Rotational integral geometry of tensor valuations

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.

Clinical Impact of Couch Top and Rails on IMRT and Arc Therapy

Purpose: To evaluate the clinical impact of the Varian Exact Couch on dose and volume coverage to targets and critical structures and tumor control probability (TCP) for 6-MV IMRT and Arc Therapy. Methods: Five clinical prostate patients were planned with both, 6-MV 8-field IMRT and 6-MV 2-field RapidArc using the Eclipse treatment planning system (TPS). These plans neglected treatment couch attenuation, as is standard clinical practice. Dose distributions were then recalculated in Eclipse with the inclusion of the Varian Exact Couch (imaging couch top) and the rails in varying configurations. The changes in dose and coverage were evaluated using the DVHs from each plan iteration. We used a tumor control probability (TCP) model to calculate losses in tumor control resulting from not accounting for the couch top and rails. We also verified dose measurements in a phantom. Results: Failure to account for the treatment couch and rails resulted in clinically unacceptable dose and volume coverage losses to the target for both IMRT and RapidArc. The couch caused average dose losses (relative to plans that ignored the couch) to the prostate of 4.2% and 2.0% for IMRT with the rails out and in, respectively, and 3.2% and 2.9% for RapidArc with the rails out and in, respectively. On average, the percentage of the target covered by the prescribed dose dropped to 35% and 84% for IMRT (rails out and in, respectively) and to 18% and 17% for RapidArc (rails out and in, respectively). The TCP was also reduced by as much as 10.5% (6.3% on average). Dose and volume coverage losses for IMRT plans were primarily due to the rails, while the imaging couch top contributed most to losses for RapidArc. Both the couch top and rails contribute to dose and coverage losses that can render plans clinically unacceptable. A follow-up study we performed found that the less attenuating unipanel mesh couch top available with the Varian Exact couch does not cause a clinically impactful loss of dose or coverage for IMRT but still causes an unacceptable loss for RapidArc. Conclusions: Both the imaging couch top and rails contribute to dose and coverage loss to a degree that, if included, would prevent the plan from meeting clinical planning criteria. Therefore, the imaging and mesh couch tops and rails should be accounted for in Arc Therapy and the imaging couch and rails only in IMRT treatment planning.

The effect of shoulder variation on IMRT and SmartArc for Head and Neck Cancer

Purpose: First, to determine an average and maximum displacement of the shoulder relative to isocenter over the course of treatment. Second, to establish the dosimetric effect of shoulder displacements relative to correct isocenter alignment on the dose delivered to the target and the surrounding structures for head and neck cancer patients. Method and Materials: The frequency of shoulder shifts of various magnitudes relative to isocenter was assessed for 4 patients using image registration software. The location of the center of the right and left humeral head relative to isocenter (usually C2) was found daily from CT on rails scans, and was compared to the location of the humeral heads relative to isocenter on the initial simulation CT. Three Baseline head and neck IMRT and SmartArc plans were generated in Pinnacle based on simulation CTs. The CT datasets (external contour and boney structures) were then modified to represent shifts of the shoulder (relative to isocenter) between 3 mm and 15 mm in the SI, AP, and LR directions. The initial plans were recalculated on the image sets with shifted shoulders. Results: On average, shoulder variation was 2-5 mm in each direction, although displacements of over 1 cm in the inferior and posterior directions occurred. Shoulder shifts induced perturbations in the dose distribution, although generally only for large shifts. Most substantially, large, superior shifts resulted in coverage loss by the 95% isodose line for targets in the lower neck. Inferior shifts elevated the dose to the brachial plexus by 0.6-4.1 Gy. SmartArc plans showed similar loss of target coverage as IMRT plans. Conclusions: The position of the shoulder can have an impact on target coverage and critical structure dose. Shoulder position may need to be considered for setup of head and neck patients depending on target location.

EVALUATION OF INTENSITY MODULATED RADIATION THERAPY (IMRT) DELIVERY ERROR DUE TO IMRT TREATMENT PLAN COMPLEXITY AND IMPROPERLY MATCHED DOSIMETRY DATA

Intensity modulated radiation therapy (IMRT) is a technique that delivers a highly conformal dose distribution to a target volume while attempting to maximally spare the surrounding normal tissues. IMRT is a common treatment modality used for treating head and neck (H&N) cancers, and the presence of many critical structures in this region requires accurate treatment delivery. The Radiological Physics Center (RPC) acts as both a remote and on-site quality assurance agency that credentials institutions participating in clinical trials. To date, about 30% of all IMRT participants have failed the RPC’s remote audit using the IMRT H&N phantom. The purpose of this project is to evaluate possible causes of H&N IMRT delivery errors observed by the RPC, specifically IMRT treatment plan complexity and the use of improper dosimetry data from machines that were thought to be matched but in reality were not. Eight H&N IMRT plans with a range of complexity defined by total MU (1460-3466), number of segments (54-225), and modulation complexity scores (MCS) (0.181-0.609) were created in Pinnacle v.8m. These plans were delivered to the RPC’s H&N phantom on a single Varian Clinac. One of the IMRT plans (1851 MU, 88 segments, and MCS=0.469) was equivalent to the median H&N plan from 130 previous RPC H&N phantom irradiations. This average IMRT plan was also delivered on four matched Varian Clinac machines and the dose distribution calculated using a different 6MV beam model. Radiochromic film and TLD within the phantom were used to analyze the dose profiles and absolute doses, respectively. The measured and calculated were compared to evaluate the dosimetric accuracy. All deliveries met the RPC acceptance criteria of ±7% absolute dose difference and 4 mm distance-to-agreement (DTA). Additionally, gamma index analysis was performed for all deliveries using a ±7%/4mm and ±5%/3mm criteria. Increasing the treatment plan complexity by varying the MU, number of segments, or varying the MCS resulted in no clear trend toward an increase in dosimetric error determined by the absolute dose difference, DTA, or gamma index. Varying the delivery machines as well as the beam model (use of a Clinac 6EX 6MV beam model vs. Clinac 21EX 6MV model), also did not show any clear trend towards an increased dosimetric error using the same criteria indicated above.

High-speed rotational atherectomy before paclitaxel-eluting stent implantation in complex calcified coronary lesions: the randomized ROTAXUS (Rotational Atherectomy Prior to Taxus Stent Treatment for Complex Native Coronary Artery Disease) trial

OBJECTIVES This study sought to determine the effect of rotational atherectomy (RA) on drug-eluting stent (DES) effectiveness. BACKGROUND DES are frequently used in complex lesions, including calcified stenoses, which may challenge DES delivery, expansion, and effectiveness. RA can adequately modify calcified plaques and facilitate stent delivery and expansion. Its impact on DES effectiveness is widely unknown. METHODS The ROTAXUS (Rotational Atherectomy Prior to TAXUS Stent Treatment for Complex Native Coronary Artery Disease) study randomly assigned 240 patients with complex calcified native coronary lesions to RA followed by stenting (n = 120) or stenting without RA (n = 120, standard therapy group). Stenting was performed using a polymer-based slow-release paclitaxel-eluting stent. The primary endpoint was in-stent late lumen loss at 9 months. Secondary endpoints included angiographic and strategy success, binary restenosis, definite stent thrombosis, and major adverse cardiac events at 9 months. RESULTS Despite similar baseline characteristics, significantly more patients in the standard therapy group were crossed over (12.5% vs. 4.2%, p = 0.02), resulting in higher strategy success in the rotablation group (92.5% vs. 83.3%, p = 0.03). At 9 months, in-stent late lumen loss was higher in the rotablation group (0.44 ± 0.58 vs. 0.31 ± 0.52, p = 0.04), despite an initially higher acute lumen gain (1.56 ± 0.43 vs. 1.44 ± 0.49 mm, p = 0.01). In-stent binary restenosis (11.4% vs. 10.6%, p = 0.71), target lesion revascularization (11.7% vs. 12.5%, p = 0.84), definite stent thrombosis (0.8% vs. 0%, p = 1.0), and major adverse cardiac events (24.2% vs. 28.3%, p = 0.46) were similar in both groups. CONCLUSIONS Routine lesion preparation using RA did not reduce late lumen loss of DES at 9 months. Balloon dilation with only provisional rotablation remains the default strategy for complex calcified lesions before DES implantation.

Novel radiotherapy techniques for involved-field and involved-node treatment of mediastinal Hodgkin lymphoma: when should they be considered and which questions remain open?

PURPOSE Hodgkin lymphoma (HL) is a highly curable disease. Reducing late complications and second malignancies has become increasingly important. Radiotherapy target paradigms are currently changing and radiotherapy techniques are evolving rapidly. DESIGN This overview reports to what extent target volume reduction in involved-node (IN) and advanced radiotherapy techniques, such as intensity-modulated radiotherapy (IMRT) and proton therapy-compared with involved-field (IF) and 3D radiotherapy (3D-RT)- can reduce high doses to organs at risk (OAR) and examines the issues that still remain open. RESULTS Although no comparison of all available techniques on identical patient datasets exists, clear patterns emerge. Advanced dose-calculation algorithms (e.g., convolution-superposition/Monte Carlo) should be used in mediastinal HL. INRT consistently reduces treated volumes when compared with IFRT with the exact amount depending on the INRT definition. The number of patients that might significantly benefit from highly conformal techniques such as IMRT over 3D-RT regarding high-dose exposure to organs at risk (OAR) is smaller with INRT. The impact of larger volumes treated with low doses in advanced techniques is unclear. The type of IMRT used (static/rotational) is of minor importance. All advanced photon techniques result in similar potential benefits and disadvantages, therefore only the degree-of-modulation should be chosen based on individual treatment goals. Treatment in deep inspiration breath hold is being evaluated. Protons theoretically provide both excellent high-dose conformality and reduced integral dose. CONCLUSION Further reduction of treated volumes most effectively reduces OAR dose, most likely without disadvantages if the excellent control rates achieved currently are maintained. For both IFRT and INRT, the benefits of advanced radiotherapy techniques depend on the individual patient/target geometry. Their use should therefore be decided case by case with comparative treatment planning.

IMRT credentialing for prospective trials using institutional virtual phantoms: results of a joint European Organization for the Research and Treatment of Cancer and Radiological Physics Center project.

BACKGROUND AND PURPOSE Intensity-modulated radiotherapy (IMRT) credentialing for a EORTC study was performed using an anthropomorphic head phantom from the Radiological Physics Center (RPC; RPC(PH)). Institutions were retrospectively requested to irradiate their institutional phantom (INST(PH)) using the same treatment plan in the framework of a Virtual Phantom Project (VPP) for IMRT credentialing. MATERIALS AND METHODS CT data set of the institutional phantom and measured 2D dose matrices were requested from centers and sent to a dedicated secure EORTC uploader. Data from the RPC(PH) and INST(PH) were thereafter centrally analyzed and inter-compared by the QA team using commercially available software (RIT; ver.5.2; Colorado Springs, USA). RESULTS Eighteen institutions participated to the VPP. The measurements of 6 (33%) institutions could not be analyzed centrally. All other centers passed both the VPP and the RPC ±7%/4 mm credentialing criteria. At the 5%/5 mm gamma criteria (90% of pixels passing), 11(92%) as compared to 12 (100%) centers pass the credentialing process with RPC(PH) and INST(PH) (p = 0.29), respectively. The corresponding pass rate for the 3%/3 mm gamma criteria (90% of pixels passing) was 2 (17%) and 9 (75%; p = 0.01), respectively. CONCLUSIONS IMRT dosimetry gamma evaluations in a single plane for a H&N prospective trial using the INST(PH) measurements showed agreement at the gamma index criteria of ±5%/5 mm (90% of pixels passing) for a small number of VPP measurements. Using more stringent, criteria, the RPC(PH) and INST(PH) comparison showed disagreement. More data is warranted and urgently required within the framework of prospective studies.

IMRT with ¹⁸FDG-PET\CT based simultaneous integrated boost for treatment of nodal positive cervical cancer

BACKGROUND To evaluate toxicity and outcome of intensity modulated radiotherapy (IMRT) with simultaneous integrated boost (SIB) to the positive lymph nodes in patients with loco-regional advanced cervical cancer (LRACC). METHODS The study population comprised ten patients with 18FDG-PET\CT positive lymph nodes (LNs), who underwent chemoradiation with IMRT and SIB. A dose of 50.4 Gy, in daily fractions of 1.8 Gy, was delivered to primary tumor and draining LNs. Primary tumor received an additional external beam boost to a total dose of 55.8 Gy. A SIB of 62 Gy, in daily fractions of 2 Gy, was delivered to the 18FDG-PET\CT positive LNs. Finally, a high dose rate brachytherapy (HDRB) boost (15 - 18 Gy) was administered to the primary tumor. The primary goal of this study was to evaluate acute and early late toxicity and loco-regional control. RESULTS The median number of irradiated LNs per patient was 3 (range: 1-6) with a median middle nodal SIB-volume of 26.10 cm3 (range, 11.9-82.50 cm3). Median follow-up was 20 months (range, 12 to 30 months). Acute and late grade 3 toxicity was observed in 1 patient. Three of the patients developed a recurrence, one in the form of a local tumor relapse, one had a paraaortic LN metastasis outside the treated volume and the last one developed a distant metastasis. CONCLUSION IMRT with SIB in the region of 18FDG-PET positive lymph nodes appears to be an effective therapy with acceptable toxicity and might be useful in the treatment of patients with locally advanced cervical cancer.

Accurate rotational constant and bond lengths of hexafluorobenzene by femtosecond rotational Raman coherence spectroscopy and ab initio calculations

The gas-phase rotational motion of hexafluorobenzene has been measured in real time using femtosecond (fs) time-resolved rotational Raman coherence spectroscopy (RR-RCS) at T = 100 and 295 K. This four-wave mixing method allows to probe the rotation of non-polar gas-phase molecules with fs time resolution over times up to ∼5 ns. The ground state rotational constant of hexafluorobenzene is determined as B 0 = 1029.740(28) MHz (2σ uncertainty) from RR-RCS transients measured in a pulsed seeded supersonic jet, where essentially only the v = 0 state is populated. Using this B 0 value, RR-RCS measurements in a room temperature gas cell give the rotational constants B v of the five lowest-lying thermally populated vibrationally excited states ν7/8, ν9, ν11/12, ν13, and ν14/15. Their B v constants differ from B 0 by between −1.02 MHz and +2.23 MHz. Combining the B 0 with the results of all-electron coupled-cluster CCSD(T) calculations of Demaison et al. [Mol. Phys.111, 1539 (2013)] and of our own allow to determine the C-C and C-F semi-experimental equilibrium bond lengths r e(C-C) = 1.3866(3) Å and r e(C-F) = 1.3244(4) Å. These agree with the CCSD(T)/wCVQZ r e bond lengths calculated by Demaison et al. within ±0.0005 Å. We also calculate the semi-experimental thermally averaged bond lengths r g(C-C)=1.3907(3) Å and r g(C-F)=1.3250(4) Å. These are at least ten times more accurate than two sets of experimental gas-phase electron diffraction r g bond lengths measured in the 1960s.

Understanding measured water rotational temperatures and column densities in the very innermost coma of Comet 73P/Schwassmann–Wachmann 3 B

Direct sublimation of a comet nucleus surface is usually considered to be the main source of gas in the coma of a comet. However, evidence from a number of comets including the recent spectacular images of Comet 103P/Hartley 2 by the EPOXI mission indicates that the nucleus alone may not be responsible for all, or possibly at times even most, of the total amount of gas seen in the coma. Indeed, the sublimation of icy grains, which have been injected into the coma, appears to constitute an important source. We use the fully-kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J., 685, 659−677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J., 732) to reproduce the measurements of column density and rotational temperature of water in Comet 73P-B/Schwassmann–Wachmann 3 obtained with a very high spatial resolution of ∼30 km using IRCS/Subaru in May 2006 (Bonev, B.P., Mumma, M.J., Kawakita, H., Kobayashi, H., Villanueva, G.L. [2008]. Icarus, 196, 241−248). For gas released solely from the cometary nucleus at a heliocentric distance of 1 AU, modeled rotational temperatures start at 110 K close to the surface and decrease to only several tens of degrees by 10–20 nucleus radii. However, the measured decay of both rotational temperature and column density with distance from the nucleus is much slower than predicted by this simple model. The addition of a substantial (distributed) source of gas from icy grains in the model slows the decay in rotational temperature and provides a more gradual drop in column density profiles. Together with a contribution of rotational heating of water molecules by electrons, the combined effects allow a much better match to the IRCS/Subaru observations. From the spatial distributions of water abundance and temperature measured in 73P/SW3-B, we have identified and quantified multiple mechanisms of release. The application of this tool to other comets may permit such studies over a range of heliocentric and geocentric distances.

Probing the Structure, Pseudorotation, and Radial Vibrations of Cyclopentane by Femtosecond Rotational Raman Coherence Spectroscopy

Femtosecond time-resolved Raman rotational coherence spectroscopy (RCS) is employed to determine accurate rotational, vibration–rotation coupling constants, and centrifugal distortion constants of cyclopentane (C⁵H¹⁰). Its lowest-frequency vibration is a pseudorotating ring deformation that interconverts 10 permutationally distinct but energetically degenerate “twist” minima interspersed by 10 “bent” conformers. While the individual twist and bent structures are polar asymmetric tops, the pseudorotation is fast on the time scale of external rotation, rendering cyclopentane a fluxionally nonpolar symmetric top molecule. The pseudorotational level pattern corresponds to a one-dimensional internal rotor with a pseudorotation constant Bps ≈ 2.8 cm⁻¹. The pseudorotational levels are significantly populated up to l = ± 13 at 298 K; <10% of the molecules are in the l = 0 level. The next-higher vibration is the “radial” ν²³ ring deformation mode at 273 cm⁻¹, which is far above the pseudorotational fundamental. Femtosecond Raman RCS measurements were performed in a gas cell at T = 293 K and in a pulsed supersonic jet at T ≈ 90 K. The jet cooling reduces the pseudorotational distribution to l < ±8 and eliminates the population of ν²³, allowing one to determine the rotational constant as A0 = B0 = 6484.930(11) MHz. This value is ∼300 times more precise than the previous value. The fit of the RCS transients reveals that the rotation–pseudorotation coupling constant αe,psB = −0.00070(1) MHz is diminutive, implying that excitation of the pseudorotation has virtually no effect on the B0 rotational constant of cyclopentane. The smallness of αe,psB can be realized when comparing to the vibration–rotation coupling constant of the ν²³ vibration, αe,23B = −9.547(1) MHz, which is about 10⁴ times larger.