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
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Background
• 50,000 die from cardiac sudden death
• Abnormal heart rhythm is its major cause
• Its mechanism is not clear
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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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3 stages of process
Bottleneck
Modeling
Simulation
Evaluation
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Various parameters
Purkinje fiber
network
Geometry
Our target
Myocardial fiber
orientation
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Previous method
• Take 2D slices from xyz direction
• Specify vectors one-by-one
• Very tedious
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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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Our contribution
• Previous work :
Only vector field on surface
• Ours :
Design of volumetric vector field
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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
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Introduction
User Interface
Stroke on the surface
Stroke crossing the model
Stroke on the cross-section
Algorithm
User Experience
Conclusion
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Stroke on the surface
• Specify fiber orientations on the surface
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Stroke crossing the model
• Cutting
• Create cross-sectional surface
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Stroke on the cross-section
• Specify fiber orientations inside the model
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Demo
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Introduction
User Interface
Algorithm
Tangent vector field
Volumetric vector field
Laplacian interpolation
User Experience
Conclusion
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Tangent vector field
Sketch
Laplacian
interpolation
Tangent
vector field
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Volumetric vector field
• Sketch
• Tangent
vector field
Laplacian
interpolation
Volumetric
vector field
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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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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
C@ 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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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
B@ 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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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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Introduction
User Interface
Algorithm
User Experience
Preliminary test
Interview
Conclusion
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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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Interview
• Positive comments
– “We need this tool!”
– “Interface is intuitive and quick.”
– “This can be a breakthrough.”
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Interview
• Points to be improved
– “Use of MRI may be needed.”
– “Cross-sectioning is not
suitable for visualizing
fiber orientation.”
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Introduction
User Interface
Algorithm
User Experience
Conclusion
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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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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.
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2007