Spatiotemporal optimisation of prostate intensity modulated proton therapy (IMPT) treatments.

Objective.In intensity modulated particle therapy (IMPT), the adoption of spatially and temporally heterogeneous dose distributions allows to decouple the fractionation scheme from the patient anatomy, so that an hypofractionated schedule can be selectively created inside the tumour, while simultaneously exploiting the fractionation effect in the healthy tissues. In this paper, the authors show the reproducibility of the method on a set of prostate patients, quantifying the dependencies of the achievable benefit with respect to conventional and hypofractionated schemes and the sensitivity of the method to setup errors and range uncertainty.Approach.On a cohort of 9 patients, non-uniform IMPT plans were optimised and compared to conventional and hypofractionated schedules. For each patient, the comparison of the three strategies has been based on the output of the cost function used to optimise the treatments. The analysis has been repeated considering differentα/ßratios for the tumour, namely 1.5, 3 and 4.5 Gy. For a single patient, setup errors and beam range uncertainty have been analysed: the plans, for each optimisation strategy, have been iteratively forward planned 500 times with randomly varying the patient position in each fraction, and 200 times for systematic range shift.Main results.An average 10% benefit has been shown for the lowestα/ßratio considered for the tumour, where the non-uniform schedule generally converges to hypofractionation; the benefit decreases to 5%-7% for higherα/ßratios, for which the non-uniform schedule always showed better outcomes with respect to the other fractionation schedules. An increased sensitivity to uncertainty, especially for setup errors, has been shown, which can be associated to the spatial non-uniformity of the dose distributions peculiar of the spatiotemporal plans.Significance.This work represents the first investigation of spatiotemporal fractionation for prostate cancer and the beginning of further investigations before clinical implementation can be considered.

Conic formulation of fluence map optimization problems.

The convexity of objectives and constraints in fluence map optimization (FMO) for radiation therapy has been extensively studied. Next to convexity, there is another important characteristic of optimization functions and problems, which has thus far not been considered in FMO literature: conic representation. Optimization problems that are conically representable using quadratic, exponential and power cones are solvable with advanced primal-dual interior-point algorithms. These algorithms guarantee an optimal solution in polynomial time and have good performance in practice. In this paper, we construct conic representations for most FMO objectives and constraints. This paper is the first that shows that FMO problems containing multiple biological evaluation criteria can be solved in polynomial time. For fractionation-corrected functions for which no exact conic reformulation is found, we provide an accurate approximation that is conically representable. We present numerical results on the TROTS data set, which demonstrate very stable numerical performance for solving FMO problems in conic form. With ongoing research in the optimization community, improvements in speed can be expected, which makes conic optimization a promising alternative for solving FMO problems.

Optimal treatment plan adaptation using mid-treatment imaging biomarkers.

Previous studies on personalized radiotherapy (RT) have mostly focused on baseline patient stratification, adapting the treatment plan according to mid-treatment anatomical changes, or dose boosting to selected tumor subregions using mid-treatment radiological findings. However, the question of how to find the optimal adapted plan has not been properly tackled. Moreover, the effect of information uncertainty on the resulting adaptation has not been explored. In this paper, we present a framework to optimally adapt radiation therapy treatments to early radiation treatment response estimates derived from pre- and mid-treatment imaging data while considering the information uncertainty. The framework is based on the optimal stopping in radiation therapy (OSRT) framework. Biological response is quantified using tumor control probability (TCP) and normal tissue complication probability (NTCP) models, and these are directly optimized for in the adaptation step. Two adaptation strategies are discussed: (1) uniform dose adaptation and (2) continuous dose adaptation. In the first strategy, the original fluence-map is simply scaled upwards or downwards, depending on whether dose escalation or de-escalation is deemed appropriate based on the mid-treatment response observed from the radiological images. In the second strategy, a full NTCP-TCP-based fluence map re-optimization is performed to achieve the optimal adapted plans. We retrospectively tested the performance of these strategies on 14 canine head and neck cases treated with tomotherapy, using as response biomarker the change in the 3'-deoxy-3'[(18)F]-fluorothymidine (FLT)-PET signals between the pre- and mid-treatment images, and accounting for information uncertainty. Using a 10% uncertainty level, the two adaptation strategies both yield a noteworthy average improvement in guaranteed (worst-case) TCP.

Compact Method for Proton Range Verification Based on Coaxial Prompt Gamma-Ray Monitoring: a Theoretical Study.

Range uncertainties in proton therapy hamper treatment precision. Prompt gamma-rays were suggested 16 years ago for real-time range verification, and have already shown promising results in clinical studies with collimated cameras. Simultaneously, alternative imaging concepts without collimation are investigated to reduce the footprint and price of current prototypes. In this manuscript, a compact range verification method is presented. It monitors prompt gamma-rays with a single scintillation detector positioned coaxially to the beam and behind the patient. Thanks to the solid angle effect, proton range deviations can be derived from changes in the number of gamma-rays detected per proton, provided that the number of incident protons is well known. A theoretical background is formulated and the requirements for a future proof-of-principle experiment are identified. The potential benefits and disadvantages of the method are discussed, and the prospects and potential obstacles for its use during patient treatments are assessed. The final milestone is to monitor proton range differences in clinical cases with a statistical precision of 1 mm, a material cost of 25000 USD and a weight below 10 kg. This technique could facilitate the widespread application of in vivo range verification in proton therapy and eventually the improvement of treatment quality.

Optimal combined proton-photon therapy schemes based on the standard BED model.

This paper investigates the potential of combined proton-photon therapy schemes in radiation oncology, with a special emphasis on fractionation. Several combined modality models, with and without fractionation, are discussed, and conditions under which combined modality treatments are of added value are demonstrated analytically and numerically. The combined modality optimal fractionation problem with multiple normal tissues is formulated based on the biologically effective dose (BED) model and tested on real patient data. Results indicate that for several patients a combined modality treatment gives better results in terms of biological dose (up to [Formula: see text] improvement) than single modality proton treatments. For several other patients, a combined modality treatment is found that offers an alternative to the optimal single modality proton treatment, being only marginally worse but using significantly fewer proton fractions, putting less pressure on the limited availability of proton slots. Overall, these results indicate that combined modality treatments can be a viable option, which is expected to become more important as proton therapy centers are spreading but the proton therapy price tag remains high.

Automation and uncertainty analysis of a method for in-vivo range verification in particle therapy.

We introduce the automation of the range difference calculation deduced from particle-irradiation induced ß(+)-activity distributions with the so-called most-likely-shift approach, and evaluate its reliability via the monitoring of algorithm- and patient-specific uncertainty factors. The calculation of the range deviation is based on the minimization of the absolute profile differences in the distal part of two activity depth profiles shifted against each other. Depending on the workflow of positron emission tomography (PET)-based range verification, the two profiles under evaluation can correspond to measured and simulated distributions, or only measured data from different treatment sessions. In comparison to previous work, the proposed approach includes an automated identification of the distal region of interest for each pair of PET depth profiles and under consideration of the planned dose distribution, resulting in the optimal shift distance. Moreover, it introduces an estimate of uncertainty associated to the identified shift, which is then used as weighting factor to 'red flag' problematic large range differences. Furthermore, additional patient-specific uncertainty factors are calculated using available computed tomography (CT) data to support the range analysis. The performance of the new method for in-vivo treatment verification in the clinical routine is investigated with in-room PET images for proton therapy as well as with offline PET images for proton and carbon ion therapy. The comparison between measured PET activity distributions and predictions obtained by Monte Carlo simulations or measurements from previous treatment fractions is performed. For this purpose, a total of 15 patient datasets were analyzed, which were acquired at Massachusetts General Hospital and Heidelberg Ion-Beam Therapy Center with in-room PET and offline PET/CT scanners, respectively. Calculated range differences between the compared activity distributions are reported in a 2D map in beam-eye-view. In comparison to previously proposed approaches, the new most-likely-shift method shows more robust results for assessing in-vivo the range from strongly varying PET distributions caused by differing patient geometry, ion beam species, beam delivery techniques, PET imaging concepts and counting statistics. The additional visualization of the uncertainties and the dedicated weighting strategy contribute to the understanding of the reliability of observed range differences and the complexity in the prediction of activity distributions. The proposed method promises to offer a feasible technique for clinical routine of PET-based range verification.

TPS(PET)-A TPS-based approach for in vivo dose verification with PET in proton therapy.

Since the interest in ion-irradiation for tumour therapy has significantly increased over the last few decades, intensive investigations are performed to improve the accuracy of this form of patient treatment. One major goal is the development of methods for in vivo dose verification. In proton therapy, a PET (positron emission tomography)-based approach measuring the irradiation-induced tissue activation inside the patient has been already clinically implemented. The acquired PET images can be compared to an expectation, derived under the assumption of a correct treatment application, to validate the particle range and the lateral field position in vivo. In the context of this work, TPSPET is introduced as a new approach to predict proton-irradiation induced three-dimensional positron emitter distributions by means of the same algorithms of the clinical treatment planning system (TPS). In order to perform additional activity calculations, reaction-channel-dependent input positron emitter depth distributions are necessary, which are determined from the application of a modified filtering approach to the TPS reference depth dose profiles in water. This paper presents the implementation of TPSPET on the basis of the research treatment planning software treatment planning for particles. The results are validated in phantom and patient studies against Monte Carlo simulations, and compared to ß(+)-emitter distributions obtained from a slightly modified version of the originally proposed one-dimensional filtering approach applied to three-dimensional dose distributions. In contrast to previously introduced methods, TPSPET provides a faster implementation, the results show no sensitivity to lateral field extension and the predicted ß(+)-emitter densities are fully consistent to the planned treatment dose as they are calculated by the same pencil beam algorithms. These findings suggest a large potential of the application of TPSPET for in vivo dose verification in the daily clinical routine.

The rationale for intensity-modulated proton therapy in geometrically challenging cases.

Intensity-modulated proton therapy (IMPT) delivered with beam scanning is currently available at a limited number of proton centers. However, a simplified form of IMPT, the technique of field 'patching', has long been a standard practice in proton therapy centers. In field patching, different parts of the target volume are treated from different directions, i.e., a part of the tumor gets either full dose from a radiation field, or almost no dose. Thus, patching represents a form of binary intensity modulation. This study explores the limitations of the standard binary field patching technique, and evaluates possible dosimetric advantages of continuous dose modulations in IMPT. Specifics of the beam delivery technology, i.e., pencil beam scanning versus passive scattering and modulation, are not investigated. We have identified two geometries of target volumes and organs at risk (OAR) in which the use of field patching is severely challenged. We focused our investigations on two patient cases that exhibit these geometries: a paraspinal tumor case and a skull-base case. For those cases we performed treatment planning comparisons of three-dimensional conformal proton therapy (3DCPT) with field patching versus IMPT, using commercial and in-house software, respectively. We also analyzed the robustness of the resulting plans with respect to systematic setup errors of ±1 mm and range errors of ±2.5 mm. IMPT is able to better spare OAR while providing superior dose coverage for the challenging cases identified above. Both 3DCPT and IMPT are sensitive to setup errors and range uncertainties, with IMPT showing the largest effect. Nevertheless, when delivery uncertainties are taken into account IMPT plans remain superior regarding target coverage and OAR sparing. On the other hand, some clinical goals, such as the maximum dose to OAR, are more likely to be unmet with IMPT under large range errors. IMPT can potentially improve target coverage and OAR sparing in challenging cases, even when compared with the relatively complicated and time consuming field patching technique. While IMPT plans tend to be more sensitive to delivery uncertainties, their dosimetric advantage generally holds. Robust treatment planning techniques may further reduce the sensitivity of IMPT plans.

SU-E-T-615: Quantifying the Benefit of Adaptive Fractionation.

PURPOSE: To quantify the benefit of adaptive fractionation, through both theoretical test cases and patient data. METHODS: We consider the effect of delivering a different fraction size based on the changes observed in the patient anatomy. Given that a fixed prescription dose must be delivered to the tumor over the course of the treatment, we find that adaptively varying the fraction size results in a lower cumulative dose to a primary organ-at-risk (OAR). We construct a one dimensional theoretical example by randomly varying the distance between the tumor and OAR, and simulate the benefit of adaptive fractionation in such a setting. Next, we test our methodology using contoured daily CT images from 5 prostate patients. RESULTS: For the theoretical example, we found about a 10% decrease in dose to the OAR when using a uniformly distributed motion model and a 20% daily fraction size deviation. In general, the amount of decrease in dose to the OAR varied significantly (5-85%) for these theoretical test cases depending on the amount of motion in the anatomy, the number of fractions, and the range of fraction sizes allowed. Preliminary results from the prostate patients indicate an average reduction in dose to the rectum of 1.4%, 3.5%, and 7.0% when using 20%, 50%, and 100% daily fraction size deviations, respectively. CONCLUSIONS: Qualitatively, the theoretical example indicates that adaptive fractionation is beneficial for disease sites in which there is significant inter-fractional motion. We also expect greater benefit when using many fractions and allowing for large daily fraction size deviations. For the prostate disease site in particular, we find that adaptive fractionation is beneficial only when allowing large daily fraction size deviations. Further research quantifying the gain for disease sites that exhibit significant inter-fractional motion, such as rectal and cervical cancers, would be useful. Partially supported by Siemens.

MO-A-213AB-07: Evaluation of Distal Dose Surface with In-Room PET for Proton Therapy Monitoring.

PURPOSE: The objective of this study is to evaluate the feasibility of proton beam treatment verification using in-room PET. As of February 2012, four patients have been studied in a clinical trial. In addition, we suggest a new method comparing the distal surface of the measured and simulated PET activities to verify the location of the distal dose surface. METHODS: Patients were scanned for 20 minutes with an in-room PET positioned next to the proton treatment head in a gantry room for beam delivery using passive scattering. The time between end of treatment and the start of the scan was within about 2 minutes. The predicted distribution of the PET activities and the proton dose distributions in the patients were also calculated using Monte Carlo (MC). Along the beam direction, the 50% fall-off positions of the maximum PET activity at each line profile were compared with the MC simulated and the measured PET images, and then the differences were assessed with root-mean-square deviation (RMSD) and mapped in the beam's eye view. RESULTS: The measured PET images showed a good spatial correlation with the simulated PET images and the proton dose distributions even though the treated volumes and locations varied between patients. The RMSD values, representing the surface differences between the measured and simulated PET, were assessed to be 4.3-5.1 mm for four patients. Some region including the penumbra showed larger differences but was excluded. CONCLUSIONS: We have explored the potential of the in-room PET for proton therapy monitoring through a clinical trial. The PET image analysis method based on MC simulations showed that the distal dose surface could be determined within a few millimeters but not within the aimed accuracy of 2-3 mm. Improvements in PET-CT image registration and biological washout modeling will most likely increase the accuracy further. NIH/NCI P01 CA021239.

4D planning over the full course of fractionation: assessment of the benefit of tumor trailing.

Tumor trailing techniques have been proposed as a method of reducing the problem of intrafraction motion in radiotherapy. However the dosimetric assessment of trailing strategies is complicated by the requirement to study dose deposition over a full fraction delivery. Common 4D planning strategies allowing assessment of dosimetric motion effects study a single cycle acquired with 4DCT. In this paper, a methodology to assess dose deposited over an entire treatment course is advanced and used to assess the potential benefit of tumor trailing strategies for lung cancer patients. Two digital phantoms mimicking patient anatomy were each programmed to follow the tumor respiratory trajectory observed from 33 lung cancer patients. The two phantoms were designed to represent the cases of a small (volume = 13.6 cm3) and large (volume = 181.7 cm3) lung lesion. Motion margins required to obtain CTV coverage by 95% of the prescription dose to 90% of the available cases were computed for a standard treatment strategy and a trailing treatment strategy. The trailing strategy facilitated a margin reduction of over 30% relative to the conventional delivery. When the dose was computed across the entire delivery for the 33 cases, the trailing strategy was found to significantly reduce the underdosage to the outlier cases and the reduced trailing margin facilitated a 15% (small lesion) and 4% (large lesion) reduction for the mean lung dose and 7% (small lesion) and 10% (large lesion) for the mean esophagus dose. Finally, for comparison an ideal continuous tracking strategy was assessed and found to further reduce the mean lung and esophagus dose. However, this improvement comes at the price of increased delivery complexity and increased reliance on tumor localization accuracy.

Extension and validation of an analytical model for in vivo PET verification of proton therapy--a phantom and clinical study.

The interest in positron emission tomography (PET) as a tool for treatment verification in proton therapy has become widespread in recent years, and several research groups worldwide are currently investigating the clinical implementation. After the first off-line investigation with a PET/CT scanner at MGH (Boston, USA), attention is now focused on an in-room PET application immediately after treatment in order to also detect shorter-lived isotopes, such as O15 and N13, minimizing isotope washout and avoiding patient repositioning errors. Clinical trials are being conducted by means of commercially available PET systems, and other tests are planned using application-dedicated tomographs. Parallel to the experimental investigation and new hardware development, great interest has been shown in the development of fast procedures to provide feedback regarding the delivered dose from reconstructed PET images. Since the thresholds of inelastic nuclear reactions leading to tissue ß+ -activation fall within the energy range of 15-20 MeV, the distal activity fall-off is correlated, but not directly matched, to the distal fall-off of the dose distribution. Moreover, the physical interactions leading to ß+ -activation and energy deposition are of a different nature. All these facts make it essential to further develop accurate and fast methodologies capable of predicting, on the basis of the planned dose distribution, expected PET images to be compared with actual PET measurements, thus providing clinical feedback on the correctness of the dose delivery and of the irradiation field position. The aim of this study has been to validate an analytical model and to implement and evaluate it in a fast and flexible framework able to locally predict such activity distributions directly taking the reference planning CT and planned dose as inputs. The results achieved in this study for phantoms and clinical cases highlighted the potential of the implemented method to predict expected activity distributions with great accuracy. Thus, the analytical model can be used as a powerful substitute method to the sensitive and time-consuming Monte Carlo approach.

The physical basis and future of radiation therapy.

The remarkable progress in radiation therapy over the last century has been largely due to our ability to more effectively focus and deliver radiation to the tumour target volume. Physics discoveries and technology inventions have been an important driving force behind this progress. However, there is still plenty of room left for future improvements through physics, for example image guidance and four-dimensional motion management and particle therapy, as well as increased efficiency of more compact and cheaper technologies. Bigger challenges lie ahead of physicists in radiation therapy beyond the dose localisation problem, for example in the areas of biological target definition, improved modelling for normal tissues and tumours, advanced multicriteria and robust optimisation, and continuous incorporation of advanced technologies such as molecular imaging. The success of physics in radiation therapy has been based on the continued "fuelling" of the field with new discoveries and inventions from physics research. A key to the success has been the application of the rigorous scientific method. In spite of the importance of physics research for radiation therapy, too few physicists are currently involved in cutting-edge research. The increased emphasis on more "professionalism" in medical physics will tip the situation even more off balance. To prevent this from happening, we argue that medical physics needs more research positions, and more and better academic programmes. Only with more emphasis on medical physics research will the future of radiation therapy and other physics-related medical specialties look as bright as the past, and medical physics will maintain a status as one of the most exciting fields of applied physics.

The reliability of proton-nuclear interaction cross-section data to predict proton-induced PET images in proton therapy.

In vivo PET range verification relies on the comparison of measured and simulated activity distributions. The accuracy of the simulated distribution depends on the accuracy of the Monte Carlo code, which is in turn dependent on the accuracy of the available cross-section data for ß(+) isotope production. We have explored different cross-section data available in the literature for the main reaction channels ((16)O(p,pn)(15)O, (12)C(p,pn)(11)C and (16)O(p,3p3n)(11)C) contributing to the production of ß(+) isotopes by proton beams in patients. Available experimental and theoretical values were implemented in the simulation and compared with measured PET images obtained with a high-resolution PET scanner. Each reaction channel was studied independently. A phantom with three different materials was built, two of them with high carbon or oxygen concentration and a third one with average soft tissue composition. Monoenergetic and SOBP field irradiations of the phantom were accomplished and measured PET images were compared with simulation results. Different cross-section values for the tissue-equivalent material lead to range differences below 1 mm when a 5 min scan time was employed and close to 5 mm differences for a 30 min scan time with 15 min delay between irradiation and scan (a typical off-line protocol). The results presented here emphasize the need of more accurate measurement of the cross-section values of the reaction channels contributing to the production of PET isotopes by proton beams before this in vivo range verification method can achieve mm accuracy.

Systematic analysis of biological and physical limitations of proton beam range verification with offline PET/CT scans.

The clinical use of offline positron emission tomography/computed tomography (PET/CT) scans for proton range verification is currently under investigation at the Massachusetts General Hospital (MGH). Validation is achieved by comparing measured activity distributions, acquired in patients after receiving one fraction of proton irradiation, with corresponding Monte Carlo (MC) simulated distributions. Deviations between measured and simulated activity distributions can either reflect errors during the treatment chain from planning to delivery or they can be caused by various inherent challenges of the offline PET/CT verification method. We performed a systematic analysis to assess the impact of the following aspects on the feasibility and accuracy of the offline PET/CT method: (1) biological washout processes, (2) patient motion, (3) Hounsfield unit (HU) based tissue classification for the simulation of the activity distributions and (4) tumor site specific aspects. It was found that the spatial reproducibility of the measured activity distributions is within 1 mm. However, the feasibility of range verification is restricted to a limited amount of positions and tumor sites. Washout effects introduce discrepancies between the measured and simulated ranges of about 4 mm at positions where the proton beam stops in soft tissue. Motion causes spatial deviations of up to 3 cm between measured and simulated activity distributions in abdominopelvic tumor cases. In these later cases, the MC simulated activity distributions were found to be limited to about 35% accuracy in absolute values and about 2 mm in spatial accuracy depending on the correlativity of HU into the physical and biological parameters of the irradiated tissue. Besides, for further specific tumor locations, the beam arrangement, the limited accuracy of rigid co-registration and organ movements can prevent the success of PET/CT range verification. All the addressed factors explain why the proton beam range can only be verified within an accuracy of 1-2 mm in low-perfused bony structures of head and neck patients for which an accurate co-registration of predominant bony anatomy is possible, as shown previously. However, most of the limitations of the current approach are conquerable. By implementing technological and methodological improvements like the use of in-room PET scanners, PET measurements could soon be used to provide proton range verification in clinical routine.

A new way of adapting IMRT delivery fraction-by-fraction to cater for variable intrafraction motion.

In this paper a technique is presented for adaptive therapy to compensate for variable intrafraction tissue motion. So long as the motion can be measured or deduced for each fraction the technique modifies the fluence profile for the subsequent fractions in a repeatable cyclic way. The fluence modification is based on projecting the dose discrepancies between the cumulative delivered dose after each fraction and the expected planned dose at the same stage. It was shown that, in general, it is best to adapt the fluence profile to moving leaves that also have been modified to 'breathe' according to some regular default motion. However, it is important to point out that, if this regular default motion were to differ too much from the variable motion at each fraction, then the result can be worse than adapting to non-breathing leaves in a dynamic MLC technique. Furthermore, in general it should always be possible to improve results by starting the adaptation process with a constrained deconvolution of the regular default motion.

Quantitative assessment of the physical potential of proton beam range verification with PET/CT.

A recent clinical pilot study demonstrated the feasibility of offline PET/CT range verification for proton therapy treatments. In vivo PET measurements are challenged by blood perfusion, variations of tissue compositions, patient motion and image co-registration uncertainties. Besides these biological and treatment specific factors, the accuracy of the method is constrained by the underlying physical processes. This phantom study distinguishes physical factors from other factors, assessing the reproducibility, consistency and sensitivity of the PET/CT range verification method. A spread-out Bragg-peak (SOBP) proton field was delivered to a phantom consisting of poly-methyl methacrylate (PMMA), lung and bone equivalent material slabs. PET data were acquired in listmode at a commercial PET/CT scanner available within 10 min walking distance from the proton therapy unit. The measured PET activity distributions were compared to simulations of the PET signal based on Geant4 and FLUKA Monte Carlo (MC) codes. To test the reproducibility of the measured PET signal, data from two independent measurements at the same geometrical position in the phantom were compared. Furthermore, activation depth profiles within identical material arrangements but at different positions within the irradiation field were compared to test the consistency of the measured PET signal. Finally, activation depth profiles through air/lung, air/bone and lung/bone interfaces parallel as well as at 6 degrees to the beam direction were studied to investigate the sensitivity of the PET/CT range verification method. The reproducibility and the consistency of the measured PET signal were found to be of the same order of magnitude. They determine the physical accuracy of the PET measurement to be about 1 mm. However, range discrepancies up to 2.6 mm between two measurements and range variations up to 2.6 mm within one measurement were found at the beam edge and at the edge of the field of view (FOV) of the PET scanner. PET/CT range verification was found to be able to detect small range modifications in the presence of complex tissue inhomogeneities. This study indicates the physical potential of the PET/CT verification method to detect the full-range characteristic of the delivered dose in the patient.

Pareto navigation: algorithmic foundation of interactive multi-criteria IMRT planning.

Inherently, IMRT treatment planning involves compromising between different planning goals. Multi-criteria IMRT planning directly addresses this compromising and thus makes it more systematic. Usually, several plans are computed from which the planner selects the most promising following a certain procedure. Applying Pareto navigation for this selection step simultaneously increases the variety of planning options and eases the identification of the most promising plan. Pareto navigation is an interactive multi-criteria optimization method that consists of the two navigation mechanisms 'selection' and 'restriction'. The former allows the formulation of wishes whereas the latter allows the exclusion of unwanted plans. They are realized as optimization problems on the so-called plan bundle -- a set constructed from pre-computed plans. They can be approximately reformulated so that their solution time is a small fraction of a second. Thus, the user can be provided with immediate feedback regarding his or her decisions. Pareto navigation was implemented in the MIRA navigator software and allows real-time manipulation of the current plan and the set of considered plans. The changes are triggered by simple mouse operations on the so-called navigation star and lead to real-time updates of the navigation star and the dose visualizations. Since any Pareto-optimal plan in the plan bundle can be found with just a few navigation operations the MIRA navigator allows a fast and directed plan determination. Besides, the concept allows for a refinement of the plan bundle, thus offering a middle course between single plan computation and multi-criteria optimization. Pareto navigation offers so far unmatched real-time interactions, ease of use and plan variety, setting it apart from the multi-criteria IMRT planning methods proposed so far.

Effects of organ motion on IMRT treatments with segments of few monitor units.

Interplay between organ (breathing) motion and leaf motion has been shown in the literature to have a small dosimetric impact for clinical conditions (over a 30 fraction treatment). However, previous studies did not consider the case of treatment beams made up of many few-monitor-unit (MU) segments, where the segment delivery time (1-2 s) is of the order of the breathing period (3-5 s). In this study we assess if breathing compromises the radiotherapy treatment with IMRT segments of low number of MUs. We assess (i) how delivered dose varies, from patient to patient, with the number of MU per segment, (ii) if this delivered dose is identical to the average dose calculated without motion over the path of the motion, and (iii) the impact of the daily variation of the delivered dose as a function of MU per segment. The organ motion was studied along two orthogonal directions, representing the left-right and cranial-caudal directions of organ movement for a patient setup in the supine position. Breathing motion was modeled as sin(x), sin4(x), and sin6(x), based on functions used in the literature to represent organ motion. Measurements were performed with an ionization chamber and films. For a systematic study of motion effects, a MATLAB simulation was written to model organ movement and dose delivery. In the case of a single beam made up of one single segment, the dose delivered to point in a moving target over 30 fractions can vary up to 20% and 10% for segments of 10 MU and 20 MU, respectively. This dose error occurs because the tumor spends most of the time near the edges of the radiation beam. In the case of a single beam made of multiple segments with low MU, we observed 2.4%, 3.3%, and 4.3% differences, respectively, for sin(x), sin4(x), and sin6(x) motion, between delivered dose and motion-averaged dose for points in the penumbra region of the beam and over 30 fractions. In approximately 5-10% of the cases, differences between the motion-averaged dose and the delivered 30-fraction dose could reach 6%, 8% and 10-12%, respectively for sin(x), sin4(x), and sin6(x) motion. To analyze a clinical IMRT beam, two patient plans were randomly selected. For one of the patients, the beams showed a likelihood of up to 25.6% that the delivered dose would deviate from the motion-averaged dose by more than 1%. For the second patient, there was a likelihood of up to 62.8% of delivering a dose that differs by more than 1% from the motion-averaged dose and a likelihood of up to approximately 30% for a 2% dose error. For the entire five-beam IMRT plan, statistical averaging over the beams reduces the overall dose error between the delivered dose and the motion-averaged dose. For both patients there was a likelihood of up to 7.0% and 33.9% that the dose error was greater than 1%, respectively. For one of the patients, there was a 12.6% likelihood of a 2% dose error. Daily intrafraction variation of the delivered dose of more than 10% is non-negligible and can potentially lead to biological effects. We observed [for sin(x), sin4(x), and sin6(x)] that below 10-15 MU leads to large daily variations of the order of 15-35%. Therefore, for small MU segments, non-negligible biological effects can be incurred. We conclude that for most clinical cases the effects may be small because of the use of many beams, it is desirable to avoid low-MU segments when treating moving targets. In addition, dose averaging may not work well for hypo-fractionation, where fewer fractions are used. For hypo-fractionation, PDF modeling of the tumor motion in IMRT optimization may not be adequate.