simulations and detection of brain aneurysmsinbios21/pdf/fall2015/yu_10232015.pdf · • stroke is...
TRANSCRIPT
• What are brain aneurysms?
• How to study brain aneurysms?
• What did we find about brain aneurysms?
Simulations and Detection of Brain Aneurysms
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
Grand Challenge Problem: Human Arterial Tree • Thomas Willis found a circulatory
anastomosis in the brain.
Circle of Willis in Brain
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
Grand Challenge Problem: Human Arterial Tree
• There are considerable anatomic variations in the Circle of Willis.
Variations in the Circle of Willis
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
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%)
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%)
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
• 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
• Numerical simulations on computers are an effective alternative approach for understanding the mechanisms behind aneurysm growth and rupture.
Why Numerical Simulations?
Simulation
Data analysis
1
2
3 4
Arterial Flow Simulations
Findings: Flow Patterns in Aneurysm
Frequency Analysis With Fourier Transform
A Mathematical Tool
5 secs
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
∞ ∞
= =
= + +∑ ∑
Example: Step Function
+
=
14 sin(t)π
≈
41 sin(t)π
+
Example: Step Function
+
=
41 sin(t)π
+4 sin(3 )3
tπ
≈
4 41 sin( ) sin(3 )3
t tπ π
+ +
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
+ + +
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=
+ −−∑
Example: Step Function
≈1
41 sin((2 1) t)(2 1)
n
ii
i π=
+ −−∑
n=50 n=6 n=250000
Fourier Transform
To express f(t) as
1 1(t) sin(kt) cos(kt)k k
k kf a b c
∞ ∞
= =
= + +∑ ∑
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
= = =
=
=⎧= ⎨
≠⎩
=⎧= ⎨
≠⎩
∫ ∫ ∫
∫
∫
∫
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
= 1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
Fourier Frequency Spectra
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
=
Fourier Frequency Spectra
1
41 sin((2 1) t)(2i 1)k
iπ
∞
=
+ −−∑
• Single Frequency Sound
Example: Sound
• Single Frequency Sound
Example: Sound
• Single Frequency Sound
Example: Sound
• Guitar Sound
Example: Sound
• Guitar Sound
Example: Sound
• Guitar Sound
Example: Sound
Findings: Aneurysm Associated Frequencies
§ The blood flow in aneurysms has stress/velocity fluctuations (20-50Hz).
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
Grand Challenge Problem: Human Arterial Tree
• Hemorrhagic strokes have a much higher death rate than ischemic strokes.
Brain (Cerebral) Aneurysm