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SU-E-J-170: Dosimetric Consequences of Uncorrected Rotational Setup Errors During Stereotactic Body Radiation Therapy (SBRT) Treatment of Pancreatic Cancers

Purpose: To explore the dosimetric consequences of uncorrected rotational setup errors during SBRT for pancreatic cancer patients. Methods: This was a retrospective study utilizing data from ten (n=10) previously treated SBRT pancreas patients. For each original planning CT, we applied rotational transformations to derive additional CT images representative of possible rotational setup errors. This resulted in 6 different sets of rotational combinations, creating a total of 60 CT planning images. The patients’ clinical dosimetric plans were then applied to their corresponding rotated CT images. The 6 rotation sets encompassed a 3, 2 and 1-degree rotation in each rotational direction and a 3-degree in just the pitch, a 3-degree in just the yaw and a 3-degree in just the roll. After the dosimetric plan was applied to the rotated CT images, the resulting plan was then evaluated and compared with the clinical plan for tumor coverage and normal tissue sparing. Results: PTV coverage, defined here by V33 throughout all of the patients’ clinical plans, ranged from 92–98%. After an n degree rotation in each rotational direction that range decreased to 68–87%, 85–92%, and 88– 94% for n=3, 2 and 1 respectively. Normal tissue sparing defined here by the proximal stomach V15 throughout all of the patients’ clinical plans ranged from 0–8.9 cc. After an n degree rotation in each rotational direction that range increased to 0–17 cc, 0–12 cc, and 0–10 cc for n=3, 2, and 1 respectively. Conclusion: For pancreatic SBRT, small rotational setup errors in the pitch, yaw and roll direction on average caused under dosage to PTV and over dosage to proximal normal tissue. The 1-degree rotation was on average the least detrimental to the normal tissue and the coverage of the PTV. The 3-degree yaw created on average the lowest increase in volume coverage to normal tissue. This research was sponsored by the AAPM Education Council through the AAPM Education and Research Fund for the AAPM Summer Undergraduate Fellowship Program.

60 APPLIED LIFE SCIENCES↗

On the Behavior of Velocity Fluctuations in Rapidly Rotating Flows

The behavior of velocity fluctuations subjected to rapid rotation is examined. The rapid rotation considered is any arbitrary combination of two basic forms of rotation, reference frame rotation and mean flow rotation. It is recognized that the two types of rotating flows differ in the manner in which the fluctuating fields are advected. The first category is comprised of flows in rotating systems of which synoptic scale geophysical flows are a good example. In this class of flows the fluctuating velocity field advects and rotates with the mean flow. In the rapid rotation limit, the Taylor-Proudman theorem describes the behavior of this class of fluctuations. Velocity fluctuations that are advected without rotation by the mean flow constitute the second category which includes vortical flows of aerodynamic interest. The Taylor-Proudman theorem is not pertinent to I his class flows and a new result appropriate to this second category of fluctuations is derived. The present development demonstrates that the fluctuating velocity fields are rendered two-dimensional and horizontally non-divergent in the limit of any large combination of reference frame rotation and mean-flow rotation. The concommitant 'geostrophic' balance of the momentum equation is, however, dependent upon the form of rapid rotation. It is also demonstrated that the evolution equations of a two-dimensional fluctuating velocity fields are frame-indifferent with any imposed mean-flow rotation. The analyses and results of this paper highlight many fundamental aspects of rotating flows and have important consequences for their turbulence closures in inertial and non-inertial frames.

Girimaji, S. S.↗

A CATALOG OF ROTATION AND ACTIVITY IN EARLY-M STARS

We present a catalog of rotation and chromospheric activity in a sample of 334 M dwarfs of spectral types M0-M4.5 populating the parameter space around the boundary to full convection. We obtain high-resolution optical spectra for 206 targets and determine projected rotational velocity, vsin i, and H{alpha} emission. The data are combined with measurements of vsin i in field stars of the same spectral type from the literature. Our sample adds 157 new rotation measurements to the existing literature and almost doubles the sample of available vsin i. The final sample provides a statistically meaningful picture of rotation and activity at the transition to full convection in the solar neighborhood. We confirm a steep rise in the fraction of active stars at the transition to full convection known from earlier work. In addition, we see a clear rise in rotational velocity in the same stars. In very few stars, no chromospheric activity but a detection of rotational broadening is reported. We argue that all of them are probably spurious detections; we conclude that in our sample all significantly rotating stars are active, and all active stars are significantly rotating. The rotation-activity relation is valid in partially and in fully convective stars. Thus, we do not observe any evidence for a transition from a rotationally dominated dynamo in partially convective stars to a rotation-independent turbulent dynamo in fully convective stars; turbulent dynamos in fully convective stars of spectral types around M4 are still driven by rotation. Finally, we compare projected rotational velocities of 33 stars to rotational periods derived from photometry in the literature and determine inclinations for a few of them.

79 ASTRONOMY AND ASTROPHYSICS↗

Rotation of solar magnetic fields for the current solar cycle 24

The rotation of solar magnetic fields for the current solar cycle 24 is investigated through a cross-correlation analysis of the Carrington synoptic maps of solar photospheric magnetic fields during Carrington rotation numbers 2076-2146 (2008 October to 2014 January). The sidereal rotation rates of positive and negative magnetic fields at some latitudes are shown, and it can be found that the positive (negative) fields generally rotate faster than the negative (positive) fields in the southern (northern) hemisphere at low latitudes. The mean rotation profiles of total, positive, and negative magnetic fields between ±60° latitudes in the time interval are also obtained. It should be noted that both of the mean rotation profiles of the positive and negative magnetic fields, as well as the mean rotation profile of the total magnetic field, exhibit a quasi-rigid rotation at latitudes above about 55°. The mean rotation rates of the positive (negative) polarity reach their maximum values at about 9°(6)° latitude in the southern (northern) hemisphere. The mean rotation profile of the total magnetic field displays an obvious north-south asymmetry, where the rotation seems to be more differential in the northern hemisphere. The latitude variation in the rotation rate differences between positive and negative magnetic fields is further studied, and it is found that magnetic fields with the same polarity as the leading sunspots at a given hemisphere rotate faster than those with the opposite polarity, except for the zones around 52° latitude of the southern hemisphere and around 35° latitude of the northern hemisphere. The implication of these results is discussed. It is clear that the obtained results can provide some observational constraints on the theoretical research of the mechanisms of differential rotation and solar cycle.

79 ASTRONOMY AND ASTROPHYSICS↗

Evaluation of Rotational Errors in Treatment Setup of Stereotactic Body Radiation Therapy of Liver Cancer

Purpose: To evaluate the dosimetric impact of rotational setup errors in stereotactic body radiotherapy (SBRT) treatment of liver tumors and to investigate whether translational shifts can compensate for rotation. Methods and Materials: The positioning accuracy in 20 patients with liver malignancies treated with SBRT was reevaluated offline by matching the patients' cone-beam computed tomography (CT) scans (n=75) to the planning CT scans and adjusting the 3 rotational angles (pitch, roll, and yaw). Systematic and random setup errors were calculated. The dosimetric changes caused by rotational setup errors were quantified for both simulated and observed patient rotations. Dose distributions recalculated on the rotated CT scans were compared with the original planned doses. Translational corrections were simulated based on manual translational registration of the rotated images to the original CT scans. The correction efficacy was evaluated by comparing the recalculated plans with the original plans. Results: The systematic rotational setup errors were -0.06 Degree-Sign {+-} 0.68 Degree-Sign , -0.29 Degree-Sign {+-} 0.62 Degree-Sign , and -0.24 Degree-Sign {+-} 0.61 Degree-Sign ; the random setup errors were 0.80 Degree-Sign , 1.05 Degree-Sign , and 0.61 Degree-Sign for pitch, roll, and yaw, respectively. Analysis of CBCT images showed that 56.0%, 14.7%, and 1.3% of treated fractions had rotational errors of >1 Degree-Sign , >2 Degree-Sign , and >3 Degree-Sign , respectively, in any one of the rotational axes. Rotational simulations demonstrated that the reduction of gross tumor volume (GTV) coverage was <2% when rotation was <3 Degree-Sign . Recalculated plans using actual patient roll motions showed similar reduction (<2%) in GTV coverage. Translational corrections improved the GTV coverage to within 3% of the original values. For organs at risk (OAR), the dosimetric impact varied case by case. Conclusion: Actual rotational setup errors in SBRT for liver tumors are relatively small in magnitude and are unlikely to affect GTV coverage significantly. Translational corrections can be optimized to compensate for rotational setup errors. However, caution regarding possible dose increases to OAR needs to be exercised.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-E-P-12: Pinnacle-Based Tool to Evaluate the Effect of Prostate Rotation as Determined by Calypso

Purpose: When the Calypso reports a large prostate rotation and one does not have the means to make corrections, it is helpful to quantify its dosimetric effects. We have devised a simple scheme to achieve this in Pinnacle TPS. If it is determined that the PTV margin is inadequate, an alternate larger-margin plan may be adapted for the day. Methods: A three-step process using the Pinnacle Image fusion module was formulated to analyze the clinical effect of prostate rotation. The process includes (1) translating the image set such that the rotational axis is about the isocenter, (2) performing 3D rotations of the structures of interest, and (3) restoring the coordinates associated with the plan. The rotated structures are imported and overlayed on the original plan for evaluation. The tool was applied to three prostate cancer patients with relatively large rotations (95 fractions total). Prostate rotations are primarily due to variations in bladder and rectal filling, which may also affect the seminal vesicles. It is difficult to estimate the perturbation of seminal vesicles for a given prostate rotation. Therefore, the Calypso-derived rotation matrix was applied only to CTV and PTV (CTV+5mm). Results: The rotations were predominantly in the pitch direction with an absolute value ranging from 0–29 degrees (Median = 10°, Average = 14.5°). For various magnitudes of rotation, the CTV V100 decreased from the original 100% to 99.6%/99%/95% for 10°/15°/29° rotations, respectively. Likewise, the PTV V100 diminished from 95% to 92%/89%/82%. Conclusion: A tool, consisting only of features within a TPS, was used to evaluate the dosimetric effect of prostate rotation. Our study shows that under large uncorrected rotations, the tumor coverage is degraded and may require intervention in the form of plan adaptation. To this end, alternate plans with variable margins can be generated in advance for daily adaption.

60 APPLIED LIFE SCIENCES↗

A Parametric Study of Erupting Flux Rope Rotation: Modeling the 'Cartwheel CME' on 9 April 2008

The rotation of erupting filaments in the solar corona is addressed through a parametric simulation study of unstable, rotating flux ropes in bipolar force-free initial equilibrium. The Lorentz force due to the external shear-field component and the relaxation of tension in the twisted field are the major contributors to the rotation in this model, while reconnection with the ambient field is of minor importance, due to the field's simple structure. In the low-beta corona, the rotation is not guided by the changing orientation of the vertical field component's polarity inversion line with height. The model yields strong initial rotations which saturate in the corona and differ qualitatively from the profile of rotation vs. height obtained in a recent simulation of an eruption without preexisting flux rope. Both major mechanisms writhe the flux rope axis, converting part of the initial twist helicity, and produce rotation profiles which, to a large part, are very similar within a range of shear-twist combinations. A difference lies in the tendency of twist-driven rotation to saturate at lower heights than shear-driven rotation. For parameters characteristic of the source regions of erupting filaments and coronal mass ejections, the shear field is found to be the dominant origin of rotations in the corona and to be required if the rotation reaches angles of order 90 degrees and higher; it dominates even if the twist exceeds the threshold of the helical kink instability. The contributions by shear and twist to the total rotation can be disentangled in the analysis of observations if the rotation and rise profiles are simultaneously compared with model calculations. The resulting twist estimate allows one to judge whether the helical kink instability occurred. This is demonstrated for the erupting prominence in the "Cartwheel CME" on 9 April 2008, which has shown a rotation of approximately 115 deg. up to a height of 1.5 Solar R above the photosphere. Out of a range of initial equilibria which include strongly kink-unstable (Phi = 5 pi), weakly kink-unstable (Phi = 3.5 pi), and kink-stable (Phi = 2.5 pi) configurations, only the evolution of the weakly kink-unstable flux rope matches the observations in their entirety.

initiation and propagation↗

MOJAVE: MONITORING OF JETS IN ACTIVE GALACTIC NUCLEI WITH VLBA EXPERIMENTS. VIII. FARADAY ROTATION IN PARSEC-SCALE AGN JETS

We report observations of Faraday rotation measures for a sample of 191 extragalactic radio jets observed within the MOJAVE program. Multifrequency Very Long Baseline Array observations were carried out over 12 epochs in 2006 at four frequencies between 8 and 15 GHz. We detect parsec-scale Faraday rotation measures in 149 sources and find the quasars to have larger rotation measures on average than BL Lac objects. The median core rotation measures are significantly higher than in the jet components. This is especially true for quasars where we detect a significant negative correlation between the magnitude of the rotation measure and the de-projected distance from the core. We perform detailed simulations of the observational errors of total intensity, polarization, and Faraday rotation, and concentrate on the errors of transverse Faraday rotation measure gradients in unresolved jets. Our simulations show that the finite image restoring beam size has a significant effect on the observed rotation measure gradients, and spurious gradients can occur due to noise in the data if the jet is less than two beams wide in polarization. We detect significant transverse rotation measure gradients in four sources (0923+392, 1226+023, 2230+114, and 2251+158). In 1226+023 the rotation measure is for the first time seen to change sign from positive to negative over the transverse cuts, which supports the presence of a helical magnetic field in the jet. In this source we also detect variations in the jet rotation measure over a timescale of three months, which are difficult to explain with external Faraday screens and suggest internal Faraday rotation. By comparing fractional polarization changes in jet components between the four frequency bands to depolarization models, we find that an external purely random Faraday screen viewed through only a few lines of sight can explain most of our polarization observations, but in some sources, such as 1226+023 and 2251+158, internal Faraday rotation is needed.

79 ASTRONOMY AND ASTROPHYSICS↗

Evaluating gyrochronology on the zero-age-main-sequence: rotation periods in the southern open cluster Blanco 1 from the Kelt-South survey

We report periods for 33 members of Blanco 1 as measured from Kilodegree Extremely Little Telescope-South light curves, the first reported rotation periods for this benchmark zero-age-main-sequence open cluster. The distribution of these stars spans from late-A or early-F dwarfs to mid-K with periods ranging from less than a day to ∼8 days. The rotation period distribution has a morphology similar to the coeval Pleiades cluster, suggesting the universal nature of stellar rotation distributions. Employing two different gyrochronology methods, we find an age of 146{sub −14}{sup +13} Myr for the cluster. Using the same techniques, we infer an age of 134{sub −10}{sup +9} Myr for the Pleiades measured from existing literature rotation periods. These rotation-derived ages agree with independently determined cluster ages based on the lithium depletion boundary technique. Additionally, we evaluate different gyrochronology models and quantify levels of agreement between the models and the Blanco 1/Pleiades rotation period distributions, including incorporating the rotation distributions of clusters at ages up to 1.1 Gyr. We find the Skumanich-like spin-down rate sufficiently describes the rotation evolution of stars hotter than the Sun; however, we find cooler stars rotating faster than predicted by a Skumanich law, suggesting a mass dependence in the efficiency of stellar angular momentum loss rate. Finally, we compare the Blanco 1 and Pleiades rotation period distributions to available nonlinear angular momentum evolution models. We find they require a significant mass dependence on the initial rotation rate of solar-type stars to reproduce the observed range of rotation periods at a given stellar mass and are furthermore unable to predict the observed over-density of stars along the upper envelope of the clusters' rotation distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

The rotation and galactic kinematics of mid M dwarfs in the solar neighborhood

Rotation is a directly observable stellar property, and it drives magnetic field generation and activity through a magnetic dynamo. Main-sequence stars with masses below approximately 0.35 M{sub ⊙} (mid-to-late M dwarfs) are fully convective, and are expected to have a different type of dynamo mechanism than solar-type stars. Measurements of their rotation rates provide insight into these mechanisms, but few rotation periods are available for these stars at field ages. Using photometry from the MEarth Project, we measure rotation periods for 387 nearby, mid-to-late M dwarfs in the northern hemisphere, finding periods from 0.1 to 140 days. The typical rotator has stable, sinusoidal photometric modulations at a semi-amplitude of 0.5%–1%. We find no period–amplitude relation for stars below 0.25 M{sub ⊙} and an anticorrelation between period and amplitude for higher-mass M dwarfs. We highlight the existence of older, slowly rotating stars without Hα emission that nevertheless have strong photometric variability. We use parallaxes, proper motions, radial velocities, photometry, and near-infrared metallicity estimates to further characterize the population of rotators. The Galactic kinematics of our sample is consistent with the local population of G and K dwarfs, and rotators have metallicities characteristic of the solar neighborhood. We use the W space velocities and established age–velocity relations to estimate that stars with P < 10 days have ages of on average <2 Gyr, and that those with P > 70 days have ages of about 5 Gyr. The period distribution is dependent on mass: as the mass decreases, the slowest rotators at a given mass have longer periods, and the fastest rotators have shorter periods. We find a lack of stars with intermediate rotation periods, and the gap between the fast and slow rotators is larger for lower masses. Our data are consistent with a scenario in which these stars maintain rapid rotation for several gigayears, then spin down quickly, reaching periods of around 100 days by a typical age of 5 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗

MO-F-CAMPUS-T-05: Correct Or Not to Correct for Rotational Patient Set-Up Errors in Stereotactic Radiosurgery

Purpose: To quantify the effect of patient rotation in stereotactic radiation therapy and establish a threshold where rotational patient set-up errors have a significant impact on target coverage. Methods: To simulate rotational patient set-up errors, a Matlab code was created to rotate the patient dose distribution around the treatment isocentre, located centrally in the lesion, while keeping the structure contours in the original locations on the CT and MRI. Rotations of 1°, 3°, and 5° for each of the pitch, roll, and yaw, as well as simultaneous rotations of 1°, 3°, and 5° around all three axes were applied to two types of brain lesions: brain metastasis and acoustic neuroma. In order to analyze multiple tumour shapes, these plans included small spherical (metastasis), elliptical (acoustic neuroma), and large irregular (metastasis) tumour structures. Dose-volume histograms and planning target volumes were compared between the planned patient positions and those with simulated rotational set-up errors. The RTOG conformity index for patient rotation was also investigated. Results: Examining the tumour volumes that received 80% of the prescription dose in the planned and rotated patient positions showed decreases in prescription dose coverage of up to 2.3%. Conformity indices for treatments with simulated rotational errors showed decreases of up to 3% compared to the original plan. For irregular lesions, degradation of 1% of the target coverage can be seen for rotations as low as 3°. Conclusions: This data shows that for elliptical or spherical targets, rotational patient set-up errors less than 3° around any or all axes do not have a significant impact on the dose delivered to the target volume or the conformity index of the plan. However the same rotational errors would have an impact on plans for irregular tumours.

60 APPLIED LIFE SCIENCES↗

Does the rotational direction of a wind turbine impact the wake in a stably stratified atmospheric boundary layer?

Stably stratified atmospheric boundary layers are often characterized by a veering wind profile, in which the wind direction changes clockwise with height in the Northern Hemisphere. Wind-turbine wakes respond to this veer in the incoming wind by stretching from a circular shape into an ellipsoid. We investigate the relationship between this stretching and the direction of the turbine rotation by means of large-eddy simulations. Clockwise rotating, counterclockwise rotating, and non-rotating actuator disc turbines are embedded in wind fields of a precursor simulation with no wind veer and in wind fields with a Northern Hemispheric Ekman spiral, resulting in six combinations of rotor rotation and inflow wind condition. The wake strength, extension, width, and deflection depend on the interaction of the meridional component of Ekman spiral with the rotational direction of the actuator disc, whereas the direction of the disc rotation only marginally modifies the wake if no veer is present. The differences result from the amplification or weakening/reversion of the spanwise and the vertical wind components due to the effect of the superposed disc rotation. They are also present in the streamwise wind component of the wake and in the total turbulence intensity. In the case of an counterclockwise rotating actuator disc, the spanwise and vertical wind components increase directly behind the rotor, resulting in the same rotational direction in the whole wake while its strength decreases downwind. In the case of a clockwise rotating actuator disc, however, the spanwise and vertical wind components of the near wake are weakened or even reversed in comparison to the inflow. This weakening/reversion results in a downwind increase in the strength of the flow rotation in the wake or even a different rotational direction in the near wake in comparison to the far wake. The physical mechanism responsible for this difference can be explained by a simple linear superposition of a veering inflow with a Rankine vortex.

17 WIND ENERGY↗

Reactive Hydrodynamics in Rotating Spherical and Cylindrical Geometry

In turbulent spray combustion among many complex interactions between local flow structures called turbulent eddies and droplets are those associated with rotation of droplets. In general, for a complete statistical description of turbulent sprays, consideration of at least four degrees of freedom respectively associated with translational, rotational, vibrational (pulsational), and internal motions of the droplet are needed. Clearly the interactions between all degrees of freedom of the droplets and those for the gaseous background field will be exceedingly complex. For example, one type of interaction between the translational and the rotational velocity of droplets results in droplet helicity, H(d) = w(d).v(d), the significance of which in turbulent spray combustion is yet to be recognized. The role of droplet rotation in turbulent spray combustion modeling and its impact on the evaporation of liquid fuel droplets was recently investigated. Also, the impact of rotation on combustion of solid particles such as is encountered in pulverized coal combustion has been emphasized. The problem of viscous flow around a rotating sphere discussed above also occurs in other areas of physical sciences such as astrophysics and geophysics. Consequently, the subject has been addressed in many classical as well as more recent investigations. According to these investigations, the rotation of a rigid sphere in an otherwise quiescent, unconfined environment results in the motion of the fluid towards the poles. The polar flows from the northern and southern hemispheres move along helical trajectories towards the equatorial plane. Eventually, the polar flows collide at the equatorial plane, thus producing a sheet of rotating fluid that is radially ejected outward on this plane. Therefore, a droplet induces a strained flow field as a result of its rotation. Since the spatial extent of equatorial jets could easily exceed many droplet diameters, interactions between neighboring droplets are enhanced as a result of their rotation. Also, the equatorial jet substantially alters the spherical geometry of the diffusion flame surface that surrounds a rotating droplet. The objective of the research is to gain more knowledge about the hydrodynamics within and around rotating spherical and cylindrical body of fluid, and the behavior of diffusion or premixed flame surfaces that could surround such symmetric body of rotating fluid.

Sohrab, Siavash H.↗

Reduction of Sample Rotation in Electrostatic Levitation

In many containerless processing systems, control of sample rotation is an important issue. Sample rotation is even more important for microgravity containerless processing systems, where the centrifugal acceleration can approach 1 g for even a small rotation rate. Prior work on rotation control by Rhim focused on driving the sample rotation at a controlled rate for droplet dynamics experiments and measurement of electrical conductivity. His technique allows controlled, fast rotation, but for many microgravity experiments the goal is zero rotation. To minimize sample rotation, two approaches are apparent: first, to identify and balance or eliminate the driving forces for undesired sample rotation, or second, implement a feedback-based rotation control loop in parallel with the position control loop. In this work, we have taken the first approach. To minimize sample rotation, the simplest approach is to identify and balance or eliminate the driving forces for undesired sample rotation. Our experiments show that the dominant driving force for rotation of machined Zr spheres in the MSFC ESL is photon pressure from the heating laser. Experimental results showing the correlation between heating power and torque are compared to theoretical predictions, and a strategy for minimizing the torque due to photon pressure is presented.

Hyers, R. W↗

Regional Moment Tensor Inversion Using Rotational Observations

There are benefits from the addition of rotational motions to translational displacements for moment tensor (MT) inversions. The rotational radiation pattern is orthogonal to the shear radiation pattern, thus incorporating rotations is equivalent to gaining another observation point on the focal sphere. We demonstrated this by simulating curl and displacement wavefields for a regional distance station. Thus, one 6-C station (3-Component translational + 3-Component rotational) gathers the same information on radiation pattern as two 3-C stations at 90° azimuth from one another along the focal plane axis, which is sometimes difficult to obtain when restricted to surface sensors. We added rotational Green's functions to a regional MT inversion scheme (long-period, time-domain, and linear inversion) by computing spatial gradients from f-κ reflectivity synthetics. For rotational data, we used Array Derived Rotations (ADR) from Piñon Flats Observatory Array and Golay array deployed during IRIS Community Wavefield Demonstration Experiment. The hope is to ultimately use compact and field deployable broadband rotational seismometers instead of ADRs. Rotational motions were predicted from well-constrained deviatoric MT solutions of nine earthquakes recorded by the arrays and other seismic networks. Additionally, we formed three station sparse datasets with (3-C and 6-C) and without rotational ground motions (3-C only) for eight earthquakes testing the benefits of including rotational waveforms in MT inversions when they are equally weighted with translational waveforms. Adding rotational motions improved the double-couple components and reduced compensated-linear-vector-dipole and isotropic components in full-MT solutions using sparse datasets with poor coverage.

58 GEOSCIENCES↗

Dynamic Collimator Angle Adjustments During Volumetric Modulated Arc Therapy to Account for Prostate Rotations

Purpose: Rotations of the prostate gland induce considerable geometric uncertainties in prostate cancer radiation therapy. Collimator and gantry angle adjustments can correct these rotations in intensity modulated radiation therapy. Modern volumetric modulated arc therapy (VMAT) treatments, however, include a wide range of beam orientations that differ in modulation, and corrections require dynamic collimator rotations. The aim of this study was to implement a rotation correction strategy for VMAT dose delivery and validate it for left-right prostate rotations. Methods and Materials: Clinical VMAT treatment plans of 5 prostate cancer patients were used. Simulated left-right prostate rotations between +15° and −15° were corrected by collimator rotations. We compared corrected and uncorrected plans by dose volume histograms, minimum dose (D{sub min}) to the prostate, bladder surface receiving ≥78 Gy (S78) and rectum equivalent uniform dose (EUD; n=0.13). Each corrected plan was delivered to a phantom, and its deliverability was evaluated by γ-evaluation between planned and delivered dose, which was reconstructed from portal images acquired during delivery. Results: On average, clinical target volume minimum dose (D{sub min}) decreased up to 10% without corrections. Negative left-right rotations were corrected almost perfectly, whereas D{sub min} remained within 4% for positive rotations. Bladder S78 and rectum EUD of the corrected plans matched those of the original plans. The average pass rate for the corrected plans delivered to the phantom was 98.9% at 3% per 3 mm gamma criteria. The measured dose in the planning target volume approximated the original dose, rotated around the simulated left-right angle, well. Conclusions: It is feasible to dynamically adjust the collimator angle during VMAT treatment delivery to correct for prostate rotations. This technique can safely correct for left-right prostate rotations up to 15°.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Three-dimensional simulation of a rotating supernova

We investigate the effects of rotation on the evolution of core-collapse supernova explosion using a 15 solar mass progenitor model with a variety of neutrino luminosity and rotational velocity. Stars should have some amount of angular momentum, which would affect stellar evolution and its final explosion. In this paper we focus on the effect of rotation on gravitational collapse of a core, on a core bounce of accreting matter, and on subsequent generation and evolution of a shock wave. We find that the rotation plays a positive role for supernova explosions. More rapidly rotating models present more rapid expansion of the shock front and more energetic explosions. When the rotational speed is moderate, the shock once stalls at about 200 km away from the center similarly to a non-rotating model. Then the rotating progenitor experiences effective neutrino heating especially around an equatorial plane and explodes even with somewhat low neutrino luminosity for which the non-rotating model cannot overcome accreting matter and finally collapses. When the rotational speed is fast, the shock expands to about 300 km immediately after the core bounce and then evolves to move outward without shock stalling. We conclude that this positive effect of rotation to explosions is dominant against some possible negative aspects, for example, lower neutrino luminosity caused by less contraction of the rotating core.

79 ASTRONOMY AND ASTROPHYSICS↗

THE INTERNAL ROTATION PROFILE OF THE B-TYPE STAR KIC 10526294 FROM FREQUENCY INVERSION OF ITS DIPOLE GRAVITY MODES

The internal angular momentum distribution of a star is the key to determining its evolution. Fortunately, stellar internal rotation can be probed through studies of rotationally split nonradial oscillation modes. In particular, the detection of nonradial gravity modes (g modes) in massive young stars has recently become feasible thanks to the Kepler space mission. Our goal is to derive the internal rotation profile of the Kepler B8V star KIC 10526294 through asteroseismology. We interpret the observed rotational splittings of its dipole g modes using four different approaches based on the best seismic models of the star and their rotational kernels. We show that these kernels can resolve differential rotation within the radiative envelope if a smooth rotational profile is assumed and if the observational errors are small. Based on Kepler data, we find that the rotation rate near the core-envelope boundary is well constrained to 163 ± 89 nHz. The seismic data are consistent with rigid rotation but a profile with counter-rotation within the envelope has a statistical advantage over constant rotation. Our study should be repeated for other massive stars with a variety of stellar parameters in order to determine the physical conditions that control the internal rotation profile of young massive stars, with the aim of improving the input physics of their models.

79 ASTRONOMY AND ASTROPHYSICS↗