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Fibre Tracking: From Raw Images To Tract Visualisation

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Fibre Tracking: From Raw Images ToTract Visualisation

T.R. Barrick

St. George’s Hospital Medical School, London, United Kingdom.

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

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

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

Section 1: Computing The Diffusion Tensor

Brownian motion

Water Diffusion

Random, translational motion

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)

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 37°C; D = 3.0 x 10-3 mm2 s-1

- 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

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

Diffusion-Weighted Images (DWI)

increasing b factor

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

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)

Possible Diffusion Tensor Image Acquisition

- 1.5T GE Signa MRI (max field 22 mT m-1)
- Diffusion-weighted axial EPI
- b=1000 s mm-2
- 12 directions
- 4 averages
- Voxel size: 2.5mm2.5mm2.8mm

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)

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

- At each voxel, D is then diagonalised

- 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.

- 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).

Diffusion Tensor Orientation and Shape

Oblate,1 2 >> 3

Prolate,1 >> 2 3

Disc

3

2

3

1

Spherical,1 2 3

v1

Anisotropic

Isotropic

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

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)

Section 2: Visualising Coloured Images

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

- 24 bit RGB images
- 3 stacked 8 bit volumes (each 256×256×N)
- Order: Red, Green, Blue
- No header
- N.B. Due to the *.shd file’s lack of a header an image with identical height must be loaded prior to loading the *.shd file

Anterior-posterior

Superior-inferior

Principal Diffusion Direction

Direction Encoded

Colour map (DEC)

Red = | vx |

Green = | vy |

Blue = | vz |

Pajevic and Pierpaoli, 1999

Shape Encoded

Colour map (SEC)

Red = 1/1 = 1

Green = 2/1

Blue = 3/1

Prolate

Oblate (Disc)

Sphere

Section 3: Streamline Tractography

- Attempt to ‘connect’ voxels on basis of directional similarity of coincident eigenvectors

Mori et al.,

Ann Neurol 1999

- Tracts generated from DTI
- Define step vector length, e.g. t = 1.0 mm
- Define tract termination criteria
- Fractional anisotropy, e.g. FA < 0.1
- Angle between consecutive eigenvectors, e.g. angle > 45°

Basser et al., 2000

Mori et al., 1999

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

Seed Point

FA <

threshold?

Diagonalise

tensor

Read

tensor

NO

Angle >

threshold?

Basser et al., 1999

Mori et al., 1999

Seed Point

FA <

threshold?

Diagonalise

tensor

Read

tensor

NO

Step distance, t,

along principal

eigenvector

Angle >

threshold?

NO

Basser et al., 1999

Mori et al., 1999

Seed Point

FA <

threshold?

Diagonalise

tensor

Read

tensor

NO

Interpolate

tensor field

Step distance, t,

along principal

eigenvector

Angle >

threshold?

NO

Basser et al., 1999

Mori et al., 1999

Seed Point

FA <

threshold?

YES

Diagonalise

tensor

Read

tensor

NO

Output

tract

vectors

Interpolate

tensor field

Step distance, t,

along principal

eigenvector

Angle >

threshold?

NO

YES

Basser et al., 2000

Mori et al., 1999

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).

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/

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

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

VECT File Format

- The conventional suffix for VECT files is ‘*.vect’.
- The files must have the following syntax:

VECT File Format

- VECT
- #edges (N) #vertices (N×2) #colours (N)
- #vertices per edge (i.e. 2, N times)
- #colours for each vector (i.e. 1, N times)
- N×2 vertices: N×6floats, s(x,y,z), e(x,y,z)
- N vector colours: N×4 floats, R G B A)

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)

VECT File Format

- Example 1: Drawing two vectors

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

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/mricro.html

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

Visualising Tractograms

- Example 2: Corticospinal pathway

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

- The conventional suffix for CQUAD files is ‘*.cquad’.
- The files must have the following syntax:

CQUAD File Format

- CQUAD
- N×4 vertices for N quadrilaterals (each consisting of N×4, x,y,z coordinates)
- Corresponding N×4 vertex colours (each consisting of N×4 floats, R G B A)

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)

- Example 4: Constructing an image slice

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)

OFF File Format

- The conventional suffix for OFF files is ‘*.off’.
- The files must have the following syntax:

OFF File Format

- OFF
- #edges #faces (N) #vertices
- Vertex positions for face N (N×3x,y,z coordinates)
- For face N,
- #vertices followed by vertex order
- Face colour (4 floats, R G B A)

OFF File Format

- Example 5: Drawing a triangle

Visualising Surfaces

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

Visualising Surfaces

- Example 6: Constructing a surface

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

- 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

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