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Investigation of structural and luminescent properties of Ce{sup 3+}/Mn{sup 2+} ions-doped Ca{sub 5}(PO{sub 4}){sub 3}F

Graphical abstract: The structural and luminescent properties FAP: Ce{sup 3+} and FAP: Ce{sup 3+}, Mn{sup 2+} were investigated in detail by the spectral measurement and theoretical calculation. The emission of Ce{sup 3+} is fitted by two Gaussian functions dashed lines in wavenumber to further confirm the Ce{sup 3+} ion simultaneously occupy the 4f and 6h sites Ca{sub 5}(PO{sub 4})F host. - Highlights: • A simple hydrothermal method has been used to prepare Ca{sub 5}(PO{sub 4}){sub 3}F: Ce{sup 3+}, Mn{sup 2+} powders with structural and luminescent analysis. • The emission of Ce{sup 3+} is fitted by two Gaussian functions to confirm the Ce{sup 3+} ion simultaneously to occupy the 4f and 6h sites in Ca{sub 5}(PO{sub 4}){sub 3}F host. • Due to an efficient energy transfer, the existence of Ce{sup 3+} (sensitizer) can dramatically enhance the green emission of Mn{sup 2+} (activator) in co-doped samples. - Abstract: Ce{sup 3+}/Mn{sup 2+} ions-doped oxyapatite calcium fluorapatite [Ca{sub 5}(PO{sub 4}){sub 3}F, FAP] has been successfully synthesized by a facile one-step hydrothermal method. The luminescent properties of Ce{sup 3+}- and Ce{sup 3+}/Mn{sup 2+}- activated FAP phosphors were investigated using the photoluminescence (PL) and photoluminescence excitation (PLE) spectra. The emission of Ce{sup 3+} was fitted by two Gaussian functions with dashed lines in wavenumber to confirm the Ce{sup 3+} ion simultaneously to occupy the 4f and 6h sites in Ca{sub 5}(PO{sub 4}){sub 3}F host, which was consistent with the calculated results of crystal field based on chemical bond theory. In addition, the existence of Ce{sup 3+} (sensitizer) can dramatically enhance the green emission of Mn{sup 2+} (activator) in Ce{sup 3+}/Mn{sup 2+} ions co-doped samples due to an efficient energy transfer from Ce{sup 3+} to Mn{sup 2+}. All of these results could help us understand the site assignments and optical properties of the rare earth ions doped in hexagonal Ca{sub 5}(PO{sub 4}){sub 3}F.

36 MATERIALS SCIENCE↗

LIKELIHOOD-FREE COSMOLOGICAL INFERENCE WITH TYPE Ia SUPERNOVAE: APPROXIMATE BAYESIAN COMPUTATION FOR A COMPLETE TREATMENT OF UNCERTAINTY

Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is an increasing burden placed on adequate modeling; systematic errors in the model will dominate where previously these were swamped by statistical errors. For example, Gaussian distributions are an insufficient representation for errors in quantities like photometric redshifts. Likewise, it can be difficult to quantify analytically the distribution of errors that are introduced in complex fitting codes. Without a simple form for these distributions, it becomes difficult to accurately construct a likelihood function for the data as a function of parameters of interest. Approximate Bayesian computation (ABC) provides a means of probing the posterior distribution when direct calculation of a sufficiently accurate likelihood is intractable. ABC allows one to bypass direct calculation of the likelihood but instead relies upon the ability to simulate the forward process that generated the data. These simulations can naturally incorporate priors placed on nuisance parameters, and hence these can be marginalized in a natural way. We present and discuss ABC methods in the context of supernova cosmology using data from the SDSS-II Supernova Survey. Assuming a flat cosmology and constant dark energy equation of state, we demonstrate that ABC can recover an accurate posterior distribution. Finally, we show that ABC can still produce an accurate posterior distribution when we contaminate the sample with Type IIP supernovae.

79 ASTRONOMY AND ASTROPHYSICS↗

A COMPREHENSIVE STUDY OF GAMMA-RAY BURST OPTICAL EMISSION. III. BRIGHTNESS DISTRIBUTIONS AND LUMINOSITY FUNCTIONS OF OPTICAL AFTERGLOWS

We continue our systematic statistical study on optical afterglow data of gamma-ray bursts (GRBs). We present the apparent magnitude distributions of early optical afterglows at different epochs (t = 10{sup 2} s, 10{sup 3} s, and 1 hr) for the optical light curves of a sample of 93 GRBs (the global sample) and for sub-samples with an afterglow onset bump or a shallow decay segment. For the onset sample and shallow decay sample we also present the brightness distribution at the peak time t{sub p} and break time t{sub b}, respectively. All the distributions can be fit with Gaussian functions. We further perform Monte Carlo simulations to infer the luminosity function of GRB optical emission at the rest-frame time 10{sup 3} s, t{sub p}, and t{sub b}. Our results show that a single power-law luminosity function is adequate to model the data with indices -1.40 {+-} 0.10, -1.06 {+-} 0.16, and -1.54 {+-} 0.22. Based on the derived rest-frame 10{sup 3} s luminosity function, we generate the intrinsic distribution of the R-band apparent magnitude M{sub R} at the observed time 10{sup 3} s post-trigger, which peaks at M{sub R} = 22.5 mag. The fraction of GRBs whose R-band magnitude is fainter than 22 mag and 25 mag and at the observer time 10{sup 3} s are {approx}63% and {approx}25%, respectively. The detection probabilities of the optical afterglows with ground-based robotic telescopes and the UV-Optical Telescope on board Swift are roughly consistent with that inferred from this intrinsic M{sub R} distribution, indicating that the variations of the dark GRB fraction among the samples with different telescopes may be due to the observational selection effect, although the existence of an intrinsically dark GRB population cannot be ruled out.

79 ASTRONOMY AND ASTROPHYSICS↗

Nanoscale measurements of proton tracks using fluorescent nuclear track detectors

Purpose: The authors describe a method in which fluorescence nuclear track detectors (FNTDs), novel track detectors with nanoscale spatial resolution, are used to determine the linear energy transfer (LET) of individual proton tracks from proton therapy beams by allowing visualization and 3D reconstruction of such tracks. Methods: FNTDs were exposed to proton therapy beams with nominal energies ranging from 100 to 250 MeV. Proton track images were then recorded by confocal microscopy of the FNTDs. Proton tracks in the FNTD images were fit by using a Gaussian function to extract fluorescence amplitudes. Histograms of fluorescence amplitudes were then compared with LET spectra. Results: The authors successfully used FNTDs to register individual proton tracks from high-energy proton therapy beams, allowing reconstruction of 3D images of proton tracks along with delta rays. The track amplitudes from FNTDs could be used to parameterize LET spectra, allowing the LET of individual proton tracks from therapeutic proton beams to be determined. Conclusions: FNTDs can be used to directly visualize proton tracks and their delta rays at the nanoscale level. Because the track intensities in the FNTDs correlate with LET, they could be used further to measure LET of individual proton tracks. This method may be useful for measuring nanoscale radiation quantities and for measuring the LET of individual proton tracks in radiation biology experiments.

60 APPLIED LIFE SCIENCES↗

Three-dimensional imaging of the ultracold plasma formed in a supersonic molecular beam

Double-resonant excitation of nitric oxide in a seeded supersonic molecular beam forms a state-selected Rydberg gas that evolves to form an ultracold plasma. This plasma travels with the propagation of the molecular beam in z over a variable distance as great as 600 mm to strike an imaging detector, which records the charge distribution in the dimensions, x and y. The ω{sub 1} + ω{sub 2} laser crossed molecular beam excitation geometry convolutes the axial Gaussian distribution of NO in the molecular beam with the Gaussian intensity distribution of the perpendicularly aligned laser beam to create an ellipsoidal volume of Rydberg gas. Detected images describe the evolution of this initial density as a function of selected Rydberg gas initial principal quantum number, n{sub 0}, ω{sub 1} laser pulse energy (linearly related to Rydberg gas density, ρ{sub 0}) and flight time. Low-density Rydberg gases of lower principal quantum number produce uniformly expanding, ellipsoidal charge-density distributions. Increase either of n{sub 0} or ρ{sub 0} breaks the ellipsoidal symmetry of plasma expansion. The volume bifurcates to form repelling plasma volumes. The velocity of separation depends on n{sub 0} and ρ{sub 0} in a way that scales uniformly with ρ{sub e}, the density of electrons formed in the core of the Rydberg gas by prompt Penning ionization. Conditions under which this electron gas drives expansion in the long axis dimension of the ellipsoid favours the formation of counter-propagating shock waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

LIKELIHOOD OF THE POWER SPECTRUM IN COSMOLOGICAL PARAMETER ESTIMATION

The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior probability derived from such a likelihood deviates considerably from the exact posterior on the largest scales probed by any survey, where the central limit theorem does not apply. We show that various forms of Gaussian likelihoods can have a significant impact on the estimation of the primordial non-Gaussianity parameter f{sub NL} from the galaxy angular power spectrum. The Gaussian plus log-normal likelihood, which has been applied successfully in analyses of the cosmic microwave background, outperforms the Gaussian likelihoods. Nevertheless, even if the exact likelihood of the power spectrum is used, the estimated parameters may be still biased. As such, the likelihoods and estimators need to be thoroughly examined for potential systematic errors.

79 ASTRONOMY AND ASTROPHYSICS↗

THE CORONAL SOURCE OF EXTREME-ULTRAVIOLET LINE PROFILE ASYMMETRIES IN SOLAR ACTIVE REGION OUTFLOWS

High-resolution spectra from the Hinode EUV Imaging Spectrometer have revealed that coronal spectral line profiles are sometimes asymmetric, with a faint enhancement in the blue wing on the order of 100 km s{sup -1}. These asymmetries could be important since they may be subtle yet diagnostically useful signatures of coronal heating or solar wind acceleration processes. It has also been suggested that they are signatures of chromospheric jets supplying mass and energy to the corona. Until now, however, there have been no studies of the physical properties of the plasma producing the asymmetries. Here we identify regions of asymmetric profiles in the outflows of AR 10978 using an asymmetric Gaussian function and extract the intensities of the faint component using multiple Gaussian fits. We then derive the temperature structure and chemical composition of the plasma producing the asymmetries. We find that the asymmetries are dependent on temperature, and are clearer and stronger in coronal lines. The temperature distribution peaks around 1.4-1.8 MK with an emission measure at least an order of magnitude larger than that at 0.6 MK. The first ionization potential bias is found to be 3-5, implying that the high-speed component of the outflows may also contribute to the slow-speed wind. Observations and models indicate that it takes time for plasma to evolve to a coronal composition, suggesting that the material is trapped on closed loops before escaping, perhaps by interchange reconnection. The results, therefore, identify the plasma producing the asymmetries as having a coronal origin.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SU-F-P-23: Setup Uncertainties for the Lung Stereotactic Body Radiation Therapy

Purpose: The Exactrack X-ray system with six degree-of-freedom (6DoF) adjustment ability can be used for setup of lung stereotactic body radiation therapy. The setup uncertainties from ExacTrack 6D system were analyzed. Methods: The Exactrack X-ray 6D image guided radiotherapy system is used in our clinic. The system is an integration of 2 subsystems: (1): an infrared based optical position system and (2) a radiography kV x-ray imaging system. The infrared system monitors reflective body markers on the patient’s skin to assistant in the initial setup. The radiographic kV devices were used for patient positions verification and adjustment. The position verification was made by fusing the radiographs with the digitally reconstructed radiograph (DRR) images generated by simulation CT images using 6DoF fusion algorithms. Those results were recorded in our system. Gaussian functions were used to fit the data. Results: For 37 lung SBRT patients, the image registration results for the initial setup by using surface markers and for the verifications, were measured. The results were analyzed for 143 treatments. The mean values for the lateral, longitudinal, vertical directions were 0.1, 0.3 and 0.3mm, respectively. The standard deviations for the lateral, longitudinal and vertical directions were 0.62, 0.78 and 0.75mm respectively. The mean values for the rotations around lateral, longitudinal and vertical directions were 0.1, 0.2 and 0.4 degrees respectively, with standard deviations of 0.36, 0.34, and 0.42 degrees. Conclusion: The setup uncertainties for the lung SBRT cases by using Exactrack 6D system were analyzed. The standard deviations of the setup errors were within 1mm for all three directions, and the standard deviations for rotations were within 0.5 degree.

60 APPLIED LIFE SCIENCES↗

A statistical analysis of avalanching heat transport in stationary enhanced core confinement regimes

We present a statistical analysis of heat transport in stationary enhanced confinement regimes obtained from flux-driven gyrofluid simulations. The probability density functions of heat flux in improved confinement regimes, characterized by the Nusselt number, show significant deviation from Gaussian, with a markedly fat tail, implying the existence of heat avalanches. Two types of avalanching transport are found to be relevant to stationary states, depending on the degree of turbulence suppression. In the weakly suppressed regime, heat avalanches occur in the form of quasi-periodic (QP) heat pulses. Collisional relaxation of zonal flow is likely to be the origin of these QP heat pulses. This phenomenon is similar to transient limit cycle oscillations observed prior to edge pedestal formation in recent experiments. On the other hand, a spectral analysis of heat flux in the strongly suppressed regime shows the emergence of a 1/f (f is the frequency) band, suggesting the presence of self-organized criticality (SOC)-like episodic heat avalanches. This episodic 1/f heat avalanches have a long temporal correlation and constitute the dominant transport process in this regime.

42 ENGINEERING↗

TH-E-BRE-03: A Novel Method to Account for Ion Chamber Volume Averaging Effect in a Commercial Treatment Planning System Through Convolution

Purpose: Fourier-based deconvolution approaches used to eliminate ion chamber volume averaging effect (VAE) suffer from measurement noise. This work aims to investigate a novel method to account for ion chamber VAE through convolution in a commercial treatment planning system (TPS). Methods: Beam profiles of various field sizes and depths of an Elekta Synergy were collected with a finite size ion chamber (CC13) to derive a clinically acceptable beam model for a commercial TPS (Pinnacle{sup 3}), following the vendor-recommended modeling process. The TPS-calculated profiles were then externally convolved with a Gaussian function representing the chamber (σ = chamber radius). The agreement between the convolved profiles and measured profiles was evaluated with a one dimensional Gamma analysis (1%/1mm) as an objective function for optimization. TPS beam model parameters for focal and extra-focal sources were optimized and loaded back into the TPS for new calculation. This process was repeated until the objective function converged using a Simplex optimization method. Planar dose of 30 IMRT beams were calculated with both the clinical and the re-optimized beam models and compared with MapCHEC™ measurements to evaluate the new beam model. Results: After re-optimization, the two orthogonal source sizes for the focal source reduced from 0.20/0.16 cm to 0.01/0.01 cm, which were the minimal allowed values in Pinnacle. No significant change in the parameters for the extra-focal source was observed. With the re-optimized beam model, average Gamma passing rate for the 30 IMRT beams increased from 92.1% to 99.5% with a 3%/3mm criterion and from 82.6% to 97.2% with a 2%/2mm criterion. Conclusion: We proposed a novel method to account for ion chamber VAE in a commercial TPS through convolution. The reoptimized beam model, with VAE accounted for through a reliable and easy-to-implement convolution and optimization approach, outperforms the original beam model in standard IMRT QA verification.

07 ISOTOPE AND RADIATION SOURCES↗

SU-C-BRC-04: Efficient Dose Calculation Algorithm for FFF IMRT with a Simplified Bivariate Gaussian Source Model

Purpose: To develop an efficient and accurate independent dose calculation algorithm with a simplified analytical source model for the quality assurance and safe delivery of Flattening Filter Free (FFF)-IMRT on an Elekta Versa HD. Methods: The source model consisted of a point source and a 2D bivariate Gaussian source, respectively modeling the primary photons and the combined effect of head scatter, monitor chamber backscatter and collimator exchange effect. The in-air fluence was firstly calculated by back-projecting the edges of beam defining devices onto the source plane and integrating the visible source distribution. The effect of the rounded MLC leaf end, tongue-and-groove and interleaf transmission was taken into account in the back-projection. The in-air fluence was then modified with a fourth degree polynomial modeling the cone-shaped dose distribution of FFF beams. Planar dose distribution was obtained by convolving the in-air fluence with a dose deposition kernel (DDK) consisting of the sum of three 2D Gaussian functions. The parameters of the source model and the DDK were commissioned using measured in-air output factors (Sc) and cross beam profiles, respectively. A novel method was used to eliminate the volume averaging effect of ion chambers in determining the DDK. Planar dose distributions of five head-and-neck FFF-IMRT plans were calculated and compared against measurements performed with a 2D diode array (MapCHECK™) to validate the accuracy of the algorithm. Results: The proposed source model predicted Sc for both 6MV and 10MV with an accuracy better than 0.1%. With a stringent gamma criterion (2%/2mm/local difference), the passing rate of the FFF-IMRT dose calculation was 97.2±2.6%. Conclusion: The removal of the flattening filter represents a simplification of the head structure which allows the use of a simpler source model for very accurate dose calculation. The proposed algorithm offers an effective way to ensure the safe delivery of FFF-IMRT.

60 APPLIED LIFE SCIENCES↗

Evolution of a Gaussian laser beam in warm collisional magnetoplasma

In this paper, the spatial evolution of an intense circularly polarized Gaussian laser beam propagated through a warm plasma is investigated, taking into account the ponderomotive force, Ohmic heating, external magnetic field, and collisional effects. Using the momentum transfer and energy equations, both modified electron temperature and electron density in plasma are obtained. By introducing the complex dielectric permittivity of warm magnetized plasma and using the complex eikonal function, coupled differential equations for beam width parameter are established and solved numerically. The effects of polarization state of laser and magnetic field on the laser spot size evolution are studied. It is observed that in case of the right-handed polarization, an increase in the value of external magnetic field causes an increase in the strength of the self-focusing, especially in the higher values, and consequently, the self-focusing occurs in shorter distance of propagation. Moreover, the results demonstrate the existence of laser intensity and electron temperature ranges where self-focusing can occur, while the beam diverges outside of these regions; meanwhile, in these intervals, there exists a turning point for each of intensity and temperature in which the self-focusing process has its strongest strength. Finally, it is found that the self-focusing effect can be enhanced by increasing the plasma frequency (plasma density).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Implementing a newly proposed Monte Carlo based small field dosimetry formalism for a comprehensive set of diode detectors

Purpose: The goal of this work was to implement a recently proposed small field dosimetry formalism [Alfonso et al., Med. Phys. 35(12), 5179-5186 (2008)] for a comprehensive set of diode detectors and provide the required Monte Carlo generated factors to correct measurement. Methods: Jaw collimated square small field sizes of side 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, and 3.0 cm normalized to a reference field of 5.0 cm x 5.0 cm were used throughout this study. Initial linac modeling was performed with electron source parameters at 6.0, 6.1, and 6.2 MeV with the Gaussian FWHM decreased in steps of 0.010 cm from 0.150 to 0.100 cm. DOSRZnrc was used to develop models of the IBA stereotactic field diode (SFD) as well as the PTW T60008, T60012, T60016, and T60017 field diodes. Simulations were run and isocentric, detector specific, output ratios (OR{sub det}) calculated at depths of 1.5, 5.0, and 10.0 cm. This was performed using the following source parameter subset: 6.1 and 6.2 MeV with a FWHM = 0.100, 0.110, and 0.120 cm. The source parameters were finalized by comparing experimental detector specific output ratios with simulation. Simulations were then run with the active volume and surrounding materials set to water and the replacement correction factors calculated according to the newly proposed formalism. Results: In all cases, the experimental field size widths (at the 50% level) were found to be smaller than the nominal, and therefore, the simulated field sizes were adjusted accordingly. At a FWHM = 0.150 cm simulation produced penumbral widths that were too broad. The fit improved as the FWHM was decreased, yet for all but the smallest field size worsened again at a FWHM = 0.100 cm. The simulated OR{sub det} were found to be greater than, equivalent to and less than experiment for spot size FWHM = 0.100, 0.110, and 0.120 cm, respectively. This is due to the change in source occlusion as a function of FWHM and field size. The corrections required for the 0.5 cm field size were 0.95 ({+-}1.0%) for the SFD, T60012 and T60017 diodes and 0.90 ({+-}1.0%) for the T60008 and T60016 diodes--indicating measured output ratios to be 5% and 10% high, respectively. Our results also revealed the correction factors to be the same within statistical variation at all depths considered. Conclusions: A number of general conclusions are evident: (1) small field OR{sub det} are very sensitive to the simulated source parameters, and therefore, rigorous Monte Carlo linac model commissioning, with respect to measurement, must be pursued prior to use, (2) backscattered dose to the monitor chamber should be included in simulated OR{sub det} calculations, (3) the corrections required for diode detectors are design dependent and therefore detailed detector modeling is required, and (4) the reported detector specific correction factors may be applied to experimental small field OR{sub det} consistent with those presented here.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

COLLIMATION AND SCATTERING OF THE ACTIVE GALACTIC NUCLEUS EMISSION IN THE SOMBRERO GALAXY

We present an analysis of a data cube of the central region of M104, the Sombrero galaxy, obtained with the GMOS-IFU of the Gemini-South telescope, and report the discovery of collimation and scattering of the active galactic nucleus (AGN) emission in the circumnuclear region of this galaxy. Analysis with PCA Tomography and spectral synthesis revealed the existence of collimation and scattering of the AGN featureless continuum and also of a broad component of the H{alpha} emission line. The collimation and scattering of this broad H{alpha} component was also revealed by fitting the [N II] {lambda}{lambda}6548, 6583 and H{alpha} emission lines as a sum of Gaussian functions. The spectral synthesis, together with a V-I image obtained with the Hubble Space Telescope, showed the existence of circumnuclear dust, which may cause the light scattering. We also identify a dusty feature that may be interpreted as a torus/disk structure. The existence of two opposite regions with featureless continuum (P.A. = -18 Degree-Sign {+-} 13 Degree-Sign and P.A. = 162 Degree-Sign {+-} 13 Degree-Sign ) along a direction perpendicular to the torus/disk (P.A. = 72 Degree-Sign {+-} 14 Degree-Sign ) suggests that this structure is approximately edge-on and collimates the AGN emission. The edge-on torus/disk also hides the broad-line region. The proposed scenario is compatible with the unified model and explains why only a weak broad component of the H{alpha} emission line is visible and also why many previous studies detected no broad H{alpha}. The technique used here proved to be an efficient method not only for detecting scattered light, but also for testing the unified model in low-luminosity AGNs.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical model based iterative reconstruction (MBIR) in clinical CT systems. Part II. Experimental assessment of spatial resolution performance

Purpose: Statistical model based iterative reconstruction (MBIR) methods have been introduced to clinical CT systems and are being used in some clinical diagnostic applications. The purpose of this paper is to experimentally assess the unique spatial resolution characteristics of this nonlinear reconstruction method and identify its potential impact on the detectabilities and the associated radiation dose levels for specific imaging tasks. Methods: The thoracic section of a pediatric phantom was repeatedly scanned 50 or 100 times using a 64-slice clinical CT scanner at four different dose levels [CTDI{sub vol} =4, 8, 12, 16 (mGy)]. Both filtered backprojection (FBP) and MBIR (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for image reconstruction and results were compared with one another. Eight test objects in the phantom with contrast levels ranging from 13 to 1710 HU were used to assess spatial resolution. The axial spatial resolution was quantified with the point spread function (PSF), while the z resolution was quantified with the slice sensitivity profile. Both were measured locally on the test objects and in the image domain. The dependence of spatial resolution on contrast and dose levels was studied. The study also features a systematic investigation of the potential trade-off between spatial resolution and locally defined noise and their joint impact on the overall image quality, which was quantified by the image domain-based channelized Hotelling observer (CHO) detectability index d′. Results: (1) The axial spatial resolution of MBIR depends on both radiation dose level and image contrast level, whereas it is supposedly independent of these two factors in FBP. The axial spatial resolution of MBIR always improved with an increasing radiation dose level and/or contrast level. (2) The axial spatial resolution of MBIR became equivalent to that of FBP at some transitional contrast level, above which MBIR demonstrated superior spatial resolution than FBP (and vice versa); the value of this transitional contrast highly depended on the dose level. (3) The PSFs of MBIR could be approximated as Gaussian functions with reasonably good accuracy. (4) Thez resolution of MBIR showed similar contrast and dose dependence. (5) Noise standard deviation assessed on the edges of objects demonstrated a trade-off with spatial resolution in MBIR. (5) When both spatial resolution and image noise were considered using the CHO analysis, MBIR led to significant improvement in the overall CT image quality for both high and low contrast detection tasks at both standard and low dose levels. Conclusions: Due to the intrinsic nonlinearity of the MBIR method, many well-known CT spatial resolution and noise properties have been modified. In particular, dose dependence and contrast dependence have been introduced to the spatial resolution of CT images by MBIR. The method has also introduced some novel noise-resolution trade-off not seen in traditional CT images. While the benefits of MBIR regarding the overall image quality, as demonstrated in this work, are significant, the optimal use of this method in clinical practice demands a thorough understanding of its unique physical characteristics.

60 APPLIED LIFE SCIENCES↗

SU-E-T-586: Optimal Determination of Tolerance Level for Radiation Dose Delivery Verification in An in Vivo Dosimetry System

Purpose: To statistically determine the optimal tolerance level in the verification of delivery dose compared to the planned dose in an in vivo dosimetry system in radiotherapy. Methods: The LANDAUER MicroSTARii dosimetry system with screened nanoDots (optically stimulated luminescence dosimeters) was used for in vivo dose measurements. Ideally, the measured dose should match with the planned dose and falls within a normal distribution. Any deviation from the normal distribution may be redeemed as a mismatch, therefore a potential sign of the dose misadministration. Randomly mis-positioned nanoDots can yield a continuum background distribution. A percentage difference of the measured dose to its corresponding planned dose (ΔD) can be used to analyze combined data sets for different patients. A model of a Gaussian plus a flat function was used to fit the ΔD distribution. Results: Total 434 nanoDot measurements for breast cancer patients were collected across a period of three months. The fit yields a Gaussian mean of 2.9% and a standard deviation (SD) of 5.3%. The observed shift of the mean from zero is attributed to the machine output bias and calibration of the dosimetry system. A pass interval of −2SD to +2SD was applied and a mismatch background was estimated to be 4.8%. With such a tolerance level, one can expect that 99.99% of patients should pass the verification and at most 0.011% might have a potential dose misadministration that may not be detected after 3 times of repeated measurements. After implementation, a number of new start breast cancer patients were monitored and the measured pass rate is consistent with the model prediction. Conclusion: It is feasible to implement an optimal tolerance level in order to maintain a low limit of potential dose misadministration while still to keep a relatively high pass rate in radiotherapy delivery verification.

61 RADIATION PROTECTION AND DOSIMETRY↗

Development of activity pencil beam algorithm using measured distribution data of positron emitter nuclei generated by proton irradiation of targets containing {sup 12}C, {sup 16}O, and {sup 40}Ca nuclei in preparation of clinical application

Purpose: The purpose of this study is to develop a new calculation algorithm that is satisfactory in terms of the requirements for both accuracy and calculation time for a simulation of imaging of the proton-irradiated volume in a patient body in clinical proton therapy. Methods: The activity pencil beam algorithm (APB algorithm), which is a new technique to apply the pencil beam algorithm generally used for proton dose calculations in proton therapy to the calculation of activity distributions, was developed as a calculation algorithm of the activity distributions formed by positron emitter nuclei generated from target nuclear fragment reactions. In the APB algorithm, activity distributions are calculated using an activity pencil beam kernel. In addition, the activity pencil beam kernel is constructed using measured activity distributions in the depth direction and calculations in the lateral direction. {sup 12}C, {sup 16}O, and {sup 40}Ca nuclei were determined as the major target nuclei that constitute a human body that are of relevance for calculation of activity distributions. In this study, ''virtual positron emitter nuclei'' was defined as the integral yield of various positron emitter nuclei generated from each target nucleus by target nuclear fragment reactions with irradiated proton beam. Compounds, namely, polyethylene, water (including some gelatin) and calcium oxide, which contain plenty of the target nuclei, were irradiated using a proton beam. In addition, depth activity distributions of virtual positron emitter nuclei generated in each compound from target nuclear fragment reactions were measured using a beam ON-LINE PET system mounted a rotating gantry port (BOLPs-RGp). The measured activity distributions depend on depth or, in other words, energy. The irradiated proton beam energies were 138, 179, and 223 MeV, and measurement time was about 5 h until the measured activity reached the background level. Furthermore, the activity pencil beam data were made using the activity pencil beam kernel, which was composed of the measured depth data and the lateral data including multiple Coulomb scattering approximated by the Gaussian function, and were used for calculating activity distributions. Results: The data of measured depth activity distributions for every target nucleus by proton beam energy were obtained using BOLPs-RGp. The form of the depth activity distribution was verified, and the data were made in consideration of the time-dependent change of the form. Time dependence of an activity distribution form could be represented by two half-lives. Gaussian form of the lateral distribution of the activity pencil beam kernel was decided by the effect of multiple Coulomb scattering. Thus, the data of activity pencil beam involving time dependence could be obtained in this study. Conclusions: The simulation of imaging of the proton-irradiated volume in a patient body using target nuclear fragment reactions was feasible with the developed APB algorithm taking time dependence into account. With the use of the APB algorithm, it was suggested that a system of simulation of activity distributions that has levels of both accuracy and calculation time appropriate for clinical use can be constructed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Implementation of EPID transit dosimetry based on a through-air dosimetry algorithm

Purpose: A method to perform transit dosimetry with an electronic portal imaging device (EPID) by extending the commercial implementation of a published through-air portal dose image (PDI) prediction algorithm Van Esch et al.[Radiother. Oncol. 71, 223-234 (2004)] is proposed and validated. A detailed characterization of the attenuation, scattering, and EPID response behind objects in the beam path is used to convert through-air PDIs into transit PDIs. Methods: The EPID detector response beyond a range of water equivalent thicknesses (0-35 cm) and field sizes (3x3 to 22.2x29.6 cm{sup 2}) was analyzed. A constant air gap between the phantom exit surface and the EPID was utilized. A model was constructed that accounts for the beam's attenuation along the central axis, the presence of phantom scattered radiation, the detector's energy dependent response, and the difference in EPID off-axis pixel response relative to the central pixel. The efficacy of the algorithm was verified by comparing predicted and measured PDIs for IMRT fields delivered through phantoms of increasing complexity. Results: The expression that converts a through-air PDI to a transit PDI is dependent on the object's thickness, the irradiated field size, and the EPID pixel position. Monte Carlo derived narrow-beam linear attenuation coefficients are used to model the decrease in primary fluence incident upon the EPID due to the object's presence in the beam. This term is multiplied by a factor that accounts for the broad beam scatter geometry of the linac-phantom-EPID system and the detector's response to the incident beam quality. A 2D Gaussian function that models the nonuniformity of pixel response across the EPID detector plane is developed. For algorithmic verification, 49 IMRT fields were repeatedly delivered to homogeneous slab phantoms in 5 cm increments. Over the entire set of measurements, the average area passing a 3%/3mm gamma criteria slowly decreased from 98% for no material in the beam to 96.7% for 35 cm of material in the beam. The same 49 fields were delivered to a heterogeneous slab phantom and on average, 97.1% of the pixels passed the gamma criteria. Finally, a total of 33 IMRT fields were delivered to the anthropomorphic phantom and on average, 98.1% of the pixels passed. The likelihood of good matches was independent of anatomical site. Conclusions: A prediction of the transit PDI behind a phantom or patient can be created for the purposes of treatment verification via an extension of the Van Esch through-air PDI algorithm. The results of the verification measurements through phantoms indicate that further investigation through patients during their treatments is warranted.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗