Transcript powerpoint slides

Analysis of Contrast-Enhanced
Dynamic MR Lung Images
Geir Torheim1,2,
Giovanni Sebastiani3, Tore Amundsen2,
Fred Godtliebsen4, Olav Haraldseth1,2
1MR
Center Medical Section, Norway, 2Norwegian University of Science and
Technology, Trondheim, Norway, 3Istituto per le Applicazioni del Calcolo,
C.N.R., Rome, Italy, 4Université de Mons-Hainaut, Mons, Belgium, and
University of Tromsø, Tromsø, Norway
Structure of the talk
• Introduction
– What is magnetic resonance imaging (MRI)?
– What is dynamic MRI ?
– Pulmonary embolism
• Dynamic Lung MRI
– Part I Motion correction
– Part II Noise reduction using Bayes
– Part III Noise reduction using novel filter
What is Magnetic Resonance Imaging?
What is Magnetic Resonance Imaging?
• The patient is placed in a magnet
– A radio signal is sent into the body
– The signal causes the body to generate a radio
signal
– The radio signal from the body is received by
antennas
• A computer turns the data into an image
What is Dynamic MR Imaging?
• A series of images is acquired over time
• The images cover the same anatomical area
• The series monitors changes with time
• Contrast agent administration
• Functional imaging of the brain
Intensity
Time
Parametric Image
Pulmonary Embolism
Cause:
Deep Vein Thrombosis
Incidence:
Mortality:
0.25 % in the Western countries
30 % of non treated (hosp.)
< 5 % of treated
Treatment:
Bleeding occurrence:
0.5-1 % (fatal)
10-30 % (non-fatal)
Pulmonary Embolism
Large vessels:
Capillary phase:
• Pulmonary angiography
• Perfusion scintigraphy
• MR angiography
• MR Perfusion Imaging
PE: A problematic diagnosis
Present imaging techniques:
– X-Ray pulmonary angiography
– perfusion and ventilation radionuclide scanning
(scintigraphy)
– spiral CT
– X-Ray peripheral venography (DVT)
• Have side effects
• Need for more accurate diagnosis
Dynamic Lung MRI
• Gives perfusion information with higher
spatial resolution than scintigraphy
• No irradiation
• Can be combined with other MRI
techniques
– MRA of lung
– MRA of lower extremities
» MRA: Magnetic Resonance Angiography
Problems in dynamic lung MRI
• Non-rigid deformation of the lungs
– Long acquisition times prohibits breath hold
• Low Signal-to-Noise-Ratio (SNR)
– Due to low tissue content in the lungs
Can post processing solve both problems ?
Part I
Motion Correction
Motion correction
• The lung was modeled as a pump, the
diaphragm being the “piston”
• An automatic method for detection of
diaphragm was constructed
Motion correction
Strategy
1 Detect diaphragm in every frame
2 Detect the rest of the lung shape
3 Combine 1 and 2 into lung masks
1
2
3
Motion correction
• The diaphragm has a parabolic shape
• The following equations were formulated:
y = a1(x - xm)2 + ym
y = a2(x - xm)2 + ym
if x <= xm
if x > xm
• These equations describe two parabolas
interconnected in the point (xm, ym)
Motion correction
• The parameters to be found are:
a1, a2, xm and ym
• The parameters were related to pixel
intensities by means of the signed X
gradient along the parametric curve
Motion correction
• To find the optimal parameters, simulated
annealing was used
• The Metropolis algorithm was implemented
• The method always accepts moves when the
energy goes down, and sometimes accepts
moves when the energy goes up
Motion correction
Simulated annealing
p=e
- ( E 2 - E1 ) /( sT )
• p is the probability of stepping to the new energy state
• E2 is the energy of the proposed state
• E1 is the current energy state
• T is temperature
• s is a scaling factor to compensate for differences in
intensity levels from one frame to the next
Motion correction
Simulated annealing
•
•
•
•
At each step, the best parameters were saved
The globally best parameters were used
The energies were collected in an array
When the standard deviation of the energies
were below a threshold, the algorithm halted
• The temperature was decreased when the
energy decreased
Motion correction
• To increase the speed and accuracy:
– A bounding box was drawn around the area of
the diaphragm
– This area was visualized by calculating the
difference between the maximum and minimum
intensity projections
Motion correction
Bounding boxes drawn on the difference image
Motion correction
Automatic detection of diaphragm
Pre contrast
Peak
Post contrast
Motion correction
• To get a good delineation of the upper parts of
the lungs, a maximum intensity projection of
all the frames was created
• A spline-based ROI was drawn manually on
the maximum intensity projection image
Motion correction
Manually drawn masks on a maximum intensity projection image
Motion correction
Mapping of pixels
am , n
= mn un
mn - u n
(ln - al ,n )
ln - u n
un
mn
am,n
ln
al,n
Reference lung
Lung to be aligned
Motion Correction
Examples Time Intensity Curves
40
40
35
30
30
Intensity
Intensity
25
20
20
15
10
10
5
0
0
0
20
40
60
80
Time (s)
Before motion correction
100
120
0
20
40
60
80
Time (s)
After motion correction
100
120
Part II
Noise reduction
Bayesian approach
Bayesian approach to Noise Reduction
• The measured image y is expressed as
y=x+e
• x is the true, noise free image
• y is the observed image
• e is Gaussian random noise
Bayesian approach to Noise Reduction
• Bayes Theorem
p ( x | y )  p ( y | x) p ( x )
• Models for p(x) and p(y|x) were formulated.
• These models require two (three)
parameters to work
Bayesian approach to Noise Reduction
• Assuming independent, Gaussian noise p(y|x)
becomes
p ( y | x) = ( 2ps )
2 -n / 2
2
2
s
exp[ y x / 2 ]
n is the number of pixels in the image.
s2 is the noise variance, estimated from a Region Of
Interest (ROI) positioned in the liver.
Bayesian approach to Noise Reduction
Assuming x can be modeled as a Markov
Random field, p(x) is given by Gibbs
distribution:


p ( x) = (1 / Z ) exp -  VC ( x)
 Cy

where Z is a constant and Vc is the potential
Bayesian approach to Noise Reduction
V was modeled as follows:
V (x ) = - b ln[p(x )]
b is a smoothing parameter
Bayesian approach to Noise Reduction
p was discretized and estimated as follows:
p
( k +1)
i

(0)
(k ) 
= p   wij p j /  w jt pt ,

j 
t
(k )
i
• wij is the value of the Gaussian density
N(0,2s2) corresponding to i-j
• pj(0) is the empirical distribution of the
neighbor differences of y
Bayesian approach to Noise Reduction
• The contrast agent is changing the contrast behavior
• Therefore, two b smoothing parameters were estimated
• The “best” parameters values were found by smoothing
two images iteratively using different b values
• The “best” value was the one which minimized the
difference between histograms from an average image and
the denoised image
Bayesian approach to Noise Reduction
Effect of smoothing parameter
Original image
b = 0.3
b = 0.15
b = 0.5
Bayesian approach to Noise Reduction
Examples Time Intensity Curves
40
40
35
30
25
Intensity
Intensity
30
20
15
10
20
10
5
0
0
0
20
40
60
80
100
Time (s)
Time intensity curve before denoising
120
0
20
40
60
80
100
Tim e (s)
Time intensity curve after denoising
120
Bayesian approach to Noise Reduction
Results
Parametric images of a patient with Pulmonary Embolism
Original data
After motion correction
After motion
correction+Bayes
Part III
Noise reduction
An alternative approach
A novel time series
1
filter
Assuming gaussian additive noise:
Z ijk = r ( xi , y j , t k ) + e ijk ,
• Z: The observed image
• r: The true image
• e: Independent identically distributed Gaussian noise
1Described
in a paper submitted to IEEE Transactions on Medical Imaging
A novel time series filter
rˆ( x p , y q , t r ) = B pqr Apqr ,
-1 - 2
B pqr = m n
n
n
 K
i =1 j =1 k =1
n
Apqr
m
n
hpi
m
K hqj K hrk Lgpqij Z ijk ,
= m -1n - 2  K hpi K hqj K hrk Lgpqij .
i =1 j =1 k =1
A novel time series filter
Khpi = Kh(xp-xi), Khqj = Kh(yq-yj), Khrk = Kh(tr-tk)
Lgpqij = Lg (Z pq - Z ij )
Kh( ) = h-1K( /h), Lg( ) = g-1L( /g)
Z ij = m
-1
m
Z
k =1
L and K are Gaussian kernels
ijk
.
A novel time series filter
• The filter can be viewed as an extension of
the Nadaraya-Watson estimator
• The extention basically consists of the L
term
• The purpose of the L term is to use only
similar curves in the smoothing process
A novel time series filter
Three parameters need to be specified:
• hxy - Controls the degree of smoothing in x-y plane
• ht - Controls the degree of smoothing along time
• g - Controls how similar curves must be in order
to be included in the smoothing
A novel time series filter
Parameter settings
g was set using the following rule:
2 2s
g=
m
m is the number of frames and s is the noise standard
deviation
A novel time series filter
Parameter settings
ht was set to a variable bandwidth function
h(t) which was found by the following
formula:
1
h(t ) = 2
2 1/ 5


r
(( ) )
hxy was found by trial and error
A novel time series filter
60
60
50
50
40
40
Signal Intensity
Signal Intensity
Examples Time Intensity Curves
30
20
30
20
10
10
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Frame Number
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Frame Number
Novel filter vs. Bayesian approach
Parametric images of a patient with Lung Embolism
After motion correction
After motion
correction+Bayes
After motion
correction+novel filter
Summary Part I
• A model based method for aligning lung
images was implemented
• The method performs well on noisy data
with little contrast
• A mask had to be drawn manually on each
slice, however, all processing on individual
frames was automatic
Summary part II
• A Bayesian noise reduction method was
implemented
• The method reduces noise without losing
much edge information
• The method is completely automatic apart
from a simple ROI drawing
• A drawback is the long processing time
Summary part III
• A novel noise reduction filter was introduced
• The new filter executes faster than the
Bayesian method
• However, parameters hxy, ht and g must be
specified
• The resulting images are more blurred than
when smoothing with the Bayesian approach
Acknowledgements
Abdel Wahad Bidar1,2
Roar Sunde1
Peter A. Rinck3
1MR
Center Medical Section, Trondheim, Norway,
2Norwegian University of Science and Technology, Trondheim, Norway,
3Université de Mons-Hainaut, Mons, Belgium
Please contact us!
Giovanni Sebastiani [email protected]
Fred Godtliebsen
[email protected]
Geir Torheim
[email protected]