A Geometric Database for Gene Expression Data

Baylor College of MedicineGregor EicheleChristina ThallerWah ChiuJames Carson

Rice UniversityTao JuJoe Warren

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– Deformable to images– Explicit modeling of anatomical boundaries– Store the expression data on the atlas– Efficient searching

• 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.

Brain Atlas: Review

• 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

Subdivision Mesh as Brain Atlas

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:

T (p4)p1

p3 p2

p4 p1= T (p1)

p3= T (p3) p2= T (p2)

T p4

ˆ

ˆ ˆ

ˆ

• Related to mesh parameterization

4 4( )p T p

Fitting Results

0

0.02

0.04

0.06

0.08

0.1

0.12

0 20 40 60 80 100

Error plot before and after global fit for 110 images.

• 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

Storing Expression With Atlas

• Database of gene expression data and deformed atlases– currently 1207 images from 110 genes.

• Web server: www.geneatlas.org – 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!

Accessing the Database via the Web

• Build 3D atlas for mouse brain – Represented as subdivision solid– Partitioned into anatomical regions by surface network– Supports fully 3D queries

• Future work– Deform the mesh onto expression images– Store the expression data onto the mesh– Efficient searching algorithm– User interface to pose 3D queries

Current Work and Future Plans

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.

• 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.

Constructing a Partitioned 3D Atlas

• Coloring of major anatomical regions in each coronal figure in the Paxino’s Atlas. (Online)

Electronic Paxino’s Atlas

• Pack uniform triangular grid into anatomic regions, annotated with colors.

• Identify and group consecutive meshes with same topology into one Layer.

2D Triangular Meshing

• Construct triangular prisms for each layer. (no topology changes)

• Color each prism by the color of the triangles.

• Crease faces: separate the volume into sub-volumes corresponding to each anatomic region.

Crease quad Crease triangle

3D Layered Mesh

Subdivided Mesh

3D Brain Anatomy

• Deform layers in z-direction to more accurately fit boundaries of anatomical regions

• Optimize surface network to fit data and bend minimally

Fit Layered Mesh

• Apply filter to high-res raw images and compute low-res 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.

Mapping Expression Data onto Atlas

• 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).

Querying the 3D Database