Download Surface-uniform sampling, possibilities and limitations

Århus, March 2002
Surface-uniform sampling (SUGOS), possibilities and limitations
H. J. G. Gundersen +45 8942 2954, [email protected]
Stereological Research Laboratory, Aarhus University, Denmark
Århus –00
The 1.5kg of human brain
is the most complicated
physical structure in the
known
universe.
It
functions according to
unknown
overall
principleswhich
nevertheless must be
based on its internal
structure,
from
macroscopic to molecular
levels. Its cortex, where
25•109
neurons
are
internally connected by
12•109 m of dendrites
and 200,000•109 oneway synapses, may be
subdivided into 50 to 100
regions, some of which
have known functions. The regions all have 6 layers of neurons, but they neither have sharp borders nor
are their position detectable on the surface. Among individuals, regions vary in extent (by 10 to 25%) and
in position (by 5 to 10mm) as does the overall pattern of cortical gyration. The thickness of layers vary 2to 3-fold as a function of both local surface curvature and of the depth of the layer. On histologic sections
locally perpendicular to the very irregular, but smooth and topologically extremely simple pial surface, the
borders between specific regions are, however, recognisable at the light microscopic level by experts.
Only uniform samples can be used for unbiased estimates. In order to allow quantitation of region
specific structures, such samples must generate sections which are always orthogonal to the local pial
surface for borders to be distinguishable. It is possible to subdivide a cortical region into a complete 2D
tessellation in such a way that all cuts are locally perpendicular to the surface. In a uniformly random
sample of such tiles (cluster or fractionator sampling) one may obtain unbiased estimates of total
volumes of regions and their layers as well as of the total number of neurons in specific layers using the
FAVER (Fixed Axis, VErtical Random) Local Stereological principle. These estimates only depend on the
orthogonal property of the sections for identifying the borders. The above complete subdivision may,
however, also be a uniformly random tessellation and the sections can be cut according to SUGOS
(Surface-Uniform, Globally Orthogonal sampling) of sections. Since the brain cortex is almost
everywhere within the positive reach of the pial surface, any point in the cortex is projected into a unique
point on the pial surface.
Using special MRI modes, one may
obtain 3D MR images of complete
brain regions with good contrast
between brain cortex and the
surrounding fluid. Also the contrast to
the underlying white matter is rather
good. The two prominent artefacts are
due to air trapped in the cortical sulci.
Next step is to develop automatic
image analysis of the 3D MR images
with
a
complete
mathematical
characterisation of the brain surface in
3D.