Validation and clinical implementation of an accurate Monte Carlo code for pencil beam scanning proton therapy.

Monte Carlo (MC)-based dose calculations are generally superior to analytical dose calculations (ADC) in modeling the dose distribution for proton pencil beam scanning (PBS) treatments. The purpose of this paper is to present a methodology for commissioning and validating an accurate MC code for PBS utilizing a parameterized source model, including an implementation of a range shifter, that can independently check the ADC in commercial treatment planning system (TPS) and fast Monte Carlo dose calculation in opensource platform (MCsquare). The source model parameters (including beam size, angular divergence and energy spread) and protons per MU were extracted and tuned at the nozzle exit by comparing Tool for Particle Simulation (TOPAS) simulations with a series of commissioning measurements using scintillation screen/CCD camera detector and ionization chambers. The range shifter was simulated as an independent object with geometric and material information. The MC calculation platform was validated through comprehensive measurements of single spots, field size factors (FSF) and three-dimensional dose distributions of spread-out Bragg peaks (SOBPs), both without and with the range shifter. Differences in field size factors and absolute output at various depths of SOBPs between measurement and simulation were within 2.2%, with and without a range shifter, indicating an accurate source model. TOPAS was also validated against anthropomorphic lung phantom measurements. Comparison of dose distributions and DVHs for representative liver and lung cases between independent MC and analytical dose calculations from a commercial TPS further highlights the limitations of the ADC in situations of highly heterogeneous geometries. The fast MC platform has been implemented within our clinical practice to provide additional independent dose validation/QA of the commercial ADC for patient plans. Using the independent MC, we can more efficiently commission ADC by reducing the amount of measured data required for low dose "halo" modeling, especially when a range shifter is employed.

A study of the beam-specific interplay effect in proton pencil beam scanning delivery in lung cancer.

BACKGROUND: For lung tumors with large motion amplitudes, the use of proton pencil beam scanning (PBS) can produce large dose errors. In this study, we assess under what circumstances PBS can be used to treat lung cancer patients who exhibit large tumor motion, based on the quantification of tumor motion and the dose interplay. MATERIAL AND METHODS: PBS plans were optimized on average 4DCT datasets using a beam-specific PTV method for 10 consecutive patients with locally advanced non-small-cell-lung-cancer (NSCLC) treated with proton therapy to 6660/180 cGy. End inhalation (CT0) and end exhalation (CT50) were selected as the two extreme scenarios to acquire the relative stopping power ratio difference (Δrsp) for a respiration cycle. The water equivalent difference (ΔWET) per radiological path was calculated from the surface of patient to the iCTV by integrating the Δrsp of each voxel. The magnitude of motion of voxels within the target follows a quasi-Gaussian distribution. A motion index (MI (>5mm WET)), defined as the percentage of target voxels with an absolute integral ΔWET larger than 5 mm, was adopted as a metric to characterize interplay. To simulate the treatment process, 4D dose was calculated by accumulating the spot dose on the corresponding respiration phase to the reference phase CT50 by deformable image registration based on spot timing and patient breathing phase. RESULTS: The study indicated that the magnitude of target underdose in a single fraction plan is proportional to the MI (p < .001), with larger motion equating to greater dose degradation and standard deviations. The target homogeneity, minimum, maximum and mean dose in the 4D dose accumulations of 37 fractions varied as a function of MI. CONCLUSIONS: This study demonstrated that MI can predict the level of dose degradation, which potentially serves as a clinical decision tool to assess whether lung cancer patients are potentially suitable to receive PBS treatment.

A benchmarking method to evaluate the accuracy of a commercial proton monte carlo pencil beam scanning treatment planning system.

AcurosPT is a Monte Carlo algorithm in the Eclipse 13.7 treatment planning system, which is designed to provide rapid and accurate dose calculations for proton therapy. Computational run-time in minimized by simplifying or eliminating less significant physics processes. In this article, the accuracy of AcurosPT was benchmarked against both measurement and an independent MC calculation, TOPAS. Such a method can be applied to any new MC calculation for the detection of potential inaccuracies. To validate multiple Coulomb scattering (MCS) which affects primary beam broadening, single spot profiles in a Solidwater® phantom were compared for beams of five selected proton energies between AcurosPT, measurement and TOPAS. The spot Gaussian sigma in AcurosPT was found to increase faster with depth than both measurement and TOPAS, suggesting that the MCS algorithm in AcurosPT overestimates the scattering effect. To validate AcurosPT modeling of the halo component beyond primary beam broadening, field size factors (FSF) were compared for multi-spot profiles measured in a water phantom. The FSF for small field sizes were found to disagree with measurement, with the disagreement increasing with depth. Conversely, TOPAS simulations of the same FSF consistently agreed with measurement to within 1.5%. The disagreement in absolute dose between AcurosPT and measurement was smaller than 2% at the mid-range depth of multi-energy beams. While AcurosPT calculates acceptable dose distributions for typical clinical beams, users are cautioned of potentially larger errors at distal depths due to overestimated MCS and halo implementation.

Evaluation of motion mitigation using abdominal compression in the clinical implementation of pencil beam scanning proton therapy of liver tumors.

PURPOSE: To determine whether individual liver tumor patients can be safely treated with pencil beam scanning proton therapy. This study reports a planning preparation workflow that can be used for beam angle selection and the evaluation of the efficacy of abdominal compression (AC) to mitigate motion. METHODS: Four-dimensional computed tomography scans (4DCT) with and without AC were available from 10 liver tumor patients with fluoroscopy-proven motion reduction by AC, previously treated using photons. For each scan, the motion amplitudes and the motion-induced variation of water-equivalent thickness (ΔWET) in each voxel of the target volume were evaluated during treatment plan preparation. Optimal proton beam angles were selected after volume analysis of the respective beam-specific planning target volume (BSPTV). M⊥80 and ΔWET80 derived from the 80th percentiles of perpendicular motion amplitude (M⊥ ) and ΔWET were compared with and without AC. Proton plans were created on the average CT to achieve target coverage similar to that of the conventional photon treatments. 4D dynamic dose calculation was performed postplan by synchronizing proton beam delivery timing patterns to the 4DCT phases to assess interplay and fractionation effects, and to determine motion criteria for subsequent patient treatment. RESULTS: Selected coplanar beam angles ranged between 180° and 39°, primarily from right lateral (oblique) and posterior (oblique) directions. While AC produced a significant reduction in mean Liver-GTV dose, any reduction in mean heart dose was patient dependent and not significant. Similarly, AC resulted in reductions in M⊥ , ΔWET, and BSPTV volumes and improved dose degradation (ΔD95 and ΔD1 ) within the CTV. For small motion (M⊥80 < 7 mm and ΔWET80 < 5 mm), motion mitigation was not needed. For moderate motion (M⊥80 7-10 mm or ΔWET80 5-7 mm), AC produced a modest improvement. For large motion (M⊥80 > 10 mm or ΔWET80 > 7 mm), AC and/or some other form of mitigation strategies were required. CONCLUSION: A workflow for screening patients' motion characteristics and optimizing beam angle selection was established for the pencil beam scanning proton therapy treatment of liver tumors. Abdominal compression was found to be useful at mitigation of moderate and large motion.

Proton computed tomography using a 1D silicon diode array.

PURPOSE: Proton radiography (PR) and proton computed tomography (PCT) can be used to measure proton stopping power directly. However, practical and cost effective proton imaging detectors are not widely available. In this study, the authors investigated the feasibility of proton imaging using a silicon diode array. METHODS: A one-dimensional silicon diode detector array (1DSDA) was aligned with the central axis (CAX) of the proton beam. Polymethyl methacrylate (PMMA) slabs were used to find the correspondence between the water equivalent thickness (WET) and 1DSDA channel number. Two-dimensional proton radiographs were obtained by translation and rotation of a phantom relative to CAX while the proton nozzle and 1DSDA were kept stationary. A PCT image of one slice of the phantom was reconstructed using filtered backprojection. RESULTS: PR and PCT images of the PMMA cube were successfully acquired using the 1DSDA. The WET of the phantom was measured using PR data. The resolution and maximum error in WET measurement are 2.0 and 1.5 mm, respectively. Structures down to 2.0 mm in size could be resolved completely. Reconstruction of a PCT image showed very good agreement with simulation. Limitations in spatial resolution are attributed to limited spatial sampling, beam collimation, and proton scatter. CONCLUSIONS: The results demonstrate the feasibility of using silicon diode arrays for proton imaging. Such a device can potentially offer fast image acquisition and high spatial and energy resolution for PR and PCT.

Beam-specific planning target volumes incorporating 4D CT for pencil beam scanning proton therapy of thoracic tumors.

The purpose of this study is to determine whether organ sparing and target coverage can be simultaneously maintained for pencil beam scanning (PBS) proton therapy treatment of thoracic tumors in the presence of motion, stopping power uncertainties, and patient setup variations. Ten consecutive patients that were previously treated with proton therapy to 66.6/1.8 Gy (RBE) using double scattering (DS) were replanned with PBS. Minimum and maximum intensity images from 4D CT were used to introduce flexible smearing in the determination of the beam specific PTV (BSPTV). Datasets from eight 4D CT phases, using ± 3% uncertainty in stopping power and ± 3 mm uncertainty in patient setup in each direction, were used to create 8 × 12 × 10 = 960 PBS plans for the evaluation of 10 patients. Plans were normalized to provide identical coverage between DS and PBS. The average lung V20, V5, and mean doses were reduced from 29.0%, 35.0%, and 16.4 Gy with DS to 24.6%, 30.6%, and 14.1 Gy with PBS, respectively. The average heart V30 and V45 were reduced from 10.4% and 7.5% in DS to 8.1% and 5.4% for PBS, respectively. Furthermore, the maximum spinal cord, esophagus, and heart doses were decreased from 37.1 Gy, 71.7 Gy, and 69.2 Gy with DS to 31.3 Gy, 67.9 Gy, and 64.6 Gy with PBS. The conformity index (CI), homogeneity index (HI), and global maximal dose were improved from 3.2, 0.08, 77.4 Gy with DS to 2.8, 0.04, and 72.1 Gy with PBS. All differences are statistically significant, with p-values <0.05, with the exception of the heart V45 (p = 0.146). PBS with BSPTV achieves better organ sparing and improves target coverage using a repainting method for the treatment of thoracic tumors. Incorporating motion-related uncertainties is essential.

Technical Note: Validation of halo modeling for proton pencil beam spot scanning using a quality assurance test pattern.

PURPOSE: The purpose of this paper is to demonstrate the utility of a comprehensive test pattern in validating calculation models that include the halo component (low-dose tails) of proton pencil beam scanning (PBS) spots. Such a pattern has been used previously for quality assurance purposes to assess spot shape, position, and dose. METHODS: In this study, a scintillation detector was used to measure the test pattern in air at isocenter for two proton beam energies (115 and 225 MeV) of two IBA universal nozzles (UN #1 and UN #2). Planar measurements were compared with calculated dose distributions based on the weighted superposition of location-independent (UN #1) or location-dependent (UN #2) spot profiles, previously measured using a pair-magnification method and between two nozzles. RESULTS: Including the halo component below 1% of the central dose is shown to improve the gamma-map comparison between calculation and measurement from 94.9% to 98.4% using 2 mm/2% criteria for the 115 MeV proton beam of UN #1. In contrast, including the halo component below 1% of the central dose does not improve the gamma agreement for the 115 MeV proton beam of UN #2, due to the cutoff of the halo component at off-axis locations. When location-dependent spot profiles are used for calculation instead of spot profiles at central axis, the gamma agreement is improved from 98.0% to 99.5% using 2 mm/2% criteria. The two nozzles clearly have different characteristics, as a direct comparison of measured data shows a passing rate of 89.7% for the 115 MeV proton beam. At 225 MeV, the corresponding gamma comparisons agree better between measurement and calculation, and between measurements in the two nozzles. CONCLUSIONS: In addition to confirming the primary component of individual PBS spot profiles, a comprehensive test pattern is useful for the validation of the halo component at off-axis locations, especially for low energy protons.

Use of a novel two-dimensional ionization chamber array for pencil beam scanning proton therapy beam quality assurance.

The need to accurately and efficiently verify both output and dose profiles creates significant challenges in quality assurance of pencil beam scanning (PBS) proton delivery. A system for PBS QA has been developed that combines a new two-dimensional ionization chamber array in a waterproof housing that is scanned in a water phantom. The MatriXX PT has the same detector array arrangement as the standard MatriXX(Evolution) but utilizes a smaller 2 mm plate spacing instead of 5mm. Because the bias voltage of the MatriXX PT and Evolution cannot be changed, PPC40 and FC65-G ionization chambers were used to assess recombination effects. The PPC40 is a parallel plate chamber with an electrode spacing of 2mm, while the FC65-G is a Farmer chamber FC65-G with an electrode spacing of 2.8 mm. Three bias voltages (500, 200, and 100 V) were used for both detectors to determine which radiation type (continuous, pulse or pulse-scanned beam) could closely estimate Pion from the ratios of charges collected. In comparison with the MatriXX(Evolution), a significant improvement in measurement of absolute dose with the MatriXX PT was observed. While dose uncertainty of the MatriXX(Evolution) can be up to 4%, it is < 1% for the MatriXX PT. Therefore the MatriXX(Evolution) should not be used for QA of PBS for conditions in which ion recombination is not negligible. Farmer chambers should be used with caution for measuring the absolute dose of PBS beams, as the uncertainty of Pion can be > 1%; chambers with an electrode spacing of 2 mm or smaller are recommended.

Experimentally validated pencil beam scanning source model in TOPAS.

The presence of a low-dose envelope, or 'halo', in the fluence profile of a proton spot can increase the output of a pencil beam scanning field by over 10%. This study evaluated whether the Monte Carlo simulation code, TOPAS 1.0-beta 8, based on Geant4.9.6 with its default physics list, can predict the spot halo at depth in phantom by incorporating a halo model within the proton source distribution. Proton sources were modelled using three 2D Gaussian functions, and optimized until simulated spot profiles matched measurements at the phantom surface out to a radius of 100 mm. Simulations were subsequently compared with profiles measured using EBT3 film in Solidwater® phantoms at various depths for 100, 115, 150, 180, 210 and 225 MeV proton beams. Simulations predict measured profiles within a 1 mm distance to agreement for 2D profiles extending to the 0.1% isodose, and within 1 mm/1% Gamma criteria over the integrated curve of spot profile as a function of radius. For isodose lines beyond 0.1% of the central spot dose, the simulated primary spot sigma is smaller than the measurement by up to 15%, and can differ by over 1 mm. The choice of particle interaction algorithm and phantom material were found to cause ~1 mm range uncertainty, a maximal 5% (0.3 mm) difference in spot sigma, and maximal 1 mm and ~2 mm distance to agreement in isodoses above and below the 0.1% level, respectively. Based on these observations, therefore, the selection of physics model and the application of Solidwater® as water replacement material in simulation and measurement should be used with caution.

Implementation of an improved dose-per-MU model for double-scattered proton beams to address interbeamline modulation width variability.

Because treatment planning systems (TPSs) generally do not provide monitor units (MUs) for double-scattered proton plans, models to predict MUs as a function of the range and the nominal modulation width requested of the beam delivery system, such as the one developed by the MGH group, have been proposed. For a given nominal modulation width, however, the measured modulation width depends on the accuracy of the vendor's calibration process and may differ from this nominal value, and also from one beamline to the next. Although such a difference can be replicated in our TPS, the output dependence on range and modulation width for each beam option or suboption has to be modeled separately for each beamline in order to achieve maximal 3% inaccuracy. As a consequence, the MGH output model may not be directly transferable. This work, therefore, serves to extend the model to more general clinic situations. In this paper, a parameterized linear-quadratic transformation is introduced to convert the nominal modulation width to the measured modulation width for each beam option or suboption on a per-beamline basis. Fit parameters are derived for each beamline from measurements of 60 reference beams spanning the minimum and maximum ranges, and modulation widths from 2 cm to full range per option or suboption. Using the modeled modulation width, we extract the MGH parameters for the output dependence on range and modulation width. Our method has been tested with 1784 patient-specific fields delivered across three different beamlines at our facility. For these fields, all measured outputs fall within 3%, and 64.4% fall within 1%, of our model. Using a parameterized linear-quadratic modulation width, MU calculation models can be established on a per-beamline basis for each double scattering beam option or suboption.

Pencil beam scanning dosimetry for large animal irradiation.

The space radiation environment imposes increased dangers of exposure to ionizing radiation, particularly during a solar particle event. These events consist primarily of low-energy protons that produce a highly inhomogeneous depth-dose distribution. Here we describe a novel technique that uses pencil beam scanning at extended source-to-surface distances and range shifter (RS) to provide robust but easily modifiable delivery of simulated solar particle event radiation to large animals. Thorough characterization of spot profiles as a function of energy, distance and RS position is critical to accurate treatment planning. At 105 MeV, the spot sigma is 234 mm at 4800 mm from the isocentre when the RS is installed at the nozzle. With the energy increased to 220 MeV, the spot sigma is 66 mm. At a distance of 1200 mm from the isocentre, the Gaussian sigma is 68 mm and 23 mm at 105 MeV and 220 MeV, respectively, when the RS is located on the nozzle. At lower energies, the spot sigma exhibits large differences as a function of distance and RS position. Scan areas of 1400 mm (superior-inferior) by 940 mm (anterior-posterior) and 580 mm by 320 mm are achieved at the extended distances of 4800 mm and 1200 mm, respectively, with dose inhomogeneity <2%. To treat large animals with a more sophisticated dose distribution, spot size can be reduced by placing the RS closer than 70 mm to the surface of the animals, producing spot sigmas below 6 mm.

Experimental characterization of two-dimensional spot profiles for two proton pencil beam scanning nozzles.

Dose calculation for pencil beam scanning proton therapy requires accurate measurement of the broad tails of the proton spot profiles for every nozzle in clinical use. By applying a pair/magnification method and merging film data, 200 mm × 240 mm dose kernels extending to 10(-4) of the central spot dose are generated for six selected energies of the IBA dedicated and universal nozzles (DN and UN). One-dimensional, circular profiles up to 100 mm in radius are generated from the asymmetric profiles to facilitate spot profile comparison. For the highest energy, 225 MeV, the output of both the DN and the UN for field sizes from 40 to 200 mm increases in parallel, slowest at the surface (∼1%) and fastest at a depth of 150 mm (∼9%). In contrast, at the lowest energy, 100 MeV, the output of the DN across the same range of field sizes increases 3-4% versus 6-7% for the UN throughout all the depths. The charge deficits in the measured depth-dose of Bragg peaks are similar between the UN and the DN. At 100 MeV, the field size factor difference at the surface between two orientations of a rectangular 40 mm × 200 mm field is 1.4% at isocentre for the DN versus 2% for the UN. Though the one-dimensional distributions are similar for the primary and tail components at different positions, the primary components of the DN spots are more elliptical 270 mm upstream than at isocentre.

Experimental characterization of two-dimensional pencil beam scanning proton spot profiles.

Dose calculations of pencil beam scanning treatment plans rely on the accuracy of proton spot profiles; not only the primary component but also the broad tail components. Four films are placed at several locations in air and multiple depths in Solidwater® for six selected energies. The films used for the primary components are exposed to 50-200 MU to avoid saturation; the films used for the tail components are exposed to 800, 8000 and 80,000 MU. By applying a pair/magnification method and merging these data, dose kernels down to 10(-4) of the central spot dose can be generated. From these kernels one can calculate the dose-per-MU for different field sizes and shapes. Measurements agree within 1% of dose-kernel-based calculations for output versus field size comparisons. Asymmetric, comet-shaped profile tails have a bigger impact at superficial depths and low energies: the output difference between two orientations at the surface of a rectangular field of 40 mm×200 mm is about 2% at the isocentre at 100 MeV. Integration of these dose kernels from 0 to 40 mm radius shows that the charge deficit in the Bragg peak chamber varies <2% from entrance to the end of range for energies <180 MeV, but exceeds 5% at 225 MeV.

A novel technique for measuring the low-dose envelope of pencil-beam scanning spot profiles.

To investigate the profile measurement capabilities of an IBA-Dosimetry scintillation detector and to assess its feasibility for determining the low-intensity tails of pencil-beam scanning spots, the responses of the scintillation detector and Gafchromic EBT2 film to a 115 MeV proton spot were measured in-air at the isocenter. Pairs of irradiations were made: one lower-level irradiation insufficient to cause saturation, and one higher-level irradiation which deliberately saturated the central region of the spot, but provided magnification of the tails. By employing the pair/magnification technique, agreement between the film and scintillation detector measurements of the spot profile can be extended from 4% of the central spot dose down to 0.01%. Gamma analysis between these measurements shows 95% and 99% agreement within a ±9 cm bound using criteria of 3 mm/3% and 5 mm/5%, respectively. Above 4%, our 115 MeV proton spot can be well-described by Gaussian function; below 4%, non-Gaussian, diamond-shaped tails predominate.

Optimization of the modelling of longitudinal dose distributions for double-scattered proton beams in a commercially-available treatment planning system.

The configuration of a treatment planning system (TPS) for double-scattering-based proton therapy requires many user inputs. Most of these are either gathered during the routine collection of commissioning data, or can be supplied by the equipment vendor; however, this is not true of all. In this study we developed a technique both to (a) expedite the extraction of those undetermined TPS parameters related to the range modulator wheels that can only otherwise be obtained by the time-consuming process of trial-and-error, and (b) demonstrate how, for a commonly-employed, commercially-available TPS, the judicious determination of such parameters can be used to optimize the resultant modelling of longitudinal dose distributions delivered by a double scattering proton therapy system. Our technique is simple to implement, robust in nature and also provides insight allowing parameters that must be contrived in that model to be related directly to physical aspects of the beam delivery system.

Fiducial markers in prostate for kV imaging: quantification of visibility and optimization of imaging conditions.

The purpose of this work is to investigate possible smaller, less-dense fiducial markers implantable into the prostate for target localization and patient repositioning verification in an on-board kV-kV imaging system on a proton gantry. The experiments used a pelvic phantom and a variety of commercially available fiducial markers: CIVCO carbon marker of ϕ; 1 × 3 mm, gold seed markers of ϕ; 0.8 × 3 mm and ϕ; 1.2 × 3 mm, and IBA Visicoil helical gold linear markers in diameters of 0.35, 0.50, 0.75 and 1.15 mm. Two orthogonal on-board kV imagers were arranged for digital radiographic imaging of the phantom through the lateral and anterior-posterior directions. The contrast-to-noise ratio (CNR) for a given marker was calculated and used as a quantitative measure of its visibility. The patient entrance skin exposure (ESE) was measured and parameterized for kVp, mAs and source-to-surface distance. The ratio of CNR to ESE was first introduced to characterize the efficiency for imaging a marker using a given x-ray technique in order to optimize the marker's visibility and simultaneously minimize the x-ray imaging dose. If CNR > 2, which corresponds to a significance p < 0.05, is required for acceptable visibility, the carbon marker and the smallest Visicoil marker are not suitable for imaging through dense bone but the others are capable of being employed in the clinic. It is predicted that other markers in development should have a greater thickness than equivalent of 0.14 mm thick gold in order to produce the acceptable visibility in the lateral kV imaging. The linear Visicoil marker of ϕ; 0.50 × 5 mm is most suitable for kV imaging in the prostate for proton therapy as it induces the least proton dose perturbation amongst the acceptable markers. An optimal range of 120-130 kVp and 40-80 mAs is determined using the maximal CNR/ESE and CNR > 2 for laterally imaging this marker in the prostate.

Comparison of secondary neutron dose in proton therapy resulting from the use of a tungsten alloy MLC or a brass collimator system.

PURPOSE: To apply the dual ionization chamber method for mixed radiation fields to an accurate comparison of the secondary neutron dose arising from the use of a tungsten alloy multileaf collimator (MLC) as opposed to a brass collimator system for defining the shape of a therapeutic proton field. METHODS: Hydrogenous and nonhydrogenous ionization chambers were constructed with large volumes to enable measurements of absorbed doses below 10(-4) Gy in mixed radiation fields using the dual ionization chamber method for mixed-field dosimetry. Neutron dose measurements were made with a nominal 230 MeV proton beam incident on a closed tungsten alloy MLC and a solid brass block. The chambers were cross-calibrated against a (60)Co-calibrated Farmer chamber in water using a 6 MV x-ray beam and Monte Carlo simulations were performed to account for variations in ionization chamber response due to differences in secondary neutron energy spectra. RESULTS: The neutron and combined proton plus γ-ray absorbed doses are shown to be nearly equivalent downstream from either a closed tungsten alloy MLC or a solid brass block. At 10 cm downstream from the distal edge of the collimating material the neutron dose from the closed MLC was (5.3 ± 0.4) × 10(- 5) Gy/Gy. The neutron dose with brass was (6.4 ± 0.7) × 10(- 5) Gy/Gy. Further from the secondary neutron source, at 50 cm, the neutron doses remain close for both the MLC and brass block at (6.9 ± 0.6) × 10(- 6) Gy/Gy and (6.3 ± 0.7) × 10(- 6) Gy/Gy, respectively. CONCLUSIONS: The dual ionization chamber method is suitable for measuring secondary neutron doses resulting from proton irradiation. The results of measurements downstream from a closed tungsten alloy MLC and a brass block indicate that, even in an overly pessimistic worst-case scenario, secondary neutron production in a tungsten alloy MLC leads to absorbed doses that are nearly equivalent to those seen from brass collimators. Therefore, the choice of tungsten alloy in constructing the leaves of a proton MLC is appropriate, and does not lead to a substantial increase in the secondary neutron dose to the patient compared to that generated in a brass collimator.

Coordination-mode control of bound nitrile radical complex reactivity: intercepting end-on nitrile-Mo(III) radicals at low temperature.

Variable temperature equilibrium studies were used to derive thermodynamic data for formation of eta(1) nitrile complexes with Mo(N[(t)Bu]Ar)(3), 1. (1-AdamantylCN = AdCN: DeltaH(degrees) = -6 +/- 2 kcal mol(-1), DeltaS(degrees) = -20 +/- 7 cal mol(-1) K(-1). C(6)H(5)CN = PhCN: DeltaH(degrees) = -14.5 +/- 1.5 kcal mol(-1), DeltaS(degrees) = -40 +/- 5 cal mol(-1) K(-1). 2,4,6-(H(3)C)(3)C(6)H(2)CN = MesCN: DeltaH(degrees) = -15.4 +/- 1.5 kcal mol(-1), DeltaS(degrees) = -52 +/- 5 cal mol(-1) K(-1).) Solution calorimetric studies show that the enthalpy of formation of 1-[eta(2)-NCNMe(2)] is more exothermic (DeltaH(degrees) = -22.0 +/- 1.0 kcal mol(-1)). Rate and activation parameters for eta(1) binding of nitriles were measured by stopped flow kinetic studies (AdCN: DeltaH(on)(++) = 5 +/- 1 kcal mol(-1), DeltaS(on)(++) = -28 +/- 5 cal mol(-1) K(-1); PhCN: DeltaH(on)(++) = 5.2 +/- 0.2 kcal mol(-1), DeltaS(on)(++) = -24 +/- 1 cal mol(-1) K(-1); MesCN: DeltaH(on)(++) = 5.0 +/- 0.3 kcal mol(-1), DeltaS(on)(++) = -26 +/- 1 cal mol(-1) K(-1)). Binding of Me(2)NCN was observed to proceed by reversible formation of an intermediate complex 1-[eta(1)-NCNMe(2)] which subsequently forms 1-[eta(2)-NCNMe(2)]: DeltaH(++)(k1) = 6.4 +/- 0.4 kcal mol(-1), DeltaS(++)(k1) = -18 +/- 2 cal mol(-1) K(-1), and DeltaH(++)(k2) = 11.1 +/- 0.2 kcal mol(-1), DeltaS(++)(k2) = -7.5 +/- 0.8 cal mol(-1) K(-1). The oxidative addition of PhSSPh to 1-[eta(1)-NCPh] is a rapid second-order process with activation parameters: DeltaH(++) = 6.7 +/- 0.6 kcal mol(-1), DeltaS(++) = -27 +/- 4 cal mol(-1) K(-1). The oxidative addition of PhSSPh to 1-[eta(2)-NCNMe(2)] also followed a second-order rate law but was much slower: DeltaH(++) = 12.2 +/- 1.5 kcal mol(-1) and DeltaS(++) = -25.4 +/- 5.0 cal mol(-1) K(-1). The crystal structure of 1-[eta(1)-NC(SPh)NMe(2)] is reported. Trapping of in situ generated 1-[eta(1)-NCNMe(2)] by PhSSPh was successful at low temperatures (-80 to -40 degrees C) as studied by stopped flow methods. If 1-[eta(1)-NCNMe(2)] is not intercepted before isomerization to 1-[eta(2)-NCNMe(2)] no oxidative addition occurs at low temperatures. The structures of key intermediates have been studied by density functional theory, confirming partial radical character of the carbon atom in eta(1)-bound nitriles. A complete reaction profile for reversible ligand binding, eta(1) to eta(2) isomerization, and oxidative addition of PhSSPh has been assembled and gives a clear picture of ligand reactivity as a function of hapticity in this system.

Thermodynamic, kinetic, and computational study of heavier chalcogen (S, Se, and Te) terminal multiple bonds to molybdenum, carbon, and phosphorus.

Enthalpies of chalcogen atom transfer to Mo(N[t-Bu]Ar)3, where Ar = 3,5-C6H3Me2, and to IPr (defined as bis-(2,6-isopropylphenyl)imidazol-2-ylidene) have been measured by solution calorimetry leading to bond energy estimates (kcal/mol) for EMo(N[t-Bu]Ar)3 (E = S, 115; Se, 87; Te, 64) and EIPr (E = S, 102; Se, 77; Te, 53). The enthalpy of S-atom transfer to PMo(N[ t-Bu]Ar) 3 generating SPMo(N[t-Bu]Ar)3 has been measured, yielding a value of only 78 kcal/mol. The kinetics of combination of Mo(N[t-Bu]Ar)3 with SMo(N[t-Bu]Ar)3 yielding (mu-S)[Mo(N[t-Bu]Ar)3]2 have been studied, and yield activation parameters Delta H (double dagger) = 4.7 +/- 1 kcal/mol and Delta S (double dagger) = -33 +/- 5 eu. Equilibrium studies for the same reaction yielded thermochemical parameters Delta H degrees = -18.6 +/- 3.2 kcal/mol and Delta S degrees = -56.2 +/- 10.5 eu. The large negative entropy of formation of (mu-S)[Mo(N[t-Bu]Ar)3]2 is interpreted in terms of the crowded molecular structure of this complex as revealed by X-ray crystallography. The crystal structure of Te-atom transfer agent TePCy3 is also reported. Quantum chemical calculations were used to make bond energy predictions as well as to probe terminal chalcogen bonding in terms of an energy partitioning analysis.

Synthesis, structure, and thermochemistry of the formation of the metal-metal bonded dimers [Mo(mu-TeAr)(CO)3(PiP3)]2 (Ar = phenyl, naphthyl) by phosphine elimination from *Mo(TePh)(CO)3(PiPr3)2.

The complexes (*TeAr)Mo(CO)3(PiPr3)2 (Ar = phenyl, naphthyl; iPr = isopropyl) slowly eliminate PiPr3 at room temperature in a toluene solution to quantitatively form the dinuclear complexes [Mo(mu-TeAr)(CO)3(PiPr3)]2. The crystal structure of [Mo(mu-Te-naphthyl)(CO)3(PiPr3)]2 is reported and has a Mo-Mo distance of 3.2130 A. The enthalpy of dimerization has been measured and is used to estimate a Mo-Mo bond strength on the order of 30 kcal mol-1. Kinetic studies show the rate of formation of the dimeric chalcogen bridged complex is best fit by a rate law first order in (*TeAr)Mo(CO)3(PiPr3)2 and inhibited by added PiPr3. The reaction is proposed to occur by initial dissociation of a phosphine ligand and not by radical recombination of 2 mol of (*TeAr)Mo(CO)3(PiPr3)2. Reaction of (*TePh)Mo(CO)3(PiPr3)2, with L = pyridine (py) or CO, is rapid and quantitative at room temperature to form PhTeTePh and Mo(L)(CO)3(PiPr3)2, in keeping with thermochemical predictions. The rate of reaction of (*TeAr)W(CO)3(PiPr3)2 and CO is first-order in the metal complex and is proposed to proceed by the associative formation of the 19 e- radical complex (*TePh)W(CO)4(PiPr3)2 which extrudes a *TePh radical.