Transcript Gene expression atlas of the mouse brain

A Geometric Database for Gene
Expression Data
Rice University
Baylor College of Medicine
Tao Ju
Joe Warren
Gregor Eichele
Christina Thaller
Wah Chiu
James Carson
Overview
• Genes are blueprints for creating proteins
• For given tissue, only a subset of genes are
generating proteins (expressed)
• New laboratory method for determining which
genes are being expressed (Eichele)
• Collect expression data over mouse brain for all
30K genes in mouse genome
• Problem: Compare expression of different images
Gene Expression Images
Example Query
Brain Atlas
• Difficulty in comparing expression images
– Variations in image
– No explicit boundaries of anatomical regions
• Solution: Brain atlas
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Deformable to images
Explicit modeling of anatomical boundaries
Store the expression data on the atlas
Efficient searching
Brain Atlas: Review
• Standard – label image with anatomical regions,
deformed onto target image using uniform grid
• Brain Warping [Toga, 1999]
• Other deformable modeling tools
• Active contours, simplex meshes, etc.
Subdivision Mesh as Brain Atlas
• Model brain as a coarse quad mesh with each quad assigned
to an anatomical region
• Edges shared by two quads from different regions defined a
network of crease edges
• Subdivision of crease edges yields a network of smooth
creases curves bounding regions
Gene Expression Database
• Collect gene expression data at key cross-sections
• Deform subdivision meshes at those cross-sections
onto expression images
– Semi-automatic fitting algorithm
• Store gene expressions back onto the mesh.
– Multi-resolution structure accelerates comparison
Mesh Fitting
• Global fitting
– Accounts for deformation resulted from imaging
• Local fitting
– Accounts for anatomical deviation and tissue distortion
in sectioning
– Minimize deviation of the mesh boundary from the
image boundary (Scattered data fitting [Hoppe, 1996])
– Relax the internal mesh vertices under energy
constraints
Minimizing Deformation Energy
• Penalize non-affine deformation of the mesh
during the fitting process
– Triangulate each quad
– Penalize deviation: p4  T ( p4 )
p1
ˆp1= T (p1)
p4
T (p4)
T
p3
p2
ˆp3= T (p3)
• Related to mesh parameterization
ˆp4
ˆp2= T (p2)
Fitting Results
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Error plot before and after global fit for 110 images.
Storing Expression With Atlas
• Automatic annotation
– Distribution: ubiquitous, scattered, regional, none.
– Strength: +++, ++, +, – Apply filter to determine distribution and strength of
expression using data stored with the mesh quads
• Optimized searching
– Using the multi-resolution structure of subdivision
mesh
– Based on Multiscale Image Searching [Chen et.al. 97]
– Works with convex norms: L1, Chi-square, etc.
– Graphical search interface
Accessing the Database via the Web
• Database of gene expression data and deformed
atlases
– currently 1207 images from 110 genes.
• Web server: www.geneatlas.org
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Viewing and downloading expression images.
Viewing atlases (using Java Applet).
Graphical interface for searching gene images.
Textual interface for searching annotation.
• It’s all online!
Current Work and Future Plans
• Build 3D atlas for mouse brain
– Represented as subdivision solid
– Partitioned into anatomical regions by surface network
– Supports fully 3D queries
• Future work
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Deform the mesh onto expression images
Store the expression data onto the mesh
Efficient searching algorithm
User interface to pose 3D queries
Conclusion
• Subdivision meshes for anatomic modeling:
– Flexible control allows easy deformation.
– Explicit modeling of region boundaries.
– Fast multi-resolution comparison of data.
Acknowledgement
This work is supported in part by:
• A training fellowship from the W.M. Keck Foundation
to the Gulf Coast Consortia through the Keck Center
for Computational and Structural Biology.
• The Burroughs Wellcome Fund, NLMT15LM07093 and
NIHP41RR02250.
• NSF grant ITR-0205671.
Constructing a Partitioned 3D Atlas
• Identify major anatomical regions in the Paxino’s
Atlas (coronal figures).
• Layout triangular mesh for each coronal figure
that conforms to region boundaries.
• Construct prisms from triangles, and fit the
subdivided volume to the underlying data.
Electronic Paxino’s Atlas
• Coloring of major anatomical regions in each
coronal figure in the Paxino’s Atlas. (Online)
2D Triangular Meshing
• Pack uniform triangular grid into anatomic regions,
annotated with colors.
• Identify and group consecutive meshes with same
topology into one Layer.
3D Layered Mesh
• Construct triangular
prisms for each layer.
(no topology changes)
• Color each prism by the
color of the triangles.
• Crease faces: separate
the volume into subvolumes corresponding
to each anatomic region.
Crease quad
Crease triangle
Subdivided Mesh
3D Brain Anatomy
Fit Layered Mesh
• Deform layers in z-direction to more accurately fit
boundaries of anatomical regions
• Optimize surface network to fit data and bend
minimally
Mapping Expression Data onto Atlas
• Apply filter to high-res raw images and compute lowres expression images
• Align images in z-direction using centers of mass,
rotate in x-y plane using line of symmetry
• Determine tilt angle of each image versus z-axis using
cross-correlation to synthetic cut of atlas
• Fit cross-sections of 3D atlas to the images using
deformable modeling methods.
• Map expression data from image back onto 3D prisms
that intersect the image plane.
Querying the 3D Database
• Specify 3D query regions using 2D layering
– Select set of triangles in 2D layer view, visualize
corresponding layer of triangular prisms in 3D.
– GUI: Separate views of selection window (2D) and
volume-viewing window (3D).
• Display of 3D search results
– Quick view of 3D expression patterns as point clouds lying
in the expression image slices.
– Optionally, view of raw 2D expression images used to
generate 3D point clouds (with links to genepaint.org).