Diffusion MRI, Tractography,and Connectivity: what machine learning can do?

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

Ting-Shuo Yo

Max Planck Institute
for Human Cognitive and Brain Sciences
Leipzig, 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.

2


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

3


Outline
● MPG/MPIs
– Max Planck Society
– Objective and Organization
– MPI - CBS
● What DWI can do
4


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.

5

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.

6

7


Outline
● MPG/MPIs
● An Introduction of DWI tractography
– Local modelling
– Fibre tracking
● What DWI can do

9


Diffusion Weighted MRI
● MRI can detect the
movement of water
molecules.
● The movement is
constrained by the
neural fibers.

10


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

11


Tractography (1)

● Local modelling:
➢ Reconstruct the fibre
orientation within each voxel

12


Tractography (2)

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

● Fibre Orientation Distribution Function
– Spherical Deconvolution

13


Tractography (3)

● Fiber tracking:
➢ Reconstruct fibre tracts by
integrating the reconstructed
local information

14


Tractography (4)

● Streamline approach
– Deterministic
– Probabilistic

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

15


Tractography (5)

● Deterministic tracking
– At each step, only
consider the most likely
direction
● Curvature threshold
● Step size
● Interpolation
● ......

16


Tractography (6)

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

17


Tractography (7)

● Probabilistic tracking and tractogram
– Probability of connection

18


Tractography (8)

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

From Kreher et al. 2008
19


Outline
● MPG/MPIs
● What DWI can do
– To reveal anatomical structure in white matter
– To construct the general brain network
– In vivo
20


White matter structure from DWI
● Product of tractography

21


Brain Network from DWI
● Hagmann 2008

22


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
23


Outline
● MPG/MPIs
● What DWI can do
● A comparison of different tractography
algorithms
– Selected algorithms
– Procedure
– Results
24


Selected Algorithms

25


Procedure

26


Results (1)

27


Results (2)

28


Results (3)

29


Results (4)

30


Results (5)

31


Results (6)

32


Results (7)

33


Results (8)

34


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

35


Results (9)

36


Outline
● MPG/MPIs
● What DWI can do
– Local model reconstruction
– Fiber tracking
– Further application
37


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.

38


ML in DWI
● Fiber tracking
– Speed up the optimization process.
– Different fiber reconstruction method.

● Probabilistic modeling of fiber tracts

39


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.

40


MICCAI'09 Fiber Cup

41


A Very Brief Review of Tractography
● Local modeling
● Fiber tracking

42


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?

43


Probability of a Fiber Tract (1)

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

44



● 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)

l−1
P t=P  x1  ∏ P  x i1∣x i 
i=1

47


Finite State Automata (1)

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

48



t={x 1 , ... , x l }
l−1
P t=P0  x l  ∏ 1−P 0  x i 
i=1

49



● How to define P0?
– # of fibers in the neighboring voxels, NB(x)
– (1-P0(xi)) ~ C(NB(xi))
P 0  x=1−C  x k

– C(NB(xi))~ C(xi) K = 20, 10, 5

l−1
P t=P0  x l  ∏ 1−P 0  x i 
i=1

l −1
P t≃∏ 1−1−C  xi k
i=1
50



● Likelihood and Log-likelihood
l−1
P t=P0  x l  ∏ 1−P 0  x i 
i=1

l −1
P t≃∏ 1−1−C  xi  k

i=1

l−1 l−1
L t≃∑ ln 1−1−C  x i k ≃∑ −1−C  xi k
i=1 i=1

Approximation with 1st order Taylor's expansion

51


Entropy of a Fiber Tract (1)

● Entropy
l
H t =∑ C  x i ⋅lnC  x i 
i=1

● Can be seen as the log-likelihood of
l l

∑ C  xi ⋅lnC  xi =ln ∏ C  x i  C xi 

i=1 i =1

52


Fiber Cup Results (2)

Max. Entropy Max. Likelihood

53


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.

54


Leipzig, Germany Saclay, Gif-sur-Yvette, France

A. Anwander M. Descoteaux
T.R. Knösche P. Fillard
T. Yo C. Poupon

55


Questions

56


Doing what the brain does - how
computers learn to listen

57


Thank You

58


Diffusion MRI, Tractography,and Connectivity: what machine learning can do?

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