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Tracking B cells from two-photon microscopy images using Sequential Monte Carlo

Tracking B cells from two-photon microscopy images using Sequential Monte Carlo

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  • 1. Tracking B and T cells from 2-photon microscopy imaging David Olivieri, Iván Gómez and Jose Faro (University of Vigo) www.milegroup.net
  • 2. Outline  Motivation for this work  Stochastic method for tracking: SMC • Theoretical aspects • Some algorithm implementation details  Results: • From simulations and animations • From real microscopy data of 2D cell motility  Conclusions (present and future work) Iván Gómez Conde
  • 3. Immune Response  Understand complex details of immune response by understanding dynamics  Several important questions related to affinity maturation process  Cell activity and interactions Iván Gómez Conde Low Affinity Low Affinity High Affinity Activation Produces antibodies Motivation
  • 4. Germinal centers  “Germinal centers” are the sites of affinity maturation  Anatomic structures (in lymph nodes) where massive proliferation of B-cells occur  Complex interactions between B and Th cells; spatial zones  Understanding dynamics in gernminal center ; better understand mechanisms of immune response Iván Gómez Conde Motivation Confocal microscopy image of GC:T-cells blue, B-cells green (photo courtesy of I. Wollenberb, IMM, Universidad de Lisboa Portugal y J. Faro, Fac. Biología, Universidad de Vigo)
  • 5. Dynamics • In vivo Data: • “2-photon Confocal microscoy” with fluorescence excitation labelling • Better elimination of background Iván Gómez Conde Motivation  Dynamics is important! • B and T cell motility in germinal centers give information of function • Useful for “Inmunologic modeling” (input & validation)
  • 6. Tracking in Videos  Tracking is hard in general! • Normally needs to be real time • many interactions: background, camera… • Methods: frame diff, homology, optical flow, particle filters  What can be learned from tracking objects? • Tracking cells is particularly difficult • Cells change shape, disappear, and stick to eachother. • complex background, Iván Gómez Conde Method
  • 7. How to Tracking cells  Cell movement: • Problems: Complex, overlaps, “random” component • BUT, flourescence color is a strong feature to track • We propose “Stochastic color based tracking”: • SMC (stochastic monte carlo) Iván Gómez Conde Method
  • 8. Software Components Method
  • 9. Stochastic tracking  Sequential Monte Carlo (smc)  Formulate tracking as an inference problem in the context of a Hidden Markov Model (HMM)  Observations (from image data)  Hidden States (object location, scale, …) Yt Yt+1 Xt Xt+1 SMC Method
  • 10. Chapman Kolmogorov Eq.  Evolution of the state (inference): • Using the Bayesian filtering distribution: Current Object State Observation Model Previous Object State Evolution Model SMC Method
  • 11. Quantities of the Model  Prior Distribution: • Initial distribution of object states  Evolution Model: • How objects move between frames  Likelihood Function: • The probability of state x given the observation y Iván Gómez Conde p(x0) p(xt | xt -1) p(yt | xt ) SMC Method
  • 12. Prior distribution  User input determines the object initial position object Iván Gómez Conde Initial selection of cells by the user SMC Method p(x0)
  • 13. Evolution model Evolution Model (second- order, auto-regressive dynamical model) SMC Method p(xt | xt -1)
  • 14. Likelihood function  Likelihood Model (Distance metric): Iván Gómez Conde SMC Method p(yt | xt )
  • 15. SMC algorithm (summary) 1. Determine initial regions (roi) to track. o From roi, store reference histogram (each node) 2. Get image samples along trajectory of cell o Determined from the dynamics (position, velocity, update) o Obtain histograms of roi; compare with reference; keep best 3. Reorder the distribution for next sampling Iván Gómez Conde SMC Method
  • 16. SMC Resampling  Resampling, we change weights Iván Gómez Conde SMC Method
  • 17. SMC Tracking pseudocode Iván Gómez Conde SMC Method
  • 18. Results: simple animation  Showing each particle  Showing tracks of max L Iván Gómez Conde Results
  • 19. Tracking Accuracy Iván Gómez Conde Results
  • 20. Time Performance Iván Gómez Conde Results
  • 21. Cells from Simulation Iván Gómez Conde Results (simulation courtesy of J. Carneiro, T. Macedo, Instituto Gulbenkian de Ciencia, Portugal)
  • 22. Cells Simulation: Ambiguities Iván Gómez Conde Results  “unstructured” SMC leads to ambiguities  Imagine two cells sticking to each other…  Just based on color, particles will sample entire region  Not sure which cell is which after contact
  • 23. Cell Ambiguities: “Present” work Iván Gómez Conde Results  Possible Solution: make constraints between particles  Conserve area and distance; & non-overlap condition Node particle Constraint Preliminary results are promising! Modify the Weights to include constraints
  • 24. 2-photon Microscopy videos Iván Gómez Conde Results (videos courtesy of C.Allen, et.al Science, 2006)
  • 25. Conclusions  SMC is a promising technique for tracking cells o Relatively easy to implement and flexible o Can use color histogram or shape! o Easily extended to handle 3D image stacks o Stochastic noise can be controlled o Present and Future: o Extend to Constrained SMC can solve ambiguities o Implementation of system of “constrained particles” for each node Iván Gómez Conde
  • 26. Many thanks for your attention