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Monte Carlo Superposition Code for Radiotherapy Dose calculations

 Abstract. The convolution/superposition calculations for radiotherapy dose distributions are traditionally performed by convolving polyenergetic energy deposition kernels with TERMA (total energy released per unit mass) precomputed in each voxel of the irradiated phantom. We propose an alternative method in which the TERMA calculation is replaced by random sampling of photon energy, direction and interaction point. Then, a direction is randomly sampled from the angular distribution of the monoenergetic kernel corresponding to the photon energy. The kernel ray is propagated across the phantom, and energy is deposited in each voxel traversed. An important advantage of the explicit sampling of energy is that spectral changes with depth are automatically accounted for. No spectral or kernel hardening corrections are needed. Furthermore, the continuous sampling of photon direction allows us to model sharp changes in fluence, such as those due to collimator tongue-and-groove. The use of explicit photon direction also facilitates modelling of situations where a given voxel is traversed by photons from many directions. Extra-focal radiation, for instance, can therefore be modelled accurately. Our method also allows efficient calculation of a multi-segment/multi-beam IMRT plan by sampling of beam angles and field segments according to their relative weights. For instance, an IMRT plan consisting of seven 14 × 12 cm2 beams with a total of 300 field segments can be computed in 15 min on a single CPU, with 2% statistical fluctuations at the isocentre of the patient's CT phantom divided into 4 × 4 × 4 mm3 voxels. The calculation contains all aperture-specific effects, such as tongue and groove, leaf curvature and head scatter. This contrasts with deterministic methods in which each segment is given equal importance, and the time taken scales with the number of segments. Thus, the Monte Carlo superposition provides a simple, accurate and efficient method for complex radiotherapy dose calculations.

Monte Carlo Formulation of Convolution/Superpostion

where the energy derivative is the cumulative energy deposited per unit solid angle in the given direction. Note that the energy deposited in the voxel depends only on the entrance and exit point.

Summary of Code features

  • Explicit photon sampling obviates the need for TERMA calculation
  • Random sampling of photon energy from the beam spectrum that depends on the radial propagation.
  • Random sampling of photon's starting postition from a Gaussian focal source, or an artbitary extra focal source
  • Sampling of monoenergetic kernel based on the sampled photon energy
  • Random sampling of kernel direction, based on angular distribution of energy around the photon interaction site.
  • No spectral hardening or kernel corrections are required.
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