Adjoint Point Detector Technique: An adjoint point detector far away from the phantom records only deterministic contributions of adjoint particles traveling perpendicular to the tube’s entrance. This entrance is shaped like the forward beam exit.
Adjoint detector disk for Legendre expansion. The direction vector of the crossing adjoint particle is translated into and .
Neutrons and gammas demand for different truncation methods to exclude zero values or steep gradients in the angular adjoint functions. By truncating the functions, fewer Legendre polynomials are needed for expansion. A typical adjoint angular function for neutrons is shown in the angular domain (a) and Legendre domain (b). A characteristic angular adjoint function for gammas in both domains is shown in (c) and (d).
Schematic overview of all steps involved in the preprocessing for the LEXT. Note that all recorded adjoint particles stored in the PTRAC file have to be read twice.
Contributions of source gammas, of 12 different energy groups which leave a diam source disk perpendicularly, to three different cells in a light water sphere. These so-called adjoint functions are obtained with APDT and forward MC which give identical results.
The adjoint functions in cell II obtained with the LEXT for different numbers of Legendre coefficients used for and . The LEXT converges towards the APDT, which is the reference when using five coefficients or more for and .
The relative errors in the adjoint functions for the LEXT and APDT. The errors of the LEXT increase with increasing number of Legendre coefficients used for and .
Head phantom with all tissues set semi-transparent, the ten OAR are light and the ten tumors dark colored.
(a) The 60 center points of the adjoint detector disks around the head. (b) These points are described with polar and azimuthal angles. (c) Orientation of the 17 adjoint detector disks and their normals, which is similarly the case at each of the 60 center points. In total there are beams simulated which can have diameters of 5, 10, and .
The relative errors in the total detector responses due to the flux of thermal neutrons in all tumors and OAR. The errors for the three methods are normalized to a maximum of 5% and averaged over 255 neutron beams after which the calculation times of the methods can be adapted and compared.
An example outcome for treatment planning with the neutron beam in Petten: for each of the 60 beam locations around the head, the maximum ratio of thermal neutrons in the tumors to thermal neutrons in the OAR is calculated out of 17 beam orientations. The larger the gray bubble the better is the ratio.
The total calculation times for the three methods for neutrons. All calculations are performed in a Windows XP command shell on a personal computer with a Pentium IV processor and of memory.
The total calculation times for the three methods for gammas. All calculations are performed in a Windows XP command shell on a personal computer with a Pentium IV processor and of memory.
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