The ‘linear – quadratic’ model of cell survival, w/ S the surviving fraction, D the dose and constants.
DWMRI/MRS Protocol: Radiobiology
The ratio has been correlated with response time for radiation damage to manifest.
For brain and/or spinal cord, ~ 2Gy indicating a late radiation response (months to years).
For tumor, ~ 10 Gy indicating an early radiation response (weeks to months).
DWMRI/MRS Protocol: Radiobiology
Patients eligible to enroll if they have a reasonable risk of suffering from RIN.
DWMRI/MRS Protocol: Enrollment Criteria 1) Kumar et al., ‘Malignant Gliomas: MR Imaging Spectrum of Radiation Therapy and Chemotherapy Induced Necrosis of the Brain After Treatment’, Radiology, 217 , 2, November 2000.
Published data 1 indicate that patients receiving a dose of 60Gy in 30 Fx have between a 5 and 24% chance of developing RIN.
Imaging Protocol: Enrollment Criteria
Biological Equivalent Dose (BED) used to determine enrollment criteria for hypo-fractionation and SRS.
5 x 6Gy required for hypo - fractionation, 21Gy for SRS.
BED = nd(1 + ) with n the
number of fractions, d the dose, and the linear quadratic constants.
Imaging Protocol: Enrollment Criteria Radiation Type Number of Fractions Minimum Radiation (Gy) SRS 1 21 Hypo-fraction 5 30 Normal Fraction 30 60 Re-treatment varies varies
'Relationship of Uncertainty in Pixel Intensity to Apparent Diffusion Coefficient Calculation‘
Narendhran Vijayakumar, Lars Ewell
American Association of Physicists in Medicine (AAPM), Minneapolis, MN 7/22/07
Purpose: To estimate how variations in pixel uncertainty can affect calculations of Apparent Diffusion Coefficients (ADCs) used in therapy evaluation .
Methods and Materials: ADCs are calculated for Volumes Of Interest (VOI) using Diffusion Weighted Magnetic Resonance Imaging (DWMRI). Uncertainties in pixel intensities, e.g. due to noise, are simulated by increasing or decreasing pixel intensities by 50% from their nominal value. The large value (50%) of variation allows trends to be observed more easily. The resulting modified DWMRI images are then used to calculate ADC for VOIs, and the variation of the ADC as a function of position and/or slice number and/or VOI size is then observed. We have analyzed DWMRI scans for a number of patients.
Results: Positive increases in pixel intensity result in lower ADC values and we hence observe the largest relative variation with this change. For the nominal ~1,500mm 3 VOI, with a +50% increase in pixel intensity, we see a maximum relative change of roughly a factor of six going from left to right compared with a factor of three for the nominal pixel intensity. Similar changes were observed for inferior – superior positions (slice number). We see a variation of X going from a 500 mm 3 to a 3,000 mm 3 VOI.
Conclusion: Positive variations in pixel uncertainty result in the largest variation of ADCs and have the most effect in the region which has low average pixel intensity. This behavior is due to less SNR in the region
See Medical Physics 34(6), 2355, June 2007 and http://www.u.arizona.edu/~lewell/pub/index.html
The Dependence of Apparent Diffusion Coefficient on B-values and Voxel Location Lars Ewell, Narendhran Vijayakumar American Society for Therapeutic Radiation and Oncology Los Angeles, CA 10/30/07 Abstract Using Diffusion Weighted Magnetic Resonance Imaging (DWMRI), it has recently become possible to calculate an Apparent Diffusion Coefficient (ADC) for a Region of Interest (ROI). If the ROI is a tumor, the ADC has found utility as a way to monitor efficacy of radiotherapy. A common method of determining an ADC uses two values of diffusion, often b=0 and 1,000 s/mm 2 . This method assumes a linear relationship between the ADC and b-values. By using three different b-values, 0, 520 and 850 s/mm 2 , we have employed linear regression to determine the ADC which should, in principal, yield a more accurate value. Utilizing axial MRI brain scans, we have divided the brain into 1cm 2 ROIs, for which we have calculated values of the ADC. Furthermore, we have subdivided the scan area into a medial/central region and a lateral/posterior/anterior region. A sample of these divisions can be seen in Figure 1. For the medial/central region, we see little difference between using two b-values (0 and 850 s/mm 2 ), and three: (Average ADC 3 )/(Average ADC 2 ) = 0.999 0.023 (SD). However, for the more lateral/posterior/anterior voxels, we see that using three b-values yields a lower result for the ADC: (Average ADC 3 )/(Average ADC 2 ) = 0.866 0.19 (SD). This difference can be seen in Figure 2, where we plot this ratio as a function of column number for central rows of voxels. We are investigating the potential reasons behind this difference, including volume averaging effects. The goal of this work is to determine how best to calculate values of ADC when monitoring efficacy of radiotherapy for brain disease. See International Journal of Radiation Oncology Biology Physics , 69(3) Supplement 1, S713, 1 November 2007 and http://www.u.arizona.edu/~lewell/pub/index.html
Method for Determining Apparent Diffusion Coefficient (ADC) Values for Cerebral Lesions from Diffusion Weighted Magnetic Resonance Imaging (DWMRI) Examinations Tim McDaniels, Lars Ewell American Association of Physicists in Medicine (AAPM), Houston TX 7/27/08 Purpose: This work involves analyzing Apparent Diffusion Coefficient (ADC) values for cerebral lesions from Diffusion Weighted Magnetic Resonance Imaging (DWMRI) examinations. The methodology presented permits transferring lesion geometry from treatment plan images to sequential DWMRI images for intensity measurement and subsequent ADC determination. Uncertainty in ADC calculation was correlated with image intensity. Method and Materials: DWMRI images were taken for several patients at specific intervals during treatment. Location of lesions were defined by the treatment plan contours and transferred to DWMRI images by use of a geometric algorithm. ADC values were calculated by a least squares line fit to DW intensities at varied b-values. ADC values for the entire volume of each lesion were calculated by a weighted sum of individual DWMRI slice values. Initially, the weighting was based on the individual slice volume compared to the total volume as determined by the number of lesion voxels in each slice. Results: Greater uncertainty in ADC values were obtained for baseline b-values (b=0) where the average image intensity was lower. The baseline intensity values were included in the weighting factor for determining the whole volume ADC value, with lower weighting given to individual slices with higher uncertainty. Conclusion: ADC values were determined for cerebral lesions outlined on treatment plan contours and transferred to DWMRI images. Corrections for variation between images and size of individual slice geometries allowed for the calculation of ADC value for whole lesion volumes. Low intensity in the baseline scans was correlated with greater uncertainty in resulting ADC values.
Comparison of Different Diffusion Weighting Techniques Using Mutual Information Registration
Submitted to ‘Magnetic Resonance in Medicine’ on 4/16/08.