The AAA of the Eclipse TPS (AAAEcl) was proposed by Ulmer et al. [83] in 2003. It is a 3D convolution/superposition algorithm based on a triple Gaussian convolution model which was preceded by the triple pencil beam model devel- oped in the mid 90s [105, 106]. The primary photons, the scattered extra-focal photons and the electrons are modeled independently. An overview of AAA dose calculation algorithm in heterogeneous media and its validation is reported by Tillikainen et al. [107, 108] and Van Esch et al. [109] have done an elaborate study on validation of AAA dose calculation algorithm against measurements in homogeneous and heterogeneous cases. This section on AAAEcl is largely drawn from Tillikainen et al. [107, 108] which gives an excellent overview of this model, Van Esch et al. [109] and Eclipse algorithms reference guide [96].
The primary photons are modeled using MC simulations and the lateral trans- port of electrons is represented with six exponential curves [84, 96]. In this multi- ple source model, the broad clinical photon beam is divided into finite beamlets
β, as shown in figure 2.2, where the intensities of the photons and electrons are different.
2.2.1 Primary source
A point source at the level of the target is the primary photon source. The incident electron beam hits the target which results in the production of bremsstrahlung photons. Photons which do not undergo any interactions in the accelerator head until they reach the patient geometry are the primary photons. The primary photon beam spectrum is generated using BEAMnrc MC system [110]. A combi- nation of mean energy radial curve and radial intensity profile are used to account for the beam hardening due to the flattening filter and variation of the photon fluence respectively. Optimisation of these two curves yield correct depth dose curves and beam profiles.
Figure 2.2: Treatment Unit Components modelled by AAA
2.2.2 Extra-focal Source
Secondary photons are generated in the components of the accelerator head which includes the flattening filter, the primary collimator and the secondary jaws. The extra-focal source with a finite width is defined just below the flattening filter and it produces a broader beam than the primary source as it is closer to the machine isocentre. The mean energy and the relative intensity of the extra-focal photon source are derived by convolving the primary fluence and a Gaussian with a width proportional to the finite source.
2.2.3 Electron contamination
Compton interactions in the head of the accelerator and the outside air between the treatment machine head and the patient surface results in the electron con- tamination. It also accounts for the photon contamination due to electron inter- actions. It is a finite source located at the plane of the target and is represented as a linear combination of two Gaussians convolved with the primary energy fluence. It is modelled with six exponential functions.
2.2.4 Volumetric dose calculation
The clinical broad beam in divided into small beamlets β and the patient ge- ometry is divided into 3D dose calculation voxels of desirable dimensions to achieve reasonable resolution. Patient CT images are imported and the mean electron density ρ is derived according to the CT machine specific electron den- sity Hounsfield unit calibration curve. The dose calculation grid is divergent and is aligned with the divergence of the photon beam.
Calculation of dose deposited by primary and secondary sources
An energy deposition density functionIβ(z,ρ) models the attenuation of the pho- ton beam and a scatter kernel Kβ(x,y,z) defines the lateral photon energy scat- ter. Each beamlet β is defined individually by the functions Iβ and Kβ. Both the primary and secondary photons are calculated in a similar method with their respective spectra, position and size of focal spot. The convolution is performed in terms of energy and the energy to dose conversion is done by scaled-water approximation.
The energy distribution from a beamlet β in the homogeneous medium is cal- culated by the convolving the photon fluence by the energy deposition density function and the scatter kernel.
Eph,β( ˜X,Y˜,Z) = Φ˜ β×Iβ(z, ρ)×Kβ(X, Y, Z) (2.6) Here ( ˜X, ˜Y, ˜Z) represents the patient coordinate system and (x,y,z) denotes the beamlet coordinate system. Φβ is the uniform photon fluence over the cross- section of the beamlet β. Iβ(z,ρ), the energy deposition function represents the area integral of the energy deposited over the spherical surface of the pencil beam at depth z.
Iβ(z) =
Z Z
hβ(t, v, z)dtdv (2.7) where hβ is the poly-energetic pencil beam kernel derived from MC simulations.
Figure 2.3: Coordinates in Patient Coordinate System and Beamlet Coordinate System on X-Z Plane
2.2.5 Inhomogeneity correction
The inhomogeneities present in the patient model are accounted for by separating them into depth directed and lateral components. The depth directed compo- nent accounts for the variation in densities along the axis of the beam whereas the lateral component considers the differences in densities in the direction perpen- dicular to that of the beam axis or in the radial direction. The heterogeneities in the tissues is accounted by the energy deposition functionIβ(z,ρ) by radiological scaling which is done by equation 2.8.
Iβ(z, ρ) =Iβ(z0) (2.8) where the radiological depth is defined in equation 2.9.
z0 = z Z 0 ρ(0,0, t) ρwater dt (2.9)
the pencil beam in a layer, pz in the phantom as given in equation 2.10.
Iβ(pz) = Φβ
Z Z
hβ(x, y, pz)dxdy (2.10) in which the photon fluence or the number of incident photons Φβ is assumed to be uniform through out the cross section of the beamlet β. On the other hand, the lateral componentkβ(θ,λ,pz) is characterised by a weighted sum of six radial exponential functions given in equation 2.11.
kβ(θ, λ,pz) = 6 X i=1 ci 1 µi e−µiλ (2.11)