Variance-based sensitivity analysis of biological uncertainties in carbon ion therapy

Technical note: Impact of beamline-specific particle energy spectra on clinical plans in carbon ion beam therapy

PURPOSE

The Local Effect Model version one (LEM I) is applied clinically across Europe to quantify the relative biological effectiveness (RBE) of carbon ion beams. It requires the full particle fluence spectrum differential in energy in each voxel as input parameter. Treatment planning systems (TPSs) use beamline-specific look-up tables generated with Monte Carlo (MC) codes. In this study, the changes in RBE weighted dose were quantified using different levels of details in the simulation or different MC codes.

METHODS

The particle fluence differential in energy was simulated with FLUKA and Geant4 at 500 depths in water in 1-mm steps for 58 initial carbon ion energies (between 120.0 and 402.8 MeV/u). A dedicated beam model was applied, including the full description of the Nozzle using GATE-RTionV1.0 (Geant4.10.03p03). In addition, two tables generated with FLUKA were compared. The starting points of the FLUKA simulations were phase space (PhS) files from, firstly, the Geant4 nozzle simulations, and secondly, a clinical beam model where an analytic approach was used to mimic the beamline. Treatment plans (TPs) were generated with RayStation 8B (RaySearch Laboratories AB, Sweden) for cubic targets in water and 10 clinical patient cases using the clinical beam model. Subsequently, the RBE weighted dose was re-computed using the two other fluence tables (FLUKA PhS or Geant4).

RESULTS

The fluence spectra of the primary and secondary particles simulated with Geant4 and FLUKA generally agreed well for the primary particles. Differences were mainly observed for the secondary particles. Interchanging the two energy spectra (FLUKA vs. GEANT4) to calculate the RBE weighted dose distributions resulted in average deviations of less than 1% in the entrance up to the end of the target region, with a maximum local deviation at the distal edge of the target. In the fragment tail, larger discrepancies of up to 5% on average were found for deep-seated targets. The patient and water phantom cases demonstrated similar results.

CONCLUSION

RBE weighted doses agreed well within all tested setups, confirming the clinical beam model provided by the TPS vendor. Furthermore, the results showed that the open source and generally available MC code Geant4 (in particular using GATE or GATE-RTion) can also be used to generate basic beam data required for RBE calculation in carbon ion therapy.

Bevacizumab is an effective treatment for symptomatic cerebral necrosis after carbon ion therapy for recurrent intracranial malignant tumours: A case report

Carbon ion therapy (CIT) is a form of particle therapy, which not only spares normal tissues but may also improve local control of recurrent intracranial tumours. Cerebral radiation necrosis (RN) is one of the most serious adverse reactions of recurrent brain tumours following reirradiation, which may lead to neurological decline or even death. Bevacizumab is an anti-vascular endothelial growth factor antibody, which has been used to treat symptomatic RN. However, studies on bevacizumab for the treatment of CIT-induced RN are sparse. The present study described two cases that were successfully treated with bevacizumab for symptomatic RN following CIT for recurrent intracranial malignant tumours. The two recurrent intracranial malignant tumours, a chondrosarcoma in the right cavernous sinus and an anaplastic meningioma in the right frontal lobe, were enrolled in a clinical trial of CIT. Both cases were treated intravenously with bevacizumab when deterioration that appeared to be symptomatic brain RN was observed. Just before CIT, enhanced magnetic resonance imaging (MRI) was performed in each case to confirm tumour recurrence. Both cases exhibited a deterioration in symptoms, as well as on MRI, at 12-month intervals following CIT. The first case underwent positron emission tomography/computed tomography to confirm no increase in fluorodeoxyglucose uptake in lesion areas. Both cases were diagnosed as having symptomatic brain RN and began intravenous administration of four cycles of 5 mg/kg bevacizumab biweekly. The patients responded well, with rapid and marked improvements on MRI, and in clinical symptoms. No tumour progression was observed 24 months after CIT. In conclusion, bevacizumab was revealed to exert marked effects on symptomatic brain RN following CIT. Notably, cycles of bevacizumab should be administered specifically based on the aim of treating brain necrosis, and long-term or prophylactic applications are not recommended.

Combining inter-observer variability, range and setup uncertainty in a variance-based sensitivity analysis for proton therapy

Margin concepts in proton therapy aim to ensure full dose coverage of the clinical target volume (CTV) in presence of setup and range uncertainty. Due to inter-observer variability (IOV), the CTV itself is uncertain. We present a framework to evaluate the combined impact of IOV, setup and range uncertainty in a variance-based sensitivity analysis (SA). For ten patients with skull base meningioma, the mean calculation time to perform the SA including 1.6 × 10⁴ dose recalculations was 59 min. For two patients in this dataset, IOV had a relevant impact on the estimated CTV D_95% uncertainty.

Variance-based sensitivity analysis for uncertainties in proton therapy: A framework to assess the effect of simultaneous uncertainties in range, positioning, and RBE model predictions on RBE-weighted dose distributions

PURPOSE

Treatment plans in proton therapy are more sensitive to uncertainties than in conventional photon therapy. In addition to setup uncertainties, proton therapy is affected by uncertainties in proton range and relative biological effectiveness (RBE). While to date a constant RBE of 1.1 is commonly assumed, the actual RBE is known to increase toward the distal end of the spread-out Bragg peak. Several models for variable RBE predictions exist. We present a framework to evaluate the combined impact and interactions of setup, range, and RBE uncertainties in a comprehensive, variance-based sensitivity analysis (SA).

MATERIAL AND METHODS

The variance-based SA requires a large number (10⁴ -10⁵ ) of RBE-weighted dose (RWD) calculations. Based on a particle therapy extension of the research treatment planning system CERR we implemented a fast, graphics processing unit (GPU) accelerated pencil beam modeling of patient and range shifts. For RBE predictions, two biological models were included: The mechanistic repair-misrepair-fixation (RMF) model and the phenomenological Wedenberg model. All input parameters (patient position, proton range, RBE model parameters) are sampled simultaneously within their assumed probability distributions. Statistical formalisms rank the input parameters according to their influence on the overall uncertainty of RBE-weighted dose-volume histogram (RW-DVH) quantiles and the RWD in every voxel, resulting in relative, normalized sensitivity indices (S = 0: noninfluential input, S = 1: only influential input). Results are visualized as RW-DVHs with error bars and sensitivity maps.

RESULTS AND CONCLUSIONS

The approach is demonstrated for two representative brain tumor cases and a prostate case. The full SA including ∼ 3 × 10 4 RWD calculations took 39, 11, and 55 min, respectively. Range uncertainty was an important contribution to overall uncertainty at the distal end of the target, while the relatively smaller uncertainty inside the target was governed by biological uncertainties. Consequently, the uncertainty of the RW-DVH quantile D₉₈ for the target was governed by range uncertainty while the uncertainty of the mean target dose was dominated by the biological parameters. The SA framework is a powerful and flexible tool to evaluate uncertainty in RWD distributions and DVH quantiles, taking into account physical and RBE uncertainties and their interactions. The additional information might help to prioritize research efforts to reduce physical and RBE uncertainties and could also have implications for future approaches to biologically robust planning and optimization.

Proton RBE dependence on dose in the setting of hypofractionation

Hypofractionated radiotherapy is attractive concerning patient burden and therapy costs, but many aspects play a role when it comes to assess its safety. While exploited for conventional photon therapy and carbon ion therapy, hypofractionation with protons is only rarely applied. One reason for this is uncertainty in the described dose, mainly due to the relative biological effectiveness (RBE), which is small for protons, but not negligible. RBE is generally dose-dependent, and for higher doses as used in hypofractionation, a thorough RBE evaluation is needed. This review article focuses on the RBE variability in protons and associated issues or implications for hypofractionation.

Analytical probabilistic modeling of RBE-weighted dose for ion therapy

Particle therapy is especially prone to uncertainties. This issue is usually addressed with uncertainty quantification and minimization techniques based on scenario sampling. For proton therapy, however, it was recently shown that it is also possible to use closed-form computations based on analytical probabilistic modeling (APM) for this purpose. APM yields unique features compared to sampling-based approaches, motivating further research in this context. This paper demonstrates the application of APM for intensity-modulated carbon ion therapy to quantify the influence of setup and range uncertainties on the RBE-weighted dose. In particular, we derive analytical forms for the nonlinear computations of the expectation value and variance of the RBE-weighted dose by propagating linearly correlated Gaussian input uncertainties through a pencil beam dose calculation algorithm. Both exact and approximation formulas are presented for the expectation value and variance of the RBE-weighted dose and are subsequently studied in-depth for a one-dimensional carbon ion spread-out Bragg peak. With V and B being the number of voxels and pencil beams, respectively, the proposed approximations induce only a marginal loss of accuracy while lowering the computational complexity from order [Formula: see text] to [Formula: see text] for the expectation value and from [Formula: see text] to [Formula: see text] for the variance of the RBE-weighted dose. Moreover, we evaluated the approximated calculation of the expectation value and standard deviation of the RBE-weighted dose in combination with a probabilistic effect-based optimization on three patient cases considering carbon ions as radiation modality against sampled references. The resulting global γ-pass rates (2 mm,2%) are [Formula: see text]99.15% for the expectation value and [Formula: see text]94.95% for the standard deviation of the RBE-weighted dose, respectively. We applied the derived analytical model to carbon ion treatment planning, although the concept is in general applicable to other ion species considering a variable RBE.

Sensitivity Analysis of the Integral Quality Monitoring System® Using Monte Carlo Simulation

The Integral Quality Monitoring (IQM) System is a real-time beam output verifying system that validates the integrity and accuracy of patient treatment plan (TP) data during radiation treatment. The purpose of this study was to evaluate the sensitivity of the IQM to errors in segment using EGSnrc/BEAMnrc Monte Carlo (MC) codes. Sensitivity analysis (SA) techniques were applied to study the significance of small alterations of field sizes (segments) on the IQM signal response. One hundred and eighty multileaf segments were analyzed with methods that include scatter plots (SP), brute force, variance-based (VAR), and standard regression coefficient SA. The segments were altered randomly within ±1, ±2, and ±3 mm leaf steps for 10 MV photon beams. SP analysis gradient and VAR maximum index are 1.045 and 0.556 for the smallest segment while the largest segment has the value of 0.018 and 0.504, respectively. The brute force and standard regression displayed maximum sensitivity indices around the unaltered segments. These tests conclusively indicated that the IQM was more sensitive to alterations of small segments compared to larger segments. This is important since small segment variation will cause a higher dose output variation that should be picked up during online beam monitoring.

Rapid implementation of the repair-misrepair-fixation (RMF) model facilitating online adaption of radiosensitivity parameters in ion therapy

INTRODUCTION

Treatment planning for ion therapy must account for physical properties of the beam as well as differences in the relative biological effectiveness (RBE) of ions compared to photons. In this work, we present a fast RBE calculation approach, based on the decoupling of physical properties and the [Formula: see text] ratio commonly used to describe the radiosensitivity of irradiated cells or organs.

MATERIAL AND METHODS

In the framework of the mechanistic repair-misrepair-fixation (RMF) model, the biological modeling can be decoupled from the physical dose. This was implemented into a research treatment planning system for carbon ion therapy.

RESULTS

The presented implementation of the RMF model is very fast, allowing online changes of [Formula: see text]. For example, a change of [Formula: see text] including a complete biological modeling and a recalculation of RBE for [Formula: see text] voxel takes 4 ms on a 4 CPU, 3.2 GHz workstation.

DISCUSSION AND CONCLUSION

The derived decoupling within the RMF model allows fast changes in [Formula: see text], facilitating online adaption by the user. This provides new options for radiation oncologists, facilitating online variations of the radiobiological input parameters during the treatment plan evaluation process as well as uncertainty and sensitivity analyses.

Future development of biologically relevant dosimetry

Proton and ion beams are radiotherapy modalities of increasing importance and interest. Because of the different biological dose response of these radiations as compared with high-energy photon beams, the current approach of treatment prescription is based on the product of the absorbed dose to water and a biological weighting factor, but this is found to be insufficient for providing a generic method to quantify the biological outcome of radiation. It is therefore suggested to define new dosimetric quantities that allow a transparent separation of the physical processes from the biological ones. Given the complexity of the initiation and occurrence of biological processes on various time and length scales, and given that neither microdosimetry nor nanodosimetry on their own can fully describe the biological effects as a function of the distribution of energy deposition or ionization, a multiscale approach is needed to lay the foundation for the aforementioned new physical quantities relating track structure to relative biological effectiveness in proton and ion beam therapy. This article reviews the state-of-the-art microdosimetry, nanodosimetry, track structure simulations, quantification of reactive species, reference radiobiological data, cross-section data and multiscale models of biological response in the context of realizing the new quantities. It also introduces the European metrology project, Biologically Weighted Quantities in Radiotherapy, which aims to investigate the feasibility of establishing a multiscale model as the basis of the new quantities. A tentative generic expression of how the weighting of physical quantities at different length scales could be carried out is presented.

Particle radiosurgery: a new frontier of physics in medicine

Radiosurgery was introduced over half a century ago for treatment of intracranial lesions. In more recent years, stereotactic radiotherapy has rapidly advanced and is now commonly used for treatments of both cranial and extracranial lesions with high doses delivered in a few, down to a single fraction. The results of a workshop on Particle radiosurgery: A new frontier of physics in medicine held at Obergurgl, Austria during August 25-29 2013 are summarized in this issue with an overview presented in this paper. The focus was laid on particle radiosurgery but the content also includes current practice in x-ray radiosurgery and the overarching research in radiobiology and motion management for extracranial lesions. The results and discussions showed that especially research in radiobiology of high-dose charged-particles and motion management are necessary for the success of particle radiosurgery.