Fast multifield optimization of the biological effect in ion therapy

The potential of mixed carbon-helium beams for online treatment verification: a simulation and treatment planning study

Objective.Recently, a new and promising approach for range verification was proposed. This method requires the use of two different ion species. Due to their equal magnetic rigidity, fully ionized carbon and helium ions can be simultaneously accelerated in accelerators like synchrotrons. At sufficiently high treatment energies, helium ions can exit the patient distally, reaching approximately three times the range of carbon ions at an equal energy per nucleon. Therefore, the proposal involves adding a small helium fluence to the carbon ion beam and utilizing helium as an online range probe during radiation therapy. This work aims to develop a software framework for treatment planning and motion verification in range-guided radiation therapy using mixed carbon-helium beams.Approach.The developed framework is based on the open-source treatment planning toolkit matRad. Dose distributions and helium radiographs were simulated using the open-source Monte Carlo package TOPAS. Beam delivery system parameters were obtained from the Heidelberg Ion Therapy Center, and imaging detectors along with reconstruction were facilitated by ProtonVDA. Methods for reconstructing the most likely patient positioning error scenarios and the motion phase of 4DCT are presented for prostate and lung cancer sites.Main results.The developed framework provides the capability to calculate and optimize treatment plans for mixed carbon-helium ion therapy. It can simulate the treatment process and generate helium radiographs for simulated patient geometry, including small beam views. Furthermore, motion reconstruction based on these radiographs seems possible with preliminary validation.Significance.The developed framework can be applied for further experimental work with the promising mixed carbon-helium ion implementation of range-guided radiotherapy. It offers opportunities for adaptation in particle therapy, improving dose accumulation, and enabling patient anatomy reconstruction during radiotherapy.

A digital male pelvis phantom series showing anatomical variations over the course of fractionated radiotherapy treatment

BACKGROUND

Daily IGRT images show day-to-day anatomical variations in patients undergoing fractionated prostate radiotherapy. This is of particular importance in particle beam treatments.

PURPOSE

To develop a digital phantom series showing variation in pelvic anatomy for evaluating treatment planning and IGRT procedures in particle radiotherapy.

METHODS

A pelvic phantom series was developed from the planning MRI and kVCT (planning CT) images along with six of the daily serial MVCT images taken of a single patient treated with a full bladder on a Tomotherapy unit. The selected patient had clearly visible yet unexceptional internal anatomy variation. Prostate, urethra, bladder, rectum, bowel, bowel gas, bone and soft tissue were contoured and a single Hounsfield Unit was assigned to each region. Treatment plans developed on the kVCT for photon, proton and carbon beams were recalculated on each phantom to demonstrate a clinical application of the series. Proton plans were developed with and without robust optimization.

RESULTS

Limited to axial slices with prostate, the bladder volume varied from 6 to 46 cm3, the rectal volume (excluding gas) from 22 to 52 cm3, and rectal gas volume from zero to 18 cm3. The water equivalent path length to the prostate varied by up to 1.5 cm . The variations resulted in larger changes in the RBE-weighted Dose Volume Histograms of the non-robust proton plan and the carbon plan compared to the robust proton plan, the latter similar to the photon plan. The prostate coverage (V100%) decreased by an average of 18% in the carbon plan, 16% in the non-robust proton plan, 1.8% in the robust proton plan, and 4.4% in the photon plan. The volume of rectum receiving 75% of the prescription dose (V75%) increased by an average of 3.7 cm3, 4.7 cm3, 1.9 cm3, and 0.6 cm3 in those four plans, respectively.

CONCLUSIONS

The digital pelvic phantom series provides for quantitative investigation of IGRT procedures and new methods for improving accuracy in particle therapy and may be used in cross-institutional comparisons for clinical trial quality assurance.

Combined BNCT-CIRT treatment planning for glioblastoma using the effect-based optimization

Objective. Boron neutron capture therapy (BNCT) and carbon ion radiotherapy (CIRT) are emerging treatment modalities for glioblastoma. In this study, we investigated the methodology and feasibility to combine BNCT and CIRT treatments. The combined treatment plan illustrated how the synergistic utilization of BNCT's biological targeting and CIRT's intensity modulation capabilities could lead to optimized treatment outcomes.Approach. The Monte Carlo toolkit, TOPAS, was employed to calculate the dose distribution for BNCT, while matRad was utilized for the optimization of CIRT. The biological effect-based approach, instead of the dose-based approach, was adopted to develop the combined BNCT-CIRT treatment plans for six patients diagnosed with glioblastoma, considering the different radiosensitivity and fraction. Five optional combined treatment plans with specific BNCT effect proportions for each patient were evaluated to identify the optimal treatment that minimizes damage on normal tissue.Main results. Individual BNCT exhibits a significant effect gradient along with the beam direction in the large tumor, while combined BNCT-CIRT treatments can achieve uniform effect delivery within the clinical target volume (CTV) through the effect filling with reversed gradient by the CIRT part. In addition, the increasing BNCT effect proportion in combined treatments can reduce damage in the normal brain tissue near the CTV. Besides, the combined treatments effectively minimize damage to the skin compared to individual BNCT treatments.Significance. The initial endeavor to combine BNCT and CIRT treatment plans is achieved by the effect-based optimization. The observed advantages of the combined treatment suggest its potential applicability for tumors characterized by pleomorphic, infiltrative, radioresistant and voluminous features.

Including Volume Effects in Biological Treatment Plan Optimization for Carbon Ion Therapy: Generalized Equivalent Uniform Dose-Based Objective in TRiP98

We describe a way to include biologically based objectives in plan optimization specific for carbon ion therapy, beyond the standard voxel-dose-based criteria already implemented in TRiP98, research planning software for ion beams. The aim is to account for volume effects—tissue architecture-dependent response to damage—in the optimization procedure, using the concept of generalized equivalent uniform dose (gEUD), which is an expression to convert a heterogeneous dose distribution (e.g., in an organ at risk (OAR)) into a uniform dose associated with the same biological effect. Moreover, gEUD is closely related to normal tissue complication probability (NTCP). The multi-field optimization problem here takes also into account the relative biological effectiveness (RBE), which in the case of ion beams is not factorizable and introduces strong non-linearity. We implemented the gEUD-based optimization in TRiP98, allowing us to control the whole dose–volume histogram (DVH) shape of OAR with a single objective by adjusting the prescribed gEUD₀ and the volume effect parameter a, reducing the volume receiving dose levels close to mean dose when a = 1 (large volume effect) while close to maximum dose for a >> 1 (small volume effect), depending on the organ type considered. We studied the role of gEUD₀ and a in the optimization, and we compared voxel-dose-based and gEUD-based optimization in chordoma cases with different anatomies. In particular, for a plan containing multiple OARs, we obtained the same target coverage and similar DVHs for OARs with a small volume effect while decreasing the mean dose received by the proximal parotid, thus reducing its NTCP by a factor of 2.5. Further investigations are done for this plan, considering also the distal parotid gland, obtaining a NTCP reduction by a factor of 1.9 for the proximal and 2.9 for the distal one. In conclusion, this novel optimization method can be applied to different OARs, but it achieves the largest improvement for organs whose volume effect is larger. This allows TRiP98 to perform a double level of biologically driven optimization for ion beams, including at the same time RBE-weighted dose and volume effects in inverse planning. An outlook is presented on the possible extension of this method to the target.

Joint Optimization of Photon-Carbon Ion Treatments for Glioblastoma

PURPOSE

Carbon ions are radiobiologically more effective than photons and are beneficial for treating radioresistant gross tumor volumes (GTV). However, owing to a reduced fractionation effect, they may be disadvantageous for treating infiltrative tumors, in which healthy tissue inside the clinical target volume (CTV) must be protected through fractionation. This work addresses the question: What is the ideal combined photon-carbon ion fluence distribution for treating infiltrative tumors given a specific fraction allocation between photons and carbon ions?

METHODS AND MATERIALS

We present a method to simultaneously optimize sequentially delivered intensity modulated photon (IMRT) and carbon ion (CIRT) treatments based on cumulative biological effect, incorporating both the variable relative biological effect of carbon ions and the fractionation effect within the linear quadratic model. The method is demonstrated for 6 glioblastoma patients in comparison with the current clinical standard of independently optimized CIRT-IMRT plans.

RESULTS

Compared with the reference plan, joint optimization strategies yield inhomogeneous photon and carbon ion dose distributions that cumulatively deliver a homogeneous biological effect distribution. In the optimal distributions, the dose to CTV is mostly delivered by photons and carbon ions are restricted to the GTV with variations depending on tumor size and location. Improvements in conformity of high-dose regions are reflected by a mean EQD2 reduction of 3.29 ± 1.22 Gy in a dose fall-off margin around the CTV. Carbon ions may deliver higher doses to the center of the GTV, and photon contributions are increased at interfaces with CTV and critical structures. This results in a mean EQD2 reduction of 8.3 ± 2.28 Gy, in which the brain stem abuts the target volumes.

CONCLUSIONS

We have developed a biophysical model to optimize combined photon-carbon ion treatments. For 6 glioblastoma patient cases, we show that our approach results in a more targeted application of carbon ions that (1) reduces dose in normal tissues within the target volume, which can only be protected through fractionation; and (2) boosts central target volume regions to reduce integral dose. Joint optimization of IMRT-CIRT treatments enable the exploration of a new spectrum of plans that can better address physical and radiobiological treatment planning challenges.

Generalized approach for radiotherapy treatment planning by optimizing projected health outcome: preliminary results for prostate radiotherapy patients

Research in cancer care increasingly focuses on survivorship issues, e.g. managing disease- and treatment-related morbidity and mortality occurring during and after treatment. This necessitates innovative approaches that consider treatment side effects in addition to tumor cure. Current treatment-planning methods rely on constrained iterative optimization of dose distributions as a surrogate for health outcomes. The goal of this study was to develop a generally applicable method to directly optimize projected health outcomes. We developed an outcome-based objective function to guide selection of the number, angle, and relative fluence weight of photon and proton radiotherapy beams in a sample of ten prostate-cancer patients by optimizing the projected health outcome. We tested whether outcome-optimized radiotherapy (OORT) improved the projected longitudinal outcome compared to dose-optimized radiotherapy (DORT) first for a statistically significant majority of patients, then for each individual patient. We assessed whether the results were influenced by the selection of treatment modality, late-risk model, or host factors. The results of this study revealed that OORT was superior to DORT. Namely, OORT maintained or improved the projected health outcome of photon- and proton-therapy treatment plans for all ten patients compared to DORT. Furthermore, the results were qualitatively similar across three treatment modalities, six late-risk models, and 10 patients. The major finding of this work was that it is feasible to directly optimize the longitudinal (i.e. long- and short-term) health outcomes associated with the total (i.e. therapeutic and stray) absorbed dose in all of the tissues (i.e. healthy and diseased) in individual patients. This approach enables consideration of arbitrary treatment factors, host factors, health endpoints, and times of relevance to cancer survivorship. It also provides a simpler, more direct approach to realizing the full beneficial potential of cancer radiotherapy.

Fluence-modulated proton CT optimized with patient-specific dose and variance objectives for proton dose calculation

Particle therapy treatment planning requires accurate volumetric maps of the relative stopping power, which can directly be acquired using proton computed tomography (pCT). With fluence-modulated pCT (FMpCT) imaging fluence is concentrated in a region-of-interest (ROI), which can be the vicinity of the treatment beam path, and imaging dose is reduced elsewhere. In this work we present a novel optimization algorithm for FMpCT which, for the first time, calculates modulated imaging fluences for joint imaging dose and image variance objectives. Thereby, image quality is maintained in the ROI to ensure accurate calculations of the treatment dose, and imaging dose is minimized outside the ROI with stronger minimization penalties given to imaging organs-at-risk. The optimization requires an initial scan at uniform fluence or a previous x-ray CT scan. We simulated and optimized FMpCT images for three pediatric patients with tumors in the head region. We verified that the target image variance inside the ROI was achieved and demonstrated imaging dose reductions outside of the ROI of 74% on average, reducing the imaging dose from 1.2 to 0.3 mGy. Such dose savings are expected to be relevant compared to the therapeutic dose outside of the treatment field. Treatment doses were re-calculated on the FMpCT images and compared to treatment doses re-recalculated on uniform fluence pCT scans using a 1% criterion. Passing rates were above 98.3% for all patients. Passing rates comparing FMpCT treatment doses to the ground truth treatment dose were above 88.5% for all patients. Evaluation of the proton range with a 1 mm criterion resulted in passing rates above 97.5% (FMpCT/pCT) and 95.3% (FMpCT/ground truth). Jointly optimized fluence-modulated pCT images can be used for proton dose calculation maintaining the full dosimetric accuracy of pCT but reducing the required imaging dose considerably by three quarters. This may allow for daily imaging during particle therapy ensuring a safe and accurate delivery of the therapeutic dose and avoiding excess dose from imaging.

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.

Modeling RBE-weighted dose variations in irregularly moving abdominal targets treated with carbon ion beams

PURPOSE

To model four-dimensional (4D) relative biological effectiveness (RBE)-weighted dose variations in abdominal lesions treated with scanned carbon ion beam in case of irregular breathing motion.

METHODS

The proposed method, referred to as bioWED method, combines the simulation of tumor motion in a patient- and beam-specific water equivalent depth (WED)-space with RBE modeling, aiming at the estimation of RBE-weighted dose changes due to respiratory motion. The method was validated on a phantom, simulating gated and free breathing dose delivery, and on a patient case, for which free breathing irradiation was assumed and both amplitude and baseline breathing irregularities were simulated through a respiratory motion model. We quantified (a) the effect of motion on the equivalent uniform dose (EUD) and the RBE-weighted dose-volume histograms (DVH), by comparing the planned dose distribution with "ground truth" 4D RBE-weighted doses computed using 4D computed tomography data, and (ii) the estimation error, by comparing the doses estimated with the bioWED method to "ground truth" 4D RBE-weighted doses.

RESULTS

In the phantom validation, the estimation error on the EUD was limited with respect to the motion effect and the median estimation error on relevant RBE-weighted DVH metrics remained within 5%. In the patient study, the estimation error as computed on the EUD was smaller than the corresponding motion effect, exhibiting the largest values in the baseline irregularity simulation. However, the median estimation error over all simulations was below 3.2% considering relevant DVH metrics.

CONCLUSIONS

In the evaluated cases, the bioWED method showed proper accuracy when compared to deformable image registration-based 4D dose calculation. Therefore, it can be seen as a tool to test treatment plan robustness against irregular breathing motion, although its accuracy decreases as a function of increasing soft tissue deformation and should be evaluated on a larger patient dataset.

Robust Optimization for Intensity Modulated Proton Therapy to Redistribute High Linear Energy Transfer from Nearby Critical Organs to Tumors in Head and Neck Cancer

PURPOSE

We propose linear energy transfer (LET)-guided robust optimization in intensity modulated proton therapy for head and neck cancer. This method simultaneously considers LET and physical dose distributions of tumors and organs at risk (OARs) with uncertainties.

METHODS AND MATERIALS

Fourteen patients with head and neck cancer were included in this retrospective study. Cord, brain stem, brain, and oral cavity were considered. Two algorithms, voxel-wise worst-case robust optimization and LET-guided robust optimization (LETRO), were used to generate intensity modulated proton therapy plans for each patient. The latter method directly optimized LET distributions rather than indirectly as in previous methods. LET-volume histograms (LETVHs) were generated, and high LET was redistributed from nearby OARs to tumors in a user-defined way via LET-volume constraints. Dose-volume histogram indices, such as clinical target volume (CTV) D_98% and D_2%-D_98%, cord D_max, brain stem D_max, brain D_max, and oral cavity D_mean, were calculated. Plan robustness was quantified using the worst-case analysis method. LETVH indices analogous to dose-volume histogram indices were used to characterize LET distributions. The Wilcoxon signed rank test was performed to measure statistical significance.

RESULTS

In the nominal scenario, LETRO provided higher LET distributions in the CTV (unit: keV/μm; CTV LET_98%: 1.18 vs 1.08, LETRO vs RO, P = .0031) while preserving comparable physical dose and plan robustness. LETRO achieved significantly reduced LET distributions in the cord, brain stem, and oral cavity compared with RO (cord LET_max: 7.20 vs 8.20, P = .0010; brain stem LET_max: 10.95 vs 12.05, P = .0007; oral cavity LET_mean: 2.11 vs 3.12, P = .0052) and had comparable physical dose and plan robustness in all OARs. In the worst-case scenario, LETRO achieved significantly higher LET_mean in the CTV, reduced LET_max in the brain, and was comparable to other LETVH indices (CTV LET_mean: 3.26 vs 3.35, P = .0012; brain LET_max: 24.80 vs 22.00, P = .0016).

CONCLUSIONS

LETRO robustly optimized LET and physical dose distributions simultaneously. It redistributed high LET from OARs to targets with slightly modified physical dose and plan robustness.

Hybrid 3D analytical linear energy transfer calculation algorithm based on precalculated data from Monte Carlo simulations

PURPOSE

The dose-averaged linear energy transfer (LET_d ) for intensity-modulated proton therapy (IMPT) calculated by one-dimensional (1D) analytical models deviates from more accurate but time-consuming Monte Carlo (MC) simulations. We developed a fast hybrid three-dimensional (3D) analytical LET_d calculation that is more accurate than 1D analytical model.

METHODS

We used the Geant4 MC code to generate 3D LET_d distributions of monoenergetic proton beams in water for all energies and used a customized error function to fit the LET_d lateral profiles at various depths to the MC simulation. The 3D LET_d calculation kernel was a lookup table of these fitted coefficients, and LET_d was determined directly from spot energies and voxel coordinates during analytical dose calculations. We validated our new method by comparing the calculated LET_d distributions to MC results using 3D Gamma index analysis with 3%/2 mm criteria in 12 patient geometries. The significance of the improvement in Gamma index analysis passing rates over the 1D analytical model was determined using the Wilcoxon rank-sum test.

RESULTS

The passing rate of 3D Gamma analysis comparing LET_d distributions from the hybrid 3D method and the 1D method to MC simulations was significantly improved from 94.0% ± 2.5% to 98.0% ± 1.0% (P = 0.0003). The typical time to calculate dose and LET_d simultaneously using an Intel Xeon E5-2680 2.50 GHz workstation was approximately 2.5 min.

CONCLUSIONS

Our new method significantly improved the LET_d calculation accuracy compared to the 1D method while maintaining significantly shorter calculation time even comparing with the GPU-based fast MC code.

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.

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.

Evaluation of Dosimetric Robustness of Carbon Ion Boost Therapy for Anal Carcinoma

Purpose

The radiation therapy treatment outcome of human papillomavirus-negative anal carcinoma may be improved by the biological effectiveness of carbon ions. However, abdominal tissue motion can compromise the precision of carbon ion therapy. This work aims to evaluate the dosimetric feasibility of carbon ion boost (CIB) therapy for anal carcinoma.

Materials and Methods

An algorithm to generate computed tomographies based on daily magnetic resonance imaging data and deformable image registration was developed. By means of this algorithm, fractional computed tomography data for 54 treatment fractions for 3 different patients with anal carcinoma were derived. The dose for a sequential CIB (CIB_seq) treatment plan was recalculated on the fractional computed tomography data and accumulated over the number of fractions. The resulting dose distributions were compared to standard intensity-modulated radiation therapy treatment with an integrated photon boost.

Results

For the investigated patient cases, similar dosimetric results for CIB_seq treatment and for intensity-modulated radiation therapy with an integrated photon boost were found. For CIB_seq treatment, bladder-filling variation had the strongest influence on the dose distribution. However, the detrimental effects on the mean target dose remained below 1 Gy (RBE) as compared to photon therapy.

Conclusion

This study shows the dosimetric feasibility of CIB therapy for anal carcinoma for the first time and gives reason for clinical exploitation of the enhanced biological effect of carbon ions for patients with human papillomavirus-negative anal cancer.

A stochastic framework for spot-scanning particle therapy

In spot-scanning particle therapy, inverse treatment planning is usually limited to finding the optimal beam fluences given the beam trajectories and energies. We address the much more challenging problem of jointly optimizing the beam fluences, trajectories and energies. For this purpose, we design a simulated annealing algorithm with an exploration mechanism that balances the conflicting demands of a small mixing time at high temperatures and a reasonable acceptance rate at low temperatures. Numerical experiments substantiate the relevance of our approach and open new horizons to spot-scanning particle therapy.

Worst case optimization for interfractional motion mitigation in carbon ion therapy of pancreatic cancer

INTRODUCTION

The efficacy of radiation therapy treatments for pancreatic cancer is compromised by abdominal motion which limits the spatial accuracy for dose delivery - especially for particles. In this work we investigate the potential of worst case optimization for interfractional offline motion mitigation in carbon ion treatments of pancreatic cancer.

METHODS

We implement a worst case optimization algorithm that explicitly models the relative biological effectiveness of carbon ions during inverse planning. We perform a comparative treatment planning study for seven pancreatic cancer patients. Treatment plans that have been generated using worst case optimization are compared against (1) conventional intensity-modulated carbon ion therapy, (2) single field uniform dose carbon ion therapy, and (3) an ideal yet impractical scenario relying on daily re-planning. The dosimetric quality and robustness of the resulting treatment plans is evaluated using reconstructions of the daily delivered dose distributions on fractional control CTs.

RESULTS

Idealized daily re-planning consistently gives the best dosimetric results with regard to both target coverage and organ at risk sparing. The absolute reduction of D 95 within the gross tumor volume during fractional dose reconstruction is most pronounced for conventional intensity-modulated carbon ion therapy. Single field uniform dose optimization exhibits no substantial reduction for six of seven patients and values for D 95 for worst case optimization fall in between. The treated volume (D>95 % prescription dose) outside of the gross tumor volume is reduced by a factor of two by worst case optimization compared to conventional optimization and single field uniform dose optimization. Single field uniform dose optimization comes at an increased radiation exposure of normal tissues, e.g. ≈2 Gy (RBE) in the mean dose in the kidneys compared to conventional and worst case optimization and ≈4 Gy (RBE) in D 1 in the spinal cord compared to worst case optimization.

CONCLUSION

Interfractional motion substantially deteriorates dose distributions for carbon ion treatments of pancreatic cancer patients. Single field uniform dose optimization mitigates the negative influence of motion on target coverage at an increased radiation exposure of normal tissue. Worst case optimization enables an exploration of the trade-off between robust target coverage and organ at risk sparing during inverse treatment planning beyond margin concepts.

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code

PURPOSE

The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons.

METHODS

The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LETt and dose-averaged LET, LETd) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LETt and LETd of protons with six different step limits ranging from 1 to 500 μm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose.

RESULTS

Simulation results showed that the step limit effect was small for LETt but significant for LETd. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LETd calculation results in the dose plateau region for small step limits. The erroneous LETd results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LETd values lead to substantial differences in the calculated RBE.

CONCLUSIONS

When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 μm, the authors recommend the use of LETt in the dose plateau region and LETd around the Bragg peak. For a large step limit, i.e., 500 μm, LETd is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LETd and LETt becomes positive.

Intensity modulated proton therapy

Intensity modulated proton therapy (IMPT) implies the electromagnetic spatial control of well-circumscribed "pencil beams" of protons of variable energy and intensity. Proton pencil beams take advantage of the charged-particle Bragg peak-the characteristic peak of dose at the end of range-combined with the modulation of pencil beam variables to create target-local modulations in dose that achieves the dose objectives. IMPT improves on X-ray intensity modulated beams (intensity modulated radiotherapy or volumetric modulated arc therapy) with dose modulation along the beam axis as well as lateral, in-field, dose modulation. The clinical practice of IMPT further improves the healthy tissue vs target dose differential in comparison with X-rays and thus allows increased target dose with dose reduction elsewhere. In addition, heavy-charged-particle beams allow for the modulation of biological effects, which is of active interest in combination with dose "painting" within a target. The clinical utilization of IMPT is actively pursued but technical, physical and clinical questions remain. Technical questions pertain to control processes for manipulating pencil beams from the creation of the proton beam to delivery within the patient within the accuracy requirement. Physical questions pertain to the interplay between the proton penetration and variations between planned and actual patient anatomical representation and the intrinsic uncertainty in tissue stopping powers (the measure of energy loss per unit distance). Clinical questions remain concerning the impact and management of the technical and physical questions within the context of the daily treatment delivery, the clinical benefit of IMPT and the biological response differential compared with X-rays against which clinical benefit will be judged. It is expected that IMPT will replace other modes of proton field delivery. Proton radiotherapy, since its first practice 50 years ago, always required the highest level of accuracy and pioneered volumetric treatment planning and imaging at a level of quality now standard in X-ray therapy. IMPT requires not only the highest precision tools but also the highest level of system integration of the services required to deliver high-precision radiotherapy.

Direct comparison of biologically optimized spread-out bragg peaks for protons and carbon ions

PURPOSE

In radiotherapy with hadrons, it is anticipated that carbon ions are superior to protons, mainly because of their biological properties: the relative biological effectiveness (RBE) for carbon ions is supposedly higher in the target than in the surrounding normal tissue, leading to a therapeutic advantage over protons. The purpose of this report is to investigate this effect by using biological model calculations.

METHODS AND MATERIALS

We compared spread-out Bragg peaks for protons and carbon ions by using physical and biological optimization. The RBE for protons and carbon ions was calculated according to published biological models. These models predict increased RBE values in regions of high linear energy transfer (LET) and an inverse dependency of the RBE on dose.

RESULTS

For pure physical optimization, protons yield a better dose distribution along the central axis. In biologically optimized plans, RBE variations for protons were relatively small. For carbon ions, high RBE values were found in the high-LET target region, as well as in the low-dose region outside the target. This means that the LET dependency and dose dependency of the RBE can cancel each other. We show this for radioresistant tissues treated with two opposing beams, for which the predicted carbon RBE within the target volume was lower than outside.

CONCLUSIONS

For tissue parameters used in this study, the model used does not predict a biologic advantage of carbon ions. More reliable model parameters and clinical trials are necessary to explore the true potential of radiotherapy with carbon ions.

Optimization for fast-scanning irradiation in particle therapy

In three-dimensional irradiation with pencil beam scanning, an extra dose is inevitably delivered to the irradiated site due to the finite reaction times of the beam delivery system, and it causes a severe distortion of the dose distribution in the target region. Since the amount of the extra dose is proportional to the beam intensity, the dose uniformity deteriorates as the beam intensity is increased in order to shorten the treatment time. In order to overcome this problem and shorten the treatment time, we have developed an optimization method in which the extra dose is integrated into the optimization process of the best weighting matrix. The effectiveness and applicability of the optimization method for spot and raster scanning irradiation were confirmed with computer simulations and also confirmed using irradiation experiments for spot scanning irradiation. The treatment time could be shortened to about one sixth of the time needed without taking the extra dose into account while obtaining the same degree of dose homogeneity in the target volume. A typical treatment time with the proposed method is about 15 s for the irradiation of a spherical target with an 80 mm diameter at 3 GyE.