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Title: Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy

Abstract

This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simulations the particles start at a source and lose energy as they travel towards the region of interest, i.e., the designated point of detection. Conversely, with adjoint Monte Carlo simulations, the so-called adjoint particles start at the region of interest and gain energy as they travel towards the source where they are detected. In this respect, the particles travel backwards and the real source and real detector become the adjoint detector and adjoint source, respectively. At the adjoint detector, an adjoint function is obtained with which numerically the same result, e.g., dose or flux in the tumor, can be derived as with forward Monte Carlo. In many cases, the adjoint method is more efficient and by that is much quicker when, for example, the response in the tumor or organ at risk for many locations and orientations of the treatment beam around the patient is required. However, a problem occurs when the treatment beammore » is mono-directional as the probability of detecting adjoint Monte Carlo particles traversing the beam exit (detector plane in adjoint mode) in the negative direction of the incident beam is zero. This problem is addressed here and solved first with the use of next event estimators and second with the application of a Legendre expansion technique of the angular adjoint function. In the first approach, adjoint particles are tracked deterministically through a tube to a (adjoint) point detector far away from the geometric model. The adjoint particles will traverse the disk shaped entrance of this tube (the beam exit in the actual geometry) perpendicularly. This method is slow whenever many events are involved that are not contributing to the point detector, e.g., neutrons in a scattering medium. In the second approach, adjoint particles that traverse an adjoint shaped detector plane are used to estimate the Legendre coefficients for expansion of the angular adjoint function. This provides an estimate of the adjoint function for the direction normal to the detector plane. In a realistic head model, as described in this paper, which is surrounded by 1020 mono-directional neutron/gamma beams and from which the best ones are to be selected, the example calculates the neutron and gamma fluxes in ten tumors and ten organs at risk. For small diameter beams (5 cm), and with comparable relative errors, forward Monte Carlo is seen to be 1.5 times faster than the adjoint Monte Carlo techniques. For larger diameter neutron beams (10 and 15 cm), the Legendre technique is found to be 6 and 20 times faster, respectively. In the case of gammas alone, for the 10 and 15 cm diam beams, both adjoint Monte Carlo Legendre and point detector techniques are respectively 2 and 3 times faster than forward Monte Carlo.« less

Authors:
; ; ; ; ;  [1];  [2];  [2];  [2];  [2];  [2]
  1. Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft (Netherlands) and Joint Research Centre of the European Commission, P.O. Box 2, 1755ZG Petten (Netherlands)
  2. (Netherlands)
Publication Date:
OSTI Identifier:
20951150
Resource Type:
Journal Article
Resource Relation:
Journal Name: Medical Physics; Journal Volume: 34; Journal Issue: 4; Other Information: DOI: 10.1118/1.2712573; (c) 2007 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
62 RADIOLOGY AND NUCLEAR MEDICINE; COMPUTERIZED SIMULATION; ERRORS; MONTE CARLO METHOD; NEUTRON BEAMS; NEUTRON CAPTURE THERAPY; OPTIMIZATION; PHANTOMS; RADIATION DOSES

Citation Formats

Nievaart, V. A., Legrady, D., Moss, R. L., Kloosterman, J. L., Hagen, T. H. J. J. van der, Dam, H. van, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, Joint Research Centre of the European Commission, P.O. Box 2, 1755ZG Petten, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, The Netherlands and Reactor Institute Delft, Delft University Technology, Mekelweg 15, 2629JB Delft, and Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft. Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy. United States: N. p., 2007. Web. doi:10.1118/1.2712573.
Nievaart, V. A., Legrady, D., Moss, R. L., Kloosterman, J. L., Hagen, T. H. J. J. van der, Dam, H. van, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, Joint Research Centre of the European Commission, P.O. Box 2, 1755ZG Petten, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, The Netherlands and Reactor Institute Delft, Delft University Technology, Mekelweg 15, 2629JB Delft, & Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft. Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy. United States. doi:10.1118/1.2712573.
Nievaart, V. A., Legrady, D., Moss, R. L., Kloosterman, J. L., Hagen, T. H. J. J. van der, Dam, H. van, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, Joint Research Centre of the European Commission, P.O. Box 2, 1755ZG Petten, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, The Netherlands and Reactor Institute Delft, Delft University Technology, Mekelweg 15, 2629JB Delft, and Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft. Sun . "Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy". United States. doi:10.1118/1.2712573.
@article{osti_20951150,
title = {Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy},
author = {Nievaart, V. A. and Legrady, D. and Moss, R. L. and Kloosterman, J. L. and Hagen, T. H. J. J. van der and Dam, H. van and Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft and Joint Research Centre of the European Commission, P.O. Box 2, 1755ZG Petten and Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft and Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, The Netherlands and Reactor Institute Delft, Delft University Technology, Mekelweg 15, 2629JB Delft and Department of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628CJ Delft},
abstractNote = {This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simulations the particles start at a source and lose energy as they travel towards the region of interest, i.e., the designated point of detection. Conversely, with adjoint Monte Carlo simulations, the so-called adjoint particles start at the region of interest and gain energy as they travel towards the source where they are detected. In this respect, the particles travel backwards and the real source and real detector become the adjoint detector and adjoint source, respectively. At the adjoint detector, an adjoint function is obtained with which numerically the same result, e.g., dose or flux in the tumor, can be derived as with forward Monte Carlo. In many cases, the adjoint method is more efficient and by that is much quicker when, for example, the response in the tumor or organ at risk for many locations and orientations of the treatment beam around the patient is required. However, a problem occurs when the treatment beam is mono-directional as the probability of detecting adjoint Monte Carlo particles traversing the beam exit (detector plane in adjoint mode) in the negative direction of the incident beam is zero. This problem is addressed here and solved first with the use of next event estimators and second with the application of a Legendre expansion technique of the angular adjoint function. In the first approach, adjoint particles are tracked deterministically through a tube to a (adjoint) point detector far away from the geometric model. The adjoint particles will traverse the disk shaped entrance of this tube (the beam exit in the actual geometry) perpendicularly. This method is slow whenever many events are involved that are not contributing to the point detector, e.g., neutrons in a scattering medium. In the second approach, adjoint particles that traverse an adjoint shaped detector plane are used to estimate the Legendre coefficients for expansion of the angular adjoint function. This provides an estimate of the adjoint function for the direction normal to the detector plane. In a realistic head model, as described in this paper, which is surrounded by 1020 mono-directional neutron/gamma beams and from which the best ones are to be selected, the example calculates the neutron and gamma fluxes in ten tumors and ten organs at risk. For small diameter beams (5 cm), and with comparable relative errors, forward Monte Carlo is seen to be 1.5 times faster than the adjoint Monte Carlo techniques. For larger diameter neutron beams (10 and 15 cm), the Legendre technique is found to be 6 and 20 times faster, respectively. In the case of gammas alone, for the 10 and 15 cm diam beams, both adjoint Monte Carlo Legendre and point detector techniques are respectively 2 and 3 times faster than forward Monte Carlo.},
doi = {10.1118/1.2712573},
journal = {Medical Physics},
number = 4,
volume = 34,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • A Monte Carlo-based treatment planning code for boron neutron capture therapy (BNCT), called NCTPLAN, has been developed in support of the New England Medical Center-Massachusetts Institute of Technology program in BNCT. This code has been used to plan BNCT irradiations in an ongoing peripheral melanoma BNCT protocol. The concept and design of the code is described and illustrative applications are presented. 32 refs., 14 figs., 4 tabs.
  • Monte Carlo based dosimetry and computer-aided treatment planning for neutron capture therapy have been developed to provide the necessary link between physical dosimetric measurements performed on the MITR-II epithermal-neutron beams and the need of the radiation oncologist to synthesize large amounts of dosimetric data into a clinically meaningful treatment plan for each individual patient. Monte Carlo simulation has been employed to characterize the spatial dose distributions within a skull/brain model irradiated by an epithermal-neutron beam designed for neutron capture therapy applications. The geometry and elemental composition employed for the mathematical skull/brain model and the neutron and photon fluence-to-dose conversion formalismmore » are presented. A treatment planning program, NCTPLAN, developed specifically for neutron capture therapy, is described. Examples are presented illustrating both one and two-dimensional dose distributions obtainable within the brain with an experimental epithermal-neutron beam, together with beam quality and treatment plan efficacy criteria which have been formulated for neutron capture therapy. The incorporation of three-dimensional computed tomographic image data into the treatment planning procedure is illustrated. The experimental epithermal-neutron beam has a maximum usable circular diameter of 20 cm, and with 30 ppm of B-10 in tumor and 3 ppm of B-10 in blood, it produces a beam-axis advantage depth of 7.4 cm, a beam-axis advantage ratio of 1.83, a global advantage ratio of 1.70, and an advantage depth RBE-dose rate to tumor of 20.6 RBE-cGy/min (cJ/kg-min). These characteristics make this beam well suited for clinical applications, enabling an RBE-dose of 2,000 RBE-cGy/min (cJ/kg-min) to be delivered to tumor at brain midline in six fractions with a treatment time of approximately 16 minutes per fraction.« less
  • A Monte Carlo simulation study has been carried out to investigate the suitability of neutron beams of various energies for therapeutic efficacy in boron neutron capture therapy. The dosimetric properties of unidirectional, monoenergetic neutron beams of varying diameters in two different phantoms (a right-circular cylinder and an ellipsoid) made of brain-equivalent material were examined. The source diameter was varied from 0.0 to 20.0 cm; neutron energies ranged from 0.025 eV up to 800 keV, the maximum neutron energy generated by a tandem cascade accelerator using 2.5-MeV protons in a {sup 7}Li(p,n){sup 7}Be reaction. Such a device is currently under investigationmore » for use as a neutron source for boron neutron capture therapy. The simulation studies indicate that the maximum effective treatment depth (advantage depth) in the brain is 10.0 cm and is obtainable with a 10-keV neutron beam. A useful range of energies, defined as those neutron energies capable of effectively treating to a depth of 7 cm in brain tissue, is found to be 4.0 eV to 40.0 keV. Beam size is shown not to affect advantage depth as long as the entire phantom volume is used in determining this depth. Dose distribution in directions parallel to and perpendicular to the beam direction are shown to illustrate this phenomenon graphically as well as to illustrate the differences in advantage depth and advantage ratio and the contribution of individual dose components to tumor dose caused by the geometric differences in phantom shape.« less
  • The energy deposition in the nucleus of cells exposed to the /sup 10/B(n, alpha)/sup 7/Li neutron capture reaction has been calculated and compared to the measured biological effect of this reaction. It was found that a considerable distribution of hit sizes to the nucleus occurs. The comparison of hit size frequency with the observed survival indicates that not every hit, independent of its size, can lead to cell death. This implies the existence of a hit size effectiveness function. The analysis shows that the location of boron relative to the radiation-sensitive volume of the cell is of great importance andmore » that average dose values alone are of limited use for predicting the biological effect of this reaction. Boron accumulating in the cell nucleus is much more efficient in cell killing than the same amount of boron uniformly distributed; its presence in one cell, however, has little effect on its neighboring cells in a tissue. When boron is present on the cell surface of a tissue (as presumably delivered by antibodies), its cell-killing effect is greatly reduced compared to that in uniform distribution. However, in this case much of the dose to one cell comes from neutron capture reactions occurring on the surface of its neighbor cells. These data have implications for the choice of boron carries in neutron capture therapy. The mathematical analysis carried out here is similar to that proposed recently for low-level exposure effects of radiation, taking mutation and/or carcinogenesis as biological effects. The results here show that high-level exposure to high-LET particles (resulting in cell killing) should be treated in an analogous manner.« less