Diffusion Tensor Imaging Lab

Diffusion Tensor Imaging Lab
Copyright David S. Tuch, 2002	HST-583, MIT

http://www.mit.edu/~dtuch

Contents

Introduction
Mathematical background
Description of acquired data
Data analysis
- Scalar visualization
- Tensor visualization
Lab report

Introduction

In recent years, diffusion tensor imaging (DTI) has emerged as a powerful method for investigating white matter architecture in health and disease. Some common applications include measuring the structural integrity of white matter, mapping white matter fiber orientation, and tracking white matter pathways.

While most MRI methods generate univariate (i.e., scalar) images, for example, T1 or T2 maps, DTI produces multivariate (i.e., tensor-valued) images. Hence, DTI poses a number of interesting image reconstruction and visualization challenges. Accordingly, while the specific objective of this lab is to familiarize you with DTI reconstruction and analysis, the more general goal is to acquaint you with multivariate data visualization and analysis.

For background reading for this lab please read:

Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H.
Diffusion tensor imaging: concepts and applications.
J Magn Reson Imaging. 2001 Apr;13(4):534-46.

Le Bihan D.
Looking into the functional architecture of the brain with diffusion MRI.
Nat Rev Neurosci. 2003 Jun;4(6):469-80.

Mathematical background

Recall that the diffusion signal E(q) is related to the diffusion tensor D by the relationship

E(q) = E(0) exp(-q^TDq)&tau (1)

where q= &gamma&deltag is the diffusion gradient wavevector, &gamma is the gyromagnetic ratio, &delta is the diffusion gradient duration, g is the diffusion gradient vector, and &tau is the effective diffusion time. The diffusion weighting is given by the b-value b=q^Tq&tau . The goal is to reconstruct the diffusion tensor D from a set of n diffusion-weighted measurements each with a diffusion wavevector q_i.

Through algebraic manipulation Eqn. 1 can be formulated as a matrix equation

s=Bd (2)

where s= - (log E(q₁) log E(q₂) ... log E(q_n))^T, d=(D₁₁ D₁₂ D₁₃ D₂₂ D₂₃ D₃₃ -log E(0))^T contains the unique elements of D flattened into a tensor with the last term appended to the end, and B is the n x 7 B-matrix. The B-matrix can thought of as an experimental design matrix based on the gradients used for the experiment. The derivation of the B-matrix is left as an exercise.

Lab question 1: Derive Eqn. 2 from Eqn. 1. In particular, derive the B-matrix for an arbitrary set of diffusion wavevectors {q₁, q₂, ..., q_n}, and a given diffusion time &tau .

The diffusion tensor coefficients d can then be estimated by applying the B-matrix pseudo-inverse to s.

d=B⁺s (3)

(If you're not familiar with the use of the matrix pseudoinverse to solve linear systems of equations you can refer to this link.) The diffusion tensor D can then be reconstructed by repartitioning d.

Thought question: In order to go from Eqn. 2 to Eqn. 3, what assumption is made on the noise distribution of s? How would you check whether this assumption is valid or not? What are some reasons it might not be valid? What are some reasons for using this assumption even if it's not valid?

The eigensystem, i.e., the eigenvectors and associated eigenvalues, of the diffusion tensor D relects the orientational structure of the tissue within a voxel. In particular, the principal eigenvector gives the local fiber direction. The fractional anisotropy metric (FA) gives a measure of the degree of diffusion anisotropy, which is correlated with the orientational coherence of the fibers within a voxel. The FA metric is defined as

FA=std(&lambda)/rms(&lambda)

where λ is the set of diffusion tensor eigenvalues, std(.) is the standard deviation, and rms(.) is the root-mean-square.

Description of acquired data

acquisition type: 2D EPI diffusion tensor image (DTI)
spatial resolution = 2x2x2mm³
averages = 6
# directions = 1 unattenuated + 6 attenuated
gradient directions = {[0 0 0], [1 1 0], [1 -1 0], [0 1 1], [0 -1 1], [1 0 1], [-1 0 1]}
repetition time (TR) = 15s
echo time (TE) = 77ms
b-value = 700s/mm²
echo type: spin-echo
image matrix size: 128 x 128 x 40 slices
static magnetic field = 1.49 Tesla

Data analysis

Scalar visualization

1. Launch Dview and open (File->Open file) the raw DTI data file: mg-0-allegra-20006-20011016-121802-4-mri.mnc

2. We first wish to analyze the relationship between the diffusion contrast and the diffusion gradient direction. Begin by binding the +/- keys to the TIME dimesion. To do so, right-click on the big viewport which shows the timecourse and select 'Bind +/- keys to this view' from the context menu. It should read '+/- keys bound to TIME' in the banner at bottom.

3. Then right-click on the small Transverse viewport at top-left and select 'Copy this view to big window' from the context menu. You should now see the Transverse view in the big viewport.

3. Step through the diffusion gradient orientations by pressing + and -. Note how the diffusion contrast changes as a function of the diffusion gradient orientation. In Lab question 2 you are asked to explain the differences in diffusion contrast for a specific anatomic point in corpus callosum.

Lab question 2: For each of the n=7 diffusion gradient orientations, measure the mean (+/- SEM) diffusion signal for a point in the left hemisphere of the genu of the corpus callosum at transverse slice Z=43.2. For each of the 7 diffusion gradients (see Description of acquired data), explain the relative diffusion signal in terms of the fiber orientation at that point in the callosum.

7. We now wish to study the fractional anisotropy (FA) maps. The diffusion tensor and FA maps were calculated before this exercise. Load the FA file: mg-0-allegra-20006-20011016-121802-4-mri-fa.mnc

8. Proceed to transverse slice Z=38.4. Consider the projection from the genu of the corpus callosum to the middle frontal gyrus. Note how the FA is high in the corpus callosum, low in the divergence to the frontal gyri, and then high again in the middle frontal gyrus.

Lab question 3: Measure the FA along a path from the genu of the corpus callosum to the middle frontal gyrus. Explain why the FA decreases in going from the callosum to the striations and then increases in the gyrus.

Tensor visualization

9. The previous exercises involved scalar visualization. We now wish to visualize the orientational information in the DTI image. Quit Dview by selecting 'File->Quit Dview' from the main menu.

10. At the unix prompt, chage directory to the Lab4 data directory: cd /afs/athena.mit.edu/course/other/hst.583/lab_data/lab4

11. Launch freediffusion by typing: /mit/hst.583/lab_sw/lab4/freediffusion

12. Load a tensor data set by selecting 'Volume->Open tensor' and then selecting the fd directory from the filechooser.

13. Here are instructions on how to navigate in the freediffusion visualizer:

Keypress j / Keypress t: toggle between joystick (position sensitive) and trackball (motion sensitive) styles.
Button 1: rotate the camera.
Button 2: pan the camera. (Note: with 2-button mice, pan is defined as -Button 1.)
Button 3: zoom the camera.
Keypress 3: toggle the render window into and out of stereo mode.
Keypress e: exit the application.
Keypress f: fly to the picked point.
Keypress r: reset the camera.

14. Proceed to slice 40 in the transverse view and identify the thalamus.

Lab question 4: In the transverse view one can identify clusters of fiber orientation in the thalamus (slice~=40). Identify 3 fiber orientation clusters in the thalamus and explain the fiber orientations in terms of your anatomical knowledge of the thalamocortical/corticothalamic projections. For example, what nucleus is the anterior-posterior (green) cluster on the medial bank of the thalamus and how is the anterior-posterior orientation consistent with the projection territory of this nucleus?

Lab report

In your report, please answer the 4 lab questions posed above. Please provide printouts of the images for questions 2 and 4. Do not hesitate to email me at 'dtuch at mit dot edu' if you have any questions.