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A 90 mins talk to introduce the contemporary research on Diffusion Weighted MRI (DWI) to audience in the field of machine learning. Date: 2009-10-20
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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
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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.
Max Planck Institute for Human Cognitive and Brain Sciences
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Outline
● MPG/MPIs● A brief introduction of DWI● What DWI can do● A comparison of different tractography algorithms● What ML can do in DWI
Max Planck Institute for Human Cognitive and Brain Sciences
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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
Max Planck Institute for Human Cognitive and Brain Sciences
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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.
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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.
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Max Planck Institute for Human Cognitive and Brain Sciences
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The MPI for CBS
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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
Max Planck Institute for Human Cognitive and Brain Sciences
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Diffusion Weighted MRI
● MRI can detect the movement of water molecules.
● The movement is constrained by the neural fibers.
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Diffusion Weighted MRI
● By posing a gradient magnetic field, the displacement in the corresponding direction can be measured.
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Tractography (1)
● Local modelling:➢ Reconstruct the fibre
orientation within each voxel
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Tractography (2)
● Diffusion propagator– Diffusion Tensor (DT)– Multiple compartment models– Persistent Angular Structure (PAS)
● Fibre Orientation Distribution Function– Spherical Deconvolution
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Tractography (3)
● Fiber tracking:➢ Reconstruct fibre tracts by
integrating the reconstructed local information
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Tractography (4)
● Streamline approach– Deterministic– Probabilistic
● Optimization for a larger region– Spin tracking– Gibbs tracking
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Tractography (5)
● Deterministic tracking– At each step, only
consider the most likely direction
● Curvature threshold● Step size● Interpolation● ......
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Tractography (6)
● Probabilistic tracking– Perform deterministic tracking for multiple times– Allow uncertainty at each step
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Tractography (7)
● Probabilistic tracking and tractogram– Probability of connection
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Tractography (8)
● Optimization for a larger region– Spin tracking– Gibbs tracking
Max Planck Institute for Human Cognitive and Brain Sciences
From Kreher et al. 2008
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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
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White matter structure from DWI● Product of tractography
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Brain Network from DWI● Hagmann 2008
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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
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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
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Selected Algorithms
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Procedure
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Results (1)
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Results (2)
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Results (3)
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Results (4)
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Results (5)
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Results (6)
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Results (7)
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Results (8)
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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
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Results (9)
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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
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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.
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ML in DWI● Fiber tracking
– Speed up the optimization process.– Different fiber reconstruction method.
● Probabilistic modeling of fiber tracts
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MICCAI'09 Fiber Cup
Max Planck Institute for Human Cognitive and Brain Sciences
● 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.
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MICCAI'09 Fiber Cup
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A Very Brief Review of Tractography
Max Planck Institute for Human Cognitive and Brain Sciences
● Local modeling● Fiber tracking
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Why are we doing this?
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● 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?
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Probability of a Fiber Tract (1)
● Fiber tract, t = { x1, x2, ...., xl }● P(t) = P( x1, x2, ...., xl )
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Probability of a Fiber Tract (2)
● 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)
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Probability of a Fiber Tract (3)
● 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)
=
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P x1∏i=1
l−1
P x i1∣x i
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Probability of a Fiber Tract (4)
● 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)
Max Planck Institute for Human Cognitive and Brain Sciences
P t =P x1∏i=1
l−1
P x i1∣x i
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Finite State Automata (1)
● Each step of fiber tracking can lead to next middle point or the terminal point.
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Finite State Automata (2)
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P t =P0 x l∏i=1
l−1
1−P0x i
t={x1 , ... , x l }
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Finite State Automata (3)
Max Planck Institute for Human Cognitive and Brain Sciences
● 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
l−1
1−1−C xik
P0x=1−C x k
K = 20, 10, 5
P t =P0 x l∏i=1
l−1
1−P0x i
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Finite State Automata (4)
● Likelihood and Log-likelihood
Max Planck Institute for Human Cognitive and Brain Sciences
P t ≃∏i=1
l−1
1−1−C xik
P t =P0 x l∏i=1
l−1
1−P0x i
L t ≃∑i=1
l−1
ln 1−1−C x ik ≃∑
i=1
l−1
−1−C xik
Approximation with 1st order Taylor's expansion
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Entropy of a Fiber Tract (1)
● Entropy
● Can be seen as the log-likelihood of
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H t =∑i=1
l
C x i⋅ln C x i
∑i=1
l
C xi⋅ln C xi=ln ∏i=1
l
C x iC xi
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Fiber Cup Results (2)
Max. Entropy Max. Likelihood
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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.
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Leipzig, Germany
A. AnwanderT.R. KnöscheT. Yo
Saclay, Gif-sur-Yvette, France
M. DescoteauxP. FillardC. Poupon
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Questions
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Doing what the brain does - how computers learn to listen
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Max Planck Institute for Human Cognitive and Brain Sciences
Thank You