Inferring cerebral white matter connectivity using the diffusion tensor model

1
Fibre Tracking From Raw Images ToTract
Visualisation
T.R. Barrick St. Georges Hospital Medical
School, London, United Kingdom.
2
Introduction

• Diffusion Tensor Magnetic Resonance Imaging has
  recently emerged as the technique of choice for
  representation of white matter pathways of the
  human brain in vivo

3
Objectives

• To show how Diffusion Tensor Images (DTIs) are
  generated from Diffusion Weighted Images (DWIs)
• To demonstrate how freely available software may
  be used to visualise coloured images and
  tractography results

4
Overview

• Section 1 Computing the DTI
• Section 2 Visualising Coloured Images
• Section 3 Streamline Tractography
• Section 4 Visualising Tractograms

5
Section 1 Computing The Diffusion Tensor
Brownian motion
6
Water Diffusion
Random, translational motion
7
Diffusion Characteristics

• In a large structure the self diffusion of water
  is more or less free (isotropy)
• In small structures such as axons the diffusion
  is restricted in some directions more than others
  (anisotropy)

8
Diffusion Coefficient (D)

• Diffusion is a time dependent process
• Molecules diffuse further from their starting
  point as time increases
• Units of D are mm2 s-1
• D is temperature dependent
• D depends species under consideration
• Water at 37C D 3.0 x 10-3 mm2 s-1

9
Diffusion-Weighting

• Make pulse sequence sensitive to diffusion
• Add additional gradients into sequence
• Spins move in gradient phase changes
• These gradients cause signal dephasing
• Results in signal loss

10
Diffusion Gradients Stejskal-Tanner Sequence
90
echo
180
RF
gradient
d
d
D
11
Diffusion Sensitivity b value

• Amount of diffusion sensitivity is called the b
  value
• b value depends on the gradient strength, G,
  duration d and separation D

12
Diffusion-Weighted Images (DWI)
increasing b factor
13
Diffusion-Weighted Images (DWI)

• Signal loss is proportional to b and D
• S(0) is signal without gradients and S(b) is
  signal with gradients

14
Diffusion Tensor Imaging (DTI)

• Acquire DWI sensitised in at least 6 different
  directions
• (x,y,0), (x,0,z), (0,y,z), (-x,y,0), (-x,0,z),
  (0,-y,z))
• Plus image without diffusion weighting (T2)

15
Possible Diffusion Tensor Image Acquisition

• 1.5T GE Signa MRI (max field 22 mT m-1)
• Diffusion-weighted axial EPI
• b1000 s mm-2
• 12 directions
• 4 averages
• Voxel size 2.5mm?2.5mm?2.8mm

16
Computation of the DTI

• Subject DWIs coregistered to image without
  diffusion weighting (Haselgrove and Moore, 1996)
• General linear model used to compute D at each
  voxel
• Uses observed diffusion weightings and the
  b-matrix of diffusion sensitisation (Basser et
  al., 1996)

17
Diffusion Tensor Imaging

• Provides a full description of the second order
  diffusion tensor,

• At each voxel, D is then diagonalised

18
Diffusion Tensor Imaging

• Eigenvalues and eigenvectors of D correspond to
  principal diffusivities and principal diffusion
  directions
• Necessarily 3 eigenvalues,
• Principal diffusivities ?1, ?2, and ?3.
• Invariant under rotation.

19
Diffusion Tensor Imaging

• For each eigenvalue the corresponding diffusion
  direction is given by the eigenvector, v1, v2,
  and v3.
• Direction of principal diffusivity is eigenvector
  corresponding to largest eigenvalue (diffusivity).

20
Diffusion Tensor Orientation and Shape
Oblate, ?1? ?2 gtgt ?3
Prolate, ?1 gtgt ?2 ? ?3
Disc
?3
?2
?3
?1
Spherical, ?1? ?2 ? ?3
v1
Anisotropic
Isotropic
21
Invariant Diffusion Measures Mean Diffusivity

• Apparent Diffusion Coefficient (ADC)
• Quantitative
• Bright pixels - high diffusion
• Uniform across WM
• Typical WM values
• ADC 0.8 x 10-3 mm2 s-1

22
Diffusion Anisotropy
ADCx
ADCy
ADCz
23
Invariant Diffusion Measures Fractional
Anisotropy

• Fractional anisotropy (Basser et al., 1996)
• Quantitative, visualizes WM
• Bright pixels - high anisotropy

Data Range 0 to 1 (isotropic to anisotropic)
24
Section 2 Visualising Coloured Images

• mri3dX Krish Singh, Aston University
• Home page
• http//www.aston.ac.uk/lhs/staff/singhkd/mri3dX/in
  dex.shtml
• Allows visualisation of
• 24 bit RGB images (shade files, .shd)
• Analyze format images (.hdr, .img)

25
Visualising Coloured Images

• 24 bit RGB images
• 3 stacked 8 bit volumes (each 256256N)
• Order Red, Green, Blue
• No header
• N.B. Due to the .shd files lack of a header an
  image with identical height must be loaded prior
  to loading the .shd file

26
mri3dX Environment
Main Window
Axial
Sagittal
Coronal
27
Principal Diffusion Direction
Direction Encoded Colour map (DEC)
Red vx Green vy Blue vz
Pajevic and Pierpaoli, 1999
28
Diffusion Tensor Shape
Shape Encoded Colour map (SEC)
Red ?1/?1 1 Green ?2/?1 Blue ?3/?1
Prolate
Oblate (Disc)
Sphere
29
Section 3 Streamline Tractography

• Attempt to connect voxels on basis of
  directional similarity of coincident eigenvectors

Mori et al., Ann Neurol 1999
30
Streamline Tractography

• Tracts generated from DTI
• Define step vector length,
  e.g. t 1.0 mm
• Define tract termination criteria
• Fractional anisotropy, e.g. FA lt 0.1
• Angle between consecutive eigenvectors, e.g.
  angle gt 45

Basser et al., 2000 Mori et al., 1999
31
Streamline Tractography

• Tracts computed in orthograde and retrograde
  directions from initial seeds
• By using multiple seed points white matter
  structures are extracted

32
Tractography Algorithm
Seed Point
Read
tensor
33
Tractography Algorithm
Seed Point
Diagonalise tensor
Read
tensor
34
Tractography Algorithm
Seed Point
Diagonalise tensor
Read
FA lt threshold?
tensor
35
Tractography Algorithm
Seed Point
Diagonalise tensor
Read
FA lt threshold?
tensor
NO
Angle gt threshold?
Basser et al., 1999 Mori et al., 1999
36
Tractography Algorithm
Seed Point
Diagonalise tensor
Read
FA lt threshold?
tensor
NO
Step distance, t, along principal eigenvector
Angle gt threshold?
NO
Basser et al., 1999 Mori et al., 1999
37
Tractography Algorithm
Seed Point
Diagonalise tensor
Read
FA lt threshold?
tensor
NO
Interpolate tensor field
Step distance, t, along principal eigenvector
Angle gt threshold?
NO
Basser et al., 1999 Mori et al., 1999
38
Tractography Algorithm
Seed Point
YES
Diagonalise tensor
Read
FA lt threshold?
tensor
NO
Output tract vectors
Interpolate tensor field
Step distance, t, along principal eigenvector
Angle gt threshold?
NO
YES
Basser et al., 2000 Mori et al., 1999
39
Section 4 Visualising Tractograms

• GeomView - interactive 3D viewing program for
  Unix and Linux (openGL)
• View and manipulate 3D objects
• Allows rotation, translation, zooming
• Geometry Center, University of Minnesota, USA
  (1992-1996).

40
GeomView

• Although the Geometry Center closed in 1998,
  GeomView is still available and continues to
  evolve
• Home page http//www.geomview.org/
• Download from
• http//www.geomview.org/download/

41
GeomView Environment
Main Window
Tool Bar
Camera Window
42
GeomView File Format

• Documentation available online
• GeomView input file format
• Object Oriented Graphics Library (OOGL)
• OOGL files may be either text (ASCII) or binary
  files

43
VECT File Format

• VECT is an OOGL format that allows visualisation
  of vectors or strings of vectors in GeomView
• Number of vectors (steps) in tractogram (N)
• Start (s) and end (e) points for each vector
• RGB colour (c) for each vector

44
VECT File Format

• The conventional suffix for VECT files is
  .vect.
• The files must have the following syntax

45
VECT File Format

• VECT
• edges (N) vertices (N2) colours (N)
• vertices per edge (i.e. 2, N times)
• colours for each vector (i.e. 1, N times)
• N2 vertices N6 floats, s(x,y,z), e(x,y,z)
• N vector colours N4 floats, R G B A)

46
VECT File Format

• Example 1 Drawing two vectors
• N 2
• Edge 1 (2 vertices v1 (1 0 0), v2 (0 1 0))
• Edge 2 (2 vertices v1 (0 1 0), v2 (0 0 1))
• Colours (absolute value DEC)
• For Edge 1 (R G B A) (1 1 0 1)
• For Edge 2 (R G B A) (0 1 1 1)

47
VECT File Format

• Example 1 Drawing two vectors

48
Visualising Tractograms

• Example 2 Corticospinal pathway

• Patient Biopsy proven right temporal
  glioblastoma
• ROIs in Brodmann Area 6 and through the base of
  the corticospinal tract

Clark et al., 2003
49
Visualising Tractograms

• Example 2 Corticospinal pathway

• Seed regions of interest drawn using
• mriCro Chris Rorden, Nottingham University

• Home page
• http//www.psychology.nottingham.ac.uk/staff/cr1/m
  ricro.html

50
Visualising Tractograms

• Example 2 Corticospinal pathway
• Streamline tractography (Basser et al., 2000)
  
• Angle threshold 45
• FA threshold 0.1
• Vector length 2.0mm
• Whole brain tractography

51
Visualising Tractograms

• Example 2 Corticospinal pathway

52
CQUAD File Format

• CQUAD is an OOGL format that allows visualisation
  of coloured quadrilaterals in GeomView
• Positions of the 4 vertices
• RGB colour for each of the 4 vertices
• For visualisation of image slices in GeomView

53
CQUAD File Format

• The conventional suffix for CQUAD files is
  .cquad.
• The files must have the following syntax

54
CQUAD File Format

• CQUAD
• N4 vertices for N quadrilaterals (each
  consisting of N4, x,y,z coordinates)
• Corresponding N4 vertex colours (each consisting
  of N4 floats, R G B A)

55
Visualising Image Slices

• Example 3 Drawing a square
• CQUAD
• 4 vertices with associated colours
• v1 (1 1 0) c1 (1 0 0 1)
• v2 (1 -1 0) c2 (1 0 0 1)
• v3 (-1 -1 0) c3 (0 1 0 1)
• v4 (-1 1 0) c4 (0 1 0 1)

56
Visualising Image Slices

• Example 3 Drawing a square

Lighting On
Lighting Off
57
Visualising Image Slices

• Example 4 Constructing an image slice

Clark et al., 2003
58
Visualising Image Slices

• Example 4 Constructing an image slice

59
OFF File Format

• OFF is an OOGL format that allows visualisation
  of polygons in GeomView
• For visualisation of triangulated surfaces output
  from the marching cubes algorithm
  (Lorenson and Cline, 1987)

60
OFF File Format

• The conventional suffix for OFF files is .off.
  
• The files must have the following syntax

61
OFF File Format

• OFF
• edges faces (N) vertices
• Vertex positions for face N (N3 x,y,z
  coordinates)
• For face N,
• vertices followed by vertex order
• Face colour (4 floats, R G B A)

62
OFF File Format

• Example 5 Drawing a triangle

63
Visualising Surfaces

• Example 6 Constructing a surface
• Draw the region of interest
• Triangulated surface patch coordinates via the
  marching cubes algorithm

64
Visualising Surfaces

• Example 6 Constructing a surface

65
Full Visualisation

• Example 7 Tractogram/Slice/Surface

Clark et al., 2003
66
Creating GeomView Movies

• Stage Tools is required
• Download http//www.geom.uiuc.edu/
  software /download/StageTools.html
• Stage Tools includes software for
• Loading and unloading image objects
• Specifying rotation, translation and zooming
  parameters to GeomView objects

67
Creating GeomView Movies
Movie created in Paint Shop Pro 7
Tiff snapshots output from GeomView
68
Conclusion

• Computation of the Diffusion Tensor from Magnetic
  Resonance Images has been described
• Freely available software has been shown to be
  capable of visualising coloured images and
  tractograms