Analysis of topographic maps from fMRI data

1
Analysis of topographic maps from fMRI data
Thomas S. Reid, Department of Physics Anthony I.
Jack, Department of Cognitive Science Robert W.
Brown, Department of Physics Case Western
Reserve University 10900 Euclid Avenue Cleveland,
OH 44106
DEPARTMENT OF PHYSICS
Brain, Mind and Consciousness Lab
Department of Cognitive Science
Abstract In recent years, a number of studies
have attempted to demonstrate the presence of
retinotopic organization in occipital, parietal
and frontal cortex. The evidence for this
topography has come from inspection of
color-coded maps based on phase-encoded visual
field stimulation. However, this method is
qualitative in nature and the maps have not been
consistent between groups and subjects, thus
leaving the important question of what this
topography looks like or whether it even exists
unanswered. Our research involves regression
analysis of BOLD fMRI data in an attempt to
establish a more quantitatively rigorous
assessment of the presence of topographical maps
on the cortical surface. Using MATLAB, we have
found that color-coded scatter plots and
superimposed gradient fields are excellent
prospects for diagnosing and visualizing
retinotopic organization in visual cortex.
Conclusions Preliminary results indicate that
our analytical method represents an excellent
prospect for a more quantitatively rigorous
assessment of retinotopic organization. Our
method not only generates more meaningful color
plots it also incorporates the novel concept of
overlaying gradient fields, from which valuable
statistics can be obtained. With relatively
little refinement, our method is very sensitive
to the presence of topography in the early visual
areas (V1, V2, etc.), as evinced in Figure 6
below. Our findings also indicate that
retinotopic organization is much weaker, if at
all present, in the extra-occipital areas (LIP,
FEF, DLPFC). However, we cannot definitively
conclude whether or not a topography is present
until we establish a false alarm rate. In
addition, we would like to use our gold standard
measure to examine the effects of changing
various cutoff parameters in our method.
Figure 1. The subject is asked to stare at the
cross in the middle of the diagram, while a
series of flickering dots is displayed in one of
the rectangular regions of the visual field,
located at 30º (up), 90º (mid), or 150º (down)
from the top of the vertical meridian. Rectangle
colors and text as well as colored arrows have
only been added as a guide to our analytical
method and are NOT seen by the subject.

• Analytical Method
• Stimulate three angles of subject's visual field,
  one at a time,
• collecting BOLD fMRI response data for each
  angle
• Create a color map (i.e. scatter plot)
• At each point on a flattened cortical surface,
  determine which stimulus angle elicited the
  greatest response
• Assign each angle its own color (See Figure 1)
• up red mid blue down green
• Place a dot of the "winning" angle's color at
  each point, with bigger dots indicating more
  significant responses (See Figure 3)
• Overlay a quiver plot (i.e. gradient field)
• At each point on the same surface, compute the
  difference in response for each of the three
  possible pairs of angles, and determine which is
  most significant
• Assign each difference its own color (See Figure
  1)
• up - down cyan up - mid mid -
  down magenta
• Place an arrow of the "winning" difference's
  color at each point, with magnitude and direction
  given by the gradient (See Figure 5)
• Run regression statistics to assess regional
  retinotopic organization (See Figure 6)

LIP
FEF
DLPFC
Figure 2. Sample color map generated by the
program Carrot on a flattened cortical surface.
Before our method, visual inspection of a diagram
like this was the only means of assessing
retinotopic organization. Proposed regions of
retinotopic organization are labeled.
Figure 3. Weighted color map generated using our
method in MATLAB on the same flattened cortical
surface as in Figure 2. Dot color indicates the
angle that, when stimulated, elicited the
greatest response. Dot size indicates the
significance of that response.
yellow
Normalized BOLD fMRI Response
a
a
Distance along flat x-axis (arbitrary units)
b
Difference in Normalized BOLD fMRI Responses
b
c
Figure 4. a. Hypothetical adjacent distributions
of predominantly mid (blue) neurons and
predominantly down (green) neurons along the
x-axis of the flattened cortical surface. b. The
difference (magenta) between mid and down
responses (i.e. blue curve minus green curve)
along the x-axis. The bigger the slope (dotted
line) in the middle region, the bigger the
x-component of the arrow placed there.
Figure 5. Close-up of color map with overlaid
gradient field in a patch of visual cortex known
to exhibit retinotopic organization. Notice
that a. the cyan arrows point from green to red
and are largest between green and red dominated
areas b. the yellow arrows point from blue to
red and are largest between blue and red
dominated areas and c. the magenta arrows point
from green to blue and are largest between green
and blue dominated areas.
Figure 6. Averages over both hemispheres in
three subjects of r2 values for all three angle
differences in various predefined cortical
regions. The three regions on the right (DLPFC,
FEF, and LIP) are proposed regions of retinotopic
organization, for which quantitative evidence has
yet to be shown. The other seven are early
visual areas already known to have retinotopic
organization.
b.
yellow