The Monte Carlo (MC) method has been shown through many research studies to calculate accurate dose distributions for clinical radiotherapy, particularly in heterogeneous patient tissues where the effects of electron transport cannot be accurately handled with conventional, deterministic dose algorithms. Despite its proven accuracy and the potential for improved dose distributions to influence treatment outcomes, the long calculation times previously associated with MC simulation rendered this method impractical for routine clinical treatment planning. However, the development of faster codes optimized for radiotherapy calculations and improvements in computer processor technology have substantially reduced calculation times to, in some instances, within minutes on a single processor. These advances have motivated several major treatment planning system vendors to embark upon the path of MC techniques. Several commercial vendors have already released or are currently in the process of releasing MC algorithms for photon and/or electron beam treatment planning. Consequently, the accessibility and use of MC treatment planning algorithms may well become widespread in the radiotherapy community. With MC simulation, dose is computed stochastically using first principles; this method is therefore quite different from conventional dose algorithms. Issues such as statistical uncertainties, the use of variance reduction techniques, the ability to account for geometric details in the accelerator treatment head simulation, and other features, are all unique components of a MC treatment planning algorithm. Successful implementation by the clinical physicist of such a system will require an understanding of the basic principles of MC techniques. The purpose of this report, while providing education and review on the use of MC simulation in radiotherapy planning, is to set out, for both users and developers, the salient issues associated with clinical implementation and experimental verification of MC dose algorithms. As the MC method is an emerging technology, this report is not meant to be prescriptive. Rather, it is intended as a preliminary report to review the tenets of the MC method and to provide the framework upon which to build a comprehensive program for commissioning and routine quality assurance of MC-based treatment planning systems.

Current clinical experience in radiation therapy is based upon dose computations that report the absorbed dose to water, even though the patient is not made of water but of many different types of tissue. While Monte Carlo dose calculation algorithms have the potential for higher dose accuracy, they usually transport particles in and compute the absorbed dose to the patient media such as soft tissue, lung or bone. Therefore, for dose calculation algorithm comparisons, or to report dose to water or tissue contained within a bone matrix for example, a method to convert dose to the medium to dose to water is required. This conversion has been developed here by applying Bragg-Gray cavity theory. The dose ratio for 6 and 18 MV photon beams was determined by computing the average stopping power ratio for the primary electron spectrum in the transport media. For soft tissue, the difference between dose to medium and dose to water is approximately 1.0%, while for cortical bone the dose difference exceeds 10%. The variation in the dose ratio as a function of depth and position in the field indicates that for photon beams a single correction factor can be used for each particular material throughout the field for a given photon beam energy. The only exception to this would be for the clinically non-relevant dose to air. Pre-computed energy spectra for 60Co to 24 MV are used to compute the dose ratios for these photon beams and to determine an effective energy for evaluation of the dose ratio.

Motion and uncertainty in radiotherapy is traditionally handled via margins. The clinical target volume (CTV) is expanded to a larger planning target volume (PTV), which is irradiated to the prescribed dose. However, the PTV concept has several limitations, especially in proton therapy. Therefore, robust and probabilistic optimization methods have been developed that directly incorporate motion and uncertainty into treatment plan optimization for intensity modulated radiotherapy (IMRT) and intensity modulated proton therapy (IMPT). Thereby, the explicit definition of a PTV becomes obsolete and treatment plan optimization is directly based on the CTV. Initial work focused on random and systematic setup errors in IMRT. Later, inter-fraction prostate motion and intra-fraction lung motion became a research focus. Over the past ten years, IMPT has emerged as a new application for robust planning methods. In proton therapy, range or setup errors may lead to dose degradation and misalignment of dose contributions from different beams -a problem that cannot generally be addressed by margins. Therefore, IMPT has led to the first implementations of robust planning methods in commercial planning systems, making these methods available for clinical use. This paper first summarizes the limitations of the PTV concept. Subsequently, robust optimization methods are introduced and their applications in IMRT and IMPT planning are reviewed.Abstract. Motion and uncertainty in radiotherapy is traditionally handled via 31 margins. The clinical target volume (CTV) is expanded to a larger planning target 32 volume (PTV), which is irradiated to the prescribed dose. However, the PTV 33 concept has several limitations, especially in proton therapy. Therefore, robust and 34 probabilistic optimization methods have been developed that directly incorporate 35 motion and uncertainty into treatment plan optimization for intensity modulated 36 radiotherapy (IMRT) and intensity modulated proton therapy (IMPT). Thereby, the 37 explicit definition of a PTV becomes obsolete and treatment plan optimization is 38 directly based on the CTV. Initial work focused on random and systematic setup errors 39 in IMRT. Later, inter-fraction prostate motion and intra-fraction lung motion became 40 a research focus. Over the past 10 years, IMPT has emerged as a new application for 41 robust planning methods. In proton therapy, range or setup errors may lead to dose 42 degradation and misalignment of dose contributions from different beams a problem 43 Robust radiotherapy planning 2 that cannot generally be addressed by margins. Therefore, IMPT has led to the first 44 implementations of robust planning methods in commercial planning systems, making 45 these methods available for clinical use. This paper first summarizes the limitations 46 of the PTV concept. Subsequently, robust optimization methods are introduced and 47 their applications in IMRT and IMPT planning are reviewed. 48 1. Introduction 49Radiotherapy aims at delivering curative doses of radiation ...

Four-dimensional (4D) radiotherapy is the explicit inclusion of the temporal changes in anatomy during the imaging, planning, and delivery of radiotherapy. Temporal anatomic changes can occur for many reasons, though the focus of the current investigation is respiration motion for lung tumors. The aim of this study was to develop 4D radiotherapy treatment-planning methodology for DMLC-based respiratory motion tracking. A 4D computed tomography (CT) scan consisting of a series of eight 3D CT image sets acquired at different respiratory phases was used for treatment planning. Deformable image registration was performed to map each CT set from the peak-inhale respiration phase to the CT image sets corresponding to subsequent respiration phases. Deformable registration allows the contours defined on the peak-inhale CT to be automatically transferred to the other respiratory phase CT image sets. Treatment planning was simultaneously performed on each of the eight 3D image sets via automated scripts in which the MLC-defined beam aperture conforms to the PTV (which in this case equaled the GTV due to CT scan length limitations) plus a penumbral margin at each respiratory phase. The dose distribution from each respiratory phase CT image set was mapped back to the peak-inhale CT image set for analysis. The treatment intent of 4D planning is that the radiation beam defined by the DMLC tracks the respiration-induced target motion based on a feedback loop including the respiration signal to a real-time MLC controller. Deformation with respiration was observed for the lung tumor and normal tissues. This deformation was verified by examining the mapping of high contrast objects, such as the lungs and cord, between image sets. For the test case, dosimetric reductions for the cord, heart, and lungs were found for 4D planning compared with 3D planning. 4D radiotherapy planning for DMLC-based respiratory motion tracking is feasible and may offer tumor dose escalation and/or a reduction in treatment-related complications. However, 4D planning requires new planning tools, such as deformable registration and automated treatment planning on multiple CT image sets.

Monte Carlo (MC) algorithms are recognized as the most accurate methodology for patient dose assessment. For intensity-modulated radiation therapy (IMRT) delivered with dynamic multileaf collimators (DMLCs), accurate dose calculation, even with MC, is challenging. Accurate IMRT MC dose calculations require inclusion of the moving MLC in the MC simulation. Due to its complex geometry, full transport through the MLC can be time consuming. The aim of this work was to develop an MLC model for photon beam MC IMRT dose computations. The basis of the MC MLC model is that the complex MLC geometry can be separated into simple geometric regions, each of which readily lends itself to simplified radiation transport. For photons, only attenuation and first Compton scatter interactions are considered. The amount of attenuation material an individual particle encounters while traversing the entire MLC is determined by adding the individual amounts from each of the simplified geometric regions. Compton scatter is sampled based upon the total thickness traversed. Pair production and electron interactions (scattering and bremsstrahlung) within the MLC are ignored. The MLC model was tested for 6 MV and 18 MV photon beams by comparing it with measurements and MC simulations that incorporate the full physics and geometry for fields blocked by the MLC and with measurements for fields with the maximum possible tongue-and-groove and tongue-or-groove effects, for static test cases and for sliding windows of various widths. The MLC model predicts the field size dependence of the MLC leakage radiation within 0.1% of the open-field dose. The entrance dose and beam hardening behind a closed MLC are predicted within +/- 1% or 1 mm. Dose undulations due to differences in inter- and intra-leaf leakage are also correctly predicted. The MC MLC model predicts leaf-edge tongue-and-groove dose effect within +/- 1% or 1 mm for 95% of the points compared at 6 MV and 88% of the points compared at 18 MV. The dose through a static leaf tip is also predicted generally within +/- 1% or 1 mm. Tests with sliding windows of various widths confirm the accuracy of the MLC model for dynamic delivery and indicate that accounting for a slight leaf position error (0.008 cm for our MLC) will improve the accuracy of the model. The MLC model developed is applicable to both dynamic MLC and segmental MLC IMRT beam delivery and will be useful for patient IMRT dose calculations, pre-treatment verification of IMRT delivery and IMRT portal dose transmission dosimetry.