Image Processing Reference
In-Depth Information
Previous related work has employed an iterative technique to create time-
of-arrival maps of a heat diffusion front [4]. Instead, we solve directly for the
steady-state concentration,
u
, which can also be thought of as a heat distribution
in the tensor field:
∇⋅ ∇ =
(
Du
)
0
(13.26)
u
, which
describes the steady-state heat flow in the tensor volume (Equation 13.2). Paths
in this divergence-free vector field can be compared using a connection strength
metric that approximates the total flow along the path:
We use this information to create the flux vector field,
j
=
−∇
∫
jt ds
|
|
(13.27)
P
where
j
is the flux along the path, and
t
the unit tangent to the path. Normalization
for the length of the path may also be included in the metric. To obtain an overall
connection strength measure between two points, the value of the maximum flow
path can be taken.
Of great interest in this method are the boundary conditions, or the locations
of sources and sinks in the tensor field. One possibility is to set a region or regions
of interest as the source, and simulate a sink at infinity. Another useful possibility
is to choose one region of interest as the source, and another as the sink. In the
experiments discussed in this chapter, we have simulated a sink at one point of interest,
and a source at another, in order to estimate the flow between the regions.
13.6.1
E
XPERIMENTS
Three experiments performed are described in the following text:
DT-MRI data acquisition:
DT-MRI scans of normal subjects were acquired
using line scan diffusion imaging [9] on a 1.5-T GE Echospeed system. The
following scan parameters were used: rectangular 22-cm field of view (FOV;
256
128 image matrix, 0.86 mm by 1.72 mm in-plane pixel size); slice
thickness
×
=
4 mm; interslice distance
=
1 mm; receiver bandwidth
=
±
6 kHz;
echo time (TE)
2500
msec); scan time (13.60 sec/section. Twenty axial slices were acquired, covering
the entire brain. This protocol provides diffusion data in six gradient directions
as well as on the corresponding T2-weighted image. All gradients and T2-
weighted images are acquired simultaneously, and thus do not need any rigid
registration prior to the tensor reconstruction process. Tensors are calculated as
described in Reference 24.
Tensor preprocessing:
We are interested in measuring connectivity in the white
matter and, consequently, to de-emphasize other regions, we multiply the tensors
by a soft mask. This is necessary to decrease the effect of the ventricles, where
neural fiber tracts are nonexistent but water diffusion is relatively unrestricted and
=
70 msec; repetition time (TR)
=
80 msec (effective TR
=
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