diffusion mri, tractography,and connectivity: what machine learning can do?

Ting-Shuo Yo

DW-MRI, Tractography, and Connectivity: what Machine Learning can do?

Max Planck Institute for Human Cognitive and Brain SciencesLeipzig, Germany

Max Planck Institute for Human Cognitive and Brain Sciences

Where the story begins

● Diffusion Weighted MRI (DWI) is a newly developed MR scanning protocol, which can detect the movement/displacement of water molecules in tissues.

● So far, the techniques used in DWI analysis are mostly deterministic and mechanical. The stochastic approaches (ML related) can bring new insights to this field.

Outline

● MPG/MPIs● A brief introduction of DWI● What DWI can do● A comparison of different tractography algorithms● What ML can do in DWI

Outline

● MPG/MPIs– Max Planck Society– Objective and Organization– MPI - CBS

● A brief introduction of DWI● What DWI can do● A comparison of different tractography algorithms● What ML can do in DWI

The Max Planck Society● The Max Planck Society for the

Advancement of Science is an independent, non-profit research organization.

● In particular, the Max Planck Society takes up new and innovative and interdisciplinary research areas that German universities are not in a position to accommodate or deal with adequately.

The Max Planck Institutes● The research institutes

of the Max Planck Society perform basic research in the interest of the general public in the natural sciences, life sciences, social sciences, and the humanities.

● Currently there are 81 MPIs.

The MPI for CBS

Outline

● MPG/MPIs● An Introduction of DWI tractographyAn Introduction of DWI tractography

– Local modelling– Fibre tracking

● What DWI can do● A comparison of different tractography algorithms● What ML can do in DWI

Diffusion Weighted MRI

● MRI can detect the movement of water molecules.

● The movement is constrained by the neural fibers.

Diffusion Weighted MRI

● By posing a gradient magnetic field, the displacement in the corresponding direction can be measured.

Tractography (1)

● Local modelling:➢ Reconstruct the fibre

orientation within each voxel

Tractography (2)

● Diffusion propagator– Diffusion Tensor (DT)– Multiple compartment models– Persistent Angular Structure (PAS)

● Fibre Orientation Distribution Function– Spherical Deconvolution

Tractography (3)

● Fiber tracking:➢ Reconstruct fibre tracts by

integrating the reconstructed local information

Tractography (4)

● Streamline approach– Deterministic– Probabilistic

● Optimization for a larger region– Spin tracking– Gibbs tracking

Tractography (5)

● Deterministic tracking– At each step, only

consider the most likely direction

● Curvature threshold● Step size● Interpolation● ......

Tractography (6)

● Probabilistic tracking– Perform deterministic tracking for multiple times– Allow uncertainty at each step

Tractography (7)

● Probabilistic tracking and tractogram– Probability of connection

Tractography (8)

● Optimization for a larger region– Spin tracking– Gibbs tracking

From Kreher et al. 2008

Outline

● MPG/MPIs● A brief introduction of DWI● What DWI can doWhat DWI can do

– To reveal anatomical structure in white matter– To construct the general brain network– In vivo

● A comparison of different tractography algorithms● What ML can do in DWI

White matter structure from DWI● Product of tractography

Brain Network from DWI● Hagmann 2008

What DWI can do● fMRI shows "where" is working.

– The "nodes" in a graph/network● DWI shows the structure of the fiber bundles.

– The “edges" in a graph/network– With further analysis, can also show "strength of

edges".● The brain network:

– The amount of nodes: 10^2– The amount of edges: 10^3

Outline● MPG/MPIs● A brief introduction of DWI● What DWI can do● A comparison of different tractography A comparison of different tractography

algorithmsalgorithms– Selected algorithms– Procedure– Results

● What ML can do in DWI

Selected Algorithms

Procedure

Results (1)

Results (2)

Results (3)

Results (4)

Results (5)

Results (6)

Results (7)

Results (8)

Quick Summary

● More connections– Local models which allow multiple fibres– Probabilistic tracking

● Consistent patterns across methods– Strong connections within a lobe– Strong connections to corpus callosum– Weak trans-callosum connections

Results (9)

Outline

● MPG/MPIs● A brief introduction of DWI● What DWI can do● A comparison of different tractography algorithms● What ML can do in DWIWhat ML can do in DWI

– Local model reconstruction– Fiber tracking– Further application

ML in DWI

● Local modeling: deconvolution approach– Assume the signals are convolution of neural

fibers and noises.– Need to “learn" the deconvolution kernel from

data defined as "one single fiber".– So far only GLM (2nd order polynomial) is used.– More sophisticated kernel methods can be used.

ML in DWI● Fiber tracking

– Speed up the optimization process.– Different fiber reconstruction method.

● Probabilistic modeling of fiber tracts

MICCAI'09 Fiber Cup

● 6 datasets:– 3 of resolution 3x3x3mm (image size: 64x64x3) and

3 b-values (650, 1500 and 2000)– 3 of resolution 6x6x6mm (image size: 64x64x1) and

3 b-values (650, 1500, 2650)● Participants have to return one single fiber per

spatial position selected.

MICCAI'09 Fiber Cup

A Very Brief Review of Tractography

● Local modeling● Fiber tracking

Why are we doing this?

● Streamline-based tractography:– Each simulation (a fiber) is a possible trajectory in

the given vector field.● What is the probability of one given fiber?● How to select the most representative fibers?

Probability of a Fiber Tract (1)

● Fiber tract, t = { x1, x2, ...., xl }● P(t) = P( x1, x2, ...., xl )

● Conditional Probability and Joint Probability– P(A|B) = P(A,B) / P(B)– P(A,B) = P(A|B) P(B)

● P(t) = P( x1, x2, ...., xl )

= P(xl| x1, ...., xl-1) P(x1, ...., xl-1)

= P(xl| x1, ...., xl-1) P(xl-1|x1, ...., xl-2) P(x1, ...., xl-2)

= P(xl| x1, ...., xl-1) P(xl-1|x1, ...., xl-2) ......P(x2|x1) P(x1)

● Assumption: fiber tracking is a 1st order Markov process– P(xi| x1, ...., xi-1) = P(xl|xi-1) – P(t) = P( x1, x2, ...., xl )

= P(xl| x1, ...., xl-1) P(xl-1|x1, ...., xl-2) ......P(x2|x1) P(x1)

= P(xl|xl-1) P(xl-1|xl-2) ......P(x2|x1) P(x1)

P x1∏i=1

P x i1∣x i

● How do we define P(xi+1|xi) and P(xi) ?– C: connection probability map– P(xi) ~ C(xi)– P(xi+1|xi) ~ C(xi+1|xi) ~ C(xi+1,xi)

P t =P x1∏i=1

P x i1∣x i

Finite State Automata (1)

● Each step of fiber tracking can lead to next middle point or the terminal point.

P t =P0 x l∏i=1

1−P0x i

t={x1 , ... , x l }

● How to define P0?– # of fibers in the neighboring voxels, NB(x)– (1-P0(xi)) ~ C(NB(xi))

– C(NB(xi))~ C(xi)

P t ≃∏i=1

1−1−C xik

P0x=1−C x k

K = 20, 10, 5

P t =P0 x l∏i=1

1−P0x i

● Likelihood and Log-likelihood

P t ≃∏i=1

1−1−C xik

P t =P0 x l∏i=1

1−P0x i

L t ≃∑i=1

ln 1−1−C x ik ≃∑

−1−C xik

Approximation with 1st order Taylor's expansion

Entropy of a Fiber Tract (1)

● Entropy

● Can be seen as the log-likelihood of

H t =∑i=1

C x i⋅ln C x i

∑i=1

C xi⋅ln C xi=ln ∏i=1

C x iC xi

Fiber Cup Results (2)

Max. Entropy Max. Likelihood

ML in DWI● Connectivity based clustering

– Brain parcellation– Brain tissue is mostly

continuous without clear segmentation, how to define regions on it?

– Perform clustering based on the connectivity matrices.

Leipzig, Germany

A. AnwanderT.R. KnöscheT. Yo

Saclay, Gif-sur-Yvette, France

M. DescoteauxP. FillardC. Poupon

Questions

Doing what the brain does - how computers learn to listen

Thank You

diffusion mri, tractography,and connectivity: what machine learning can do?

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brain sciences tractography

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