Gamma Evaluation Combined with Isocenter Optimal Matching in Intensity Modulated Radiation Therapy Quality Assurance

박진호,최진화,박석원,박광우,박성호 한국물리학회 2015 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.67 No.12

Two-dimensional (2D) dose comparisons are widely performed by using a gamma evaluation with patient-specific intensity modulated radiation therapy quality assurance (IMRT QA) or dose delivery quality assurance (DQA). In this way, a pass/fail determination is made for a particular treatment plan. When gamma evaluation results are close to the failure criterion, the pass/fail decision may change applying a small shift to the center of the 2D dose distribution. In this study, we quantitatively evaluated the meaning of such a small relative shift in a 2D dose distribution comparison. In addition, we propose the use of a small shift for a pass/fail criterion in gamma analysis, where the concept of isocenter optimal matching (IOM) is applied to IMRT QA of 20 patients. Gamma evaluations were performed to compare two dose distributions, one with and the other without IOM. In-house software was developed in C++ in order to find IOM values including both translational and rotational shifts. Upon gamma evaluation failure, further investigation was initiated using IOM. In this way, three groups were categorized: group 1 for ‘pass’ on gamma evaluation, group 21 for ‘fail’ on the gamma evaluation and ‘pass’ on the gamma the evaluation with IOM, and group 22 for ‘fail’ on the both gamma evaluations and the IOM calculation. IOM results revealed that some failures could be considered as a ‘pass’. In group 21, 88.98% (fail) of the averaged gamma pass rate changed to 90.45% (pass) when IOM was applied. On average, a ratio of 1 was reduced by 11.06% in 20 patients. We propose that gamma evaluations that do not pass with a rate of 85% to 90% may be augmented with IOM to reveal a potential pass result.

Some Generalized Gamma Distribution

Saralees Nadarajah,Arjun K. Gupta 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.1

Gamma distributions are some of the most popular models for hydro-logical processes. In this paper, a very exible family which contains thegamma distribution as a particular case is introduced. Evidence of exibil-ity is shown by examining the shape of its pdf and the associated hazardrate function. A comprehensive treatment of the mathematical propertiesis provided by deriving expressions for thenth moment, moment generatingfunction, characteristic function, Renyi entropy and the asymptotic distri-bution of the extreme order statistics. Estimation and simulation issues arealso considered. Finally, a detailed application to drought data from theState of Nebraska is illustrated.AMS 2000 subject classications.Primary 33C90; Secondary 62E99.Keywords.Drought modeling, gamma distribution, generalized gamma distribution.1. IntroductionA random variable X is said to have the standard gamma distribution if itsprobability density function (pdf) is given byf(x) =x1 exp( x)()(1.1)forx > 0, > 0 and > 0. Gamma distributions are some of the most popularmodels for hydrological processes (Yue, 2001; Yueet al., 2001; Shiauet al., 2006;references therein). The aim of this paper is to introduce a generalization of(1.1) that could have much wider applicability in hydrology. The generalizationis given by the pdff(x) = Cx1(x + z)exp( x) (1.2)Received May 2006; accepted September 2006.1Corresponding author. School of Mathematics, University of Manchester, Manchester M601QD, U.K. (e-mail: saralees.nadarajah@manchester.ac.uk)

A Modified Hybrid Gamma and Generalized Pareto Distribution for Precipitation Data

김용구,Hyeongang Kim,이규원,민기홍 한국기상학회 2019 Asia-Pacific Journal of Atmospheric Sciences Vol.55 No.4

This study introduces a modified hybrid gamma and generalized Pareto distribution. Prior to this, we define a general spliced distribution and its corresponding gamma distribution, which is part of the head, and a generalized Pareto (GP) distribution, which is part of the tail. We then examine the threshold conditions for the modified hybrid gamma and GP distribution and defined probability density function. Also, we derive the negative log-likelihood function of the modified hybrid gamma and GP distribution and estimate approximate maximum likelihood estimates using the differential evolution algorithm for each simulation to minimize it. Moreover, by presenting the mean square error for each sample size, the model is evaluated according to the size of the sample. Finally, we use daily observed summer precipitation for Seoul, Korea, from 1961 to 2011, which includes 4692 data sets.We use 2051 data sets corresponding to wet conditions. As a result, the estimated threshold of the modified hybrid gamma and GP distribution is 0.1455. After deriving Fisher information through the Hessian matrix, we also present the standard error of the maximum likelihood estimator.

Statistical Properties of Kumaraswamy Exponentiated Gamma Distribution

L. S. Diab,Hiba Z. Muhammed 한국신뢰성학회 2015 International Journal of Reliability and Applicati Vol.16 No.2

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the r<SUP>th</SUP> moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

An Interpretation of the Mixture of Poisson Distributions with a Gamma Distributed Parameter

Suneung Ahn 한국산업경영시스템학회 2003 한국산업경영시스템학회 학술대회 Vol.2003 No.춘계

Used as a mixing distribution for an unknown Poisson parameter, the gamma distribution leads to the negative binomial distribution. The hyperparameters of the gamma distribution have their own meanings according to what the Poisson parameter represents. Different sources in the randomness of the Poisson parameter give different interpretations of the negative binomial distribution.

Applying Conventional and Saturated Generalized Gamma Distributions in Parametric Survival Analysis of Breast Cancer

Yavari, Parvin,Abadi, Alireza,Amanpour, Farzaneh,Bajdik, Chris Asian Pacific Journal of Cancer Prevention 2012 Asian Pacific journal of cancer prevention Vol.13 No.5

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

Two-dimensional Measurement of the Prompt-gamma Distribution for Proton Dose Distribution Monitoring

이한림,박종훈,김한성,김찬형,김승훈 한국물리학회 2013 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.63 No.7

In proton therapy, accurate monitoring of the in-vivo proton dose distribution is essential in orderto deliver the planned dose to the tumor volume within a minimal safety margin. Recently,a strong correlation between the distributions of the proton dose and the prompt gammas wasfound, and various prompt-gamma distribution-measurement systems, including collimation-basedsystems, Compton cameras, knife-edge imaging systems, and ion vertex imaging systems, have beenproposed. In the present study, the feasibility of proton dose distribution monitoring was testedusing a two-dimensional measurement system for prompt gammas. The measurement system, developedin the present study, incorporates a vertically-aligned one-dimensional array of gamma sensors,a parallel multi-hole collimator, a precision movement system, and a digitizer- and LabVIEW-basedautomatic data acquisition system. A 45-MeV proton beam of 0.5 nA was delivered to a polymethylmethacrylate (PMMA) phantom, and the two-dimensional prompt-gamma distribution was measuredusing the developed system. The proton beam range could be quantitatively determined towithin a 1.6-mm error by sigmoidal curve-fitting with the Boltzmann equation. A comparison of theprompt-gamma distribution as measured by our detection system with the proton dose distributionas measured independently by using Gafchromic EBT films positioned inside the PMMA phantomshowed good agreement. Both results imply that it is, indeed, possible to confirm the patient’sproton dose distribution by using two-dimensional prompt-gamma measurements.

Peroxisome Proliferator-Activated $Receptor-{\gamma}$ 2 $(PPAR{\gamma}2)$ Pro12Ala (P12A) 유전자 다형성이 한국여성의 체지방분포에 미치는 영향

김길수,최선미,양현성,윤유식,신승우,Kim, Kil-Soo,Choi, Sun-Mi,Yang, Hyun-Sung,Yoon, Yoo-Sik,Shin, Seun-Uoo 한방비만학회 2004 한방비만학회지 Vol.4 No.1

Objectives: The effects of peroxisome proliferator-activated receptor ${\gamma}2\;(PPAR{\gamma}2)$ Pro12Ala (P12A) polymorphism on body mass index (BMI) and type 2 diabetes are well documented; however, until now, only a few studies have evaluated the effects of this polymorphism on body fat distribution. This study was conducted to elucidate the effects of this polymorphism on computed tomography (CT)-measured body fat distribution and other obesity-related parameters in Korean female subjects. Methods & Results: The frequencies of $PPAR{\gamma}2$ genotypes were: PP type, 93.0%; PA type, 6.8%; and AA type, 0.2%. The frequency of the A allele was 0.035. Body weight (P .012), BMI (P .012), and waist-to-hip ratio (WHR) (P .001) were significantly higher in subjects with PA/AA compared with subjects with PP. When body composition was analyzed by bioimpedance analysis, lean body mass and body water content were similar between the 2 groups. However, body fat mass (P .003) and body fat percent (P .025) were significantly higher in subjects with PA/AA compared with subjects with PP. Among overweight subjects with BMI of greater than 25, PA/AA was associated with significantly higher abdominal subcutaneous fat (P .000), abdominal visceral fat (P .031), and subcutaneous upper and lower thigh adipose tissue (P .010 and .013). However, among lean subjects with BMI of less than 25, no significant differences associated with $PPAR{\gamma}2$ genotype were found, suggesting that the fat-accumulating effects of the PA/AA genotype were evident only among overweight subjects, but not among lean subjects. When serum lipid profiles, glucose, and liver function indicators were compared among overweight subjects, no significant difference associated with $PPAR{\gamma}2$ genotype was found. Changes in body weight, BMI, WHR, and body fat mass were measured among overweight subjects who finished a 1-month weight lose program of a hypocaloric diet and exercise; no significant differences associated with $PPAR{\gamma}2$ genotype were found. Conclusions: The results of this study suggest that the $PPAR{\gamma}2$ PA/AA genotype is associated with increased subcutaneous and visceral fat areas in overweight Korean female subjects, but does not significantly affect serum biochemical parameters and outcomes of weight loss programs.

Monte Carlo simulations on the local density inhomogeneities of sub- and supercritical carbon dioxide: Statistical analysis based on the Voronoi tessellation

Yoon, Tae Jun,Ha, Min Young,Lee, Won Bo,Lee, Youn-Woo Elsevier 2017 The Journal of supercritical fluids Vol.119 No.-

<P><B>Abstract</B></P> <P>Monte Carlo (MC) simulations were performed to understand the statistical aspects of the local density distributions of sub- and supercritical CO<SUB>2</SUB> along the VLE line and at <I>T<SUB>r</SUB> </I> =1.02 which were obtained from the Voronoi tessellation. From the statistical analysis, the local density distribution of CO<SUB>2</SUB> (<I>v</I>) and CO<SUB>2</SUB> (<I>l</I>) along the VLE line was assumed to be represented by an Inverse Gamma distribution and a Normal distribution respectively. An Inverse Gamma-Normal mixture model was then proposed as a statistical model for the representation of the local density distributions of CO<SUB>2</SUB> (<I>sc</I>). For the density distribution of CO<SUB>2</SUB> (<I>sc</I>) at <I>T<SUB>r</SUB> </I> =1.02, the mixture model was well fitted to the distribution. The mixture model could also find out the gas-to-liquid transition point located at <SUB> ρ r </SUB> ≅ 0.92 . In addition, the <I>mean</I> local densities were correlated to the conventional concept of the <I>effective</I> local density.</P> <P><B>Highlights</B></P> <P> <UL> <LI> MC simulations were used to study the density augmentation of supercritical CO<SUB>2</SUB>. </LI> <LI> Voronoi tessellation was performed to obtain the local densities of molecules. </LI> <LI> The density distributions of CO<SUB>2</SUB> (<I>v</I>) were fitted to an Inverse Gamma distribution. </LI> <LI> The density distributions of CO<SUB>2</SUB> (<I>l</I>) were fitted to a Normal distribution. </LI> <LI> An Inverse Gamma-Normal mixture were used as the density distribution of CO<SUB>2</SUB> (<I>sc</I>). </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>

Statistical Properties of Kumaraswamy Exponentiated Gamma Distribution

Diab, L.S.,Muhammed, Hiba Z. The Korean Reliability Society 2015 International Journal of Reliability and Applicati Vol.16 No.2

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.