APPLICATIONS OF MONTE CARLO METHODS IN BIOLOGY, MEDICINE AND OTHER FIELDS OF SCIENCE Edited by Charles J. Mode Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science Edited by Charles J. Mode Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Ana Nikolic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic First published February, 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science Edited by Charles J. Mode p. cm. ISBN 978-953-307-427-6 free online editions of InTech Books and Journals can be found at www.intechopen.com Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Preface IX Bias Monte Carlo Methods in Environmental Engineering 1 Albert S. Kim Monte-Carlo Simulation of a Multi-Dimensional Switch-Like Model of Stem Cell Differentiation 25 M. Andrecut Application of Monte Carlo Simulation and Voxel Models to Internal Dosimetry 41 Sakae Kinase, Akram Mohammadi and Masa Takahashi Applications of Monte Carlo Simulation in Modelling of Biochemical Processes 57 Kiril Ivanov Tenekedjiev, Natalia Danailova Nikolova and Krasimir Kolev Applications to Development of PET/SPECT System by Use of Geant4 77 Yoshiyuki Hirano Applying Dynamic Monte Carlo Simulation for Living Free Radical Polymerization Processes: Emphasis on Atom Transfer Radical Polymerization (ATRP) 95 Mamdouh A. Al-Harthi Monte Carlo Simulations for Beam Delivery Line Design in Radiation Therapy with Heavy Ion Beams 115 Faiza Bourhaleb, Andrea Attili and Germano Russo A Monte Carlo Simulation for the Construction of Cytotoxic T Lymphocytes Repertoire 131 Filippo Castiglione Contents Contents VI Application of Monte Carlo Simulation in Treatment Planning for Radiation Oncology 147 Kin Chan, Soo Min Heng and Robert Smee Dosimetric Characteristics of the Brachytherapy Sources Based on Monte Carlo Method 155 Mahdi Sadeghi, Pooneh Saidi and Claudio Tenreiro Evaluation of the Respiratory Motion Effect in Small Animal PET Images with GATE Monte Carlo Simulations 177 Susana Branco, Pedro Almeida and Sébastien Jan Fiber-optic Raman Probe Coupled with a Ball Lens for Improving Depth-resolved Raman Measurements of Epithelial Tissue: Monte Carlo Simulations 201 Zhiwei Huang Monte Carlo Simulations of Powerful Neutron Interaction with Matter for the Goals of Disclosure of Hidden Explosives and Fissile Materials and for Treatment of Cancer Diseases versus their Experimental Verifications 217 V.A. Gribkov, S.V. Latyshev, R.A. Miklaszewski, M. Chernyshova, R. Prokopowicz, M. Scholz, K. Drozdowicz, U. Wiącek, B. Gabańska, D. Dworak, K. Pytel, A. Zawadka, M. Ramos Aruca, F. Longo, G. Giannini and C. Tuniz HERWIG: a Monte Carlo Program for QCD at LHC 243 Giuseppe Marchesini Monte Carlo Simulation of TLD Response Function: Scatterd Radiation Application 265 Seied Rabie Mahdavi, Alireza Shirazi, Ali Khodadadee, Mostafa Ghaffory and Asghar Mesbahi Monte Carlo Implementations of Two Sex Density Dependent Branching Processes and their Applications in Evolutionary Genetics 273 Charles J. Mode, Towfique Raj and Candace K. Sleeman Monte Carlo Modeling of Light Propagation in Neonatal Skin 297 J.A. Delgado Atencio, S.L. Jacques and S. Vázquez y Montiel Monte-Carlo Simulation of Ionizing Radiation Tracks 315 Ianik Plante and Francis A. Cucinotta Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Contents VII Monte Carlo Simulation Tool of Evanescent Waves Spectroscopy Fiber – Optic Probe for Medical Applications (FOPS 3D) 357 Daniel Khankin, Shlomo Mark and Shaul Mordechai Strain Effects in p-type Devices using Full-Band Monte Carlo Simulations 371 Valérie Aubry-Fortuna, Karim Huet, T.T. Trang Nghiêm, Arnaud Bournel, Jérôme Saint-Martin and Philippe Dollfus Utilizing Monte Carlo Simulation for Valuation: the Case of Barrier Options under Stochastic Interest Rates 387 Snorre Lindset A rapidly Mixing Monte Carlo Method for the Simulation of Slow Molecular Processes 399 V. Durmaz, K. Fackeldey and M. Weber Chapter 19 Chapter 20 Chapter 21 Chapter 22 Pref ac e During the last seven or so decades, Monte Carlo simulation methods have been ap- plied in various fi elds including business, economics, engineering and virtually every fi eld of the physical and biological sciences such as chemistry, physics, genetics, biolog- ical evolution and stochastic models of epidemics of infectious diseases in human and other populations. Monte Carlo methods have also had a profound eff ect on the devel- opment of several branches of mathematical sciences such as statistics and numerical analysis. In statistics the phrase, Markov Chain Monte Carlo Methods, denotes a class of methods for estimating parameters within the Bayesian paradigm, and in numeri- cal analysis a widely accepted method for estimating the value of a multi-dimensional integral is known as Monte Carlo integration. But, Monte Carlo methods are, funda- mentally, anchored in pure mathematics and are part of such fi elds as number theory and abstract algebra which underlie the computer generation of “random” numbers. It is beyond the scope of this brief preface to go into the mathematical details underlying the generation of random numbers, but suffi ce it to say that an investigator should be aware that the random generator being utilized has passed numerous statistical tests for randomness, even though we know the sequence of “random” numbers have been computed by a purely sequential deterministic procedure that is repeatable. More de- tails of these procedures will be briefl y discussed at the end of this preface. That this volume is an eclectic mix of applications of Monte Carlo methods in many fi elds of research should not be surprising, because of the ubiquitous use of these methods in many fi elds of human endeavor. In an a empt to focus a ention on a man- ageable set of applications, the main thrust of this book is to emphasize applications of Monte Carlo simulation methods in biology and medicine. But it became necessary, due to the acceptance of a large number of papers for publication, to also accommodate a few other papers that may contain ideas that are potentially applicable to biology and medicine or of general scientifi c interest. Chapter 1 is devoted to a paper by A. Kim on Monte Carlo methods in environmental engineering which center around such issues as expected sacristy of fossil fuels and the designing of new paradigms for environmentally friendly, green, or zero-emission processes to eliminate potential adverse eff ects on nature from undesired technologi- cal by-products. A paper by M. Andrecut on applications of Monte Carlo methods to multi-dimensional switch-like model of stem cell diff erentiation provides the content of chapter 2 and is of basic interest in biology and medicine due to its focus on gene regulatory systems. Chapter 3 contains a paper by S. Kinase et al. on voxel models and their application to internal dosimetry. X Preface A paper by K. I. Tenekedjiev et al. on applications of Monte Carlo methods in modeling biochemical process makes up the content of chapter 4. Dynamic models of complex metabolic systems are typically multi-parametric and non-linear. The stochastic nature of the data necessitates the use of non-linear regression models and other statistical procedures to estimate the many parameters from data. Chapter 5 contains a paper by Y. Hirano on the application of Monte Carlo methods to problem in bio-medical imag- ining, and chapter 6 is devoted to a paper by M. A. Al-Harthi on applying Monte Carlo methods in simulating free radical polymerization processes. The contents of chapter 7 is a paper by F. Bourhaleb et al. on the use of Monte Carlo sim- ulation methods for beam delivery line design in radiation therapy in heavy ion beams. The immune systems of vertebrates are very complex systems that have evolved a set of mechanisms to destroy potential pathogens that individuals may encounter, and chapter 8 is devoted to a paper by F. Castiglione on the Monte Carlo simulation of cy- totoxic T lymphocytes repertoire. A paper by K. Chan et al. on the application of Monte Carlo simulation methods in treatment planning for radiation oncology constitutes the content of chapter 9. The implantation of radioactive particles in organs to treat cancer is a familiar term for many people who have developed cancer. A paper by M. Sadeghi et al. on applying Monte Carlo methods on dosimetric characteristics of brachytherapy sources provides the content of chapter 10. The rapid growth in genetics and molecular biology com- bined with the development of techniques for genetically engineering small animals has increased interest in vivo imaging of small animals. The contents of chapter 11 are a paper by S. Branco et al. on using Monte Carlo methods in the evaluation of respira- tory motion eff ect in small animals by PET and other images. Raman spectroscopy is a vibrational spectroscopic technique capable of optically probing bio-molecular chang- es in tissues and is useful in diagnosing cancers in early stages. Chapter 12 contains a paper by Z. Huang on applying Monte Carlo methods to fi ber-optic Raman probes with a ball lens for improving Raman measurements in epithelial tissue. Chapter 13 contains a paper by V. A. Gribkov et al. on the Monte Carlo simulation of powerful neutron interactions with ma er. Among the goals of such simulation experi- ments is the disclosure of hidden explosives and fi ssile materials, methods for treat- ing cancer and the comparison of real and simulated data. Monte Carlo simulation so ware may be used for the partial description of particle physics production at high energy such as those arising at the LHC (large hadron collider) in CERN, Switzer- land. The content of chapter 14 is a paper by G. Marchesini on such so ware. Thermo- luminescence dosimetries (TLDs) are routinely used for in-vivo dosimetry as well as in other applications in medicine and industry. Chapter 15 is devoted to a paper by S. R. Mahdavi et al. on the Monte Carlo simulation of the response function in sca ered radiation applications. The development of stochastic models accommodating two sexes and population den- sity is an area of theoretical evolutionary genetics of considerable interest. Chapter 16 is devoted to a paper by C. J. Mode et al. on the Monte Carlo implementation of a two sex density dependant branching process, which is very diffi cult to analyze mathemati- cally due to its complexity but its Monte Carlo implementation is straight forward. This paper also contains a description of embedding a non-linear deterministic model in a [...]... great importance in chemical engineering processes Since a polymer can be viewed as a linear connection of many identical monomers, trial movement of a polymer requires constraints such as sequence, bond length, and bond angle of associated monomers 20 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science Mapping the movement of a polymer chain is an interesting problem de... Explain.” (a) Solution using logical thinking The probability that A will be released is 2 because two out of the three will be released The 3 decision of the parole board is independent of A’s knowledge Therefore, A still has a 2/3 chance of being released 8 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science (b) Solution using conditional probability The probability of. .. uniform, random, or mixed manner throughout the mall A station assigned to Leia2 is located between a parking lot and 1 2 The largest shopping mall in Honolulu, Hawaii, the fifteenth largest shopping mall in the United States, and the largest open-air shopping center in the world Hawaiian female name, meaning child of heaven 14 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science. .. to deal with fundamentals of probability and statistics and see how these are used in thermodynamics in order to deeply understand natural and engineered phenomena? What are the likelihood, chances, and probabilities in nature? 2 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science 1.1 Probability The primary objective of this chapter is to introduce how to use statistical... a specific Hamiltonian as the sum of kinetic and potential energies of N 12 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science particles in a conservative field, i.e., H= N ∑ i =1 − − → → Pi · Pi → + V −i r 2mi (46) and using the in nitesimal relationship of the Helmholtz free energy dF = μdN − PdV − SdT (47) the rest of four variables in the canonical ensemble are calculated... is also of interest, because a brief account of the history of a statistical sampling process, which became known as the Monte Carlo method, is contained in this paper The contents of chapter 18 are a paper by I Plante and F A Cucinotta on the Monte Carlo simulation of ionizing radiation tracks The contents of this paper have applications in medicine consisting of not only in the detection of cancer... environmental engineering now vigorously extends from providing conventional sanitation guidelines to contributing crucial information to environmental policy-making and futurological issues Unlike other engineering and closely related disciplines (such as chemical engineering, electrical engineering, material science, and computer and information sciences), environmental engineering deals with poorly or incompletely... always be one You don’t think the winning probability on door #1 has changed Then, there is only one possibility, i.e., the 6 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science probability of door #3 moved to that of door #2 So, if you switch to door #2, your winning chance will be doubled: from 1/3 to 2/3 So, you are switching now! (b) Solution using conditional probability... enough information at the micro-mechanics level from which we can √ definitely say that “The probability of tossing heads on the damaged coin is 2/2 and that of √ tails is 1 − 2/2.” There are many important features in tossing the damaged coin: tosser’s specific way of flipping the coin into air, the number of spins before landing, the landing conditions such as falling velocity and bouncing angle, all of. .. − V (r ) and ΔWFB = k B T ln C C (78) (79) (80) 18 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science If the maximum displacement Δrmax is set to be small, then C /C can be approximated using the Taylor expansion If we consider terms only in the x-coordinate, C C = x η sinh[η + Δη ] η + Δη sinh[η ] (81) where η = βλFx Δrmax and Δη = βλΔFx Δrmax Using 1 sinh t = 1 . APPLICATIONS OF MONTE CARLO METHODS IN BIOLOGY, MEDICINE AND OTHER FIELDS OF SCIENCE Edited by Charles J. Mode Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of. probability include tossing a coin and rolling a dice, and the following questions are often asked: What is the 2 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science Number. H 3 ) = P ( S 1 ) P ( H 3 ) = 1 3 · 1 2 = 1 6 (16) because we select one door out of three and the host opens one out of the two remaining doors. 6 Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science