volumetric

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7th Symposium on
Smart Graphics
A Sketch-based Interface
for Modeling Myocardial
Fiber Orientation
Kenshi Takayama1
Ryo Haraguchi3
1The
Takeo Igarashi1,2
Kazuo Nakazawa3
University of Tokyo
2JST SORST
3National Cardiovascular Center
Research Institute
Introduction
Background
Related work
Basic idea
User Interface
Algorithm
User Experience
Conclusion
SG
2007
Background
• 50,000 die from cardiac sudden death
• Abnormal heart rhythm is its major cause
• Its mechanism is not clear
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2007
Simulation approach
Mathematical model
X
dVi
= f i (Vi ; X i ) +
dt
• jElucidation
di j ¢(V
¡ Vi )
j 2 N (i )
dX i
= Gi (Vi ; X i )
dt
1 X
±i = x i ¡
xj
jN i j j 2 N
• Prediction
• Education
(' 0)
i
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2007
3 stages of process
Bottleneck
Modeling
Simulation
Evaluation
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2007
Various parameters
Purkinje fiber
network
Geometry
Our target
Myocardial fiber
orientation
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2007
Previous method
• Take 2D slices from xyz direction
• Specify vectors one-by-one
• Very tedious
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2007
Related work
• Vector field design on surfaces
[Praun et al,00]
[Zhang et al,06]
[Turk,01]
[Fisher et al,07]
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2007
Our contribution
• Previous work :
Only vector field on surface
• Ours :
Design of volumetric vector field
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2007
Basic idea
• Observation
– “Myocardial fibers are parallel
to the surface of the heart”
• Two-step algorithm
Step 1: Construct
tangent vector field
Step 2: Construct
volumetric vector field
SG
2007
Introduction
User Interface
Stroke on the surface
Stroke crossing the model
Stroke on the cross-section
Algorithm
User Experience
Conclusion
SG
2007
Stroke on the surface
• Specify fiber orientations on the surface
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2007
Stroke crossing the model
• Cutting
• Create cross-sectional surface
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2007
Stroke on the cross-section
• Specify fiber orientations inside the model
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2007
Demo
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2007
Introduction
User Interface
Algorithm
Tangent vector field
Volumetric vector field
Laplacian interpolation
User Experience
Conclusion
SG
2007
Tangent vector field
Sketch
Laplacian
interpolation
Tangent
vector field
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2007
Volumetric vector field
• Sketch
• Tangent
vector field
Laplacian
interpolation
Volumetric
vector field
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2007
Laplacian interpolation
• Minimize Laplacian
1 X
X
1
= x i ¡ ± = x ¡x j (' 0) x
j
jNi i j j 2 Ni
jN j
i
i
(' 0)
j 2 Ni
neighbor
i = (1; : : : ; n)
i
=
(1;
:
:
:
;
n)
• Satisfy constraint
Laplacian
x k i = bi
x k i = bi
i = (1; : : : ; m)
i = (1; : : : ; m)
neighbor
xi
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2007
0
1
0
x1
1
0
1
¢¢¢ 1 ¢¢¢
b1
B
C
Laplacian
interpolation
@
AB C = @ A
@ A
¢¢¢ 1 ¢¢¢
bm
xn
• Matrix form
0
1
0 1
1
¡ 1 ¢¢¢ j N 1 j ¢¢¢
0
B
C
B C
B
C0 1
B C
B
C x1
B C
B
C
B C
1
B ¢¢¢
CB C B 0C
¢¢¢
¡
1
B
jN n j
CB C ' B C
B
[email protected] A
B C
B
C
B C
B ¢¢¢
C xn
B b1 C
1
¢¢¢
B
C
B C
@
A
@ A
bm
¢¢¢
1
¢¢¢
µ ¶
µ ¶
L
C
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2007
BB¢¢¢
C B C BB 0CC
C
¢¢¢
¡
1
BB
jN n j
C B x C ' BB b CC
C
BB ¢¢¢ 1
C @ n A BB 1 CC
¢¢¢
C
[email protected] Laplacian interpolation
C
B AC
A
@
B ¢¢¢
C
B
C
x
b
n
1
¢¢¢
B
C
Bb 1 C
¢¢¢
1
¢¢¢A
@
@m A
• Matrix form
µ ¶
µ ¶
bm
¢¢¢
1L
¢¢¢ 0
µ C¶ x ' µ b ¶
L
0
µ ¶x'
µ ¶
C
b
¡ T
¢
¡
¢
L
0
T
T
T
• Least-square
solution
L
C µ ¶ x= L
C µ ¶
C
b
¡ T
¢
¡
¢
L
0
T
T
T
L
C
C
x= L
b
T C
T
T
(L L + C C)x = C b
T
T
T
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2007
C
b
Laplacian
µ ¶ interpolation
µ ¶
¢
¡
¢
L
0
T
T
T
T
L • Sparse
C linear system
C
x= L
C
b
T
T
T
(L L + C C)x = C b
T
Precomputable
T
x = (L L + C C)
¡ 1
T
C b
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2007
Introduction
User Interface
Algorithm
User Experience
Preliminary test
Interview
Conclusion
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2007
Preliminary test
• Asked a physician* to try our system
• Sample model by him
– In about 8 minutes
• Sample simulation result
* T. Ashihara, MD, PhD,
Shiga University of
Medical Science
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2007
Interview
• Positive comments
– “We need this tool!”
– “Interface is intuitive and quick.”
– “This can be a breakthrough.”
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2007
Interview
• Points to be improved
– “Use of MRI may be needed.”
– “Cross-sectioning is not
suitable for visualizing
fiber orientation.”
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2007
Introduction
User Interface
Algorithm
User Experience
Conclusion
SG
2007
Conclusion
• Novel method for modeling
myocardial fiber orientation
• 2-step scheme (our contribution)
– Surface  Volume
• Preliminary user study
with a physician
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2007
Future work
•
•
•
•
Test other interpolation algorithms
More formal user test
Use of MRI
Peeling UI
• Other applications
– Fibers in wood
– Particle animation
[Owada et al,04]
Thank you.
SG
2007
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