Dose prescription with spatial uncertainty for peripheral lung SBRT

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 hours 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.

Section: Discussionmentioning

confidence: 99%

“…Spatial robustness of the solutions (Unkelbach et al 2018) was ensured by considering the initial unscattered fluence, ( ) F , ijk uns to be distributed over a probability kernel (Bedford et al 2019, Bedford 2023 having N (= 64) points:…”

Section: Boltzmann Solvermentioning

confidence: 99%

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

Bedford

2024

“…A simple means of robust treatment planning (Unkelbach et al 2018 ) was incorporated by considering the clinical target volume (CTV) to have a spatial probability distribution (Bedford et al 2019 ). In practice, this was carried out by shifting the unscattered fluence in the opposite direction to the direction of target volume motion.…”

Section: Methodsmentioning

confidence: 99%

“…i j k ( )As this led to a combination of 4913 points, which was computationally demanding, the kernel was resampled by casting the points onto a regular grid of resolution 2 mm and then selecting the voxels with the highest 64 intensities, with rescaling to ensure conservation of energy (Bedford et al 2019). The result was a kernel consisting of 64 coordinates and probabilities.…”

Section: Inclusion Of Spatial Uncertaintymentioning

confidence: 99%

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

Bedford

2023

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.

“…SBRT has been gaining in importance in recent years and use of an accurate dose calculation is important due to the small PTV with steep dose gradients. For the case of lung SBRT, the PTV margin is frequently composed of low-density lung material, so that differences in dose occur between the PTV and the gross tumour volume (GTV) or internal target volume (ITV) (Lacornerie et al 2014, Lebredonchel et al 2017, so that alternative methods of prescription have been sought, avoiding the PTV (Bedford et al 2018). The accurate calculation of dose in this situation is therefore particularly important.…”

Section: Stereotactic Body Radiotherapymentioning

confidence: 99%

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

Bedford

2019

Over the last decade, dose calculations which solve the linear Boltzmann transport equations have been introduced into clinical practice and are now in widespread use. However, knowledge in the radiotherapy community concerning the details of their function is limited. This review gives a general description of the linear Boltzmann transport equations as applied to calculation of absorbed dose in clinical radiotherapy. The aim is to elucidate the principles of the method, rather than to describe a particular implementation. The literature on the performance of typical algorithms is then reviewed, in many cases with reference to Monte Carlo simulations. The review is completed with an overview of the emerging applications in the important area of MR-guided radiotherapy.