•  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