Geometrydriven Visualization of Microscopic Structures in Biology

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Geometry-driven Visualization of Microscopic
Structures in Biology

• Kishore Mosaliganti, Raghu Machiraju
• Computer Science and Engineering,
• Kun Huang
• Biomedical Informatics,
• Gustavo Leone
• Human Cancer Genetics

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Presentation Overview

• Biological motivation
• Structure and pattern in biology
• N-point correlation functions
• Density, arrangements and spatial distributions
• Segmentation and 3D visualization
• Useful transfer functions
• Applications
• Light and phase-contrast microscopy

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Component Distributions

• Rb phenotyping studies
• Mouse placenta tissue layer visualization
• Tissue layers differ in spatial distributions
• Characteristic packing of RBCs, nuclei, cytoplasm
  - phases
• Differ in porosity, volume fractions, sizes and
  arrangement

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Component Arrangements

• PTEN phenotyping studies
• Mammary duct visualization
• 2D projections of a complex tortuous 3D object
• Concentric arrangement of epithelial cells
• Linear separation model of cells

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Component Packing
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• Cancer therapy - proliferation of mutated cell
  lines
• Identifying and tracking clonal populations
• Clustering of mutated cells into colonies
• Exponential growth across frames
• Colonies separated by white space

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Geometric and Statistical Estimators

• Ability to measure
• Arrangement geometries
• Packing density
• Multiphase mixtures
• Similar to material microstructure
  characterization
• Spatial statistics, signal processing and
  astrology

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2-Point Correlation Functions
k
Microstructure, with phase 0 and 1

• Definition Pki1i2 - Probability that a line
  segment of length k in the microstructure has
  vertices in phase i1, i2 ?0,1
• Four possible 2-pcfs namely Pk00, Pk01, Pk10 and
  Pk11

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N-Point Correlation Functions

• Multiphase material with m component phases
• Place a N-sided regular polyhedron with edge
  length k
• Definition The probability that all the
  N-vertices lie in phase (i1,i2,,iN) is defined
  as an N-point correlation function, Pki1i2iN
• Polygonal models of separation

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Results Segmentation
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Multiphase Segmentations
Tissue Segmentation
Component Segmentation
Original

• Identify homogenous phase components
• nuclei, RBC, cytoplasm, background
• Estimate component distributions
• Image windowing, sampling
• Tensor feature classification
• K-NN, HOSVD classifier

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Detecting Arrangements
Mammary ducts segmentation
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Density Distributions
Clonal populations
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Results Visualization
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Constructing Feature Spaces

• Define suitable transfer functions in the feature
  space of the N-pcfs
• Different features spaces for exploration
• Polygonal models of separation (N2, 3)
• Separation lengths (k)

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Mouse Mammary Ducts

• Deletion of PTEN induces morphological change
• Wildtype and mutant 2D serial-section image
  stacks
• Each dataset has dimensions 20Kx20Kx500
• Goal Detect morphology change using automated
  tools

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Mouse Mammary ducts
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Choosing optimal tessellations

• Divide the image into salient regions
• Tessellated region houses a single cell/nuclei
• Tessellation lines split nuclei clusters
  consistently
• Bayesian framework to generate optimal parameters
• Lies on a high gradient, shortest length
• Similar to a Voronoi tessellation

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3D Cellular Reconstructions
Before using cellular segmentation
Using N-pcfs and cellular segmentations
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Mouse Placenta Phenotyping
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Morphometric Differences
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Morphometric Differences
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Conclusions

• N-point correlation functions as estimators
• Density
• Arrangement patterns
• Spatial distributions
• Provides feature space
• Tissue segmentation
• Tracking meta-objects
• 3D Visualization

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Acknowledgements

• Firdaus Janoos
• Lee Cooper
• Randall Ridgway
• Okan Irfanoglu

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Algorithm
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Implementation

• Sliding-window

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Performance

• Running time O(S x O)
• S Sample size
• O Image domain
• Does not depend on N and k
• N higher-order polygonal models
• Different characteristic signatures
• k depends on the microstructure
• Usually a range of values explored
• O Sufficient to capture the distribution
• Places limits on the resolution
• S Larger the better

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Validation
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Image-1
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Image-2
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Image-3
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Segmentation Validation
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Results Tracking
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Tracking Clonal Colonies
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• Cells and Colonies
• - Track entire colony and not cells
• - Cells are very close to each other

• Our Approach
• Use spatial relationships and attributes of
  cells in colonies
• Correspondence and membership problems solved
  in derived functional space

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Our Approach
Preprocess
Detect Cells (Nuclei)
Compute Spatial Correlation Manifold
Colonies
Partition Manifold
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Tracking on 2-pcf manifolds
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Voronoi Segmentations
Clonal Populations