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

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 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 2 / 24

Objectives To track the morphology of cells and reconstruct their movements: V. Peschetola et al. Cytoskeleton , 2013 3 / 24

What is our signature Pure geometric math models: Pure geometric math models: Pure geometric math models: Particle tracking: Particle tracking: Particle tracking: Resolution of the data matters The morphology of cells are not Typically no cell-setting is considered considered Manually tracking is slow It is a complicated procedure to Automatic tracking algorithms obtain the results are often flawed Segmentation is suboptimal Computational power and for real data advanced numerical methods Tracking through patten have to be included for 3-D recognition is challenging real-life cell tracking 4 / 24

Our optimal control model The volume conserved mean curvature flow: � V V V ( x x x , t ) = ( − σ H ( x x x , t ) + η ( x x x , t ) + λ V ( t )) v v v ( x x , t ) on Γ( t ) , t ∈ (0 , T ] , x Γ(0) = Γ 0 . The phase-field approximation of the above equation - Allen-Cahn:  x , t ) − 1 x , t )) − 1 ∂ t φ ( x x x , t ) = △ φ ( x x ǫ 2 G ′ ( φ ( x x ǫ ( c G η ( x x x , t ) − λ ( t )) in Ω × (0 , T ] ,   ν = 0 on ∂ Ω × (0 , T ] , ∇ φ · ν ν Ω = φ 0 in Ω .  φ ( · , 0)  5 / 24

Our optimal control model cont. The objective functional: � T J ( φ, η ) = 1 � x + θ � x )) 2 dx x , t ) 2 dx ( φ ( x x x , T ) − φ obs ( x x x η ( x x x xdt , 2 2 Ω 0 Ω and now we solve the minimisation problem: min η J ( φ, η ) , with J given above . 6 / 24

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. 7 / 24

Toy model for proving concepts A circle becomes two ellipses. Initial data Desired data 8 / 24

Toy model for proving concepts 9 / 24

Toy model for proving concepts cont. A circle becomes 4 children circles. Initial data Desired data 10 / 24

Toy model for proving concepts cont. 11 / 24

Toy model for proving concepts cont. 12 / 24

Real world application Two segmented cell images. Initial data Desired data 13 / 24

Real world application cont. 14 / 24

Real world application cont. 15 / 24

3-D simulation (a) (b) (c) (d) 16 / 24

3-D simulation cont. 17 / 24

IBiDi data 18 / 24

IBiDi data cont. 19 / 24

Issues with basic segmentation 20 / 24

Our simple solution to segmentation 21 / 24

Particle tracking N. Stuurman. Mtrack2 at valelab.ucsf.edu , 2009 22 / 24

Particle tracking cont. 23 / 24

The end Thank you. 24 / 24