prof. rosemary a. renaut dr. hongbin guo & dr. haewon nam...
TRANSCRIPT
� � � � �� � �� � � � � � � � � �� � ��� � ��� � � �
� � � � � ��� �� � � � � � �� �� � � � � ��� � � � � � � �
� � � � � � �� � � � ��
��� !#" $ %'& ! " ( ! ( ( & ! % ( ! %'& ! "
) & � ! � & * ! %,+ &
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
•
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•
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•
! � � � � � � � �� � � � � � � � � � � �#" � � � � � �
•
$ � � � � � � � � " % � � � & � � � � � � � � � � �" � �#" � � � � � �•
' �� � � ��
•
� � � � � � � �� � � � �� % ( � � " � ' �" � � � � � � ��� �
•
( � � �� � � � � � � $� � � � � � � � � � ��) � � �
•
$� � � � � � ��� � � �+* � � � � ��� � �
– 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
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– 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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– p.36
Voxel-by-voxel CMRgl comparison (24 subjects)
– p.37
Conclusion
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