Post on 03-Aug-2015
Tracking B and T cells
from 2-photon microscopy imaging
David Olivieri, Iván Gómez and Jose Faro
(University of Vigo)
www.milegroup.net
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
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
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)
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)
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
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
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
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
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
Prior distribution
User input determines the object initial position
object
Iván Gómez Conde
Initial selection
of cells by the
user
SMC Method
p(x0)
Evolution model
Evolution Model (second-
order, auto-regressive
dynamical model)
SMC Method
p(xt | xt -1)
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
Cells from Simulation
Iván Gómez Conde
Results
(simulation courtesy of J. Carneiro, T. Macedo, Instituto
Gulbenkian de Ciencia, Portugal)
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
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
2-photon Microscopy videos
Iván Gómez Conde
Results
(videos courtesy of C.Allen, et.al
Science, 2006)
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