Diffusion Imaging and Fibre Tractography
Diffusion Imaging and Fibre Tractography
My research involves both acquisition of magnetic resonance imaging
(MRI) data and postprocessing techniques. Specifically, I am working
on an MRI modality called diffusion imaging, and use computer vision
techniques to infer white matter fibre connectivity in the central
nervous system (CNS) from the base MRI images. Diffusion imaging is a
method for measuring the displacement distribution of water molecules
in vivo. From the displacement distribution, we can infer the
fibre orientation or orientations in each imaging volume element (or
voxel). With suitable postprocessing techniuqes, we can
reconstruct 3D white mater fibre bundles from these displacement
distributions, along with the uncertainty associated with these
connections.
Below is a pictorial decription of diffusion imaging and
postprocessing techniques. For further information, please see these
references.
Diffusion MRI background




Diffusion is the random thermal motion of molecules. With MRI, we can
measure the magnitude and direction of the diffusion of
water molecules in vivo.

When there is oriented fibre structure, the diffusing water molecules
will move preferentially parallel to the fibre direction.



Diffusion Imaging involves acquiring a series of diffusion weighted
images (DWIs) and from them inferring something about the
underlying tissue structure. The diffusion displacement
distribution, including magnitude and directional
information, can be calculated from the DWIs.

A diffusion weighted image is one in which the signal intensity
is decreased in the direction of an applied diffusion sensitizing
gradient. Above, we see that the difference in the signal
decrease when the diffusion sensitizing gradient is applied
parallel or perpendicular to the white matter fibre tract direction.



Diffusion tensor imaging (DTI) is done by fitting the diffusion
probability density function (pdf) to a 3D Gaussian function, which
can be described with a second order tensor. The eigenvector
corresponding to the largest eigenvalue of the diffusion tensor will
lie along the direction of maximal diffusion.

With the tensor model, it can be difficult to describe the fibre
architecture in voxels in which there are multiple fibre
directions. However, the diffusion pdf can be measured at high angular
resolution to obtain information about multiple subvoxel fiber
directions. There are a number of new methods that have been proposed
for measuring the diffusion pdf at high angular resolution (HARD
techniques). These include qspace methods such as diffusion spectrum
imaging (DSI), persistent angular structure (PAS) reconstruction,
multitensor reconstruction, and Qball imaging (QBI).



From this diffusion pdf, we hope to infer the fibre orientation
pdf. This can be done by simply extracting the maxima of the
diffusion pdf, or by more sophisticated modeling and statistics.

Diffusion orientation distribution function (ODF), or
projection of the diffusion pdf on the surface of the sphere.



redgreenblue (RGB) map showing the direction of the principle
eigenvector of the diffusion tensor.

The diffusion ODF shown in the region of interest outlined in the
RGB map (far left). Left: QBI reconstruction. Right: DTI
reconstruction. This ROI contains fibres from both the superior
longitudinal fasciculus and the corpus collosum. The topmost ODF
indicates that in some voxels, there is significant partial volume
averaging of fibre directions, in which case the tensor model does not
clearly show their directions.



Fibre tractography: tracts of the corpus callosum

Maximum intensity projection (MIP) of uncertainty associated with fibre connections.

Projects
 characterization of complex subvoxel fibre geometries
 mathematics of fibre tract reconstruction
 validation of tractography using phantoms
 cross validation of diffusion MRI tractography and other
tracttracing methods
 registration, distortion correction, and denoising of diffusion
MRI data
 acquisition of high signal, high spatial resolution, high angular
resolution, distortion free diffusion MRI data
 applications of diffusion imaging: these include multiple
sclerosis, CJD, stroke, brain tumours, epilepsy, scizophrenia, and
basic neuroanatomical research, e.g. investigation of pathways
involved in language, vision, audition.