Extraction of Cerebral
Vasculature from Anatomical
MRI
Andreas Deistung, University of Jena
Jurgen Reichenbach, University of Jena
Marek Kocinski, TUL
Piotr Szczypinski, TUL
Andrzej Materka, TUL
2
The purpose of our research
Vascular Tree Generation
(geometry, flow, pressure drop, viscosity)
3D MRI Data
3D segmentation of a vessel 3D model of a vessel
Pressure drop & flow simulation
comparison
Mesh generation
3
What we focus on
3D MRI data(selected cross-section)
The 3D vascular model
Knowledge-Based Extraction of Cerebral Vasculaturefrom Anatomical MRI
4
The algorithm
1. Multiscale vessel enhancementa. Gaussian filtering
b. Hessian matrix computation
c. Vesselness function
2. Center-line extractiona. 3D Segmentation
b. Skeletonization
3. Surface smoothing with tube-like deformable models
5
Gaussian Filtering
• Derivatives of image L is a convolution with derivatives of Gaussian:
( ) ( ) ( )sGLssL ,, xx
xxx ∂
∂∗=
∂
∂ γ
The D-dimensional Gaussian is defined:
( ) 2
2
2
22
1, s
De
s
sG
x
x−
=π
Where γ is a normalization parameter and s is a scale parameter . For a typical diameter of a vessel smin=0.2, smax=2.
maxmin sss ≤≤
6
• A Taylor expansion of the image L in the neighborhood of point x0
( ) ( )000000
xxxxxx δδδδ s
T
s
TsLsL ,0,0,, Η+∇+≈+
ss 0,0, , Η∇
where:
is a gradient and Hessian matrix of an imagecomputed at x0 coordinates, at scale s.
Multiscale vessel enhancement
7
Multiscale vessel enhancement
• Hessian matrix computed at coordinates x0:
• Eigenvalues are sorted
• The eigenvector of the highest eigenvalueindicate a direction of the vessel at coordinates x0
=
zzzyzx
yzyyyx
xzxyxx
LLL
LLL
LLL
H
123 λλλ ≤≤
8
Blob like structures:
Plate-like structures:
Hessian norm: ∑≤
=Η=3
2
j
jFS λ
32
1
λλ
λ
⋅=BR
3
2
λ
λ=AR
3D 2D
2
1
λ
λ=BR
−
Multiscale vessel enhancement
9
Vesselness function
( ) ( )γγ ,max 00maxmin
sVVsss ≤≤
=
( )
−−
−
−−=
2
2
2
2
2
2
0
2exp1
2exp
2exp1
0
,
c
SRRsV BA
βαγ
λ2>0 and λ3>0
Vesselness function :
( )
−−
−=
2
2
2
2
0
2exp1
2exp
0
,
c
SRsV B
βγ
λ2 >0
3D case:
2D case:
Finally:
10
Multiscale Filtering Results
Slide before filtering Vesselness function representation
11
Axial, coronal and sagittal planes of the
multi-scale enhancement filtered volume.
Maximum intensity projections through
the 3D volume.
Multiscale Filtering Results
12
3D Visualization Results
Visualisation of a selected vessel after
3D vesselness function thresholding
and data segmentation with flood-fill
(seed growing) algorithm.
The surface is rough and uneven.
Applying a surface smoothing methods
is needed.
13
Center-line extraction resultsthe first step for surface smoothing with deformable models
after masking and thresholding
after applying a skeletonization
algorithm
Vesselness function
14
Plans for the future work
• Improving a 3D data filtering algorithm,
• Applying tube-like deformable models for surface smoothing,
• Modelling a viscosity, blood flow andpressure drop.
15
References:
• Knowledge-Based Extraction of Cerebral Vasculature from Anatomical MRI – L.R.
Ostergaard, O.V. Larsen, J. Haase, F.V. Meer, A.C. Evans, D.L. Collins
• Multiscale vessel enhancement filtering– A.F.Frangi, W.J. Niessen, K.L. Vincken, M.A. Viergever
• Edge Detection and Ridge Detection with Automatic Scale Selection – T.
Lindberg
16
Thank you for your attention
