prof. rosemary a. renaut dr. hongbin guo & dr. haewon nam...

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� � � � �� � �� � � � � � � � � �� � ��� � ��� � � �

� � � � � ��� �� � � � � � �� �� � � � � ��� � � � � � � �

� � � � � � �� � � � ��

��� !#" $ %'& ! " ( ! ( ( & ! % ( ! %'& ! "

) & � ! � & * ! %,+ &

Prof. Rosemary A. Renaut

Dr. Hongbin Guo & Dr. Haewon Nam

Department of Mathematics and Statistics, Arizona State Univerisity

Dr. Kewei Chen

Banner Good Samaritan PET center, Phoenix

Supported by: Arizona Alzheimer’s Research Center and NIH BIBIB

April 2005– p.1

OUTLINE

��� � ��� � � �� � � � � � � � � � ��� � � � � � � � ���

� � � � � � � �� � � � � � � � �� � � �� � � � ��� ���

! � � � � � � � �� � � � � � � � � � � �#" � � � � � �

$ � � � � � � � � " % � � � & � � � � � � � � � � �" � �#" � � � � � �•

' �� � � ��

� � � � � � � �� � � � �� % ( � � " � ' �" � � � � � � ��� �

( � � �� � � � � � � $� � � � � � � � � � ��) � � �

$� � � � � � ��� � � �+* � � � � ��� � �

– p.2

1. Ultimate Goal

��� �� � � �� � �� � �� � �� � � � �� �� � � � � � � � � � � � � � � � � � � � � ��

– p.3

Output Data of One Slice

−5

0

5

x 10−4

−5

0

5

x 10−3

−0.01

0

0.01

−0.02

0

0.02

−0.02

0

0.02

0.04

0.06

−0.0200.020.040.06

−0.0200.020.040.06

−0.0200.020.040.060.08

−0.04−0.0200.020.04

−0.01

0

0.01

0.02

−0.01

0

0.01

0.02

−0.01

0

0.01

0.02

−5051015

x 10−3

−5051015

x 10−3

0

5

10

15

x 10−3

0

5

10

15

x 10−3

0

10

20

x 10−3

0

10

20

x 10−3

0

0.01

0.02

0

0.01

0.02

0

0.01

0.02

0.03

0 10 20−5

0

5

10x 10

−4

Time frame0 20 40

−5

0

5

10x 10

−4

Time in minutes

Averageconcentration

Average concentration

� ��� �� �� � � � � � � � � ��� � � �� � �� � � � ��

�� � � ��� � �� ��� �� � � � � �� � � � �� �� � �� � �

� �� � � � �� � ��

– p.4

What is the FDG Tracer Model?

� � � � u(t) � � � � � � � � � � ��� �� � � � � � � � � � � �� � � ��� ��

� � � � y(t)= y1(t) + y2(t) � � � � � � � � �� � � � � � �� � � � � � � � �� � ��

� � �

� � � � � � �

� � �

K1−→

k2←−

� � �

� � � � � � �

y1(t)

k3−→

k4←−

� � ��

� � � � �� �

y2(t)

�� � � ��

y1 = K1u(t)− (k2 + k3)y1(t) + k4y2(t)

y2 = k3y1(t)− k4y2(t). (1)

• K1

� � �

k2

� � � � � � �� � � �• k3

� � �

k4

� � � �� � � � �� � � � � � � ��� � � � �� � � � �� � � � � � �

� � � � �� K1k3

k2+k3

Cp

LC= K

Cp

LC, � �� � �� � �� �� � � � �� � � �� �� �� � �

� � �� � u(t) � � �

y(t) � � � �� �

K1, k2, k3, k4

� � �

K.

– p.5

The Solution of the FDG Tracer Model

� � � � � �

K = (K1, k2, k3, k4) �

y(t) = u(t) ⊗(

c1(K)e−λ1(K)t + c2(K)e−λ2(K)t)

,

� � � � �

� � � � � � �� � �� � &� � � � ��� ���

� � � � � � � � ) � � � � � � � � � � k4

� � � � � �� 0 �� � � � � � � � � � � � � � � � � & � ��) & � �) � � � � � � � � � � �

� � � � � � � " � � � � � 60 � � � � � �� � � �) � � � � � � � � " � � � � " � �� � �� & � � � � � � � � � � � �

�� � � � � � � � �

k4 ��� � � � � � � � � �

y(t) = u(t) ⊗

(

K1k3

k2 + k3+

K1k2

k2 + k3e−(k2+k3)t

)

. (2)

�� � � � � � � ��� � � � � �� � � � � � � � ��� � � � � � � � � � � � � �� � � � � � � �� �

�� � �� � �

u(t) � � � � � �� � �� � �� � �� � �

y(t) ! � � � � � � � � � � � � � � � �

�" � � � � � � � �#– p.6

What are issues with this parameter estimation problem?

� * � � �� � ��� � �� � � � � � � � � � �� � � � ��� � � � � � � � � � � � �* � � � ��) �

� � � � � � � � � � � � �� � � !� � & � � " � � � �� � � � � � ��� � � � � � � � � � � �� � � � � � � � � �

� � � � � � � �� � � � � � � � � �

$� � � �� � � � � � � � � � � � � � � � ��) � � � � � �* � � � � � & ��•

$ � � � � � � � � " � � � � � � �� � � � ��� � � ��� � � � � � � � � � � � �) � � � �" �� � � � � � � � �� � � � � �

� � � � � � � � ��

� � � � � ! � � � � � � � � � ��� � � �� � � � � � � � � � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � � � � � � �� � �� � �� � � � � �

– p.7

Representative input/output

0 5 10 15 20 250

2

4

6

8

10

time in minutes

dens

ity

0 5 10 15 20 25−0.01

0

0.01

0.02

0.03

0.04

time in minutes

freq

uenc

y

� � � � % � � � � � �� � � � ��� � u(t) �

' �" � � % � � �� � � �� � � � ��� � � y(t)

�� � 6 � � * � � � �

� � � � � � � � � � � � � ) � � � � � � � � � � � � � �� � " � � � � � t21 = 25m�� � � �� � � � ��� � � � � � � " � � � � � � � � & � � � � � � � � � � � � � � � � " � � � � � � � � � ∆t22 = 30m�

– p.8

Approximate Input Function–Arterial Blood Samples

0 10 20 30 40 50 600

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

Blood samples for t< 3 minutes

Blood samples for whole 60 minutes

� � � � � � � � � � �� � � ��� � ubs(tj), j = 1, 2, · · · , 34.

– p.9

2. Some Methods for Identifying the Input

��� �� �� �� � � � �� � � � � � � � � � � � � � � � " � � � � � � � � & � � � & ��

� � � � � � � � � � � � � � � � � � � �� � � � ��� � �� � � � � �

��� � � � � � � � � � � � � � �� � � �

� � � � � � � "

� � � � � � � � � � � � � � � � � � ��� � � & � � � � � � � � � � �� � �� � � � �� � � � � � � � � � � ��� � � � � � � �� %

uPhelps = A1eλ1(t−τ) + A2e

λ2(t−τ) + A3eλ3(t−τ),

� �

uFeng = (A1(t − τ0) − A2 − A3)eλ1(t−τ0) + A2e

λ2(t−τ0) + A3eλ3(t−τ0).

' �� � � � �� � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � �

� ( � � " � � � � � � & � � � � � � � �� � � � ��� � � �� � � � �� � � � � � " � � � � � �� � � � � � � � �) � �

� � � " � � � � � � � � � �� � ��

� � �� � � � �� � � �

– p.10

� � � � � � � � � � � � �� � � � � � � � � � �

20 40 60 80 100 120

20

40

60

80

100

120

20 40 60 80 100 120

20

40

60

80

100

120

20 40 60 80 100 120

20

40

60

80

100

120

20 40 60 80 100 120

20

40

60

80

100

120

0 0.5 1 1.5 20

1

2

3

4

5

0 0.5 1 1.5 20

1

2

3

4

5

0 0.5 1 1.5 20

1

2

3

4

5

0 0.5 1 1.5 20

1

2

3

4

5

� � � �� � 26 � � �

27 � � � � �� � � 1154� � � � �� � � � �� � � �� � � � � � � � ��

�� � � �� � � �� � �� � � �

��� � � � � �� �� � � � ��� � � �� � � � � � � � � � � � � � � � � � �

� � � � � � � ��� � � �� � � � � � � � � � � � � �� �

��� � � ��

� � ��� � � �� � �� � � � � � � �� � ��� � �� � � � � � � � � � � � � �� � � � �� ��

– p.11

Time Activity Curve of Blood Region

10−2

10−1

100

101

102

0

1

2

3

4

5

6

7

8

9

10Blood samplesAverage CA−ROI TACEstimated input functionLinear interpolation points

(τ, θ v(τ))$� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � �� � � � � � � � � � � � � � � � �� � � �� � �

�� � � � � � � � � & � � � " � � � � � � � � � � � � � � &

� �) �� � & � � � � � � � �� � � � � �� � � � � � � � � �

� � � �� � � � ��� ��� � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � & � � � " � � � � � �

� � � � � � � � � � & � �) � � � � � � � � � � � � � � � �

' � (� � � � � � � � � � � � � �� � � � � � � �

& � � � � � � � � � � � � � � � � � � � � � � � �� �

� � � �� � � � � � � � � � � � � � � � � � � �� � � �

� � � � � � � � � � � � � � � �� � � � � �� � � � �

� �� � � � � � � � � " � � � � � � � � � � ��

– p.12

� �� ��� � � � � � � � � � � � � �

�� ��� � � � � � �

� � � � ) � � � � & � �) & � �) � � � � � � � � �� � � � � � � � � � � � � � � � � � � �•

� � � � � � � � � & � �) � � � " � � � � � � � � � �)ue(t, θ, λ, δ) =

0 t ≤ τ0,

θv(τp)((t−τ0)(τp−τ0)

) τ0 < t ≤ τp

θ(v(τ)(t−τp)+v(τp)(τ−t)

(τ−τp) ) τp < t ≤ τ

θv(τ)e−λ(t−τ)δ

t > τ

.

� � � � � � � � � � � � �� � � � � � � � � � � � � � �

θ � λ � � �

δ � � � � � � � � � � � � � � �� τ � τ0 � τp�

θ

� � �� � � �� �� � � � � � � � � � � � &� � � � � � �� � & � � � � � � ��) � � � � � � � � � �� � � � � ��� �

– p.13

� � � � �� � � � � � � � � � � � �� �� � � � � � �� � � �

� � � � � � � � � � � � � � � � � � � � & � � � ��� � � � � � � �� � � � � � � � � � � � � � � �� � �� � � � � � � � � � �

� � � � � � � � � � �� � � � � � � � � � " � & � � � � � � � �� � � �� �� � � � � � � � � � � �� � � � � � � � � � �

�� � � � � � � �

� �� � � � � � � � � � � � � � � �τ uPhelps uFeng uExp uPExp

1 1.53(−2)

8.0(−3)

5.23(−2)

1.0(−2)

3.65(−1)

1.1(−1)

1.79(−2)

1.1(−2)

2 1.44(−2)

6.2(−3)

1.59(−2)

7.3(−3)

2.75(−1)

9.7(−2)

1.69(−2)

9.9(−3)

3 1.48(−2)

7.4(−3)

1.51(−2)

7.7(−3)�

2.42(−1)

8.3(−2)

1.67(−2)

1.0(−2)

4 1.49(−2)

6.5(−3)

1.44(−2)

7.4(−3)�

2.50(−1)

8.7(−2)

1.68(−2)

1.0(−2)

– p.14

Do numbers tell everything?

10−2

100

102

0

2

4

6

8

10−2

100

102

0

2

4

6

8

10−2

100

102

0

2

4

6

8

10−2

100

102

0

2

4

6

8

blood samplenew−IF Feng−IFTri−exp−IF

� � � � � � �� � � � � �* � � � � � � � � � � � � � � � � � � " � � � �* � �� � �� � � � �" � � t � � � � � � � � �

� � � � " � � � � � � �� � � � � � � ��� � % � � � � � � �� � � �� � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� � � � � � � �) τ �– p.15

3.Simultaneous Estimate Algorithm(SIME)

$� � � �� � � � ��� � � � � � � � � � � ��� � � %

minx,α

Φ(x, α) =3

i=1

n∑

j=1

wj

[

yTACi (tj) − αi · yi(tj) − (1 − αi) · ue(tj , θ)

]2.

• αi

� � �� � � � �� � � � � � � � & � � � �� � � � � � � �� � � � � � � � � � � & � � � � � � � � � � � �� � �" �

� � � � � �

� � � � �� � � � � � � � � � � � �� � � � � � � � � � � � � � � �� � � �) � yi

� � � � � �� � � �� � & ��

� � � � � � � � � �� � � � � � � � � � � " �•

� ��� � � & � � � � � � � � � Φ

� �� � � � � � � � � � � � � ��) � � � � � � � � � � �� � �

ue

minλ,δ

3∑

i=1

[

θv(τ)e−λ(ti−τ)δ

− ubs(ti)]2

.

– p.16

Intelligent Clustering of Voxel Data to Remove Noise

−1 0 1 20

5000

10000

15000

Density

Fre

quen

cy

Subject:4248, Slice:16, t=23 Seconds

� −20 −10 0 10 20 30 40 50 600

500

1000

1500

Density

Fre

quen

cy

Subject: 4248, Slice:16, t=43 seconds

−10 −5 0 5 10 15 20 25 300

500

1000

1500

2000

2500

3000

Density

Fre

quen

cy

Subject:4248, Slice:16, t=5.75 minutes

� −10 0 10 20 30 40 500

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Density

Fre

quen

cy

Subject: 4248, Slice : 16, t=45min

� � � � � � � � � ��� � �� � � � � � � �� � � �� � � � � � � �� � � � � � � �� � �� � � � �� � �� � � �� � � � �

t = 23 �� �� � � � 43 �� �� � � � 5.75 � � � � � � � � � � � �� � � � �� � � �� 45 � � �

� ��� �� � ��� � � �� � � �� � �

– p.17

Cluster curves: An Example

0 5 10 15 20 25 30 35 40 450

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045Averaged curves using clustering methods

time in minutes

conc

entr

atio

n va

lues

curve1curve2curve3curve4curve5

– p.18

Validating Clustering of Voxel Data

� � � � � �

$ � � � � � � � � " � � � � � � � � � � � � � � � � � � � � �

$ � � � � � � � � " � �� � � �� � � ��) � � � � �� � � � � � � � � � � � � � � � � � � �� � ��� � � � � �

� � � � � � � � � � � � " � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� % � �� � � � � ��� � �� � � � � � � � � � � � � � � � � � � � � �

$ � � � � � � � � " �#" � � � � � � � �� � � � � � � � �� � � � � � ��� � � � � � � � � � � � � � � � � � � � � � � ��

� �

� � � � � � � � � � � � � � � � � � � � � � � � � � �" � � � � � � � � � � � � � ��

$� � � � � � ��� � �

!�� � � � � � � �� � � � � � � � � � � � � � � � � �#" � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � "

– p.19

Comparison of Recovered Input and Measured Data

0 0.5 1 1.50

2

4

6

8

10

12

0<t<1.5

time (min.)

estimated input function

blood samples

� 10−2

10−1

100

101

102

0

2

4

6

8

10

12

log of time (min.)

estimated input function

blood samples

� 10−2

10−1

100

101

102

0

2

4

6

8

10

12

Shifted to alignment

log of time (min.)

estimated input function

blood samples

� � � � �� � � �� � � � ��� � �� � � � � � � � �) � �� � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � �� � ( � � � � � � � � � � � � � � � � � � � � �� �� � � � � � � � � � � � � � � � � � � � � � � �� � ��

� � � � � � � � � � � � � � � � � � " � & � � � � � � " � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � �

� � � � � � � �� � � � � � � � � � � � � � � � � � � � �� � � �� � � � �� � � � � � � � � � � � �) � � � � � � & � �� � � �

� � � � � � � � � � � � � � � � � � �� � ��� � �� � ��

– p.20

Representative Shifted Comparisons

10−2

10−1

100

101

102

0

2

4

6

8

10

121206

10−2

10−1

100

101

102

0

2

4

6

8

10

121227

10−2

10−1

100

101

102

0

2

4

6

8

10

12

140817

10−2

10−1

100

101

102

0

1

2

3

4

5

6

7

8

91154

� � � � � � �� � � � � � � �� � � � � � � ue �� � � � � � � � � � �� � � � � � � � � � � � � � � �� � � ��� � � � � � ubs

�� � � � � � �� � � � � � � �� � �� � � � �� � � � �� � � �� � � ��

– p.21

� � � � �� � �� � �� � � � � � � � � � � � �� � � � � ��

� � �� � � θ λ δ α1 α2 α3

1206 2.049 0.923 0.233 0.930 0.931 0.926

1227 4.000 1.438 0.158 0.952 0.956 0.953

817 2.843 0.691 0.241 0.935 0.935 0.919

1154 2.730 0.872 0.237 0.958 0.957 0.960

1208 1.790 0.518 0.318 0.912 0.915 0.912

1231 2.294 0.828 0.265 0.938 0.932 0.929

1245 2.287 0.350 0.364 0.928 0.929 0.922

827 3.190 0.797 0.257 0.935 0.934 0.928

1264 3.000 1.558 0.152 0.939 0.952 0.934

1078 4.000 0.889 0.260 0.961 0.963 0.963

1188 2.246 0.628 0.247 0.930 0.925 0.914

1234 3.543 0.781 0.277 0.941 0.941 0.943

1086 4.000 1.121 0.189 0.961 0.960 0.958

1191 3.781 0.792 0.257 0.942 0.940 0.941

� �� � � 3.100 0.89 0.239 0.941 0.939 0.936– p.22

Validation by Quantification

0 0.05 0.1 0.150

0.05

0.1

0.15

K1 , y=0.61x+0.049 ( r=0.64774, p=0.0019)

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25

k2 , y=0.68x+0.03 (r=0.94, p=3.25e−9)

0 0.05 0.10

0.02

0.04

0.06

0.08

0.1

0.12

k3 , y=0.92x+0.005 (r=0.87, p=3.48e−7)

0 0.02 0.04 0.060

0.01

0.02

0.03

0.04

0.05

0.06

0.07

K , y=1.02x+5.5e−05 (r=0.996, p<1.2e−16)

– p.23

4. Observations from Results

� � � �� � � � � � � � � � K

� � � � � � �� � � � � � � � � � �� � � � � � � �� � � � � � � � � � � � �

� � � �� � � ��

� � � �� � � � � � � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � �� � �) � � � � � � � � � �� � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � ��

�� � � � � � � � �) � � � � � � � � �) � � � � � � � � � � � � �� � � � � �� � � �� �� � � � � � � � � � � �

0.25 � � � & � � � " ��

� � � � � � & � � � � �� � � � � � � � � � � �� � � � � � � � � �� � � �� �� �� � � � � � � �� � � � � � � � � � � �� � � ��)

� � � � � � � �– p.24

Additional Comments on the Optimization

$� � � � � � � � �� ( � � � �� � � � � � � � �� � � � �� � � � � � � � �� �� � � � � � � � � � ��� � � ��� ���

$ � � � � � � �� � & �� $ � � � � � � � � " � �� & � � �� � � �� � � � � �� � � � � � � �� � � � � � � � ��

0

0.005

0.01

0.015

0.02

0.025

0.03

k4 − no bounds imposed FLS

20 40 60 80

10

20

30

40

50

60

700

0.01

0.02

0.03

0.04

k4 − using bounds from Feng, 1995

20 40 60 80

10

20

30

40

50

60

70

0

0.005

0.01

0.015

0.02

0.025

k4 − using bounds from Piert, 1996

20 40 60 80

10

20

30

40

50

60

700

0.01

0.02

0.03

0.04

k4 − using bounds derived from clustering

20 40 60 80

10

20

30

40

50

60

70 �

0

0.02

0.04

0.06

0.08

0.1K − no bounds imposed FLS

20 40 60 80

10

20

30

40

50

60

700

0.01

0.02

0.03

0.04

0.05

0.06

0.07

K − using bounds from Feng, 1995

20 40 60 80

10

20

30

40

50

60

70

0

0.01

0.02

0.03

0.04

0.05

0.06

K − using bounds from Piert, 1996

20 40 60 80

10

20

30

40

50

60

70

0.02

0.04

0.06

0.08

K − using bounds derived from clustering

20 40 60 80

10

20

30

40

50

60

70

– p.25

Some Remaining Issues

� � � �� � � � � � ��� � � � � � � � � � �� & � � � � � � � � � �� � � � � � � � � � � � �� � � � � � ��� �

�� � � � � � � � � �

' � � � & � � � � � � � � � � � � � " % � � � � � � � � � � � � �� & � � � � � � � � � � ��) � � � � � � � � � � � �

� � � � � �� � � � � � ��� � � � ( � � " � � � ��) � � � � � �� � � � � �� � � � � � � ��) � � � � � � �) � � " $

� �" ��� ��� � ' �� � � � �" � � � � � � ��� � � � � � ' � � �� � �� � � �� � � � � � � �) $ � �� � � �

� � � �) � � � �

( � � �� � � � � � � $� � � � � � � � � � ��) � � � �� � � � � � � �) $ � � � ��

– p.26

5. MR -PET Image Registration: Initial Work

� � � � � � � � � � � �" � � � � � � ��� � � � � � � � ' � � � � � � � � � � � � � � � � � � � �� � � � � �

� � � � � � � � � � � � � � �� � ��� � � � � � � � " � � � � � � � � � � ��

� � �� � � ( � �� � � � � ��� � � � * � � ��� � � � � � ( � � � � � � � � � � " �� �� � � � � � � � � � � � � � � �

� � � � ��

T1−MR

20 40 60 80 100 120

20

40

60

80

100

120

200

400

600

Clustered PET

20 40 60 80 100 120

20

40

60

80

100

1201

2

3

4

Registered Image using Bspline

20 40 60 80 100 120

20

40

60

80

100

120

200

400

600

Difference of PET and registered MR

20 40 60 80 100 120

20

40

60

80

100

120 −0.5

0

0.5

� * � � � � � � � � � � � ' � � � � � � � " � � � � " � ( � � � � � � � � � �

� � � � � �� � � � � � �� � �� � � � � � � � �

– p.27

6. Independent Component Analysis for the ROI

� � � � � � � � � � � �� � � � � � � ��� � � � � � � � � � � � � � �� � �ABTAC(t) = α · u(t) + β · y(t)

�� � � & � � � " � � � � � � � �" ��� � � $�

� � $ � � � � � � � � � �" � ��� � � � � � � � � � � $�

y(t) �� $ � � � � � �� � ��

� � � � � � � �� α

� � �

β

� � �� � � � �� � � � � � � � � &� � � � � � � � � � � � � � & � � � � � � ��

� �� � � � � � & � ��) �

� � � � � � � � � � � � � � � � � � �� � �u(t)

�� � � � & � �� � α � � �

β

�) � � � � � � � � � � �� �� $ � � � � � �� � ��

( � � $ � � � � � � $ � � � � � � � � � � � � � � � �� � � � � � � � ��) � � � � � � � � �� � � � � � � � �) �

� � � � �� " � �� � �( � � �� � � � � � � $� � � � � � � � � � ��) � � � � ( $ � � � � � � � $ � �� � � �

� � � �) �

– p.28

ICA Theory

! � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� �

� � � � � � � � � �� � � � � � � � � � �� �� � � � � * � �

� � � � � � �" � � � � �

� � � � � � � � � � � � � �� �� � � � � � � � � � �� � � � � � � & �� � � � � � � � � � � � � � � � � � � �

� � � � � �� �

� � � � � � � � � �� �� � � � �� � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � �" � � � � � �� � � � �

� � � � � � �" ��� � � �

� � � � � & � � � � � � � �� � � � � � � �� � �" � � � � � � � � � � �� � � � � �� � � � �� � � � � � � � � � � � � �

� � � � � & �� � � � � �" ��� ��

– p.29

ICA Procedure

!� � � � � � � � � � � � � � % � � ' � � � � �� � � � ��� � �� � � � � � � � � � � � � � � � � � � � � � � �� �� � � � �

� � � � � � �� � � � � � � � � � � � � � &� � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � �) �

� � � � � � � �� � � $ � �� � ( $ � � � ��) � � � �•

!� � � � � � � � � � � � � � ( $ � & � � � � �� � � � � � �� �

20 � � �� � � � �� � � � � � � �)

� � � � �� � � � � � � & �� � � ��

$� � � � � � � � � � � � � � � � &� � � � � � � � � � � � � � & � � � � � � �� �

– p.30

ICA Setting Determination and Validation

� & � � � � � � �� �� � � � �� � � � � � � � � � � � � � � &� � � � � � ��� � � � � � � � � � � � � � � � ��� ���

� � � � � � � � � � � � � � � � �� � � � � � � � �� � � � �� � � � �� � � � � � � � �) � �" � � � � � � � � � ��� ���

� � � � � � � � � � � � � � � � �� � � � � � �� � �� � � � �� � � � � � � � � � � � � � � � � � � � �" ��� �

� � � � � � ��� ���

$� � � � � � � � � � � � " � � � � � & � � ( � � � � �� � � � � � � & � � ( $ �� � � � � �) � � � � �

� � � � � � � " �

$� � � � � � � � � � � � � �� � � � � � � � $ � '" � �

K

� � � � � ( $ � � � � � �� � � � ��� � ��

� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � ���

– p.31

7. Results of ICA defined ROI : Subvolume

– p.32

ICA Determined Carotid Artery Region: Whole Brain

– p.33

Blood-sampled and ICA image-derived input functions

� � � � � � � " � � � � � � � � � � � � � � � � � � � �� �� � & ��

– p.34

Voxel-by-voxel CMRgl (K) comparison for one subject

� �� � � �� � � � � � �� � � ��� �� � �� � � �� � � � � � � � ��� � �� ��

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– p.35

Global CMRgl comparison (24 subjects)

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u(t)�

– p.36

Voxel-by-voxel CMRgl comparison (24 subjects)

– p.37

Conclusion

( � � " � � � � � & � � � � � � � �� � � � ��� � � & � � ��� � � � � � � � � � � � � & � � � � � � � � � � �� � �

�� � � � � � � � � " � � � � � � � � � � � � � � � � � � � � � � � � ( $ � � � � � � ' � (� � � � �* � � � � � � �

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k3�

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– p.38

References

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– p.39

References

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References

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– p.41

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