A Geometric Database for Gene Expression Data

1. A Geometric Database for Gene Expression Data Rice University Tao Ju Joe Warren Baylor College of Medicine Gregor Eichele Christina Thaller Wah Chiu James Carson

2. 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

3. Gene Expression Images

4. Example Query

5. 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

6. 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.

7. 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

8. 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

9. 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

10. Minimizing Deformation Energy • Penalize non-affine deformation of the mesh during the fitting process • Triangulate each quad • Penalize deviation: • Related to mesh parameterization

11. Fitting Results Error plot before and after global fit for 110 images.

12. 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

13. 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 • 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!

14. 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 • Deform the mesh onto expression images • Store the expression data onto the mesh • Efficient searching algorithm • User interface to pose 3D queries

15. Conclusion • Subdivision meshes for anatomic modeling: • Flexible control allows easy deformation. • Explicit modeling of region boundaries. • Fast multi-resolution comparison of data.

16. 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.

17. 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.

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

19. 2D Triangular Meshing • Pack uniform triangular grid into anatomic regions, annotated with colors. • Identify and group consecutive meshes with same topology into one Layer.

20. 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 sub-volumes corresponding to each anatomic region. Crease quad Crease triangle

21. Subdivided Mesh

22. 3D Brain Anatomy

23. 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

24. Mapping Expression Data onto Atlas • 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.

25. 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).