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Fulltext Monte Carlo method with heuristic adjustment for irregularly shaped food product volume measurement

Siswantoro J, Prabuwono AS, Abdullah A, Idrus B

ScientificWorldJournal, 2014;2014:683048.
PMID: 24892069 DOI: 10.1155/2014/683048

Volume measurement plays an important role in the production and processing of food products. Various methods have been proposed to measure the volume of food products with irregular shapes based on 3D reconstruction. However, 3D reconstruction comes with a high-priced computational cost. Furthermore, some of the volume measurement methods based on 3D reconstruction have a low accuracy. Another method for measuring volume of objects uses Monte Carlo method. Monte Carlo method performs volume measurements using random points. Monte Carlo method only requires information regarding whether random points fall inside or outside an object and does not require a 3D reconstruction. This paper proposes volume measurement using a computer vision system for irregularly shaped food products without 3D reconstruction based on Monte Carlo method with heuristic adjustment. Five images of food product were captured using five cameras and processed to produce binary images. Monte Carlo integration with heuristic adjustment was performed to measure the volume based on the information extracted from binary images. The experimental results show that the proposed method provided high accuracy and precision compared to the water displacement method. In addition, the proposed method is more accurate and faster than the space carving method.

Matched MeSH terms: Monte Carlo Method*
Stochastic lead time demand estimation via Monte Carlo simulation technique in supply chain planning

Mahdavi M, Mahdavi M

Sains Malaysiana, 2014;43:629-636.

This paper considers a Monte Carlo simulation based method for estimating cycle stocks (production lot-sizing stocks) in a typical batch production system, where a variety of products is scheduled for production at determined periods of time. Delivery time is defined as the maximum lead time and pre-assembly processing time of the product's raw materials in the method. The product's final assembly cycle and delivery time, which were obtained via the production schedule and supply chain simulation, respectively, were both considered to estimate the demand distribution of product based on total duration. Efficient random variates generators were applied to model the lead time of the supply chain's stages. In order to support the performance reliability of the proposed method, a real case study is conducted and numerically analyzed.

Matched MeSH terms: Monte Carlo Method
Single-machine Integrated Production Preventive Maintenance Scheduling: A Simheuristic Approach

Nurul Nadiah Abdul Halim, S. Sarifah Radiah Shariff, Siti Meriam Zahari

MATEMATIKA, 2020;36(2):113-126.
MyJurnal

Preventive maintenance (PM) planning becomes a crucial issue in the real world of the manufacturing process. It is important in the manufacturing industry to maintain the optimum level of production and minimize its investments. Thus, this paper focuses on multiple jobs with a single production line by considering stochastic machine breakdown time. The aim of this paper is to propose a good integration of production and PM schedule that will minimize total completion time. In this study, a hybrid method, which is a genetic algorithm (GA), is used with the Monte Carlo simulation (MCS) technique to deal with the uncertain behavior of machine breakdown time. A deterministic model is adopted and tested under different levels of complexity. Its performance is evaluated based on the value of average completion time. The result clearly shows that the proposed integrated production with PM schedule can reduce the average completion time by 11.68% compared to the production scheduling with machine breakdown time.

Matched MeSH terms: Monte Carlo Method
Fulltext Determination of neutronic parameters of RTP core using mcnp code

Mohamad Hairie Rabir, Usang, Mark Dennis, Naim Syauqi Hamzah, Julia Abdul Karim, Mohd Amin Sharifuldin Salleh

Jurnal Sains Nuklear Malaysia, 2013;25(1):45-59.
MyJurnal

The 1 MW TRIGA MARK II research reactor at Malaysian Nuclear Agency achieved initial
criticality on June 28, 1982. The reactor is designed to effectively implement the various fields of
basic nuclear research, manpower training, and production of radioisotopes. This
paperdescribes the reactor parameters calculation for the PUSPATI TRIGA REACTOR (RTP);
focusing on the application of the developed reactor 3D model for criticality calculation,
analysis of power and neutron flux distribution and depletion study of TRIGA fuel. The 3D
continuous energy Monte Carlo code MCNP was used to develop a versatile and accurate full
model of the TRIGA reactor. The consistency and accuracy of the developed RTP MCNP model
was established by comparing calculations to the experimental results and TRIGLAV
code.MCNP and TRIGLAV criticality prediction of the critical core loading are in a very good
agreement with the experimental results.Power peaking factor calculated with TRIGLAV are
systematically higher than the MCNP but the trends are the same.Depletion calculation by both
codes show differences especially at high burnup.The results are conservative and can be
applied to show the reliability of MCNP code and the model both for design and verification of
the reactor core, and future calculation of its neutronic parameters.

Matched MeSH terms: Monte Carlo Method
Fulltext The performance of classical and robust logistic regression estimators in the presence of outliers

Habshah, M., Syaiba, B.A.

Pertanika Journal of Science & Technology, 2012;20(2):313-325.
MyJurnal

It is now evident that the estimation of logistic regression parameters, using Maximum LikelihoodEstimator (MLE), suffers a huge drawback in the presence of outliers. An alternative approach is touse robust logistic regression estimators, such as Mallows type leverage dependent weights estimator(MALLOWS), Conditionally Unbiased Bounded Influence Function estimator (CUBIF), Bianco andYohai estimator (BY), and Weighted Bianco and Yohai estimator (WBY). This paper investigates therobustness of the preceding robust estimators by using real data sets and Monte Carlo simulations. Theresults indicate that the MLE behaves poorly in the presence of outliers. On the other hand, the WBYestimator is more efficient than the other existing robust estimators. Thus, it is suggested that the WBYestimator be employed when outliers are present in the data to obtain a reliable estimate.

Matched MeSH terms: Monte Carlo Method
Fulltext Power and neutron flux calculation for the puspati triga reactor using MCNP

Mohamad Hairie Rabir, Julia Abdul Karim, Mohd Amin Sharifuldin Salleh

Jurnal Sains Nuklear Malaysia, 2012;24(1):22-32.
MyJurnal

The Malaysian 1 MW TRIGA MARK II research reactor at Malaysian Nuclear Agency is designed to effectively implement the various fields of basic nuclear research, manpower training, and production of radioisotopes for their use in agriculture, industry, and medicine. This study deals with the calculation of neutron flux and power distribution in PUSPATI TRIGA REACTOR (RTP) 14th core configuration. The 3-D continuous energy Monte Carlo code MCNP was used to develop a versatile and accurate full model of the TRIGA core and fuels. The model represents in detailed all components of the core with literally no physical approximation. Continuous energy cross-section data from the more recent nuclear data as well as S (α, β) thermal neutron scattering functions distributed with the MCNP code were used. Results of calculations are analyzed and discussed.

Matched MeSH terms: Monte Carlo Method
Fulltext Criticality calculation in triga Mark II puspati reactor using Monte Carlo code

Jamro, Rafhayudi, Abdul Aziz Mohamed, Megat Harun Al-Rashid, Julia Abd Karim, Hafizal Yazid, Azraf Azman, et al.

Journal of Nuclear and Related Technologies, 2008;2008(2):65-71.
MyJurnal

A Monte Carlo simulation of the Malaysian nuclear reactor has been performed using MCNP Version 5 code. The purpose of the work is the determination of the multiplication factor (k eff ) for TRIGA Mark II research reactor in Malaysia based on Monte Carlo method. This work has been performed to calculate the value of k eff for two cases, which are the control rod either fully withdrawn or fully inserted to construct a complete model of the TRIGA Mark II PUSPATI Reactor (RTP). The RTP core was modeled as close as possible to the real core and the results of k eff from MCNP5 were obtained. When the control-fuel rods were fully inserted, the k eff value indicates the RTP reactor was in the subcritical condition with a value of 0.98370 ± 0.00054. When the control-fuel rods were fully withdrawn the value of k eff value indicates the RTP reactor is in the supercritical condition, that is 1.10773 ± 0.00083.

Matched MeSH terms: Monte Carlo Method
Analysis of t-year return level for partial duration rainfall series

Ling WS, Noriszura Ismail

Sains Malaysiana, 2012;41:1389-1401.

This paper aims to estimate the Generalized Pareto Distribution (GPD) parameters and predicts the T-year return levels of extreme rainfall events using the Partial Duration Series (PDS) method based on the hourly rainfall data of five stations in Peninsular Malaysia. In particular, the GPD parameters are estimated using five methods namely the method of Moments (MOM), the probability weighted moments (PWM), the L-moments (LMOM), the Trimmed L-moments (TLMOM) and the Maximum Likelihood (ML) and the performance of the T-year return level of each estimation method is analyzed based on the RMSE measure obtained from Monte Carlo simulation. In addition, we suggest the weighted average model, a model which assigns the inverse variance of several methods as weights, to estimate the T-year return level. This paper contributes to the hydrological literatures in terms of three main elements. Firstly, we suggest the use
of hourly rainfall data as an alternative to provide a more detailed and valuable information for the analysis of extreme rainfall events. Secondly, this study applies five methods of parametric approach for estimating the GPD parameters and predicting the T-year return level. Finally, in this study we propose the weighted average model, a model that assigns the inverse variance of several methods as weights, for the estimation of the T-year return level.

Matched MeSH terms: Monte Carlo Method
Preliminary study on bayesian extreme rainfall analysis: a case study of Alor Setar, Kedah, Malaysia

Annazirin Eli, Mardhiyyah Shaffie, Wan Zawiah W

Sains Malaysiana, 2012;41:1403-1410.

Statistical modeling of extreme rainfall is essential since the results can often facilitate civil engineers and planners to estimate the ability of building structures to survive under the utmost extreme conditions. Data comprising of annual maximum series (AMS) of extreme rainfall in Alor Setar were fitted to Generalized Extreme Value (GEV) distribution using method of maximum likelihood (ML) and Bayesian Markov Chain Monte Carlo (MCMC) simulations. The weakness of ML method in handling small sample is hoped to be tackled by means of Bayesian MCMC simulations in this study. In order to obtain the posterior densities, non-informative and independent priors were employed. Performances of parameter estimations were verified by conducting several goodness-of-fit tests. The results showed that Bayesian MCMC method was slightly better than ML method in estimating GEV parameters.

Matched MeSH terms: Monte Carlo Method
Performance of two-samples pseudo-median procedure

Nor Aishah Ahad, Sharipah Soaad Syed Yahaya, Abdul Rahman Othman

Sains Malaysiana, 2012;41:1149-1154.

This article investigates the performance of two-sample pseudo-median based procedure in testing differences between groups. The procedure is a modification of the one-sample Wilcoxon procedure using the pseudo-median of differences between group values as the central measure of location. The test was conducted on two groups with moderate sample
sizes of symmetric and asymmetric distributions. The performance of the procedure was measured in terms of Type I error and power rates computed via Monte Carlo methods. The performance of the procedure was compared against the t-test and Mann-Whitney-Wilcoxon test. The findings from this study revealed that the pseudo-median procedure performed very
well in controlling Type I error rates close to the nominal value. The pseudo-median procedure outperformed the MannWhitney-Wilcoxon test and is comparable to the t-test in controlling Type I error and maintaining adequate power.

Matched MeSH terms: Monte Carlo Method
Sensitivity analysis of the refinement to the mann-whitney test

Abdul Rahman Othman, Lai CH

Sains Malaysiana, 2014;43:1095-1100.

The aim of researchers when comparing two independent groups is to collect large normally distributed samples unless they lack the resources to access them. In these situations, there are a myriad of non-parametric tests to select, of which the Mann Whitney U test is the most commonly used. In spite of its great advantages of usage, the U test is capable of producing inflated Type I error when applied in situation of heterogeneity or distinct variances. This current study will present a viable alternative called the refined Mann-Whitney test (RMW). A Monte Carlo evaluation test is conducted on RMW using artificial data of various combinations of extreme test conditions. This study reviews that the RMW test justified its development by enhancing the performance of the U test. The RMW test is able to control well its Type I error rates even though it has a lower power.

Matched MeSH terms: Monte Carlo Method
A monte carlo simulation study on high leverage collinearity-enhancing observation and its effect on multicollinearity pattern

Habshah Midi, Bagheri A, Rahmatullah Imon A

Sains Malaysiana, 2011;40:1437-1447.

Outliers in the X-direction or high leverage points are the latest known source of multicollinearity. Multicollinearity is a nonorthogonality of two or more explanatory variables in multiple regression models, which may have important influential impacts on interpreting a fitted regression model. In this paper, we performed Monte Carlo simulation studies to achieve two main objectives. The first objective was to study the effect of certain magnitude and percentage of high leverage points, which are two important issues in tending the high leverage points to be collinearity-enhancing observations, on the multicollinarity pattern of the data. The second objective was to investigate in which situations these points do make different degrees of multicollinearity, such as moderate or severe. According to the simulation results, high leverage points should be in large magnitude for at least two explanatory variables to guarantee that they are the cause of multicollinearity problems. We also proposed some practical Lower Bound (LB) and Upper Bound (UB) for High Leverage Collinearity Influential Measure (HLCIM) which is an essential measure in detecting the degree of multicollinearity. A well-known example is used to confirm the simulation results.

Matched MeSH terms: Monte Carlo Method
Utilizing 3D Slicer to incorporate tomographic images into GATE Monte Carlo simulation for personalized dosimetry in yttrium-90 radioembolization

Abdul Hadi MFR, Abdullah AN, Hashikin NAA, Ying CK, Yeong CH, Yoon TL, et al.

Med Phys, 2022 Dec;49(12):7742-7753.
PMID: 36098271 DOI: 10.1002/mp.15980

PURPOSE: Monte Carlo (MC) simulation is an important technique that can help design advanced and challenging experimental setups. GATE (Geant4 application for tomographic emission) is a useful simulation toolkit for applications in nuclear medicine. Transarterial radioembolization is a treatment for liver cancer, where microspheres embedded with yttrium-90 (90 Y) are administered intra-arterially to the tumor. Personalized dosimetry for this treatment may provide higher dosimetry accuracy compared to the conventional partition model (PM) calculation. However, incorporation of three-dimensional tomographic input data into MC simulation is an intricate process. In this article, 3D Slicer, free and open-source software, was utilized for the incorporation of patient tomographic images into GATE to demonstrate the feasibility of personalized dosimetry in hepatic radioembolization with 90 Y.
METHODS: In this article, the steps involved in importing, segmenting, and registering tomographic images using 3D Slicer were thoroughly described, before importing them into GATE for MC simulation. The absorbed doses estimated using GATE were then compared with that of PM. SlicerRT, a 3D Slicer extension, was then used to visualize the isodose from the MC simulation.
RESULTS: A workflow diagram consisting of all the steps taken in the utilization of 3D Slicer for personalized dosimetry in 90 Y radioembolization has been presented in this article. In comparison to the MC simulation, the absorbed doses to the tumor and normal liver were overestimated by PM by 105.55% and 20.23%, respectively, whereas for lungs, the absorbed dose estimated by PM was underestimated by 25.32%. These values were supported by the isodose distribution obtained via SlicerRT, suggesting the presence of beta particles outside the volumes of interest. These findings demonstrate the importance of personalized dosimetry for a more accurate absorbed dose estimation compared to PM.
CONCLUSION: The methodology provided in this study can assist users (especially students or researchers who are new to MC simulation) in navigating intricate steps required in the importation of tomographic data for MC simulation. These steps can also be utilized for other radiation therapy related applications, not necessarily limited to internal dosimetry.

Matched MeSH terms: Monte Carlo Method
The application of graphene/h-BN metamaterial in medical linear accelerators for reducing neutron leakage in the treatment room

Hassanpour M, Hassanpour M, Rezaie M, Khezripour S, Faruque MRI, Khandaker MU

Phys Eng Sci Med, 2023 Sep;46(3):1023-1032.
PMID: 37219796 DOI: 10.1007/s13246-023-01269-w

Neutrons can be generated in medical linear accelerators (Linac) due to the interaction of high-energy photons (> 10 MeV) with the components of the accelerator head. The generated photoneutrons may penetrate the treatment room if a suitable neutron shield is not used. This causes a biological risk to the patient and occupational workers. The use of appropriate materials in the barriers surrounding the bunker may be effective in preventing the transmission of neutrons from the treatment room to the outside. In addition, neutrons are present in the treatment room due to leakage in the Linac's head. This study aims to reduce the transmission of neutrons from the treatment room by using graphene/hexagonal boron nitride (h-BN) metamaterial as a neutron shielding material. MCNPX code was used to model three layers of graphene/h-BN metamaterial around the target and other components of the linac, and to investigate its effect on the photon spectrum and photoneutrons. Results indicate that the first layer of a graphene/h-BN metamaterial shield around the target improves photon spectrum quality at low energies, whereas the second and third layers have no significant effect. Regarding neutrons, three layers of the metamaterial results in a 50% reduction in the number of neutrons in the air within the treatment room.

Matched MeSH terms: Monte Carlo Method
Fulltext A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection

Apenteng OO, Ismail NA

PLoS One, 2015;10(7):e0131950.
PMID: 26147199 DOI: 10.1371/journal.pone.0131950

The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS.

Matched MeSH terms: Monte Carlo Method*
Biological polymeric shielding design for an X-ray laboratory using Monte Carlo codes

Tajudin SM, Tabbakh F

Radiol Phys Technol, 2019 Sep;12(3):299-304.
PMID: 31302871 DOI: 10.1007/s12194-019-00522-w

Photon irradiation facilities are often shielded using lead despite its toxicity and high cost. In this study, three Monte Carlo codes, EGS5, MCNPX, and Geant4, were utilized to investigate the efficiency of a relatively new polymeric base compound (CnH2n), as a radiation shielding material for photons with energies below 150 keV. The proposed compound with the densities of 6 and 8 g cm-3 were doped with the weight percentages of 8.0 and 15.0% gadolinium. The probabilities of photoelectric effect and Compton scattering were relatively equal at low photon energies, thus the shielding design was optimized using three Monte Carlo codes for the conformity of calculation results. Consequently, 8% Gd-doped polymer with thickness less than 2 cm and density of 6 g cm-3 was adequate for X-ray room shielding to attenuate more than 95% of the 150-keV incident photons. An average dose rate reduction of 88% can be achieved to ensure safety of the radiation area.

Matched MeSH terms: Monte Carlo Method*
Fulltext Monte Carlo dose calculation in dental amalgam phantom

Aziz MZ, Yusoff AL, Osman ND, Abdullah R, Rabaie NA, Salikin MS

J Med Phys, 2015 Jul-Sep;40(3):150-5.
PMID: 26500401 DOI: 10.4103/0971-6203.165080

It has become a great challenge in the modern radiation treatment to ensure the accuracy of treatment delivery in electron beam therapy. Tissue inhomogeneity has become one of the factors for accurate dose calculation, and this requires complex algorithm calculation like Monte Carlo (MC). On the other hand, computed tomography (CT) images used in treatment planning system need to be trustful as they are the input in radiotherapy treatment. However, with the presence of metal amalgam in treatment volume, the CT images input showed prominent streak artefact, thus, contributed sources of error. Hence, metal amalgam phantom often creates streak artifacts, which cause an error in the dose calculation. Thus, a streak artifact reduction technique was applied to correct the images, and as a result, better images were observed in terms of structure delineation and density assigning. Furthermore, the amalgam density data were corrected to provide amalgam voxel with accurate density value. As for the errors of dose uncertainties due to metal amalgam, they were reduced from 46% to as low as 2% at d80 (depth of the 80% dose beyond Zmax) using the presented strategies. Considering the number of vital and radiosensitive organs in the head and the neck regions, this correction strategy is suggested in reducing calculation uncertainties through MC calculation.

Matched MeSH terms: Monte Carlo Method
Studies of Charm Quark Diffusion inside Jets Using Pb-Pb and pp Collisions at sqrt[s_{NN}]=5.02 TeV

Sirunyan AM, Tumasyan A, Adam W, Ambrogi F, Asilar E, Bergauer T, et al.

Phys Rev Lett, 2020 Sep 04;125(10):102001.
PMID: 32955327 DOI: 10.1103/PhysRevLett.125.102001

The first study of charm quark diffusion with respect to the jet axis in heavy ion collisions is presented. The measurement is performed using jets with p_{T}^{jet}>60 GeV/c and D^{0} mesons with p_{T}^{D}>4 GeV/c in lead-lead (Pb-Pb) and proton-proton (pp) collisions at a nucleon-nucleon center-of-mass energy of sqrt[s_{NN}]=5.02 TeV, recorded by the CMS detector at the LHC. The radial distribution of D^{0} mesons with respect to the jet axis is sensitive to the production mechanisms of the meson, as well as to the energy loss and diffusion processes undergone by its parent parton inside the strongly interacting medium produced in Pb-Pb collisions. When compared to Monte Carlo event generators, the radial distribution in pp collisions is found to be well described by pythia, while the slope of the distribution predicted by sherpa is steeper than that of the data. In Pb-Pb collisions, compared to the pp results, the D^{0} meson distribution for 4

Matched MeSH terms: Monte Carlo Method
Population pharmacokinetic modelling of intravenous immunoglobulin in patients with predominantly antibody deficiencies

Lee JL, Mohd Saffian S, Makmor-Bakry M, Islahudin F, Alias H, Noh LM, et al.

Br J Clin Pharmacol, 2021 07;87(7):2956-2966.
PMID: 33377197 DOI: 10.1111/bcp.14712

AIMS: There is considerable interpatient variability in the pharmacokinetics (PK) of intravenous immunoglobulin G (IVIG), causing difficulty in optimizing individual dosage regimen. This study aims to estimate the population PK parameters of IVIG and to investigate the impact of genetic polymorphism of the FcRn gene and clinical variability on the PK of IVIG in patients with predominantly antibody deficiencies.
METHODS: Patients were recruited from four hospitals. Clinical data were recorded and blood samples were taken for PK and genetic studies. Population PK parameters were estimated by nonlinear mixed-effects modelling in Monolix®. Models were evaluated using the difference in objective function value, goodness-of-fit plots, visual predictive check and bootstrap analysis. Monte Carlo simulation was conducted to evaluate different dosing regimens for IVIG.
RESULTS: A total of 30 blood samples were analysed from 10 patients. The immunoglobulin G concentration data were best described by a one-compartment model with linear elimination. The final model included both volume of distribution (Vd) and clearance (CL) based on patient's individual weight. Goodness-of-fit plots indicated that the model fit the data adequately, with minor model mis-specification. Genetic polymorphism of the FcRn gene and the presence of bronchiectasis did not affect the PK of IVIG. Simulation showed that 3-4-weekly dosing intervals were sufficient to maintain IgG levels of 5 g L-1 , with more frequent intervals needed to achieve higher trough levels.
CONCLUSIONS: Body weight significantly affects the PK parameters of IVIG. Genetic and other clinical factors investigated did not affect the disposition of IVIG.

Matched MeSH terms: Monte Carlo Method
Fulltext Determination optimal aperture parameters for neutron collimator design using MCNP code

Wagiran, Husin, Supramaniam, Thiagu, Azali Mohamad, Abdul Aziz Mohamed, Faridah M. Idris

Journal of Nuclear and Related Technologies, 2009;2009(2):49-62.
MyJurnal

Neutron aperture is one of the collimator components in a neutron radiography facility. The optimum design of neutron aperture is very importance in order to obtain largest L/D ratio with highest thermal neutron flux and low gamma-rays at the image plane. In this study, the optimization of neutron aperture parameters were done using Monte Carlo N-Particle Transport Code, version five (MCNP5). This code has a capability to simulate the neutron, photon, and electron or coupled of neutron/photon/electron transport, including the capability to calculate eigen values for critical system. The aperture parameters concerned in this study are the selection of best aperture material, aperture thickness, aperture position and aperture center hole diameter. In these simulations, vacuum beam port medium was applied.

Matched MeSH terms: Monte Carlo Method

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