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

Inverse planning of lung radiotherapy with photon and proton beams using a discrete ordinates Boltzmann solver

Objective. A discrete ordinates Boltzmann solver has recently been developed for use as a fast and accurate dose engine for calculation of photon and proton beams. The purpose of this study is to apply the algorithm to the inverse planning process for photons and protons and to evaluate the impact that this has on the quality of the final solution.Approach.The method was implemented into an iterative least-squares inverse planning optimiser, with the Boltzmann solver used every 20 iterations over the total of 100 iterations. Elemental dose distributions for the intensity modulation and the dose changes at the intermediate iterations were calculated by a convolution algorithm for photons and a simple analytical model for protons. The method was evaluated for 12 patients in the heterogeneous tissue environment encountered in radiotherapy of lung tumours. Photon arc and proton arc treatments were considered in this study. The results were compared with those for use of the Boltzmann solver solely at the end of inverse planning or not at all.Main results.Application of the Boltzmann solver at the end of inverse planning shows the dose heterogeneity in the planning target volume to be greater than calculated by convolution and empirical methods, with the median root-mean-square dose deviation increasing from 3.7 to 5.3 for photons and from 1.9 to 3.4 for proton arcs. Use of discrete ordinates throughout inverse planning enables homogeneity of target coverage to be maintained throughout, the median root-mean-square dose deviation being 3.6 for photons and 2.3 for protons. Dose to critical structures is similar with discrete ordinates and conventional methods. Time for inverse planning with discrete ordinates takes around 1-2 h using a contemporary computing environment.Significance.By incorporating the Boltzmann solver into an iterative least squares inverse planning optimiser, accurate dose calculation in a heterogeneous medium is obtained throughout inverse planning, with the result that the final dose distribution is of the highest quality.

A discrete ordinates Boltzmann solver for application to inverse planning of photons and protons

The aim of this work is to develop a discrete ordinates Boltzmann solver that can be used for calculation of absorbed dose from both photons and protons within an inverse planning optimiser, so as to perform accurate dose calculation throughout the whole of the inverse planning process. With photons, five transport sweeps were performed to obtain scattered photon fluence, and unscattered electron fluence was then obtained and used as a fixed source for solution of the electron transport equations. With protons, continuous slowing down was treated as a fixed source, and five transport sweeps were used to calculate scattered fluence. The total electron or proton fluence was multiplied by the stopping power ratio for the transport medium to obtain absorbed dose. The method was evaluated in homogeneous media and in a lung case where the planning target volume was surrounded by low-density lung material. Photon arc, proton passive scattering and proton arc treatments were considered. The results were compared to a clinically validated convolution dose calculation for photons, and with an analytical method for protons. In water-equivalent media, the discrete ordinates method agrees with the alternative algorithms to within 2%. Convergence is found to be sufficiently complete for water-, lung- and bone-equivalent materials after five iterations. The dose calculated by the relatively simple angular quadrature is seen to be very close to that calculated by a more comprehensive quadrature. For inhomogeneous lung plans, the method shows more heterogeneity of dose to the planning target volume than the comparative methods. The discrete ordinates Boltzmann solver provides a general framework for dose calculation with both photons and protons. The method is suitable for incorporation into an inverse planning optimiser, so that accurate dose calculation in a heterogeneous medium can be obtained throughout inverse planning, with the result that the final dose distribution is as predicted by the optimiser.

Accuracy of Acuros[Formula: see text] BV as determined from GATE monte-carlo simulation

The American Association of Physicists in Medicine's Task Group No.43 has provided a standardised dose calculation methodology that is now the international benchmark for all brachytherapy dosimetry publications and treatment planning systems. However, limitations in this methodology has seen the development of Model-Based Dose Calculation Algorithms (MBDCA). In 2009, Varian (Varian Medical Systems, Palo Alto, CA, USA) released Acuros[Formula: see text] BrachyVision (ABV) which calculates dose by explicitly solving the Linear Boltzmann Transport Equation. In this study we have assessed the accuracy of ABV dose calculations within a range of materials relevant to high dose rate brachytherapy with an iridium-192 ([Formula: see text]Ir) source. Accuracy assessment has been achieved by implementing a modelled GamaMed Plus [Formula: see text]Ir source within a series of phantoms using the GEANT4 Application for Emission Tomography (GATE) to calculate dose for comparison with dose as determined by ABV. Comparisons between GATE and ABV were made using point-to-point profile comparisons and 1D gamma analysis. Source validation results yielded good agreement with published data. Spectrum and TG43U1 comparisons showed no major differences, with TG43U1 comparisons agreeing within ± 1%. Point-to-point comparisons showed large differences between GATE and ABV near the source and in low density materials. 1D gamma analysis pass criteria of 2%/1 mm and 2%/2 mm yielded passing rates ranging between 51.72-100% and 62.07-100% respectively. A critical analysis of this study's results suggest that ABV is unable to accurately calculate doses in low density materials. Furthermore, spatial accuracy of dose near the source is within 2 mm.

The effect of material assignment in nasal cavity on dose calculation for nasopharyngeal carcinoma (NPC) using Acuros XB

PURPOSE

To evaluate the effect of material assignment in nasal cavity on dose calculation for the volumetric modulated arc therapy (VMAT) of nasopharyngeal carcinoma (NPC) using Acuros XB (AXB) algorithm.

METHODS

The VMAT plans of 30 patients with NPC were calculated using AXB with material auto-assignment of nasal cavity to lung and reassignment to air respectively. The doses to the planning target volumes (PTVs) overlapping with nasal cavity with material auto-assignment of lung (AXB_Lung) were compared to the values obtained when nasal cavity was reassigned to air (AXB_Air) under the dose-to-medium (D_m ) reporting mode of AXB.

RESULTS

For dose calculated under AXB_Lung, the D_98% , D_2% , and D_mean of the PTV_69.96 _Air Cavity (PTV of prescription dose 69.96 Gy overlapping with nasal cavity) were on average 16.1%, 1.6%, and 8.6% larger than that calculated under AXB_Air, respectively. Up to 19.5% difference in D_98% , 3% difference in D_2% , and 11.2% difference in D_mean were observed in the worst cases for PTV_69.96 . Similar trend was observed for the PTV₅₉₄₀ _Air Cavity, in which the D_98% , D_2% , and D_mean calculated under AXB_Lung were on average 14.7%, 2.5%, and 10.2% larger than that calculated under AXB_Air, respectively. In the worst cases, the difference observed in D_98% , D_2% , and D_mean could be up to 17.7%, 4.5%, and 12.7%, respectively.

CONCLUSIONS

Significant dose difference calculated by AXB between the material assignment of lung and air in nasal cavity for NPC cases might imply the possibility of underdosage to the PTVs that overlap with inhomogeneity. Therefore, attention should be put to ensure that accurate material assignment for dose calculation under AXB such that optimal dosage was given for tumor control.

The radiobiological effect of using Acuros XB vs anisotropic analytical algorithm on hepatocellular carcinoma stereotactic body radiation therapy

The purpose of this work was to study the radiobiological effect of using Acuros XB (AXB) vs Analytic Anisotropic Algorithm (AAA) on hepatocellular carcinoma (HCC) stereotactic body radiation therapy (SBRT). Seventy SBRT volumetric modulated arc therapy (VMAT) plans for HCC were calculated using AAA and AXB respectively with the same treatment parameters. Published tumor control probability (TCP) and normal tissue complication probability (NTCP) models were used to quantify the effect of dosimetric difference between AAA and AXB on TCP, NTCP and uncomplicated tumor control probability (UTCP). There was an average decrease of 2.5% in 6-month TCP. Normal liver has the largest average decrease in NTCP which was 59.7%. Bowels followed with 26.6% average decrease in NTCP. Duodenum, stomach and esophagus had 10.2%, 5.1%, and 4.3% average decrease in NTCP. There was an average decrease of 1.8% and up to 7.2% in 6-month UTCP. There was an overall decrease in TCP, NTCP, and UTCP for HCC SBRT plans calculated using AXB compared to AAA which could be clinically significant.

The effect on tumour control probability of using AXB algorithm in replacement of AAA for SBRT of hepatocellular carcinoma located at lung-liver boundary region

Objective:

To retrospectively analyze the clinical impact on stereotactic body radiation therapy (SBRT) for hepatocellular carcinoma (HCC) located at lung–liver boundary due to the use of Acuros XB algorithm (AXB) in replacement of anisotropic analytical algorithm (AAA).

Methods:

23 SBRT volumetric modulated arc therapy (VMAT) plans for HCC located at lung–liver boundary were calculated using AAA and AXB respectively with the same treatment parameters. The dose–volume data of the planned target volumes (PTVs) were compared. A published tumour control probability (TCP) model was used to calculate the effect of dosimetric difference between AAA and AXB on tumour control probability.

Results:

For dose calculated by AXB (Dose to medium), the D95% and D98% of the PTV were on average 2.4 and 3.1% less than that calculated by AAA. For dose calculated by AXB (dose to water), the D95% and D98% of the PTV were on average 1.8%, and 2.7% less than that calculated by AAA. Up to 5% difference in D95% and 8% difference in D98% were observed in the worst cases. The significant decrease in D95% calculated by AXB compared to AAA could result in a % decrease in 2 year TCP up to 8% in the worst case (from 46.8 to 42.9%).

Conclusion:

The difference in dose calculated by AAA and AXB could lead to significant difference in TCP for HCC SBRT located at lung–liver boundary region.

Advances in knowledge:

The difference in calculated dose and tumour control probability for HCC SBRT between AAA and AXB algorithm at lung–liver boundary region was compared.

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

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.

CONCLUSIONS

The dose quantity used in MV photon optimization can affect plan robustness. D_w,w distributions from convolution/superposition algorithms are robust but may not provide sufficient radiation transport accuracy in some cases. D_m,m and D_w,m from advanced algorithms can compromise robustness because their different responses to some composition heterogeneities introduce additional fluence compensations. D_ref,m* offers advantages in plan optimization and evaluation, producing accurate and robust plans without increasing complexity. D_ref,m* can be easily implemented as a built-in feature of the TPS and can facilitate and simplify the treatment planning process when using advanced algorithms. Final reporting can be kept in D_m,m or D_w,m for clinical correlations.

Dose Calculation Algorithms for External Radiation Therapy: An Overview for Practitioners

Radiation therapy (RT) is a constantly evolving therapeutic technique; improvements are continuously being introduced for both methodological and practical aspects. Among the features that have undergone a huge evolution in recent decades, dose calculation algorithms are still rapidly changing. This process is propelled by the awareness that the agreement between the delivered and calculated doses is of paramount relevance in RT, since it could largely affect clinical outcomes. The aim of this work is to provide an overall picture of the main dose calculation algorithms currently used in RT, summarizing their underlying physical models and mathematical bases, and highlighting their strengths and weaknesses, referring to the most recent studies on algorithm comparisons. This handy guide is meant to provide a clear and concise overview of the topic, which will prove useful in helping clinical medical physicists to perform their responsibilities more effectively and efficiently, increasing patient benefits and improving the overall quality of the management of radiation treatment.

A new dose quantity for evaluation and optimisation of MV photon dose distributions when using advanced algorithms: proof of concept and potential applications

Advanced algorithms used in MV photon radiotherapy model radiation transport in any media. They represent a step forward but introduce new uncertainties and questions, including whether to report the doses to water (D_w,m) or medium (D_m,m) voxels, and the impact of fluence changes introduced by surrounding media. These aspects can compromise consistency between both reporting modes and with previous algorithms in which clinical experience is based. This study introduces a new dose quantity, the dose-to-reference-like medium, to overcome the aforementioned shortcomings. It is linked to a reference medium, water in this study (D_w,m*), and defined as the absorbed dose in a voxel of this reference medium surrounded by a reference-like medium with the same radiation transport characteristics as the original one. We propose to derive D_w,m* distributions by post-processing D_w,m or D_m,m applying a correction factor (CF) to each voxel which depends on its composition. We present and justify a simple and straightforward method to obtain CFs that only involves two phantoms with the same density: one with the considered composition and the other with that of the reference medium. A proof of concept was performed in a clinical environment for Acuros XB (AXB) advanced algorithm and 6 MV photon beams. The CFs were derived for the tissues characterised in Acuros. D_w,m* was compared to D_w,m, D_m,m, and D_w,w from AAA analytical algorithm for some virtual and clinical cases. All the previous quantities presented limitations that can be solved by D_w,m*. This new quantity allows the applicability of evaluation parameters, traceability to clinical experience, and isolation of heterogeneity effects to identify optimum plans, offering useful characteristics for plan evaluation and optimisation in clinical practice. Additionally, it also has potential applications in automated treatment planning and multi-centre activities such as clinical trials, audits, benchmarking, and shared models for automation.