Deterministic photon transport calculations in general geometry for external beam radiation therapy

Williams, Mark L.; Ilas, Dan; Sajo, Erno; Jones, Dean B.; Watkins, K. E.

doi:10.1118/1.1621135

Cited by 13 publications

(8 citation statements)

References 12 publications

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“…In addition, the deterministic method has the highest computational efficiency among the three methodologies. Although deterministic photon dose estimation has been widely used in the field of radiation therapy 28 – 32 , its use has not been fully investigated for CT imaging. Because CT imaging is fundamentally different from radiation therapy, in terms of X-ray photon energy, interaction mechanisms, beam shape, and source trajectory, a CT-specific approach to deterministic photon dose calculation is required.…”

Section: Introductionmentioning

confidence: 99%

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Norris

Liu

2020

Sci Rep

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In this study, cone-beam single projection and axial CT scans are modeled with a software package-DOCTORS, which solves the linear Boltzmann equation using the discrete ordinates method. Phantoms include a uniform 35 cm diameter water cylinder and a non-uniform abdomen phantom. Series simulations were performed with different simulation parameters, including the number of quadrature angles, the order of Legendre polynomial expansions, and coarse and fine mesh grid. Monte Carlo simulations were also performed to benchmark DOCTORS simulations. A quantitative comparison was made between the simulation results obtained using DOCTORS and Monte Carlo methods. The deterministic simulation was in good agreement with the Monte Carlo simulation on dose estimation, with a root-mean-square-deviation difference of around 2.87%. It was found that the contribution of uncollided photon fluence directly from the source dominates the local absorbed dose in the diagnostic X-ray energy range. The uncollided photon fluence can be calculated accurately using a 'ray-tracing' algorithm. The accuracy of collided photon fluence estimation is largely affected by the pre-calculated multigroup cross-sections. The primary benefit of DOCTORS lies in its rapid computation speed. Using DOCTORS, parallel computing with GPU enables the cone-beam CT dose estimation nearly in real-time. In X-ray attenuation-based CT imaging, the mechanisms responsible for a material's attenuation are primarily the photoelectric effect and Compton and Rayleigh scattering 1-3. These interactions determine the energy transfer between photons and material as well as the photon distribution throughout the CT system. A complete description of the photon distribution and energy transfer is essential for estimating patient dose and for designing an optimized CT system. Stochastic methods (e.g., Monte Carlo simulation) have been used extensively in the past 4-20 , and are generally considered to be the gold standard for estimating photon distributions and CT doses. However, they require a large number of particle histories and, therefore, a lengthy computation time is needed to reduce statistical uncertainty to an acceptable level. There is, however, no statistical error associated with deterministic methods, so they can be comparatively efficient in large regions where the highly resolved spatial fluence must be known to within a tight uncertainty bound. While hybrid stochastic-deterministic methods advantageously combine Monte Carlo and deterministic techniques and are more computationally efficient than a pure Monte Carlo simulation, they result in a cumbersome computational framework, due to the combination of two different methodologies, and can also have lengthy computation times 21, 22. We have explored three methodologies including Monte Carlo, hybrid Monte Carlo, and deterministic methods to solve photon transport problems 23-27 , and have found that the deterministic method provides accurate results that are comparable to a Monte Carlo simulation. In addition, the ...

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Section: Introductionmentioning

confidence: 99%

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Norris

Liu

2020

Sci Rep

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“…Finally, a third physical quantity was required to calculate the delivered dose: the local particle fluence. For this, a simple deterministic approximation was used, incorporating the inverse‐square law and exponential decay in accordance with the attenuation of the beam in water 17 . Equation gives the first order (uncollided) angularly independent fluence approximation at r if the accelerator target is represented by a point source at location

r_{0}

.…”

Section: Methodsmentioning

confidence: 99%

“…For this, a simple deterministic approximation was used, incorporating the inverse-square law and exponential decay in accordance with the attenuation of the beam in water. 17 Equation (1) gives the first order (uncollided) angularly independent fluence approximation at r if the accelerator target is represented by a point source at location r 0 . Exponential decay resulting from the attenuation of the material is dictated by the optical distance τ (the mean free path length of water) and Q A ðr 0 , EÞ is the energy dependent photon source intensity at r 0 .…”

Section: B Data Channelsmentioning

confidence: 99%

Radiation dose calculation in 3D heterogeneous media using artificial neural networks

Keal

Santos²,

Penfold³

et al. 2021

Medical Physics

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External beam radiotherapy (EBRT) treatment planning requires a fast and accurate method of calculating the dose delivered by a clinical treatment plan. However, existing methods of calculating dose distributions have limitations. Monte Carlo (MC) methods are accurate but can take too long to be clinically viable. Deterministic approaches are quicker but can be inaccurate under certain conditions, particularly near heterogeneities and air interfaces. Neural networks trained on MCderived data have the potential to reproduce dose distributions that agree closely with the MC method while being significantly quicker to deploy. Methods: In this work we present a framework for training machine learning models capable of directly calculating the dose delivered to a point in three-dimensional (3D) heterogeneous media given only spatially local information. The framework consists of three parts. First, we describe a novel method of randomly generating 3D heterogeneous geometries using simplex noise. Dose distributions for training were obtained by importing these geometries into a MC simulation. The second and third parts of the framework are precalculated data channels, aligned with the patient computed tomography (CT) image, to be used as input to the model. These data channels are a computationally efficient way of encoding the parameters of an incident radiation beam while also allowing the model to learn from data that would otherwise be outside of its receptive field. Results: We demonstrate the viability of the framework by a training small, fully connected neural network model to reproduce dose distributions from megavoltage photon beams. The trained network displayed excellent agreement with MC dose distributions in randomly generated geometries with an average gamma index (3%/3 mm) pass rate of 94.7% and an average error of 1.45% of peak dose. Finally, the network was used to calculate the dose in a patient CT image, on which the network was not trained, producing similarly impressive results. Conclusions: A novel method of generating training data for learned radiation dosimetry models has been introduced, along with preprocessing steps that allow even simple models to reproduce accurate dose distributions for EBRT. More importantly, we have demonstrated that a model trained using the proposed framework can generalize from the training data to predicting the therapeutic dose in realistic media.

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“…For applications in medical physics, it apparently does not take advantage of the well-defined pixel geometry, basically a three-dimensional cuboid array. The TRANSMED code 6 , on the other hand, uses the structured orthogonal mesh and solves the integral form of the transport equation on the discrete direction lines by the method of characteristics ͑MOC͒. Multistep collision sources are employed in which a sequential equation of the uncollided, the first-collision, the second-collision, and collided sources are solved.…”

Section: Methodsmentioning

confidence: 99%

“…Several authors have reported their external beam radiotherapy calculations based on deterministic transport equations. [6][7][8][9] Williams et al 6 have described a deterministic method based on the BTE to perform three-dimensional photon transport calculations of a LINAC head and phantom or patient geometry using the TRANSMED code. The method of characteristics was used for integration of the transport equation and the angular flux was decomposed into multistep collision flux, such as the uncollided, first-collision, second-collision and collided flux.…”

Section: Introductionmentioning

confidence: 99%

Deterministic photon kerma distribution based on the Boltzmann equation for external beam radiation therapy

2008

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A photon transport algorithm for fully three-dimensional radiotherapy treatment planning has been developed based on the discrete ordinates (SN) solution of the Boltzmann equation. The algorithm is characterized by orthogonal adaptive meshes, which place additional points where large gradients occur and a procedure to evaluate the collided flux using the representation of spherical harmonic expansion instead of the summation of the volume-weighted contribution from discrete angles. The Boltzmann equation was solved in the form of SN spatial, energy, and angular discretization with mitigation of ray effects by the first-collision source method. Unlike existing SN codes, which were designed for general purpose for multiparticle transport in areas such as nuclear engineering, our code is optimized for medical radiation transport. To validate the algorithm, several examples were employed to calculate the photon flux distribution. Numerical results show good agreement with the Monte Carlo calculations using EGSnrc.

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Deterministic photon transport calculations in general geometry for external beam radiation therapy

Cited by 13 publications

References 12 publications

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Photon fluence and dose estimation in computed tomography using a discrete ordinates Boltzmann solver

Radiation dose calculation in 3D heterogeneous media using artificial neural networks

Deterministic photon kerma distribution based on the Boltzmann equation for external beam radiation therapy

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