![Page 1: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/1.jpg)
• What are brain aneurysms?
• How to study brain aneurysms?
• What did we find about brain aneurysms?
Simulations and Detection of Brain Aneurysms
![Page 2: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/2.jpg)
Grand Challenge Problem: Human Arterial Tree • A complete human arterial tree
delivers the oxygen and nutrition to the whole body.
Circle of Willis in Brain
![Page 3: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/3.jpg)
Grand Challenge Problem: Human Arterial Tree • Thomas Willis found a circulatory
anastomosis in the brain.
Circle of Willis in Brain
![Page 4: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/4.jpg)
Grand Challenge Problem: Human Arterial Tree • Thomas Willis found a circulatory
anastomosis in the brain. • Circle of Willis can preserve the
brain blood supply.
Circle of Willis in Brain
![Page 5: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/5.jpg)
Grand Challenge Problem: Human Arterial Tree
• There are considerable anatomic variations in the Circle of Willis.
Variations in the Circle of Willis
![Page 6: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/6.jpg)
Grand Challenge Problem: Human Arterial Tree • There are considerable anatomic variations in
the Circle of Willis. • Such defects may be related to different
cardiovascular diseases.
Variations in the Circle of Willis
![Page 7: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/7.jpg)
Grand Challenge Problem: Human Arterial Tree
• Stroke is a sudden interruption of the blood supply to the brain.
Stroke Related with Brain Arteries
Ischemic stroke (80%) Hemorrhagic stroke (20%)
![Page 8: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/8.jpg)
Grand Challenge Problem: Human Arterial Tree
• Stroke is a sudden interruption of the blood supply to the brain.
• 80% of strokes are caused by an abrupt blockage of an artery. 20% of strokes are caused by bleeding into brain tissue when a blood vessel bursts.
Stroke Related with Brain Arteries
Ischemic stroke (80%) Hemorrhagic stroke (20%)
![Page 9: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/9.jpg)
Grand Challenge Problem: Human Arterial Tree
• Unruptured brain aneurysms are typically completely with no symptom.
• Brain aneurysms are associated with complicated blood flow patterns.
Brain (Cerebral) Aneurysm
![Page 10: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/10.jpg)
• The current clinical technology could not provide detailed in vivo measurements for intra-aneurysm flow patterns.
• For aneurysm detection, expensive and inconvenient.
Why Numerical Simulations?
MRI results
![Page 11: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/11.jpg)
• Numerical simulations on computers are an effective alternative approach for understanding the mechanisms behind aneurysm growth and rupture.
Why Numerical Simulations?
![Page 12: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/12.jpg)
Simulation
Data analysis
1
2
3 4
Arterial Flow Simulations
![Page 13: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/13.jpg)
Findings: Flow Patterns in Aneurysm
![Page 14: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/14.jpg)
Frequency Analysis With Fourier Transform
A Mathematical Tool
5 secs
![Page 15: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/15.jpg)
Sum of Sines and Cosines
Our building block:
Add enough of them to get any periodic function f(t) you want!
1,sin( ),sin(2 ),sin(3 ),...,sin(k ),...cos( ),cos(2 ),cos(3 ),..., cos(k ),...t t t tt t t t
1 1( ) sin(k ) cos(k )k k
k kf t a b t c t
∞ ∞
= =
= + +∑ ∑
![Page 16: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/16.jpg)
Example: Step Function
+
=
14 sin(t)π
≈
41 sin(t)π
+
![Page 17: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/17.jpg)
Example: Step Function
+
=
41 sin(t)π
+4 sin(3 )3
tπ
≈
4 41 sin( ) sin(3 )3
t tπ π
+ +
![Page 18: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/18.jpg)
Example: Step Function
+
=
4 41 sin(t) sin(3 )3
tπ π
+ +4 sin(5 )5
tπ
≈
4 4 41 sin(t) sin(3 ) sin(5 )3 5
t tπ π π
+ + +
![Page 19: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/19.jpg)
Example: Step Function
+
=
4 sin(7 )7
tπ
≈
3
1
41 sin((2 1) t)(2 1)i
ii π=
+ −−∑
4
1
41 sin((2 1) t)(2 1)i
ii π=
+ −−∑
![Page 20: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/20.jpg)
Example: Step Function
≈1
41 sin((2 1) t)(2 1)
n
ii
i π=
+ −−∑
n=50 n=6 n=250000
![Page 21: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/21.jpg)
Fourier Transform
To express f(t) as
1 1(t) sin(kt) cos(kt)k k
k kf a b c
∞ ∞
= =
= + +∑ ∑
![Page 22: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/22.jpg)
Fourier Transform
To express f(t) as Orthogonal properties:
1 1(t) sin(kt) cos(kt)k k
k kf a b c
∞ ∞
= =
= + +∑ ∑
2 2 2
0 0 02
0
2
0
2
0
1 2 , sin(x) 0, cos(x) 0;
sin(jt) cos(kt)d 0;
, whensin(jt)sin(kt)d ;
0, when
, whencos(jt) cos(kt)d ;
0, when
dt dt dt
t
j kt
j k
j kt
j k
π π π
π
π
π
π
π
π
= = =
=
=⎧= ⎨
≠⎩
=⎧= ⎨
≠⎩
∫ ∫ ∫
∫
∫
∫
![Page 23: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/23.jpg)
To express f(t) as Fourier spectrums:
1 1(t) sin(kt) cos(kt)k k
k kf a b c
∞ ∞
= =
= + +∑ ∑
2
0
2
0
2
0
(t)
2
(t)sin(kt)dt
(t) cos(kt)dt
k
k
f dta
fb
fc
π
π
π
π
π
π
=
=
=
∫
∫
∫
Fourier Transform
![Page 24: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/24.jpg)
= 1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
Fourier Frequency Spectra
![Page 25: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/25.jpg)
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
![Page 26: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/26.jpg)
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
![Page 27: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/27.jpg)
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
![Page 28: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/28.jpg)
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
![Page 29: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/29.jpg)
• Single Frequency Sound
Example: Sound
![Page 30: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/30.jpg)
• Single Frequency Sound
Example: Sound
![Page 31: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/31.jpg)
• Single Frequency Sound
Example: Sound
![Page 32: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/32.jpg)
• Guitar Sound
Example: Sound
![Page 33: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/33.jpg)
• Guitar Sound
Example: Sound
![Page 34: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/34.jpg)
• Guitar Sound
Example: Sound
![Page 35: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/35.jpg)
Findings: Aneurysm Associated Frequencies
§ The blood flow in aneurysms has stress/velocity fluctuations (20-50Hz).
![Page 36: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/36.jpg)
Future Direction: Detecting Aneurysms § The blood flow in aneurysms has stress/velocity fluctuations (20-50Hz). § May analyze the murmurs to detect the brain arterial defects and aneurysms.
Sound data collected
![Page 37: Simulations and Detection of Brain Aneurysmsinbios21/PDF/Fall2015/Yu_10232015.pdf · • Stroke is a sudden interruption of the blood supply to the brain. • 80% of strokes are caused](https://reader034.vdocument.in/reader034/viewer/2022042316/5f052aee7e708231d4119c0f/html5/thumbnails/37.jpg)
Grand Challenge Problem: Human Arterial Tree
• Hemorrhagic strokes have a much higher death rate than ischemic strokes.
Brain (Cerebral) Aneurysm