To evaluate a radiotherapy planning system, comparisons of measured and calculated dose distributions are required, and quantitative evaluations need to be performed.
As a rst approximation to de ne a quantitative evaluation method, dose dierence was used as acceptance criterion. A distribution of dose dierences can be represented to identify the regions where the calculated dose and the measurement dier. This criterion can be used in low gradient areas but is inadequate in high gradient regions, where a small spacial shift results in a large dose dierence.
The sensitivity of the dose dierence method to high dose gradients led to the development of a new tool called Distance-to-agreement (DTA) [Van Dyk et al., 1993]. The DTA is the evaluation of the distance between a measured data point and the nearest point in the calculated distribution that exhibits the same dose. However, in small dose gradient regions, small dose dierences can lead to high DTA values.
Because of the complementary sensitivity of these methods, both evaluation images were merged to create a more complete evaluation criterion, the gamma evaluation [Low et al., 1998, Low and Dempsey, 2003, Depuydt et al., 2002].
Figure 1.27: Schematic representation of the gamma evaluation method between the reference dose
(rr,Dr) and the calculated dose (rc,Dc). The criteria is de ned by an ellipsoid of acceptance determined
by the dose dierence tolerance ∆DM and the DTA tolerance ∆dM [Depuydt et al., 2002].
The gamma method, presented by Low et al. [Low et al., 1998], compares two dose distributions: The reference dose (Dr(r)) and the calculated dose that needs to be evaluated (Dc(r)). The acceptance criteria are denoted by ∆DM for the dose dierence and ∆dM for the DTA. For a reference point at position rr with a dose Dr, the surface representing these acceptance criteria
1.9. Gamma evaluation is an ellipsoid de ned as:
1 = s ∆r2 ∆d2M + ∆D2 ∆DM2 (1.7)
Where ∆r is the distance between the reference and the calculated point and ∆D is the dose dierence at the position rcrelative to the reference dose Dr in rr.
∆r =|rr−rc| (1.8)
∆D = Dc(rc) − Dr(rr) (1.9)
The calculated dose will t the gamma evaluation if at least one point (rc, Dc) of its dose distribution is contained inside the ellipsoid of acceptance showed in gure 1.27, ie. one point for which Γr(rc, Dc) ≡ s ∆r2 ∆d2 M + ∆D 2 ∆D2 M ≤ 1 (1.10)
The pass-fail criterion becomes: • γ(rr) ≤ 1, calculation passes. • γ(rr) > 1, calculation fails.
For example, if a 3%-3 mm criterion is considered, points passing this criterion will be the ones located at 3 mm or less from a point in which dose dierence with the reference is 3% or less.
Gamma evaluation limits depend on the type of radiotherapy and the location of the tumor. For a stereotactic brain treatment, with high precision systems and with organs at risk very close, it would be suitable a 1%-1 mm criterion. However, for IORT these precision requirements are not so restrictive, because the surgeon limits the treatment area and protects the organs at risk. Therefore, in IOERT it is reasonable to consider suitable a dosimetric study when 95% of the points pass the 3%-3 mm limit [Alber et al., 2008]. Nevertheless, this approximation can not be considered in a dose evaluation for the Intrabeam R, because of the rapid decrease of the dose.
In this case, this limit can vary from 2%-1 mm [Nwankwo et al., 2013], to 2%-2 mm [Clausen et al., 2012] or even 10%-1 mm [Chiavassa et al., 2014]. In this thesis we have considered dierent limits, depending on the voxel size used.
Chapter 2
Monte Carlo methods in
radiotherapy
2.1 Introduction
Determination of a dose distribution inside a patient or a phantom is of crucial importance to be able to determine the eectiveness of a radiotherapy treatment and to evaluate the eects of radiation in matter. Any dose measuring method will be only an estimation, because dose deposition will depend on the irradiated medium, and by introducing any dosimetry system the medium will be modi ed. This estimation of the dose can be measured with dierent dosimetry techniques (ionization chambers, radiochromic lms, etc.), or calculated with numerical methods that implement dierent models of the interaction of radiation with matter.
The use of calculation algorithms in dosimetry allows the estimation of absorbed dose distributions inside irradiated volumes. These algorithms are based in radiation transport models that describe the mechanisms responsible for the transport and the interaction of radiation with matter. There are two main trends of dose calculation algorithms based in dierent mathematical models of energy deposition: one is a deterministic strategy based in Boltzmann equation and the other is based in Monte Carlo (MC) simulations.
In the deterministic approach, the model is built from a coupled set of equations (known as Boltzmann equation) that describe how a variety of dierent types of particles travel through a material. This technique works adequately in homogeneous media but has some problems with heterogeneities [Wang et al., 1996, Ding et al., 2005], which are specially important in radiotherapy dosimetry.
In the last years, Monte Carlo methods are becoming widely used. Monte Carlo simulation of radiation transport uses the probability distributions governing the individual interactions of electrons and photons in materials to simulate the random trajectories or histories of individual particles. These methods are more precise than the deterministic models, specially in complex media, but very time consuming.
In this chapter we will explain the basic concepts of MC methods and their application in radiotherapy. We will also describe the main MC codes used in radiation transport, specially the ones that have been used in this thesis.