Calculation of absorbed dose in radiotherapy by solution of the linear Boltzmann transport equations

Bedford, James L.

doi:10.1088/1361-6560/aaf0e2

Cited by 22 publications

(17 citation statements)

References 83 publications

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“…The linear Boltzmann equation has been used to model transport processes in a large variety of applications [e.g. 44,50,10,3]. Computational methods in radiation therapy require a discretization of the sevendimensional phase space.…”

Section: Introductionmentioning

confidence: 99%

“…These discretizations can be grouped into deterministic and stochastic approaches. Deterministic approaches [3,13], such as the spherical harmonics (P N ) [9] and the discrete ordinates (S N ) [56,16] method for the angular discretization, are computationally efficient. However, stochastic Monte Carlo methods are increasingly preferred for radiation therapy due to their accuracy and flexibility [58,23].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

Stammer¹,

Burigo²,

Jäkel³

et al. 2022

Preprint

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Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or initial conditions. Monte Carlo methods are often used to solve transport problems especially for applications which require high accuracy. In these cases, common non-intrusive solution strategies that involve repeated simulations of the problem at different points in the parameter space quickly become infeasible due to their long run-times. Intrusive methods however limit the usability in combination with proprietary simulation engines. In [51], we demonstrated the application of a new nonintrusive uncertainty quantification approach for Monte Carlo simulations in proton dose calculations with normally distributed errors on realistic patient data. In this paper, we introduce a generalized formulation and focus on a more in-depth theoretical analysis of this method concerning bias, error and convergence of the estimates. The multivariate input model of the proposed approach further supports almost arbitrary error correlation models. We demonstrate how this framework can be used to model and efficiently quantify complex auto-correlated and time-dependent errors.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

Stammer¹,

Burigo²,

Jäkel³

et al. 2022

Preprint

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“…MC algorithms simulate the random trajectories of individual particles while LBTE describes radiation transport macroscopically. 7,8 In these algorithms, voxel doses can be reported as water voxels surrounded by medium (D w,m ) or medium voxels surrounded by medium (D m,m ). Advanced algorithms have overcome most of the issues of C/S algorithms,and their use is explicitly recommended when their performance is notably superior.…”

Section: Introductionmentioning

confidence: 99%

“…Advanced algorithms, based on Monte Carlo (MC) or the linear Boltzmann transport equation (LBTE), model the physics of radiation transport in any media. MC algorithms simulate the random trajectories of individual particles while LBTE describes radiation transport macroscopically 7,8 . In these algorithms, voxel doses can be reported as water voxels surrounded by medium ( D w,m ) or medium voxels surrounded by medium ( D m,m ).…”

Section: Introductionmentioning

confidence: 99%

Impact of the dose quantity used in MV photon optimization on dose distribution, robustness, and complexity

et al. 2021

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Purpose: Convolution/superposition algorithms used in megavoltage (MV) photon radiotherapy model radiation transport in water, yielding dose to water-in-water (D w,w ). Advanced algorithms constitute a step forward, but their dose distributions in terms of dose to medium-in-medium (D m,m ) or dose to water-in-medium (D w,m ) can be problematic when used in plan optimization due to their different dose responses to some atomic composition heterogeneities. Failure to take this into account can lead to undesired overcorrections and thus to unnoticed suboptimal and unrobust plans. Dose to reference-like medium (D ref,m* ) was recently introduced to overcome these limitations while ensuring accurate transport. This work evaluates and compares the performance of these four dose quantities in planning target volume (PTV)-based optimization. Methods: We considered three cases with heterogeneities inside the PTV: virtual phantom with water surrounded by bone; head and neck; and lung. These cases were planned with volumetric modulated arc therapy (VMAT) technique, optimizing with the same setup and objectives for each dose quantity. We used different algorithms of the Varian Eclipse treatment planning system (TPS): Acuros XB (AXB) for D m,m and D w,m , and Analytical Anisotropic Algorithm (AAA) for D w,w . D ref,m* was obtained from D m,m distributions using an in-house software considering water as the reference medium (D w,m* ). The optimization process consisted of: (1) common first optimization, (2) dose distribution computed for each quantity, (3) re-optimization, and (4) final calculation for each dose quantity. The dose distribution, robustness to patient setup errors, and complexity of the plans were analyzed and compared. Results: The quantities showed similar dose distributions after the optimization but differed in terms of plan robustness. The cases with soft tissue and high-density heterogeneities followed the same pattern. For AXB D m,m , cold regions appeared in the heterogeneities after the first optimization. They were compensated in the second optimization through local fluence increases, but any positional mismatch impacted robustness, with clinical target volume (CTV) variations from the nominal scenario around +3% for bone and up to +7% for metal. For AXB D w,m the pattern was inverse (hot regions compensated by fluence decreases) and more pronounced, with CTV dose variations around -7% for bone and up to -17% for metal. Neither AXB D w,m* nor AAA D w,w presented these dose inhomogeneities, which resulted in more robust plans. However, D w,w differed markedly from the other quantities in the lung case because of its lower radiation transport accuracy. AXB D m,m was the most complex of the four dose quantities and AXB D w,m* the least complex, though we observed no major differences in this regard.

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“…The few Monte Carlo codes approved for clinical implementation compromise accuracy for calculation speed and are not generally considered true Monte Carlo codes. Some researchers have reported the accuracy of the AXB algorithm for dose computation to be on par with that of Monte Carlo, with the advantage of increased calculation speed [10]. In clinical radiotherapy, dose calculation accuracy may affect treatment outcomes of tumor control and toxicities.…”

Section: Introductionmentioning

confidence: 99%

Dosimetric Comparison between Varian Halcyon Analytical Anisotropic Algorithm and Acuros XB Algorithm for Planning of RapidArc Radiotherapy of Cervical Carcinoma

Mbewe

Shiba

2021

Progress in Medical Physics

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Purpose: The Halcyon radiotherapy platform at Groote Schuur Hospital was delivered with a factory-configured analytical anisotropic algorithm (AAA) beam model for dose calculation. In a recent system upgrade, the Acuros XB (AXB) algorithm was installed. Both algorithms adopt fundamentally different approaches to dose calculation. This study aimed to compare the dose distributions of cervical carcinoma RapidArc plans calculated using both algorithms.Methods: A total of 15 plans previously calculated using the AAA were retrieved and recalculated using the AXB algorithm. Comparisons were performed using the planning target volume (PTV) maximum (max) and minimum (min) doses, D95%, D98%, D50%, D2%, homogeneity index (HI), and conformity index (CI). The mean and max doses and D2% were compared for the bladder, bowel, and femoral heads.Results: The AAA calculated slightly higher targets, D98%, D95%, D50%, and CI, than the AXB algorithm (44.49 Gy vs. 44.32 Gy, P=0.129; 44.87 Gy vs. 44.70 Gy, P=0.089; 46.00 Gy vs. 45.98 Gy, P=0.154; and 0.51 vs. 0.50, P=0.200, respectively). For target min dose, D2%, max dose, and HI, the AAA scored lower than the AXB algorithm (41.24 Gy vs. 41.30 Gy, P=0.902; 47.34 Gy vs. 47.75 Gy, P<0.001; 48.62 Gy vs. 50.14 Gy, P<0.001; and 0.06 vs. 0.07, P=0.002, respectively). For bladder, bowel, and left and right femurs, the AAA calculated higher mean and max doses.Conclusions: Statistically significant differences were observed for PTV D2%, max dose, HI, and bowel max dose (P>0.05).

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Calculation of absorbed dose in radiotherapy by solution of the linear Boltzmann transport equations

Cited by 22 publications

References 83 publications

Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

Impact of the dose quantity used in MV photon optimization on dose distribution, robustness, and complexity

Dosimetric Comparison between Varian Halcyon Analytical Anisotropic Algorithm and Acuros XB Algorithm for Planning of RapidArc Radiotherapy of Cervical Carcinoma

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