TD15-Applications of Monte-Carlo Methods in Medical Physics

Chen-Shou Chui and Lu Wang

Memorial Sloan-Kettering Cancer Center, New York City, New York.

Monte Carlo method has been used to solve radiation transport problems. It simulates the physical processes by random sampling from appropriate probability distributions. Potentially, it is the most accurate method for problems involving inhomogeneities.

The method is based on two mathematical principles: the Law of Large Numbers and the Central Limit Theorem. The former states that the sample mean approaches the expected value as the sample size increases. The latter gives us a confidence interval on the sample standard deviation. For radiation transport problems, the simulation involves two major components: ‘transport’ and ‘interaction’. The ‘transport’ component selects the step size of a particle to the next interaction; and performs geometry checking and possible energy deposition along the step. The ‘interaction’ component decides the type of the interaction; and samples the energy and direction of the outgoing particles.

Monte Carlo has been applied to many problems in medical physics, including simulation of the therapy machine head; the calculation of correction factors used in chamber theory; the generation of dose kernels; and dose calculation in heterogeneous media. Prior to clinical application, Monte Carlo method needs to be validated empirically. Results from Monte Carlo have been compared to measurements in homogeneous flat and hemisphere phantoms; and in inhomogeneous phantoms imbedded with low and high density materials.

After empirical validation, Monte Carlo methods have been applied to dose calculations for head/neck and lung treatments. These two sites are expected to show the greatest effects of anatomic inhomogeneities on dose. Results from Monte Carlo were compared to that using a pencil beam model. For head/neck treatment using 6 MV photons, the difference between the two methods was in general small. For lung treatment using 6 MV photons, the PTV coverage was degraded by about a few percent while the normal organs (lungs, cord) were not much affected. For lung treatment using 15 MV photons, however, the PTV coverage was significantly degraded, by over 10%. This is due to the increased range of the secondary electrons in low density volumes (lungs) which was not properly accounted for in the pencil beam model.  Similar results were observed for both conventional and IMRT treatments. Additional comparisons were also made for treatments involving metal prosthesis and for electron beams.

In conclusion, Monte Carlo can be applied to many medical physics problems to give accurate results. Moreover, it provides a powerful tool for analysis which cannot be easily done with measurement. The drawback, however, is that it requires long computation time in order to achieve good statistics.