Benchmark experiment to verify Monte Carlo numerical simulations for radiation transport

Motivation

To prepare a patient’s irradiation at radiotherapy facilities, a treatment plan has to be drawn up. For this purpose, different algorithms are used to calculate the dose distribution in the patient and to optimize it in such a way that a maximum therapeutic outcome can be achieved with minimum side-effects. Due to the complexity of modern irradiation methods and to the required accuracy of each irradiation process, Monte Carlo simulation methods are increasingly used to calculate the dose distributions.

Monte Carlo simulations

With the aid of Monte Carlo simulation methods, it becomes possible to solve the problem of the penetration of radiation through matter numerically, whereas it is not possible or very difficult to solve analytically. Hereby, a large number of random experiments are carried out with the aid of computers; each of these experiments corresponds to an elementary process of the interaction of radiation with matter. By analyzing a large number of such random experiments, statements can be made with regard to the expectation values of various quantities which are of interest, e. g., the absorbed dose or the spectral particle fluence.

In principle, such Monte Carlo simulation methods make it possible to reproduce an actual experiment very accurately. In practice, however, various approximations or simplifications occur which are due either to an incomplete knowledge of the simulated elementary processes (e. g. use of approximation formulae for the interaction cross sections) or of the actual experiment (inaccurate knowledge of the irradiate geometry or of the materials penetrated by radiation), or which have been introduced to reduce the computing time (so-called "variance reduction methods"). The effects of these approximations and simplifications on the results of the simulation are often difficult to estimate. It is therefore very important to check the validity of simulation algorithms. This is done within the scope of so-called "benchmark experiments" in which calculated results are compared to measurements.

Verification of Monte Carlo simulation algorithms

Since Monte Carlo simulation algorithms provide mean values of the quantities which are of interest - e.g. the mean absorbed dose which is deposited by an electron or a photon in a certain volume -, the calculated quantities usually cannot be directly compared to measurements. In most cases, the problem is bypassed by comparing the relative changes of a quantity when varying a parameter - instead of comparing the absolute values of this quantity. For example, the relative development of calculated and measured depth dose distributions can be compared after both curves have been normalized to the maximum. In the case of such normalizations, however, the information on whether the Monte Carlo simulation has also determined the absolute dose values correctly is lost. Since the absolute dose distribution in the patient is, however, of particular interest when planning the irradiation in radiotherapy, it is essential to verify Monte Carlo simulation algorithms.

Benchmark experiment

For the absolute verification of Monte Carlo simulation algorithms, the mean absorbed dose which is generated by a linear accelerator per inciding electron has to be determined. This experimentally determined value can then be compared to the mean absorbed dose per electron calculated by means of a Monte Carlo simulation directly, without any normalization.

Such a benchmark experiment was recently performed at PTB's research accelerator within the scope of a doctoral dissertation. The research accelerator allows the properties of the electron beam to be characterized with great accuracy. These properties - such as, e.g., the spectral fluence of the electrons or the beam divergence - are needed, on the one hand, as input data for the Monte Carlo simulation, to be able to reproduce the actual experiment in the simulation as accurately as possible. On the other hand, the precise knowledge of the beam current (i.e. the number of electrons inciding on the target per unit of time) allows the mean dose per inciding electron to be determined from the total measured dose.

The basic preconditions for this comparison are: a very detailed modelling of the experiment in the Monte Carlo simulation which requires, among other things, an exact knowledge of all the materials occurring and of the geometric dimensions, a precise characterization of the properties of the electron beam as well as a precise measurement of the absorbed dose.

The benchmark experiment is aimed at determining the ratio of mean absorbed dose per inciding electron calculated by means of a Monte Carlo simulation to the mean absorbed dose per inciding electron obtained by measurement with a relative standard measurement uncertainty of approx. 1 %.

The realization and the results of the experiment are described in detail in a dissertation.