Computer in
Nuclear Medicine
Liang-Chih Wu
National PET/Cyclotron Center
Department of Nuclear Medicine
Taipei Veterans General Hospital
Radionuclide Image Processing
• Filtering, noise reduction
• Extraction of diagnostic information
• Enhancement of image presentation
– Parametric images
– 3D display/rendering
– Image fusion
Planar Image Analysis
• Conventional flow: data acquisition,
display, ROI, TAC, parameters,
report
• Global vs regional function analysis
• Model analysis, image processing,
reporting
• Modeling: Physiological, physical,
mathematical
Fundamental steps in image processing
problem
domain
result
data
acquisition
preprocessing
knowledge base
segmentation
recognition and
interpretation
representation
and description
核醫影像分析流程
整體功能分析
===================
ROI, TAC, Parameter
模式分析
============
生理, 物理,
數學模式
局部功能分析
===================
Parametric Images
報告
=============
images, ROIs,
curves,
parameters
Mean Transit Time

MTT 
 f (t )tdt
0

 f (t )dt
If f(t)=ae-bt then
MTT  1 / b
f ( MTT )  a / e  0.368a
0

The area under f(t), A  
0
A area
 MTT  
a height
a
f (t )dt   aMTT
b
T Half
f (t1 / 2 )  a / 2  ae
t1 / 2
 bt1/ 2
ln 2

 0.693MTT
b
Exponential Fit
simple exponential fit:
f (t )  a 2
 t / t1/ 2
 ae
power exponential fit:
f (t )  a 2
 ( t / t1/ 2 ) s
 t / MTT
Transfer Function Analysis
O(t)
I(t)
H(t)
O(t)=I(t)*H(t)
Ideal Case (Impulse Function)
q0  q,
q
k
H(t), k
q2  q1 (1  k ),
qi  q(1  k )
 qe
q1  q0 (1  k ),
 bi
i
...
qi  qi 1 (1  k ).
Real Case
q0  I 0 ,
I(t)
H(t), k
q1  q0 (1  k )  I1 ,
i 1
qi  I 0 (1  k )  I1 (1  k )  ...  I i
i
i
  I j (1  k )i  j .
j 0
q2  q1 (1  k )  I 2 ,
...
qi  qi 1 (1  k )  I i .
qi = Ii * (1-k)i where * means convolution
Summary
• The ventricular function is the
convolution of the atria function and a
transfer function (1-k)i.
(1  k )  e
i
ib
e
k  1 e
iln(
b
1
)
1 k
1
)0
where b  ln(
1 k
EF by MTTD
• If O(t)=I(t)*H(t),then
MTT(O)=MTT(I)+MTT(H),where
MTT(.) means mean transit time.
• If h(t)=e-bt, then MTT(h)=1/b.
• From the above equations, we have
1
b
MTT (O )  MTT ( I )
Parametric Images
• Physiological
• Mathematical
• Descriptive
Fourier Analysis
• If f(t) is a periodic function with
fundamental frequency , it can be
rewritten as follows:
• f(t) = A0
average value
•
+ A1cos(t+1)
1st harmonic
•
+ A2cos (2t+2) 2nd harmonic
•
+…
Graphic
representation
of Fourier
analysis
Fourier Analysis in NM Images
• Let I(x,y,t) = I1(x,y), I2(x,y),…, In(x,y) be
the original dynamic series of images.
The function I(x,y,t) can be rewritten as:
• I(x,y,t) = A0(x,y)
•
+ B1(x,y)sin(t)+C1(x,y)cos(t)
•
+ B2(x,y)sin(2t)+C2(x,y)cos(2t)
•
+…
Fourier Analysis in NM Images
A0 = Ii/n
Bj = 2Iisin(j2(i-1)/n)/n
Cj = 2Iicos(j2(i-1)/n)/n
Where A0, Bj, Cj, and Ii are the simplified
notation of A0(x,y), Bj(x,y), Cj(x,y), and
Ii(x,y) respectively.
• amplitude = sqrt(B2+C2),
• phase = arctan(-B/C)
•
•
•
•
Phase Analysis
• The dynamic series of images I(x,y,t) can
then be expressed as
• I(t) = A0 + A1cos(t+1) + A2cos(2t+1)
•
+…
• 1st harmonic Fourier analysis of the study
is equivalent to fitting a sinusoidal
function Acos(t+) to the data on pixelby-pixel basis.
Phase analysis of dynamic radionuclide images
Physiological Meaning
of Phase Analysis
• Amplitude: volume change, regional
contractility
• Phase: coordination of motion, sequence
of change
Issues in PET Image Analysis
•
•
•
•
•
3D Image Rendering
Image Fusion/Registration
Image Correction
Image Reconstruction
Quantitation/Modeling
Visualization of Whole-Body PET
STEP 1: Data Interpolation
16 bits projection data
128 x 128 x 2 bytes x 15
256 x 256 x 2 bytes x 48.75
15 x 6.5 mm = 9.75 cm
Interpolation
Serial PET slices
15 images
256 x256 x2 bytes x48.75 xN
PET volume 1
Interpolation
Serial PET slices
15 images
PET volume 2
Whole-Body
PET data volume
Interpolation
Serial PET slices
15 images
PET volume N
Visualization of Whole-Body PET
STEP 2 : Maximum Value Projection
16 Bits
MVP Image Buffer
8 Bits
X-Buffer
8 Bits
Y-Buffer
8 Bits
Z-Buffer
Maximum Value
Projection
Value window size
and center value
Position of MVP Image
Whole-Body
PET Volume Data
8 Bits MVP
Display Frame
Buffer
sagittal
image
coronal
image
transaxial
image
Integration Display of Whole-Body PET Data
PET Transmission scan
PET Emission Scan
正子斷層 Emission + Transmission
全身正子斷層檢查應用
IMIS 影像融合對準處理
病患MRI 影像
IMIS 工作站
DICOM Server
放射線部 影像伺服器
醫院網路
透過醫院內網路,
調出病人相關影像資料
病患PET影像
DICOM Server
核醫部 影像伺服器
Realignment and Fusion Display of MRI and PET Images
STEP 1
Interpolation
Interpolation
Resizing
Serial PET slices
PET volume
Serial MRI slices
STEP 2
MRI volume
Transformation
PET volume
Yes
Is aligned
No
Re-sliced PET volume
Optimization
algorithm
MRI: gray scale
PET: rainbow color scale
MRI volume
Artifact Introduced by the Movement Between
Transmission Scan and Emission Scan
Enhanced Contour Finding Method for Attenuation
Correction of PET Brain Images
The ratio of count value between frontal and posterior lobe
areas was improved 11-15%.
The contribution of variable skull-thickness consideration is 3-7%
and the head-holder is about 6-9%.
Corrected with
transmission scan
Corrected with
contour-finding method
Corrected with enhanced
contour-finding method
Tracer Distribution in Brain over Time
Tracer Distribution in Heart over Time
N-13 ammonia
Fluorodeoxyglucose Model
Three Compartment Model
Plasma FDG
Cp
k1
Tissue FDG
Ce
k2
k3
Tissue FDG-6-P
Cm
k4
dCe (t )
 k1C p (t )  (k2  k3 )Ce (t )  k4Cm (t )
dt
dCm (t )
 k3Ce (t )  k4Cm (t )
dt
Cg
k1k3
MRGlc 
LC k2  k3
Parameter Estimation
•
•
•
•
•
•
Nonlinear least squares method
Autoradiographic approach
Patlak graphic approach
Weighted integration projection method
Linear least squares method
Generalized linear least squares method
Conclusion
• Physiology, physics, mathematics, and
computer technology are the key to
radionuclide image processing.