Transcript Relationship of Uncertainty in Pixel Intensity to Apparent Diffusion Coefficient... American Association of Physicists in Medicine, Minneapolis, MN 7/22/07 Abstract Narendhran Vijayakumar

Relationship of Uncertainty in Pixel Intensity to Apparent Diffusion Coefficient Calculation
1
Vijayakumar
Narendhran
and Lars
2
Ewell
American Association of Physicists in Medicine, Minneapolis, MN 7/22/07
Abstract
Scan Set: 3017
4.50
Area 150 mm^2
Using Diffusion Weighted Magnetic Resonance Image (DWMRI) scans, it is possible to
calculate an Apparent Diffusion Coefficient (ADC) for a Region of Interest (ROI). The change
in magnitude of an ADC over time has found utility for evaluation of radiotherapy efficacy. The
amount of diffusion is varied using the parameter know as the ‘b-value’. By intentionally
changing the pixel intensity on DWMRI scans, we have investigated how uncertainties in pixel
intensities can affect the ADC value.
ADC Value [1e-03] (mm^2/s)
4.00
Slope = ADC
Area 300 mm^2
Area 600 mm^2
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
8
9
10
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Slice Number
Figure7: ADC calculated for different area of ROI shows that there is minimal variation.
Introduction
Figure2: ROI of area 306 mm2 (with No shift) for
ADC pixel variation calculation.
Figure1: Graphical representation of ADC.
Scan Set: 2956
Scan Set: 3017
In order to determine the effect of uncertainty on different regions (White and Dark), the
pixel intensity of the images b=520 s/mm2 and b=850 s/mm2 were varied by ±50% from their
nominal value. Then ADC was calculated for a Region Of Interest (ROI) of area 300 mm2.
The ROI was shifted across the ventricles from left to right in increments of 5 pixels. The ROI
is shown in the Figure 2. The obtained ADC data is normalized to the minimum ADC value
and the resulting plots are shown in Figures 3, 4 and 5.
The area of the ROI was varied from 150mm2 to 600mm2. The ADC for this fixed ROI (no
shift) across different slice was calculated and the resulting plots are shown in Figure 7.
7.00
10.00
(-50% Variation)
(-50% Variation)
9.00
No Variation
6.00
No Variation
8.00
Normalized ADC Value
1  Ii 
ADC   ln  
bi  I 0 
Effect of Uncertainty - Region
Normalized ADC Value
Apparent Diffusion Coefficient (ADC) gives a measure of water mobility in a tissue. It is
used in estimating the efficacy of radiation therapy. It is hypothesized that as effective
radiation therapy progresses, the cellular breakdown of cancer cells results in the increased
mobility of water. The calculation of ADC requires at least two images, one without diffusion
weighting (b=0) and other with diffusion weighting (b>0). The ADC is given by [1]
(+50% Variation)
7.00
6.00
5.00
4.00
3.00
(+50% Variation)
5.00
4.00
3.00
2.00
2.00
1.00
Where bi  b-value of the ith data point.
Ii  Pixel intensity of the ith data point.
I0 Pixel intensity of the image without diffusion weighting (b=0).
1.00
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-15
-10
-5
0
5
Shift (Pixels)
10
15
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25
-30
30
-25
-20
-15
-10
-5
0
5
10
15
20
25
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Shift (Pixels)
Figure3: ADC variation for the ROI shifted across the ventricles of the brain for
scan set 3017.
Figure4: ADC variation for the ROI shifted across the ventricles of the brain for
scan set 2956.
A graphical representation of ADC is shown in figure1. Using linear regression line fit is
achieved with minimum error, the slope of the line gives ADC.
Scan Set: 3040
Scan Set: 3017
4.50
No Variation
4.00
Normalized ADC Value
(+50% Variation)
Methods and Materials
ADCs are calculated for a Region of Interest (ROI) using Diffusion Weighted Magnetic
Resonance Imaging (DWMRI). Uncertainties in pixel intensities, e.g. due to noise, are
simulated by increasing/decreasing pixel intensities by 50% from their nominal value. We
specifically varied the pixel intensity by ±50%, because this large variation allows us to
observe the trends more easily. The resulting modified DWMRI images are then used to
calculate ADC for ROIs. IDL® software was used for all our calculations. Eight bit DWMRI
images of dimension 256X256 pixels which corresponds to 300mmx300mm was used for
calculation.
Table 1: Characteristics of DWMRI used in ADC calculation
Scan Set
Slice Thickness
(mm)
Slice Spacing
(mm)
Number of
slices
7.0
Diffusion Values
used for calculating
ADC
(s/mm2)
b=0,520 & 850
2916
5.0
2956
2994
5.0
5.0
7.0
7.0
b=0,520 & 850
b=0,520 & 850
4
6
3017
3040
5.0
5.0
7.0
7.0
b=0,520 & 850
b=0,520 & 850
6
6
1Department
of Electrical and Computer Engineering, University of Arizona
2Department
of Radiation Oncology, University of Arizona
5
3.50
3.00
2.50
2.00
1.50
ADC Value [1.0e-3] (mm^2/s)
(-50% Variation)
4.50
No Variation
4.00
Variation in b=520 (s/mm^2)
Variation in b=850 (s/mm^2)
3.50
3.00
Effect of Uncertainty – Diffusion Weight
In order to study the effect of uncertainty of pixel intensity and how different b-values are
affected, the pixel intensity was varied separately for b=520s/mm2, and then b=850s/mm2. Using
linear regression, ADC for images b=0 s/mm2, b=520 s/mm2 (positive 50% pixel variation) and
b=850 s/mm2 was calculated. Similarly using the images b=0 s/mm2 , b=520 s/mm2 and b=850
s/mm2 (positive 50% pixel variation) ADC was calculated. The result shown in Figure 6 shows that
the positive variation in pixel intensity causes more variation in ADC for image with higher diffusion
weighting.
2.50
2.00
Conclusion
1.50
1.00
0.50
0.00
1.00
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-25
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-5
0
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Shift (Pixels)
Figure5: ADC variation for the ROI shifted across the ventricles of the brain for
scan set 3040
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-20
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-10
-5
0
5
10
15
20
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Shift (pixels)
Figure6: Positive variation in pixel intensity of higher diffusion weighting
(b= 850 s/mm2) results in more variation of the ADC, than with lower diffusion
weighting (b=520 s/mm2).
30
Positive increase in pixel intensity results in lower ADC values and we hence observe the largest
relative variation with this change. For positive pixel variations, a maximum relative change of roughly
a factor of 9 (Figure 3) was observed compared to a factor of 5 for the nominal pixel intensity. The
increase in pixel intensity resulted in a lower ADC value and hence the relative variations were
greatest. Minimal variation in ADC was observed when ROI area is varied from 150mm2 to 600 mm2
as shown in Figure 7.
As the signal intensity is low in diffusion weighted image b=850 s/mm2 when compared to b=520
s/mm2, addition of noise in the image b=850 s/mm2 causes more relative variation in ADC value. This
clearly shows that the image with low signal intensity gets affected the most by noise.
Reference
[1]. Rebecca J. Theilmann, Rebecca Bordersy, Theodore P. Trouard, Guowei Xia, Eric Outwater,
James Ranger-Mooreb, Robert J. Gillies, and Alison Stopeck. Changes in Water Mobility Measured
by Diffusion MRI Predict Response of Metastatic Breast Cancer to Chemotherapy. Neoplasia 2004