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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. 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 256 X 256 pixels which corresponds to 300mmx300mm was used for calculation. In order to determine the effect of uncertainty on different regions (White and Dark), the pixel intensity of the images b=520 s/mm 2 and b=850 s/mm 2 were varied by ±50% from their nominal value. Then ADC was calculated for a Region Of Interest (ROI) of area 300 mm 2. 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 150mm 2 to 600mm 2. The ADC for this fixed ROI (no shift) across different slice was calculated and the resulting plots are shown in Figure 7. Abstract Introduction Methods and Materials Effect of Uncertainty - Region Relationship of Uncertainty in Pixel Intensity to Apparent Diffusion Coefficient Calculation Narendhran Vijayakumar 1 and Lars Ewell 2 American Association of Physicists in Medicine, Minneapolis, MN 7/22/07 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 150mm 2 to 600 mm 2 as shown in Figure 7. As the signal intensity is low in diffusion weighted image b=850 s/mm 2 when compared to b=520 s/mm 2, addition of noise in the image b=850 s/mm 2 causes more relative variation in ADC value. This clearly shows that the image with low signal intensity gets affected the most by noise. Conclusion 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/mm 2, and then b=850s/mm 2. Using linear regression, ADC for images b=0 s/mm 2, b=520 s/mm 2 (positive 50% pixel variation) and b=850 s/mm 2 was calculated. Similarly using the images b=0 s/mm 2, b=520 s/mm 2 and b=850 s/mm 2 (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. Effect of Uncertainty – Diffusion Weight Figure2: ROI of area 306 mm 2 (with No shift) for ADC pixel variation calculation. 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] Where b i b-value of the i th data point. I i Pixel intensity of the i th data point. I 0 Pixel intensity of the image without diffusion weighting (b=0). 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. 1 Department of Electrical and Computer Engineering, University of Arizona 2 Department of Radiation Oncology, University of Arizona Figure1: Graphical representation of ADC. Slope = ADC Scan SetSlice Thickness (mm) Slice Spacing (mm) Diffusion Values used for calculating ADC (s/mm 2 ) Number of slices 29165.07.0b=0,520 & 8505 29565.07.0b=0,520 & 8504 29945.07.0b=0,520 & 8506 30175.07.0b=0,520 & 8506 30405.07.0b=0,520 & 8506 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. Figure5: ADC variation for the ROI shifted across the ventricles of the brain for scan set 3040 Figure6: Positive variation in pixel intensity of higher diffusion weighting (b= 850 s/mm 2 ) results in more variation of the ADC, than with lower diffusion weighting (b=520 s/mm 2 ). Table 1: Characteristics of DWMRI used in ADC calculation Figure7: ADC calculated for different area of ROI shows that there is minimal variation. 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

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