Simulating Differential Dosimetry

1. Simulating Differential Dosimetry M. E. Monville1, Z. Kuncic2,3,4, C. Riveros1, P. B.Greer1,5 (1)University of Newcastle, (2) Institute of Medical Physics, (3) School of Physics, (4) University of Sydney, (5) Calvary Mater Hospital

2. INTRODUCTION This study is aimed at implementing novel tools for dose delivery real-time verification PROGRAM OBJECTIVE • Predict time resolved dose during treatment • Prompt remedial actions • Spare patients from error consequences PROGRAM OUTLINE • Analytical model forward prediction • Real time comparison of delivered dose against analytical calculated dose • Stochastic model • Off-line comparison of analytical calculated dose against stochastic predicted dose

3. Materials Monte Carlo differential dosimetry prediction tool • Built on BEAMnrc and DOSXYZnrc • Designed to validate the analytical model predictions BEAMnrc Generate the phase-space file input to DOSXYZ • Uses variance reduction techniques • Directional Bremsstrhalung Splitting • Bremsstrahlung Cross-Section Enhancement • Simulate primary and secondary particles interaction with the Linac head components • Transport particles from the phase-space file through the phantom • Simulate primary and secondary particles interaction with the phantom • Generate the 3D dose distribution in the phantom • Use variance reduction techniques • 2000 photon splitting • 2000 charged particles splitting DOXYZnrc

4. Methods Underlying Idea Bins may be smaller equal or bigger than MLC file segments MLC file is broken into a number of bins For each bin perform a simulation pair  BEAM + DOSXYZ whichgenerates the 3D dose distribution Add up the 3D dose matrix contributed by all segments Save results and clean-up Four Methods to Break Mlc File into Bins • Dynamic Full MLC Use custom BEAM version • Static Segmented Use standard BEAM • Stuffed Static Segmented Use standard BEAM • Dynamic Segmented Use standard BEAM

5. Dynamic Full MLC For each bin run a dynamic BEAM simulation using the whole MLC file. Leaves pattern constrained to span only the bin width by drawing random numbers from the bin width MLC file indices sequence is the CDF for the MLC leaf positions probability • A random number uniformly distributed in [0,1] uniquely identifies a segment through inversion of the CDF • The leaf positions at the random point are obtained through linear interpolation of known leaf positions at the nearest control points Seg0.3506_0.3571 Seg0.1299_0.1364 Seg0.5390_0.5455 Seg0.7338_0.7403

6. Static Segmented For each segment run static BEAM simulation using the segment leaves pattern. The cumulative dose contributed by all segments is approximated by the staircase pattern which assumes the leaf positions are kept constant over the segment. Conceptually similar to the approximation of a Riemann integral through a Riemann sum Num. bins = 10

7. Stuffed Static Segmented Similar to Static Segmented The MLC file is enriched with an arbitrary number of fictitious segments whose leaf positions are obtained through linear interpolation of leaf positions of original adjacent segments. The limit of the Riemann sum approaches the integral value as the number of bins grows bigger … likewise the staircase cumulative dose approaches the total delivered dose as the number of segments grows bigger Num. bins = 100 Num. bins = 1000

8. Dynamic Segmented The N-segment MLC file is broken into N-1 MLC files containing only two consecutive segments whose indices are set respectively to 0 and 1 Run a dynamic BEAM simulation for each 2-segment MLC file  the leaf positions is dynamically computed by interpolation of the 2-segment leaf patterns Example: MLC file made up of the first two originally consecutive segment_0.0000 and segment_0.0065 Seg0.0065 Seg1.000 Seg0.0000 Intermediate interpolated leaf positions

9. Validation Results Compute the cumulative dose by adding up the dose contributed by each segment • Monte Carlo Validation Compare the cumulative dose against the dose from a standard dynamic simulation • Measurements Validation Compare the cumulative dose against the calibrated Epid measurements left –side: Standard dynamic simulation right-side:Dynamic Full MLC method using variance-reduction DBS & BCSE Dynamic Full MLC simulation Cumulative dose contributed by 155 segments

10. Conclusion • Our novel tool is fully automated • It is designed to run in modern distributed calculus computer clusters with optimum usage of the available computational power • Two methods are still in the Monte Carlo framework validation stage Work in Progress Computation Improvements • We are changing the process scheduling scheme to port our tool to small cluster systems • We plan to incorporate parallel BEAM and DOSXYZ into our tool Application extensions • We need to incorporate the Step-and-Shoot radiation delivery procedure • We need to deal with delivery circumstances when the dose rate is not constant like Linac beam hold-offs