (exterior) leadfield nodes

Mon Sep 28 15:16:24 CEST 2015

  Dear community,

  My name is Jan I am based at Nicolaus Copernicus University in Toruń
  (Poland), where I study CogSci, I am also member of small research
  group focused on on neuronal activity indices and reconstruction
  methods.  FieldTrip has turned out to be the most convenient and
  capable toolbox for the work we have done so far :)

  However, we have a question in respect of forward modelling.  We had
  a close look into some properties of leadfields and we are anxious
  if the features revealed are unusual, alarming or just standard and
  irrelevant?

  We have found that some leadfield nodes have norm (calculations
  described below) tremendously higher than the neighbouring nodes.
  Also some nodes are column-wise highly correlated.

  We obtained very similar results for both =icosahedron642= and
  random =sphere-like= triangulations.

  We have produced 2 volume conduction models and 2 corresponding
  leadfields that were based on =icosahedron642= or random
  =sphere-like meshes= geometry.  Radia for { 'brain' 'skull' 'scalp'
  } were [ 88 92 100 ].

  Electrodes (162, =icosahedron162=) were placed uniformly around the
  scalp All geometrical units were in mm.  Conductivity was expressed
  in in S/mm.

  We used =dipoli= and =openmeeg= methods with ft_prepare_headmodel

*  #+BEGIN_SRC matlab :eval no :exports code    cfg                 =
[];    cfg.method          = 'openmeeg';    cfg.conductivity    =
sel_msh02.cond    sel_vol02_openmeeg  = ft_prepare_headmodel( cfg,
sel_msh02.bnd );  #+END_SRC*

  and

*  #+BEGIN_SRC matlab :eval no :exports code    cfg                 =
[];    cfg.method          = 'dipoli';    cfg.conductivity    =
sel_msh02.cond    sel_vol02_dipoli    = ft_prepare_headmodel( cfg,
sel_msh02.bnd );  #+END_SRC*

  The laedfield was created using the following settings

*  #+BEGIN_SRC matlab :eval no :exports code    cfg                   =
[];    cfg.elec              = sel_elec00;    cfg.grid.unit         =
'mm';    cfg.grid.xgrid        = -110:5:110;       % Specify in mm!
cfg.grid.ygrid        = -110:5:110;       % Specify in mm!
cfg.grid.zgrid        = -110:5:110;       % Specify in mm!
cfg.reducerank        = 'no';    cfg.vol               =
sel_vol02_dipoli;    sel_lfg02_dipoli      = ft_prepare_leadfield(cfg);
cfg.vol               = sel_vol02_openmeeg;    sel_lfg02_openmeeg    =
ft_prepare_leadfield(cfg);  #+END_SRC*

** Norm

   Next, we plotted norm of the leadfields expressed as

   $norm(H) = sum(sum(abs(H)))$

   [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_712_leadfield-norms_openmeeg.png
]]

   On the figure above norm for OPENMEEG created leadfield is
   expressed by colour and marker size.  It is quite evident that
   leadfields with very high norm are distributed on the externals of
   the grid.

   [[file:img/fig_711_leadfield-norms_dipoli.png]]

   Same problem arises with DIPOLI leadfield, but to much smaller
   extent.  My it pose a serious threat to both spatial filters and
   some activity indices (such as power of LCMV filter).

   The following histograms also show the same feature of the
   leadfields.  Please note that the horizontal axis contains
   log(norm(H)) so the values spread is more dramatic than it appears
   at the first glace.

   [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_722_leadfield-normHist_openmeeg.png
]]

   [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_721_leadfield-normHist_dipoli.png
]]

** Correlation

   We also investigated correlation between columns of each leadfield
   node.  We suspect that this feature can also have deleterious efect
   on performance of some spatial filters and neuronal activity
   indices.

   Following scatterplots show this using color and marker size which
   reflect the absolute value of correlation coefficient between
   second and third column of each leadfield node (change of columns
   in consideration does not alleviate the problem.

   OPENMEEG
   [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_732_leadfield-corrCoefs_openmeeg.png
]]

   DIPOLI
   [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_731_leadfield-corrCoefs_dipoli.png
]]

** Differences between leadfields

   Futhermore we checked correlation between solutions provided by
   DIPOLI and OPENMEEG.  Here we calculated correlation coefficients
   between the two leadfield grids with respect to nodes of the same
   position inside the ``brain''.

   Following plot shows only leadfield nodes for which the absolute
   value of correlation coefficient was lower than 0.1.

   This shows that solutions for the nodes that are located deep
   inside brain are highly correlated.  The main differences between
   the leadfields are distributed at the exterior of the grid.

   [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_800_leadfield-corrCoefs-DIPOLI-vs-OPENMEEG.png
]]

** MATLAB figures

   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_666_triangulation-meshes.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_700_electrode-positions-and-labels.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_701_leadfield-geometry_dipoli.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_702_leadfield-geometry_openmeeg.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_711_leadfield-norms_dipoli.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_712_leadfield-norms_openmeeg.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_721_leadfield-normHist_dipoli.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_722_leadfield-normHist_openmeeg.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_731_leadfield-corrCoefs_dipoli.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_732_leadfield-corrCoefs_openmeeg.fig
]]
   * [[
https://github.com/nikadon/lfgTesting001/blob/master/img/fig_800_leadfield-corrCoefs-DIPOLI-vs-OPENMEEG.fig
]]

   Details of the MATLAB implementation for the above can be found on
   https://github.com/nikadon/lfgTesting001/blob/master/lfgTesting001.org

   Thank you in advance for any help or comments...

   Best,
   Jan
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