한양대학교 원자력공학과 김 찬 형 제44회 춘계의학물리학회 & Geant4 Workshop (충무, 마리나 리조트, ) Monte Carlo 원리 및 응용

History Definition Stochastic calculation technique using random numbers  ‘Statistical sampling technique’ History Development started in 1946 at Los Alamos  Suggested by Stanislaw Ulam in 1946  Development directed by John von Neumann First complete MC test on ENIAC in 1947  9 neutron transport problems “Monte Carlo” Named by Nicholas Metropolis Name of a quarter in Monaco (city state) Common feature - randomly selected numbers are used in both Monte Carlo technique and gambling

Random Numbers Computer-generated numbers Pseudo random number Linear-congruent method rand() function in MATALB TM  Numbers between 0 and 1  Random, but also uniform RW3USB (speed: 1.5 Mbit/sec, Dimensions: 8 cm x 5.5 cm x 2.5 cm)

Radiation Transport Simulation Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle 10 x y z x y z x y z

Radiation Transport Simulation Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Radioisotope (isotropic) x y z particle direction (cosine distribution) Pencil beam/ Beam polar, azimuthal angles fixed Use physics models and cross section data to sample direction, flight distance, etc.

Radiation Transport Simulation Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Use physics models and cross section data to sample direction, flight distance, etc. Single energy No sampling Multiple energies (e.g 60 Co) 1.17 MeV (50 %) 1.33 MeV (50 %) MeV 1.33 MeV Polyenergetic (e.g. X-rays) Integration CDF Energy sampling

Radiation Transport Simulation Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle d=? interaction p(d) d Distance Sampling

Radiation Transport Simulation Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Collision point coordinate

Radiation Transport Simulation Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Example Photoelectric effect : 30 % Compton scattering : 50 % Pair production : 20 % Photoelectric effect (30 %) 0.8 Compton scattering (50 %) Pair production (20 %)

Radiation Transport Simulation Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle

Radiation Transport Simulation Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle “Acceptance-rejection” method Klein-Nishina cross section Photon energy

In Reality - More Complicated Production of secondary particles photon  electron electron  electron; electron  photon (Bremsstrahlung X-ray) positron  511 keV annihilation photons Characteristic X-rays Heterogeneous 3-D geometry Need to calculated the distance between the particle and a surface in a given direction Voxel model, polygon model Non-analog simulation Russian roulette/particle splitting Forced collision Implicit capture Exponential transform

Application Examples at RIDoL

Texas A&M University 1 MW MTR converted type TRIGA reactor as modeled in MCNP The fission product was modeled by “average fission product” and repeated adjustment. High- temperature neutron cross section was used to model the reactor at full power. Nuclear Reactor Simulation C.H. Kim, S.Y. Jang and W.D. Reece. Monte Carlo modeling of the Texas A&M University Research Reactor. Nucl. Tech. 145(1):1-10 (2004)

Radiation Shielding Analysis IBA Cyclotron 18/19 Cyclotron X Y Target Cyclotron 상층 벽 상층 1 Y Z Calculated dose distribution at exterior surface of side wall and bottom of upper floor (MCNP mesh tally used) Target modeling (MCNPX) MCNPX modeling Kyu Seok Seo, Chan Hyeong Kim, “Shielding Calculations of Accelerator Facility for Medical Isotope Production using MCNPX Code,” Korean Journal of Medical Physics, 15(4): (2004) side wall

Varian 2100C LINAC as modeled in BEAMnrc PTW30013 Farmer-type ion chamber as modeled in EGSPP Result for 6, 9, 12 MeV electron beams LINAC Simulation Chul Hee Min, Seong Hoon Kim, Dong Oh Shin, Chan-Hyeong Kim. A preliminary study on the calculation of TG-51 beam quality correction factor for low-energy electron beams. Japanese Journal of Medical Physics. 25S(3-1): (2005)

Compton Camera Simulation Geant4 simulation Hee Seo, So Hyun An, Jong Kyung Kim, Chan Hyeong Kim. Monte Carlo Study of a Double Scattering Compton Camera with GEANT4, Nuclear Instruments and Methods in Physics Research A. 580: (2007) Double-scattering Compton Imager (DOCI)

CIS - Compton Imaging Simulator Se Hyung Lee, Hee Seo, and Chan Hyeong Kim, CCSC: a GUI-based Integrated Simulation Code for Monte Carlo Simulation of Compton Camera, Nuclear Technology (in press)

Prompt Gamma Measurement System Chul-Hee Min, Chan Hyeong Kim, Min-Young Youn, Jong-Won Kim. Prompt gamma measurements for locating the dose fall- off region in the proton therapy. Applied Physics Letters. 89: (2006)

2D Prompt Gamma Imaging

Organ Dose Calculations C. H. Kim*, J. H. Jeong, W. E. Bolch, K. W. Cho and S. B. Hwang, "A polygon-surface reference Korean male phantom (PSRK-Man) and its direct implementation in Geant4 Monte Carlo simulation", Phys. Med. Biol., 56: (2011) HDRK-Man and HDRK-Woman PSRK-Man

4D Monte Carlo Simulation 4D-CT Images Polygon Phantom 4D Monte Carlo Simulation Technique Moving Respiratory Organs 4D Computational Human Phantoms for Medical Applications

Other Simulations Cases Chest X-ray simulation 125 I seed source TG-43 dosimetry Prompt gamma head-and-neck system Effective dose measurement system Industrial SPECT system Proton radiography system MOSFET dosimeter Landmine detection system GEVI imaging system