A clinical application of fair value estimate (FVE) for R50%: Separating overlapping 50% isodose volumes in single isocenter multiple targets SRS.

In the treatment of single isocenter multiple targets (SIMT) stereotactic cranial cases with linac-based, multi-leaf collimated delivery, one encounters cases when the 50% isodose clouds (IDC50%s) of planning target volumes (PTVs) in close proximity overlap and cannot easily be separated. In such cases, it is difficult to assign an IDC50% to each individual PTV, which is necessary to allow evaluation of individual PTV intermediate dose spill for comparison to established intermediate dose spill metrics for plan quality assessment. The Fair Value Estimate (FVE) for R50% (R50%FVE ) is a method to unambiguously apportion the overlapping volume of IDC50% to allow calculation of the intermediate dose spill metric R50% (defined as volume of IDC50% / volume of PTV). Full application of R50%FVE requires knowing the surface area of the PTVs. Since surface area information is not always available, we develop a spherical PTV approximation to R50%FVE-sphere and compare this to R50%FVE . Then we apply the R50%FVE-sphere to clinical data from the University of Alabama, Birmingham (UAB) that catalogs 68 PTVs from various SIMT plans with overlapping IDC50%. The UAB dataset reports intermediate dose spill as Falloff Index. While Falloff Index looks mathematically equivalent to R50%, the Falloff Index attributes the "entire overlapping IDC50% of PTVs in close proximity" to each individual PTV in the cluster. R50%FVE-sphere provides a value that is conceptually correct and numerically smaller relative to the Falloff Index data reported by UAB in all cases. This reprocessing of the UAB data places many of the PTVs with very high intermediate dose spill within recently proposed R50% guidelines.

How to estimate R50% for cranial SRS/SRT cases with overlapping 50% isodose volumes: A proposed system.

Inevitably in clinical stereotactic cranial single isocenter multiple target cases treated with linac-based multi-leaf collimated (MLC) delivery, one encounters planning target volumes (PTVs) in close proximity with overlapping 50% isodose clouds (IDC50%). In such cases, it is very difficult to separate the IDC50% attributable to each individual target and, thus, assess the intermediate dose conformality or R50%. Such scenarios happen regardless of what metric is used to measure intermediate dose spill. Now that universal standards for intermediate dose spill have been proposed, it is important to have a consistent method for apportioning these overlapping IDC50% volumes to allow comparison with the proposed standards when multiple PTVs have overlapping IDC50%. We propose a systematic method for apportioning the IDC50% of multiple targets with overlapping IDC50% based on the relative surface area of each target volume; we call this the fair value estimate (FVE). This FVE system of apportionment is tested for reasonableness by comparing the apportionment of multiple target single isocenter stereotactic treatment with widely spaced targets where the IDC50% can be obviously assigned to demonstrate that the FVE results are very similar to the actual R50% results. We then demonstrate how the FVE system would be applied to cases with overlapping IDC50%. We propose this FVE system for consideration by the cranial stereotactic community for apportioning the intermediate dose spill when that intermediate dose spill overlaps among multiple targets.

A measure of SRS/SRT plan quality: Quantitative limits for intermediate dose spill (R50%) in linac-based delivery.

Stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) of multiple cranial targets using a single isocenter on conventional C-arm linear accelerators are rapidly developing clinical techniques. However, no universal guidelines for acceptable intermediate dose spill limits are currently available or widely accepted. In this work, we propose an intermediate dose spill guidance range for cranial SRS/SRT delivered on C-arm linacs with MLC collimation for single PTV plans and single isocenter multiple target plans with PTV volumes in the range 0.02-57.9 cm3 . We quantify intermediate dose spill with the R50% metric (R50% = volume of 50% of prescription isodose cloud / volume of PTV) and test the proposed range using three clinical data sets, containing both 6 MV and 10 MV beams, previously published by other authors. Our proposed lower limit of R50% (LowerR50%) and upper limit of acceptable R50% (UpperR50%) bound over 90% of the clinical data used in this study, yet still provide a challenging benchmark for optimization and plan assessment of linac-based, MLC collimated SRS/SRT.

Efficient optimization of R50% when planning multiple cranial metastases simultaneously in single isocenter SRS/SRT.

Simultaneous optimization of multiple Planning Target Volumes (PTVs) of varying size and location in the cranium is a non-trivial task. The rate of dose falloff around PTV structures is variable and depends on PTV characteristics such as the volume. The metric R50% is one parameter that can be used to quantify dose falloff achieved in a given treatment plan. An important treatment planning question is how to construct optimization conditions that result in the efficient production of acceptable plan outcomes considering metrics such as R50%. Guidance provided in literature suggests generating multiple shell control structures around each PTV. The constraints applied to these shells can vary significantly depending on PTV volume. Additionally, there is no clear guidance on how to prospectively determine objective constraints for the optimization shells to achieve a specified goal of R50%. Based on physical principles and empirical evidence, we provide clear quantitative guidance on how to translate the desired R50% outcome into appropriately sized optimization structures around PTVs via an equation that depends on a desired goal for R50% and the volume of PTV. Optimization schema are also provided that allow the goal R50% to be approached or achieved for all PTVs individually. We demonstrate the application of the methodology using commercially available treatment planning software and radiotherapy treatment equipment.

The surface area effect: How the intermediate dose spill depends on the PTV surface area in SRS.

PURPOSE: Stereotactic radiosurgery (SRS) is rapidly becoming the standard of care for many intracranial targets. The characteristics of the planning target volume (PTV) can affect the intermediate dose spill and thus normal brain volume dose which is correlated with brain toxicity. R50% (volume receiving 50% of prescription dose divided by PTV volume) is a useful metric to quantify the intermediate dose spill. We propose a novel understanding of how the PTV surface area (SAPTV ) affects the intermediate dose spill of SRS treatments. METHODS: Using a phantom model provided by a computed tomography (CT) of the IROC Head Phantom® and Eclipse® Treatment Planning System, we investigate the relationship of R50% and SAPTV in single-target SRS treatments. The planning studies are conducted for SRS treatments on a Varian TrueBeam® linear accelerator with high-definition MLC and a 6 MVFFF beam mode. These data are analyzed to ascertain trends in R50% related to SAPTV . Since SAPTV is not available as a structure property in the Eclipse RTPS, we introduce an Eclipse script to extract PTV surface area of arbitrary-shaped PTVs. We compare a physically reasonable theoretical prediction of R50%, R50%Analytic , to the R50% achieved in treatment planning studies. RESULTS: The SRS phantom study indicates good correlation between the plan R50% and SAPTV . A near-linear relationship of plan R50% vs SAPTV is observed as predicted by the R50%Analytic model. Agreement between plan R50% values and R50%Analytic predictions is good for all but the very smallest PTV volumes. CONCLUSIONS: We demonstrate dependence of the intermediate dose spill measured by R50% on the SAPTV . We call that dependence the surface area effect. This dependence is explicit in the R50%Analytic prediction model. The predicted value of R50%Analytic for a given PTV could be used for guidance during SRS treatment plan optimization, and plan evaluation for that PTV.

An analytical expression for R50% dependent on PTV surface area and volume: A cranial SRS comparison.

The intermediate dose spill for a stereotactic radiosurgery (SRS) plan can be quantified with the metric R50%, defined as the 50% isodose cloud volume (VIDC50% ) divided by the volume of the planning target volume (PTV). By coupling sound physical principles with the basic definition of R50%, we derive an analytical expression for R50% for a spherical PTV. Our analytical expression depends on three quantities: the surface area of PTV (SAPTV ), the volume of PTV (VPTV ), and the distance of dose drop-off to 50% (Δr). The value of ∆r was obtained from a simple set of cranial phantom plan calculations. We generate values from our analytical expression for R50% (R50%Analytic ) and compare the values to clinical R50% values (R50%Clinical ) extracted from a previously published SRS data set that spans the VPTV range from 0.15 to 50.1 cm3 . R50%Analytic is smaller than R50%Clinical in all cases by an average of 15% ± 7%, and the general trend of R50%Clinical vs VPTV is reflected in the same trend of R50%Analytic . This comparison suggests that R50%Analytic could represent a theoretical lower limit for the clinical SRS data; further investigation is required to confirm this. R50%Analytic could provide useful guidance for what might be achievable in SRS planning.

Cleaning the dose falloff in lung SBRT plan.

PURPOSE: To investigate a planning technique that can possibly reduce low-to-intermediate dose spillage (measured by R50%, D2cm values) in lung SBRT plans. MATERIALS AND METHODS: Dose falloff outside the target was studied retrospectively in 102 SBRT VMAT plans of lung tumor. Plans having R50% and/or D2cm higher than recommended tolerances in RTOG protocols 0813 and 0915 were replanned with new optimization constraints using novel shell structures and novel constraints. Violations in the RTOG R50% value can be rectified with a dose constraint to a novel shell structure ("OptiForR50"). The construction of structure OptiForR50% and the novel optimization criteria translate the RTOG goals for R50% into direct inputs for the optimizer. Violations in the D2cm can be rectified using constraints on a 0.5 cm thick shell structure with inner surface 2cm from the PTV surface. Wilcoxon signed-rank test was used to compare differences in dose conformity, volume of hot spots, R50%, D2cm of the target in addition to the OAR doses. A two-sided P-value of 0.05 was used to assess statistical significance. RESULTS: Among 102 lung SBRT plans with PTV sizes ranging from 5 to 179 cc, 32 plans with violations in R50% or D2cm were reoptimized. The mean reduction in R50% (4.68 vs 3.89) and D2cm (56.49 vs 52.51) was statistically significant both having P < 0.01. Target conformity index, volume of 105% isodose contour outside PTV, normal lung V20, and mean dose to heart and aorta were significantly lowered with P < 0.05. CONCLUSION: The novel planning methodology using multiple shells including the novel OptiForR50 shell with precisely calculated dimensions and optimizer constraints lead to significantly lower values of R50% and D2cm and lower dose spillage in lung SBRT plans. All plans were successfully brought into the zone of no RTOG violations.

An analytical expression for R50% dependent on PTV surface area and volume: a lung SBRT comparison.

In stereotactic body radiation therapy (SBRT), R50% is a common metric for intermediate dose spill and is defined in RTOG 0915 as the ratio of 50% isodose cloud volume (IDC50%) to the planning target volume (PTV). By coupling sound physical principles with the basic definition of intermediate dose spill, we derive an exact analytical expression for R50% for the case of a spherical volume. This expression for R50% depends on three quantities: the surface area of PTV (SAPTV ), the volume of PTV (VPTV ), and the dose gradient Δr. Validity of our analytical expression for R50% was confirmed via direct comparison to peer-reviewed, multi-institutional, diverse clinical data. The comparison of our R50% values computed from our analytical expression to the clinical data yielded an average percent difference of 3.8 ± 4.5%.

A physically meaningful relationship between R50% and PTV surface area in lung SBRT.

PURPOSE: We propose a novel understanding of two characteristics of the planning target volume (PTV) that affect the intermediate-dose spill in lung stereotactic body radiation therapy (SBRT) as measured by R50%. This phantom model research investigates two characteristics of the PTV that have a marked effect on the value of R50%: the mean dose deposited within the PTV (Dav ) and the surface area of the PTV (SAPTV ). METHODS: Using a phantom model provided by a CT of the IROC Thorax-Lung Phantom® (IROC Houston QA Center, Houston, TX) and Eclipse® Treatment Planning System (Varian Medical Systems, Palo Alto, CA), we investigate the two characteristics for spherical and cylindrical PTVs. A total of 135 plans with tightly controlled PTV characteristics are employed. A lower bound for R50% (R50%min∆r ) is derived and clearly establishes a relationship between R50% and SAPTV that has not been fully appreciated previously. RESULTS: The study of PTV Dav revealed a local minimum for R50% as a function of the PTV Dav at Dav  ≈ 110% of Rx dose. As PTV Dav increases above this local minimum, R50% increases; while for PTV Dav less than this local minimum, the R50% value also increases. The study of PTV surface area (SAPTV ) demonstrated that as the SAPTV increases, the R50% increases if the PTV volume stays the same. The SAPTV result is predicted by the theoretical investigation that yields the R50% lower bound, R50%min∆r . CONCLUSIONS: This research has identified two characteristics of the PTV that have a marked influence on R50%: PTV Dav and SAPTV . These characteristics have not been clearly articulated in the vast body of previous research in SBRT. These results could help explain plans that cannot meet the RTOG criteria for R50%. With further development, these concepts could be extended to provide additional guidance for creating acceptable SBRT plans.

Analysis of R50% location dependence on LINAC-based VMAT cranial stereotactic treatments.

Stereotactic radiosurgery (SRS) and stereotactic radiation therapy (SRT) techniques are used to deliver high doses per fraction to various types of intra-cranial targets. LINAC-based solutions are growing in prevalence due to recent advances in technologies such as high-definition multi-leaf collimators and volumetric arc therapy radiation delivery. A wide variety of clinical pathologies including intracranial metastases, meningioma, glioblastoma, arteriovenous malformation, acoustic neuroma, and trigeminal neuralgia have been successfully treated using SRS/SRT techniques. These lesions can be in virtually at any location within the cranium. Several publications have shown a wide dispersion of intermediate dose conformality (intermediate dose spill) indices such as the Paddick Gradient Index or R50% for lesions of a specific volume. A complete explanation of this dispersion is lacking but location has been suggested as a contributing factor. While prior studies of PTV location in SRS/SRT are retrospective in nature, we have conducted a prospective study to ascertain the potential effects of location within the cranium on plan intermediate dose conformality as measured by R50% while controlling for lesion volume, lesion shape, prescription (Rx) dose, and Rx isodose surface. Lesion volumes utilized in this study are consistent with metastatic disease presentation. Results indicate only a weak relationship between intermediate dose conformality as measured by R50% and the lesion location when considering nine different, strategically placed lesions. Close proximity to critical structures can reduce the degree of conformality, but the effect appears to be minimal. Single isocenter multiple target cases were studied in addition to single target plans. All critical structure doses observed in this study were found to be within the recommendations of AAPM Task Group report 101. Lesion location does not appear to be a significant contributing factor to the observed variation of dose conformality seen in several SRS/SRT publications.

A Dose Falloff Gradient Study in RapidArc Planning of Lung Stereotactic Body Radiation Therapy.

INTRODUCTION: Radiation Therapy Oncology Group (RTOG) report #0813 and 0915 recommends using D2cm and R50% as plan quality metrics for evaluation of normal tissue sparing in stereotactic body radiation therapy (SBRT) of lung lesion. This study introduces dose falloff gradient (DFG) as a tool for analyzing the dose beyond the planning target volume (PTV) extending into normal tissue structures. In ascertaining the impact of PTV size and SBRT planning techniques in DFG, this study questions the independence of the RTOG recommended metrics. MATERIALS AND METHODS: In this retrospective study, 41 RapidArc lung SBRT plans with 2 or 3 complete or partial arcs were analyzed. PTV volumes ranged between 5.3 and 113 cm3 and their geographic locations were distributed in both lungs. 6MV, 6 MV-FFF, 10 MV, or 10 MV-FFF energies were used. RTOG-0915 metrics conformity index, homogeneity index, D2cm, R50%, and HDloc were evaluated. DFG was computed from the mean and maximum dose in seven concentric 5 mm wide rings outside the PTV. DFG was investigated against the volume of normal lung irradiated by 50% isodose volume. Treatment plans with alternate energy and couch rotations were generated. RESULTS: The dose falloff beyond PTV was modeled using a double exponential fit and evaluated for relationship with intermediate lung dose. Photon energy and beam configuration had a minimal impact on the dose falloff outside. The product of normalized D2cm and R50% was estimated to have a slowly varying value. CONCLUSIONS: Dose falloff outside PTV has been studied as a function of radial distance and ascertained by intermediate dose to normal lung. DFG can serve as a complementary plan quality metric.

Technical Note: A planning technique to lower normal tissue toxicity in lung SBRT plans based on two likely dependent RTOG metrics.

PURPOSE: Intermediate- and low-dose falloff in stereotactic body radiotherapy (SBRT) of lung tumor is known to relate to normal tissue toxicity. The purpose is twofold to analyze the relation between RTOG parameters (namely, R50%, D2cm) in lung SBRT plans and to explore planning methods that correlate with higher than acceptable dose to normal tissue. METHODS: RTOG recommended target dose coverage, conformity index, homogeneity index, R50%, and D2cm were evaluated retrospectively in 105 lung tumor SBRT plans. Deviations in R50% and D2cm were correlated with parameters including prescription dose, tumor location, number of beams or arcs, beam configuration (coplanar or noncoplanar), type of treatment plan (3D-CRT, IMRT or volumetric arc therapy), and shortest distance to the chest wall. RESULT: All plans met the target coverage, conformity index, homogeneity index, and critical organ dose tolerance objectives. Dose falloff product (DFP) of R50% and D2cm has a small variance and small dependence on PTV. Low correlation between DFP and PTV suggests that R50% and D2cm are not independent. Coplanar beam placement was found to be prevalent among plans with large deviations in R50%, D2cm. CONCLUSION: This study questions the independence of the two RTOG recommended metrics, R50% and D2cm in lung SBRT plans, and suggests that noncoplanar beams may provide better normal tissue sparing by reducing the intermediate dose falloff.

A topographic leaf-sequencing algorithm for delivering intensity modulated radiation therapy.

Topographic treatment is a radiation therapy delivery technique for fixed-gantry (nonrotational) treatments on a helical tomotherapy system. The intensity-modulated fields are created by moving the treatment couch relative to a fan-beam positioned at fixed gantry angles. The delivered dose distribution is controlled by moving multileaf collimator (MLC) leaves into and out of the fan beam. The purpose of this work was to develop a leaf-sequencing algorithm for creating topographic MLC sequences. Topographic delivery was modeled using the analogy of a water faucet moving over a collection of bottles. The flow rate per unit length of the water from the faucet represented the photon fluence per unit length along the width of the fan beam, the collection of bottles represented the pixels in the treatment planning fluence map, and the volume of water collected in each bottle represented the delivered fluence. The radiation fluence per unit length delivered to the target at a given position is given by the convolution of the intensity distribution per unit length over the width of the beam and the time per unit distance along the direction of travel that an MLC leaf is open. The MLC opening times for the desired dose profiles were determined using a technique based on deconvolution using a genetic algorithm. The MLC opening times were expanded in terms of a Fourier series, and a genetic algorithm was used to find the best expansion coefficients for a given dose distribution. A series of wedge shapes (15, 30, 45, and 60 deg) and "dose well" test fluence maps were created to test the algorithm's ability to generate topographic leaf sequences. The accuracy of the leaf-sequencing algorithm was measured on a helical tomotherapy system using radiographic film placed at depth in water equivalent material. The measured dose profiles were compared with the desired dose distributions. The agreement was within +/- 2% or 2 mm distance-to-agreement (DTA) in the high dose gradient regions for all test cases. The central axis measured dose was between 3.6% and 4.2% higher than the expected dose for the wedge cases. For the "dose well" test cases, the calculated and measured doses agreed to within +/- 0.5% at the peak and within +/- 1.6% in the "dose well." The topographic leaf-sequencing algorithm produced deliverable dose distributions that agreed well with the calculated dose distributions. This delivery technique could be used for treatment of whole intact breast. However, additional work is needed to further improve the algorithm in order to get better agreement between the calculated, deliverable, and measured dose distributions.

Out-of-field dosimetry measurements for a helical tomotherapy system.

Helical tomotherapy is a rotational delivery technique that uses intensity-modulated fan beams to deliver highly conformal intensity-modulated radiation therapy (IMRT). The beam-on time needed to deliver a given prescribed dose can be up to 15 times longer than that needed using conventional treatment delivery. As such, there is concern that this delivery technique has the potential to increase the whole body dose due to increased leakage. The purpose of this work is to directly measure out-of-field doses for a clinical tomotherapy system. Peripheral doses were measured in-phantom using static fields and rotational intensity-modulated delivery. In-air scatter and leakage doses were also measured at multiple locations around the treatment room. At 20 cm, the tomotherapy peripheral dose dropped to 0.4% of the prescribed dose. Leakage accounted for 94% of the in-air dose at distances greater than 60 cm from the machine's isocenter. The largest measured dose equivalent rate was 1 x 10(-4) Sv/s in the plane of gantry rotation due to head leakage and primary beam transmission through the system's beam stopper. The dose equivalent rate dropped to 1 x 10(-6) Sv/s at the end of the treatment couch. Even though helical tomotherapy treatment delivery requires beam-on times that are 5 to 15 times longer than those used by conventional accelerators, the delivery system was designed to maximize shielding for radiation leakage. As such, the peripheral doses are equal to or less than the published peripheral doses for IMRT delivery on other linear accelerators. In addition, the shielding requirements are also similar to conventional linear accelerators.

Simulation of Charged Particle Trajectories in the Neutron Decay Correlation Experiment abBA.

The proposed neutron decay correlation experiment, abBA, will directly detect the direction of emission of decay protons and electrons as well as providing spectroscopic information for both particles. In order to provide this information, the abBA experiment incorporates spatially varying electric and magnetic fields. We report on detailed simulations of the decay particle trajectories in order to assess the impact of various systematic effects on the experimental observables. These include among others; adiabaticity of particle orbits, tracking of orbits, reversal of low energy protons due to inhomogeneous electric field, and accuracy of proton time of flight measurements. Several simulation methods were used including commercial software (Simion), custom software, as well as analytical tools based on the use of adiabatic invariants. Our results indicate that the proposed field geometry of the abBA spectrometer will be substantially immune to most systematic effects and that transport calculations using adiabatic invariants agree well with solution of the full equations of motion.