that is a 3D vector representing the length and orien-
tation of the candidate in each axis; so, s = (x, l).
Given a configuration of marked points (c), the
model, h, is composed by a prior term, f , and a data
term g (Descombes et al., 2004),
h(c) = f (c)g(c) (1)
The prior term models the length of the candidates
and relations between them, while the data term takes
into account the intensity along the candidate, as well
as the intensity after each of its ending voxels.
In order to select the configuration of candidates
corresponding to real dilated VRS, Descombes em-
ployed a Reversible Jump Markov Chain Monte Carlo
algorithm with simulation annealing to globally op-
timize the model. Diverging from Descombes, who
have used a geometrical cooling schedule, we have
chosen to follow an exponential cooling schedule
(equation (2)), as described in (Murphy, 2012), be-
cause we have found that it provided better conver-
gence.
T
t
= T
0
C
t
, (2)
where T
t
is the temperature at iteration t, T
0
is the ini-
tial temperature, defined as T
0
= 1, and C is the cool-
ing rate, defined as C = 0.8.
2.4 Visualization Application
In order to facilitate the observation and analysis of
the detected dilated VRS, we developed a graphical
application as presented in Figure 4. Common to all
three panels is a section that allows the user to select
the desired panel (Figure 4(a)-I). The main panel (Fig-
ure 4(a)) has a section to select the image to be loaded
and the image with detected VRS. There, it is, also,
possible to turn on or off the layer with the detected
dilated VRS and to check the counting of the detected
structures (II). In III, we present the 3D reconstruc-
tion of the selected dilated VRS in the viewers (IV)
with the image of the ROI that has the detected VRS
overlaid.
The application permits to visualize the 3D recon-
struction of the ROI, as well as the detected VRS, as
depicted in Figure 4(b) for the basal ganglia. Finally,
the ROI with the detected VRS overlaid is, also, re-
constructed (Figure 4(c)).
3 RESULTS AND DISCUSSION
The database used for the detection of dilated VRS
was acquired at the Hospital of Braga, Portugal, from
9 elderly patients, whose mean age was 69.4, that had
a clinical minor stroke within 6 months of the cere-
bral MRI acquisition and had at least one vascular
risk factor as hypertension, diabetes or high choles-
terol levels. For each of them there was available
a 3D T1-weighted MPRAGE sequence (176 sagit-
tal slices, matrix 256 X 256, 1 mm isotropic reso-
lution, TR 2730 ms, TE 3.48 ms), acquired with a
Siemens Avanto 1.5 T scanner. To segment the tissues
of our MPRAGE sequence images, we used the Ran-
dom Forest that was trained to participate in Grand
Challenge on MR Brain Image Segmentation (MR-
BrainS
1
). Although the intensity range is different,
the normalization procedure permitted to normalize
the intensities between both databases.
3.1 Tool
Figure 4 depicts the potential of the proposed tool.
With it, physicians can easily retrieve the number
of dilated VRS for each ROI, as well as inspect the
scan of the subject to confirm if it presents abnormal-
ities related to small vessel diseases, or others, which
would allow a better understanding of the correlation
between dilated VRS and those abnormalities. 3D re-
construction of the detected dilated VRS may be use-
ful to provide insight into the spatial distribution of
those structures, as well as if there exists any correla-
tion between the distribution and the diseases, while
3D reconstruction of the ROI permits to confirm if
it was well extracted. The 3D reconstruction of the
ROI, or brain, with VRS overlaid is useful to under-
stand if its propagation through the brain parenchyma
coincide with the perforating arteries.
When the FLAIR sequence is available, the
method to segment tissues is able to segment WM
lesions. This potentiality makes the tool capable to
measure its number and volume, which may be use-
ful for studies that hypothesize a correlation between
dilated VRS and WM lesions.
3.2 Detection of Dilated VRS
The first row of Figure 5(a) and Figure 5(b) show
some examples of dilated VRS detected by the al-
gorithm in the basal ganglia and cerebral WM, re-
spectively. In both cases, the examples seem to have
properties of dilated VRS, such as the low intensity,
surrounded by normal tissue, and small size. In the
second row of Figure 5(a) and Figure 5(b) is shown
the 3D reconstruction of each detected VRS, which
allows the physicians to observe the tortuosity; the
green mark is located in the voxel that was selected
1
http://mrbrains13.isi.uu.n
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