Clinical CT-based calculations of dose and positron emitter distributions in proton therapy using the FLUKA Monte Carlo code

Abstract

Clinical investigations on post-irradiation PET/CT (positron emission tomography/computed tomography) imaging for in vivo verification of treatment delivery and, in particular, beam range in proton therapy are underway at Massachusetts General Hospital (MGH). Within this project, we have developed a Monte Carlo framework for CT-based calculation of dose and irradiation-induced positron emitter distributions. Initial proton beam information is provided by a separate Geant4 Monte Carlo simulation modelling the treatment head. Particle transport in the patient is performed in the CT voxel geometry using the FLUKA Monte Carlo code. The implementation uses a discrete number of different tissue types with composition and mean density deduced from the CT scan. Scaling factors are introduced to account for the continuous Hounsfield unit dependence of the mass density and of the relative stopping power ratio to water used by the treatment planning system (XiO (Computerized Medical Systems Inc.)). Resulting Monte Carlo dose distributions are generally found in good correspondence with calculations of the treatment planning program, except a few cases (e.g. in the presence of air/tissue interfaces). Whereas dose is computed using standard FLUKA utilities, positron emitter distributions are calculated by internally combining proton fluence with experimental and evaluated cross-sections yielding 11C, 15O, 14O, 13N, 38K and 30P. Simulated positron emitter distributions yield PET images in good agreement with measurements. In this paper, we describe in detail the specific implementation of the FLUKA calculation framework, which may be easily adapted to handle arbitrary phase spaces of proton beams delivered by other facilities or include more reaction channels based on additional cross-section data. Further, we demonstrate the effects of different acquisition time regimes (e.g., PET imaging during or after irradiation) on the intensity and spatial distribution of the irradiation-induced beta+-activity signal for the cases of head and neck and para-spinal tumour sites.

Figure 1

Used additional cross-sections values (lines) interpolated from experimental (Iljinov et al 1991, Kitwanga et al 1989, Albouy et al 1962, Kettern et al 2004, Sisterson et al 1978, EXFOR 2005) and evaluated (IAEA 2001) data for proton induced reactions on O, N, P and Ca yielding ¹⁴O, ¹³N, ¹¹C, ³⁰P and ³⁸K positron emitters.

Figure 2

MC calculated dose deposition (left) against the planned treatment (right). The top raw shows a posterior-anterior field delivering 0.9 GyE to a pituitary adenoma (where GyE stands for ⁶⁰Co equivalent dose, i.e., for protons 1 GyE = 1.1 Gy). The bottom raw depicts a lateral portal irradiating a clivus chordoma at 0.96 GyE. The rainbow colour-bar displays dose values in mGy. The black-white colour-bar represents the HU map arbitrary rescaled for display purposes.

Figure 3

MC calculated dose deposition (left) against the planned treatment (right). The top raw shows a posterior-anterior field delivering 2 GyE to a primitive neuroectodermal tumor. In this example no transaxial grouping was used (cf. text). The bottom raw depicts a posterior-anterior irradiation of a T-spine chondrosaroma at 0.6 GyE. Interpretation of the colour-bar is the same as in figure 2.

Figure 4

Comparison between MC (solid line) and TP (dotted line) calculated depth dose deposition (top) and lateral field dimension (bottom) for the lateral cranial field of figure 2, bottom (left panel) and the posterior-anterior field of figure 3, top (right panel). For the cranial case, the depth profile is sampled along the main beam axis, while the lateral profile is taken at a lateral shift of 20 mm along the horizontal axis of figure 2 to exclude the nasal cavity. In the extra-cranial case, both profiles are taken at a −10 mm shift along the horizontal axis of figure 3 to traverse highly inhomogeneous tissue. Statistical uncertainties deduced from the independent MC runs are shown by error bars (reported for every two data points to reduce the data density). The corresponding CT profiles are shown by the grey dotted lines.

Figure 5

MC calculated positron emitter production (left column, top to bottom: ¹¹C, ¹³N, ³⁰P; right column, top to bottom: ¹⁵O, ¹⁴O and ³⁸K) for the lateral field of figure 2, bottom, using the same statistics of the dose delivery. The rainbow colour-bar displays the number of produced isotopes normalised to the application of the prescribed dose.

Figure 6

MC calculated positron emitter production (left column, top to bottom: ¹¹C, ¹³N, ³⁰P; right column, top to bottom: ¹⁵O, ¹⁴O and ³⁸K) for the posterior-anterior field of figure 3, top, using half the statistics of the dose delivery. The colour-bar has the same meaning of figure 5.

Figure 7

MC calculated average activity in 2 min acquisition starting immediately (left) or 10 min (right) after 20 s delivery of the same treatment fields of figure 2. The system response function of a PET scanner was mimicked by a 3D Gaussian convolution kernel. The colour-bar refers to activity concentration in Bq/ml for the delivery of the prescribed dose.

Figure 8

Similar to figure 7, MC calculated activity for 2 min acquisition starting immediately (left) or 10 min (right) after 20 s proton irradiation for the extra-cranial cases depicted in figure 3.

Figure 9

Profiles corresponding to the lateral cranial field (i.e., horizontal axis) of figure 5 (left panel) and to the posterior-anterior extra-cranial field (i.e., vertical axis) of figure 6 (right panel), taken at the 0 mm and −10 mm lateral positions, respectively (cf. corresponding dose profiles in figure 4). The top panel shows MC calculated individual positron emitter production density (coloured solid lines), separating the major yield of ¹¹C from proton interaction on carbon (dotted red line). The bottom panel depicts corresponding normalised activity depth profiles (solid) calculated for 2 minutes acquisition starting 0 (red), 5 (green), 10 (blue) and 15 (magenta) minutes after beam delivery. Dotted coloured lines additionally show the activity resulting from a reduction of the carbon tissue composition by 20%. The CT profiles are shown by the light grey dashed lines.

Figure 10

Similar to figure 9, comparison between individual positron emitter production density (left) and resulting activity acquired in different imaging scenarios (right) for the same lateral dose profile of figure 4 (bottom, right) sampled in the highly inhomogeneous spine region (cf. dashed CT profile) of an extra-cranial field. Again, the red dotted line in the left panel separates the major contribution to the main ¹¹C production from proton interaction on carbon. The almost indistinguishable solid and dotted lines in the right panel depict normalised activity profiles in different imaging scenarios using the stoichiometric calibration of (Schneider et al 2000) or assuming a 20% reduction in carbon composition, respectively.