White Matter Fibre Tract Likelihood Evaluated using Normalized RMS Diffusion Distance

References
[1] R. Duda, P. Hart. Pattern Recognition and Scene Analysis. NY: Wiley, 1973.
[2] G.J.M. Parker et al. IPMI 2001, 106-120,2001. [3] E.A.H. von dem Hagen, R.M. Henkelman. Proc. 9th
Theory
Our contribution is a modification of the algorithm intro-
duced by Parker et al [2], based on level set methods.
The algorithm works with either DTI data or higher angu-
[3] should yield better results would more closely reflect the
underlying tract structure.
Prior to tracking, we classify tissue and CSF with a
Bayesian classifier [1], and scale the speed F by the frac-
ISMRM, 1528, 2001.
defined preferred direction, the tract will still be assigned
relatively high likelihood. Cases where one would want to
traverse such voxels occur when there is volume averaging
oluftifiobnreofdDire¡ cθt¢iφo£ns(ei.ng.acDqTuIisaitciqounissiutisoinngs),loawndancagsuelsarwrheseore-
single voxels are corrupted by noise.
Methods
We demonstrate the algorithm with diffusion tensor data,
பைடு நூலகம்
orientation, instead of only along the fibre direction. More
work will be done to sharpen the maxima of the RMS dif-
fusion distance surface, to make it more resemblant of the
D¯
if
¡
D
θn ¢
φn £¦¥
D¯
if
¡
D
θn
¢
φn
£¦§
D¯ ¢
(1)
the scalar diffusion coefficient measured
¢ φ£ at x, and D¯ is the average value of D
Figure 1: Schematic of tracking algorithm: 2D projection of surface evolution and tract reconstruction using RMS diffusion distance surface. Putative tracts are created by gradient descent through the
lar resolution diffusion coefficient measurements. From a
seed point or region, a surface S is propagated outward
along its normal with speed F. We desire S to propa-
The algorithm currently produces an artifactual¡
out of tracts (see figure 3). This arises because D
fanning
θ¢ φ£ has
values greater than D¯ within a finite solid angle of a fibre
Discussion
We have presented a fibre tracking algorithm that al-
lows for subvoxel volume averaging of fibre directions.
The algorithm assumes that crossing of tracts is minimal:
spond to the dominant direction of diffusion in all voxels
through which they pass will be assigned high likelihood.
If a single voxel along the tract does not have a clearly
gate faster along tracts. Voxels reached quickly will be
assigned high likelihood of connection to the seed. We
propose a new speed function equal to the normalized
tDhe¡ θs¢ uφr£ f,asciemSulwatiilnlgfltohwe
along all diffusion
maxima of water
of the along
surface branch-
ing tracts. Further work should be done to restrain the flow
RMS¡
nˆ
diffusion distance per
1¢ θn ¢ φn £ to S, evaluated
unit time along at position x on
the S:
normal
¤
F
0
where
¡
D
θ¢
φ¡ £
oinvedriraelclti¡ oθn¢ φ£
1 .
is
¢θ
D¡ θn ¢ φn£
such that crossing points are not interpreted as branching
points. Use of regional priors regarding tract curvature
could potentially help in this case.
White Matter Fibre Tract Likelihood Evaluated using Normalized RMS Diffusion Distance
JENNIFER S.W. CAMPBELL, KALEEM SIDDIQI, AND G. BRUCE PIKE
McGill University, Montre´al, Que´bec, Canada
i.e., the RMS diffusion surface is assumed to be an ellip-
soid. We note, however, that measurement of the ADC
abtechaiguhseerthaengsuurlafarcreesDol¡ uθt¢ iφo£n
Figure 2: Evolution of surface S from a seed in the thalamus using speed function F from equation 1.
Figure 3: Putative tracts with high likelihood: pyramidal tract (blue) and anterior (green) and posterior (red) projections from the thalamus. Tracts shown connect user-defined seeds to user-defined ROIs.
surface representing probability of existence of fibre struc-
ture.
Finally, further investigation is needed into what threshold
of likelihood corresponds to anatomically valid tracts.
Introduction
Many algorithms have been proposed for tracking white matter fibres using the principle eigenvector of the diffusion tensor. These approaches can fail when fibres cross or branch at a subvoxel scale. We present a modification of existing tracking schemes that allows for subvoxel branching by using the RMS diffusion distance. The algorithm produces putative tracts as well as a scalar measure of the likelihood of existence for each tract.
tional tissue content, constraining the flow to tissue.
Results
Figure 2 shows an example of the evolution of the surface S. Figure 3 shows putative tracts from user-defined seeds in the thalamus and the brainstem to user-defined regions of interest.
surface time of arrival map¡ T ¡ x¢ y¢ z£ as in [2]. We assign
a likelihood L to the tract σ s£ given by
¡ L σ£
¡¡
F
©σ¨
σ
s£
¢ t¡ s££
ds
ds
¢
(2)
σ¨ s
where t is the tangent to σ. Tracts whose tangents corre-