Analysis of Contrast-Enhanced Dynamic MR Lung Images

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, andUniversity 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?

• 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 Magnetic Resonance Imaging?

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

Time

Intensity

Parametric Image

Pulmonary Embolism

Cause: Deep Vein Thrombosis

Incidence: 0.25 % in the Western countriesMortality: 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 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

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

1 Detect diaphragm in every frame

2 Detect the rest of the lung shape

3 Combine 1 and 2 into lung masks

Motion correctionStrategy

1 32

Motion correction

• The diaphragm has a parabolic shape

• The following equations were formulated:

y = a1(x - xm)2 + ym if x <= xm

y = a2(x - xm)2 + ym 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 correctionSimulated annealing

• 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

)/()( 12 sTEEep

Motion correctionSimulated 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 Post contrastPeak

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 correctionMapping of pixels

un

mn

ln

un

am,n

al,n

)( ,, nlnnn

nnnnm al

ulum

ma

Reference lung Lung to be aligned

Motion CorrectionExamples Time Intensity Curves

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100 120

Time (s)

Inte

ns

ity

0

10

20

30

40

0 20 40 60 80 100 120

Time (s)

Inte

ns

ity

Before motion correction After motion correction

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

• Bayes Theorem


)()|()|( xxyyx ppp

• Models for p(x) and p(y|x) were formulated.

• These models require two (three) parameters to work


]2/exp[)2()|( 22

2/2 xyxy np

• Assuming independent, Gaussian noise p(y|x) becomes

n is the number of pixels in the image.

2 is the noise variance, estimated from a Region Of Interest (ROI) positioned in the liver.

Assuming x can be modeled as a Markov Random field, p(x) is given by Gibbs distribution:


)(exp)/1()( xx

CCVZp

where Z is a constant and Vc is the potential

V was modeled as follows:


)(ln)( pV

is a smoothing parameter

• wij is the value of the Gaussian density N(0,22) corresponding to i-j

• pj(0) is the empirical distribution of the

neighbor differences of y


p was discretized and estimated as follows:

j t

ktjtjij

ki

ki pwpwpp ,/ )()0()()1(

• The contrast agent is changing the contrast behavior

• Therefore, two smoothing parameters were estimated

• The “best” parameters values were found by smoothing two images iteratively using different 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 ReductionEffect of smoothing parameter

Original image = 0.15

= 0.5 = 0.3

Time intensity curve before denoising Time intensity curve after denoising

0

10

20

30

40

0 20 40 60 80 100 120

Time (s)

Inte

ns

ity

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100 120

Time (s)

Inte

nsi

ty

Bayesian approach to Noise ReductionExamples Time Intensity Curves

Parametric images of a patient with Pulmonary Embolism

Original data After motion correction After motion correction+Bayes

Bayesian approach to Noise ReductionResults

Part III

Noise reduction

An alternative approach

A novel time series filter1

,),,( ijkkjiijk tyxZ

Assuming gaussian additive noise:

• Z: The observed image

• : The true image

• : Independent identically distributed Gaussian noise

1Described in a paper submitted to IEEE Transactions on Medical Imaging

A novel time series filter

,),,(ˆ pqrpqrrqp ABtyx

n

i

n

j

m

kijkgpqijhrkhqjhpipqr ZLKKKnmB

1 1 1

21 ,

n

i

n

j

m

kgpqijhrkhqjhpipqr LKKKnmA

1 1 1

21 .


Khpi = Kh(xp-xi), Khqj = Kh(yq-yj), Khrk = Kh(tr-tk)

ZZ ijpqggpqij LL

Kh( ) = h-1K( /h), Lg( ) = g-1L( /g)

Z

m

kijkij Zm

1

1 .

L and K are Gaussian kernels


• 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


• 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

Three parameters need to be specified:

g was set using the following rule:

A novel time series filterParameter settings

mg

22

m is the number of frames and is the noise standard deviation

A novel time series filterParameter settings

5/12 ))((1

2)( th

ht was set to a variable bandwidth function h(t) which was found by the following formula:

hxy was found by trial and error

A novel time series filter Examples Time Intensity Curves

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Frame Number

Sig

na

l In

ten

sity

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Frame Number

Sig

na

l In

ten

sity

Parametric images of a patient with Lung Embolism

Novel filter vs. Bayesian approach

After motion correction After motion correction+novel filter

After motion correction+Bayes

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]

Documents

Analysis of Contrast-Enhanced Dynamic MR Lung Images