Abstract— White matter fibre tractography is a non-invasive
method for reconstructing three dimensional trajectories of
fibre pathways. Fast Marching is one of fibre tracking methods
in which co-linearity of principal eigenvectors determines the
speed of front's evolution. In this algorithm effect of tensor’s
eigenvalues are not considered. In the current work, the speed
function of standard fast marching was modified by
considering the strength of tensor’s eigenvectors. The proposed
speed function has an adaptive Fractional Anisotropy (FA)
weighted factor which can be set by type of brain’s
environments (i.e. isotropic and anisotropic regions). This
modification was found to have high accuracy for detecting
fibres by reducing false pathways. The proposed method has
performed high accuracy in detection of fibre crossing.
Index Term – Diffusion Tensor Imaging (DTI), fibre
tractography, Fast Marching (FM), FA Weighted Fast
Marching (FAW-FM), adaptive weighted factor, Fibre
crossing.
I. INTRODUCTION
iffusion Tensor Imaging (DTI) is a non-invasive tool,
which measures random motion of particles that has
been called diffusion or “Brownian motion”. In isotropic
environments, molecules spread out equally in all directions
whereas diffusion is restricted with myelin sheath of axons
in anisotropic regions such as brain white matter. Diffusion
in parallel direction of white matter tracts is at least twice
F. Dargi is with the Department of Medical Physics & Biomedical
engineering, Medical Sciences/University of Tehran, and with the Research
Center for Science and Technology in Medicine, Tehran, Iran. (email:
dargi@razi.tums.ac.ir)
M. A. Oghabian is with the Department of Medical Physics &
Biomedical engineering, Medical Sciences/University of Tehran, and with
the Research Center for Science and Technology in Medicine, Tehran, Iran.
(email: oghabian@sina.tums.ac.ir)
A. Ahmadian is with the Department of Medical Physics & Biomedical
engineering, Medical Sciences/University of Tehran, and with the Research
Center for Science and Technology in Medicine, Tehran, Iran. (email:
ahmadian@sina.tums.ac.ir)
H. Soltanian Zadeh is with the Control and Intelligent Processing Center
of Excellence, Department of Electrical and Computer Engineering,
University of Tehran, Tehran, Iran and the Image Analysis Laboratory,
Department of Radiology, Henry Ford Heath System, Detroit, MI, USA.
(emails: hszadeh@ut.ac.ir, hamids@rad.hfh.edu)
M. Zarei is with the Department of Clinical Neurology, University of
Oxford and with the Oxford Center for Functional Magnetic Resonance
Imaging of the Brain. (email: mojtaba@fmrib.ox.ac.uk)
A. Boroomand is with the Department of Medical Physics & Biomedical
engineering, Medical Sciences/University of Tehran, and with the Research
Center for Science and Technology in Medicine, Tehran, Iran. (email:
boroomand@razi.tums.ac.ir)
faster than perpendicular directions [1]. Diffusion properties
of neural pathways can be obtained by this imaging
technique, where a symmetric 2
nd
-order tensor is assigned to
each image voxel. Principal eigenvector of each voxel’s
tensor represents direction of diffusion [2].
One of the most important applications of DTI is white
matter tractography, which non-invasively reconstructs three
dimensional trajectories of white matter fibre pathways.
Until now several tractography algorithms have been used to
reconstruct neural pathways. The first fibre tractography
method has been called Principal Diffusion Direction (PDD)
techniques, which start tracking from user defined seed
voxel and follow its principal eigenvector direction to enter
next voxel. Tracking line is propagated until some stopping
criterions are met. Other same algorithms are streamlines
algorithms that reconstruct three dimensional trajectories
from main eigenvector of each voxel using Runge-Kutta and
Euler integration methods for solving differential equations
in vector field of DTI. These techniques have discretization
error for reconstructing fibres. Mori et al. [4] implemented
FACT algorithm which eliminates this error.
Global energy minimization algorithms are other
tractography methods. Fast marching algorithm [5] is the
basic one in this classification. In this algorithm a front is
propagated from a seed point or volume of interest using
defined speed function. The spreading speed is largest in
parallel direction of fibre pathways. In this method a narrow
band is defined around selected voxels which its voxels are
candidate for front to propagate to them. Flow-based surface
evolution fibre tracking method is an extension of fast
marching consists of using all diffusion tensor information.
This modification uses HARDI data in multiple direction
cases [6]. Advanced fast marching is another modification.
In this algorithm, four different speed functions based on a
predefined threshold for their anisotropic index are
determined for connecting any two voxels [7].
In previous fast marching based algorithms, only
directions of eigenvectors determined the speed value and
the arrival time of entrance to next voxel. An FA threshold
was considered during the tractography for not entering to
isotropic areas. In this paper, we consider the effect of
tensor’s strength as well as directions of eigenvectors in DTI
data. Thus, if speed values for entering two candidate voxels
are equal or close to each other, velocity will be determined
by the product of Fractional Anisotropy (FA) values of both
selected voxel and candidate one.
Modified Fast Marching Tractography Algorithm and Its Ability to
Detect Fibre Crossing
F. Dargi, M. A. Oghabian, Member, IEEE, A. Ahmadian, Senior Member, IEEE,
H. Soltanian Zadeh, Senior Member, IEEE, M. Zarei, and A. Boroomand
D
Proceedings of the 29th Annual International
Conference of the IEEE EMBS
Cité Internationale, Lyon, France
August 23-26, 2007.
ThC03.3
1-4244-0788-5/07/$20.00 ©2007 IEEE 319