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Fibre Tracking: From Raw Images To Tract Visualisation. T.R. Barrick St. George’s Hospital Medical School, London, United Kingdom. Introduction.

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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


Overview

  • 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


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


Diffusion Gradients: Stejskal-Tanner Sequence

90°

echo

180°

RF

gradient

d

d

D


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: 2.5mm2.5mm2.8mm


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)


Diffusion Tensor Imaging

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

  • At each voxel, D is then diagonalised


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.


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).


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


Diffusion Anisotropy

ADCx

ADCy

ADCz


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)


Visualising Coloured Images

  • 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


mri3dX Environment

Main Window

Axial

Sagittal

Coronal


Right-left

Anterior-posterior

Superior-inferior

Principal Diffusion Direction

Direction Encoded

Colour map (DEC)

Red = | vx |

Green = | vy |

Blue = | vz |

Pajevic and Pierpaoli, 1999


Diffusion Tensor Shape

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


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 < 0.1

    • Angle between consecutive eigenvectors, e.g. angle > 45°

Basser et al., 2000

Mori et al., 1999


Streamline Tractography

  • Tracts computed in orthograde and retrograde directions from initial seeds

  • By using multiple seed points white matter structures are extracted


Tractography Algorithm

Seed Point

Read

tensor


Tractography Algorithm

Seed Point

Diagonalise

tensor

Read

tensor


Tractography Algorithm

Seed Point

FA <

threshold?

Diagonalise

tensor

Read

tensor


Tractography Algorithm

Seed Point

FA <

threshold?

Diagonalise

tensor

Read

tensor

NO

Angle >

threshold?

Basser et al., 1999

Mori et al., 1999


Tractography Algorithm

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


Tractography Algorithm

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


Tractography Algorithm

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 Environment

Main Window

Tool Bar

Camera Window


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


e

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


CQUAD File Format

  • 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)


Visualising Image Slices

  • Example 3: Drawing a square

Lighting On

Lighting Off


e

Visualising Image Slices

  • Example 4: Constructing an image slice

Clark et al., 2003


Visualising Image Slices

  • 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


Full Visualisation

  • Example 7: Tractogram/Slice/Surface

Clark et al., 2003


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


Creating GeomView Movies

Tiff snapshots output

from GeomView

Movie created in

Paint Shop Pro 7


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


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