Visualizing Fiber Tractsin the Brain

Using Diffusion Tensor Data

Masters Project Presentation

Yoshihito Yagi

Thursday, July 28th, 10:00 a.m.

499 Dirac Science Library

What does a brain look like?

• A brain is composed of fibers, which connect the cortex to other parts of the brain and the spinal chord.

• When lesions or tumors appear in the interior of the white matter of the brain, fibers might go around them, and it makes lesions and tumors visible.

• Until now, in order to see fibers we had to cut into a brain.

Diffusion Tensor (DT) MRI

• DT-MRI can be used to reconstruct fibers inside brain noninvasively.

• There are two visualization methods using DT-MRI.– Glyph-based visualization– Fiber tracking method

Glyph-Based Visualization

• 2D and 3D arrays of glyphs.

Fiber Tracking

• Fiber Tracking can visualize the white matter connectivity.

What is a tensor?

• A tensor with rank 2, dimension 3 is just a 3x3 matrix.

• A matrix is used to represent the diffusion of water inside tissue.

zzzyzx

yzyyyx

xzxyxx

DDD

DDD

DDD

Diffusion of Water

• How the diffusion MRI relates to the diffusion of water is not fully understood.

• The diffusion of microstructures is limited by the boundary of the long structure.

• The diffusion is more along one direction than the others.

eigenvalues and eigenvectors

• In this project, a matrix is symmetric positive definite.

• There are only six distinct values.• A matrix has 3 eigenvectors, , and 3 positive

real number eigenvalues, , where .

zzzyzx

yzyyyx

xzxyxx

DDD

DDD

DDD

zyyzzxxzyxxy DDDDDD ,,where

321 ,, eee

321 ,, 321

Anistropic Diffusion

• Diffusion can be characterized by three anisotropic diffusion properties.

Westin et.al proposed three measurements: Cl, Cp, Cs.

.,, 332211 ebeger

Liner Anisotropic Diffusion, Cl

• If , then the diffusion occurs almost entirely along the e1 direction.

• Define Cl that is 1 when the previous situation holds, and is less than 1 otherwise.

0321

1)00(

)0(

)(

)(

1

1

321

21

lC

Planar Anisotropic Diffusion, Cp

• If , then the diffusion is along 2 directions, e1 and e2.

• Define Cp that is 1 when the previous situation holds, and is less than 1 otherwise.

0321

1)0(

)0(2

)(

)(2

22

2

321

32

pC

Spherical Anisotropic Diffusion, Cs

• i.e., Isotropic Diffusion.

• If , then the diffusion occurs in every direction.

• Define Cs such that:

321

1)(

3

)(

3

333

3

321

3

sC

What do these regions look like?

• The regions of large Cl, Cp, Cs.

• The region of white matter, like the corpus callosum, has a large Cl.

• Fibers exist where Cl is large, and they are parallel due to a linear diffusion.

Fiber Tracking Algorithm

• A fiber starts at the point where Cl is large, and it is integrated along e1.

• e1 is the largest diffusion.

Problem

• Long integration leads you to the point where Cl is small.

Tensorline

• This is proposed by Weinstein et al.

• This used two additional vectors, Vin and Vout to calculate a propagation vector.

• If Cl is small, then Vin has more weight.

inout VDV ))1(()1(1 outinllprop VwVwCeCV

where weightwvectornpropagatiopreviousVin :,:

The Goal of This Project

• Our goal is to make pictures which look like those of dissected brains in the book.

• We are improving realism in the display.

Realistic Illumination

• Realistic illumination means global illumination (GI) which is the technique used to simulate indirect illumination.

• Problem – GI uses surfaces instead of lines.

• Solution – Around each line, create a polygonal mesh.

Global vs. Local

Cut-away

• In all the preparations of the brains, we see that the brain has been cut into, in order to see the interior.

• We use the same strategy.

Cut-away algorithm

• We create an isosurface mesh of the basic anatomical MRI data, which yields the cortex of the brain.

• There are a mesh S and two planes H1 and H2.

Cut-away images and movie

• We clip the isosurface of the cortex in order to see inside the isosurfaces of Cl and Cp.

• See a movie.

Global vs. Local

Density and radius of fibers

• Since these fibers are merely suggestive of the actual anatomy of the white matter, their density and radius are free parameters.

Changing the density of fibers

• The number of fibers are 300, 600, 1200

• The radius of fibers is 0.3

Placing more fibers and shrinking their radius

• The number of fibers are 300, 600, 1200.

• The radius of fibers are 0.6, 0.3, 0.15.

Interactive exploration of data

• We implement several interactive tools which enable a user to manipulate data.

• See a movie.

Highlighting fibers

• If fibers are passing through active regions of the cortex, then they are highlighted.

• The activated regions can be found from functional MRI.

Highlighting fibers

• Highlighting fibers intersect with triangular meshes.

Novel Contribution

1. Highlighting fibers

2. Intersection of a fiber with a cortex triangular mesh

3. Global illumination

Laboratory for Mathematics in Imaging at Harvard Medical School.

• We have collaborated with Gordon Kindleman at LMI. In fact, We use his brain data to construct 3D images.

• Next year, Dr. Banks will spend fall 2005 at LMI in order to integrate the tools from this project into their clinical protocols.

Thanks

• Dr. Banks (Adviser)

• Dr. Ouimet, Dr. Liu (Committee)

• Beason (Ray Tracer Pane)

• Ji, Saka,Connor, Reece (Review my report)