Using the Fourth Dimension to Distinguish Between Structures for Anisotropic Diffusion Filtering in 4D CT Perfusion Scans - Longitudinal Registration and Shape Modeling - page 76

The HDCS filter [ 15 , 16 ] can be used to filter noise from CT scans, while
preserving as much structure as possible. This 3D anisotropic diffusion filter
combines edge enhancing diffusion (EED) and coherence enhancing diffusion
(CED) [ 17 , 18 ] proposed by Weickert [ 10 , 11 ] using a continuous switch. Since this
filter enhances vessels (CED) and reduces noise (EED), we propose to extend this
filter to 4D by integrating the fourth dimension into the finite difference scheme
that determines the first-derivatives used to determine the structure tensor. Our
approach consists of the following steps:

1. Perform 3D Gaussian smoothing with scale ˃ on each 3D sequential scan
within the 4D CT perfusion data.
2. For each voxel

x within the 3D spatial domain, determine:

) using equation ( 2 ), for each neighboring voxel ʾ within the dis-
cretization scheme.
(b) the first-order derivatives ʴu/ʴx , ʴu/ʴy and ʴu/ʴz ,usingaforwardfinite
difference scheme.
(c) the structure tensor elements and the gradient magnitude squared (used
to determine the first eigenvalue ( ʻ e 1 ) of the EED diffusion tensor [ 15 ]).
3. Perform the conventional steps: smooth the structure tensor elements with
scale ˁ and determine the eigenvalues and eigenvectors of the structure tensor
and the eigenvalues of the EED, CED and HDCS diffusion tensor [ 15 ].
4. Apply the HDCS diffusion filter of which the diffusion tensor is based on
structures detected using information present in the 4th dimension, to each
3D sequential scan within the 4D CT perfusion scan.

(a) ʶ ( ʾ, x

3 Experiments and Results

The proposed time-intensity profile similarity (TIPS) anisotropic diffusion filter
was applied to 20 patient cerebral CTP scans (scanned every 2 s during 60 s at 80
kVp and 150 mAs), acquired on a Philips Brilliance 64-slice CT scanner during
injection of 40 ml of (300 mg I/ ml) contrast agent at 5 ml/s, and reconstructed
with 0.625 mm thick sections. The filter parameters were set as follows. The
˃ and ˁ were set to 0.5 and 1.0 respectively for all patient scans, to preserve
small vessels. The time step size ( ˄ ) was set to 0.03 based on the voxel size
(0.43x0.43x0.625 mm) as described in [ 15 ]. The regularization parameter ʱ and
the contrast parameter for the CED diffusion tensor ( ʻ c ) were set as described
in [ 15 ] to be 0.001 and 15.0. The contrast parameters of the EED ( ʻ e )and
HDCS ( ʻ h ) diffusion tensors varied for each of the patient CTP scans and are
dependent on the sum of squared difference between the time-intensity profiles.
They were determined within a region of interest in the white matter, selected
on the temporal average image of the CTP data. The average first eigenvalue of
the structure tensor ( μ 1 ) and the average gradient magnitude were determined
within the ROI and used to set ʻ h and ʻ e respectively. The number of iterations
( ʷ ) was set to be 30 for all patient CTP scans.
Arteriograms and venograms were derived from the original and filtered CTP
scans using the method proposed in [ 4 ]. To assess the performance of the TIPS