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Whole cell tracking and movement reconstruction through an optimal - - PowerPoint PPT Presentation

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Whole cell tracking and movement reconstruction through an optimal control problem Feng Wei Yang with Anotida Madzvamuse and Chandrasekhar Venkataraman University of Sussex F.W.Yang@sussex.ac.uk 8 June 2015 at IBiDi 1 / 24 Outline Whole

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Whole cell tracking and movement reconstruction through an optimal control problem

Feng Wei Yang with Anotida Madzvamuse and Chandrasekhar Venkataraman

University of Sussex F.W.Yang@sussex.ac.uk

8 June 2015 at IBiDi

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Outline

Whole cell tracking through optimal control problem

The mathematical model Toy models for proving concepts Real world application 3-D simulation

IBiDi data

Our automatic segmentation algorithm Particle tracking results

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Objectives

To track the morphology of cells and reconstruct their movements:

  • V. Peschetola et al. Cytoskeleton, 2013

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What is our signature

Particle tracking: Particle tracking: Particle tracking: The morphology of cells are not considered Manually tracking is slow Automatic tracking algorithms are often flawed

Segmentation is suboptimal for real data Tracking through patten recognition is challenging

Pure geometric math models: Pure geometric math models: Pure geometric math models: Resolution of the data matters Typically no cell-setting is considered It is a complicated procedure to

  • btain the results

Computational power and advanced numerical methods have to be included for 3-D real-life cell tracking

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Our optimal control model

The volume conserved mean curvature flow:

  • V

V V (x x x, t) = (−σH(x x x, t) + η(x x x, t) + λV (t))v v v(x x x, t) on Γ(t), t ∈ (0, T], Γ(0) = Γ0.

The phase-field approximation of the above equation - Allen-Cahn:

     ∂tφ(x x x, t) = △φ(x x x, t) − 1

ǫ2 G ′(φ(x

x x, t)) − 1

ǫ(cGη(x

x x, t) − λ(t)) in Ω × (0, T], ∇φ · ν ν νΩ = 0 on ∂Ω × (0, T], φ(·, 0) = φ0 in Ω.

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Our optimal control model cont.

The objective functional:

J(φ, η) = 1 2

  • Ω

(φ(x x x, T) − φobs(x x x))2 dx x x + θ 2 T

  • Ω

η(x x x, t)2dx x xdt,

and now we solve the minimisation problem:

minηJ(φ, η), with J given above.

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Obtaining solutions

We are using one of the most efficient solution methods, combining most advanced adaptive techniques. Meanwhile, parallelism is employed and the computation has been carried out on large computer cluster with multiple number of computational cores.

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Toy model for proving concepts

A circle becomes two ellipses. Initial data Desired data

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Toy model for proving concepts

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Toy model for proving concepts cont.

A circle becomes 4 children circles. Initial data Desired data

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Toy model for proving concepts cont.

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Toy model for proving concepts cont.

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Real world application

Two segmented cell images. Initial data Desired data

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Real world application cont.

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Real world application cont.

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3-D simulation

(a) (b) (c) (d)

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3-D simulation cont.

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IBiDi data

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IBiDi data cont.

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Issues with basic segmentation

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Our simple solution to segmentation

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Particle tracking

  • N. Stuurman. Mtrack2 at valelab.ucsf.edu, 2009

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Particle tracking cont.

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The end

Thank you.

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