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A Monte Carlo Program Package for Predicting Physical Enhancement from Nanomaterials Under X-Ray Irradiation

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A Monte Carlo Program Package for Predicting Physical Enhancement from Nanomaterials Under X-Ray Irradiation Appendix A A Monte Carlo Program Package for Predicting Physical Enhancement from Nanomaterials Under X-Ray Irradiation Introduction This appendix describes a theoretical modeling package developed by the Guo group at UC Davis. The package uses a Monte Carlo method to calculate physical enhancement by nanomaterials under X-ray irradiation. A Matlab version was created and published in 2007 by Guo et al. [1], and the Mathematica package was first published in 2012 by Guo et al. [2]. The current package uses the Geant4 code to calculate electron emission from atoms in nanomaterials upon X-ray absorption and the NOREC code to calculate energy deposition in water by electrons. Shapes of nanomaterials are created in a number of C++ programs, and visualization and implementation are done in homemade Mathematica programs. The whole package is called LLSG, using the initial letters of the last names of the authors who helped develop the package (Lee-Lu-Sharmah-Guo). As shown in Chap. 2, there are several ways to model physical enhancement. The fundamental physical principles to model physical enhancement by nanomaterials under X-ray irradiation are similar to those of atoms and the bulk, which have been successfully developed over the last century. The main difference between modeling nanomaterials and other materials is that the shape of nanostructures needs to be considered. These shapes modify the energy spectrum of electrons released from the nanomaterials under X-ray irradiation. Many packages are now available to calculate physical enhancement, although some are more user-friendly than others. A brief summary of these packages is given in Sect. 2.3.3. As stated above, Guo et al. [1–3] developed the Monte Carlo-based simulation package to calculate enhancement generated from different nanostructures when irradiated by ionizing radiation such as X-rays. Prior to the work published in 2012, calculations performed in the Guo group, with all the physical processes considered, were done with homemade programs similar to that of PENELOPE [4]. In the 2012 publication, the atomic processes were replaced with Geant4 v. 9.6, and energy deposition in water was performed using NOREC. The remaining homemade part © Springer International Publishing AG, part of Springer Nature 2018 465 T. Guo, X-ray Nanochemistry, Nanostructure Science and Technology, https://doi.org/10.1007/978-3-319-78004-7 466 Appendix A A Monte Carlo Program Package... was transformed from the Matlab code to the C++ code that created the shapes of nanomaterials from which electrons were emitted as a result of interactions between X-rays and nanomaterials. Mathematica was chosen for its features of visualization and implementation. The combined program is the LLSG package. The main contribution of LLSG is the use of nanomaterials of various shapes and compositions. Geant4 and other similar packages have basic shape features to predict physical enhancement of nanostructures. However, they are often not ade- quate to model complicated nanostructures demanded by X-ray nanochemistry research. It is important to point out that many of the existing modeling calculations predict only energy deposition enhancement. They, including the LLSG package shown here, do not calculate the amounts of reactive oxygen species or other properties such as DNA damage or hydroxylation or polymerization reactions using the quantum chemistry methods. There are several packages such as Geant4-DNA or PARTRAC that have incorporated some chemical or biochemical features are briefly reviewed in Chap. 2, although neither package includes actual molecular (quantum) simulations to model actual biochemical reactions. Description of the Simulation Method The package developed by Guo et al. [2] calculates physical enhancement by nanostructures of different shapes, compositions, and assemblies. The central parts of the simulation are X-ray absorption by nanomaterials, electron emission from nanomaterials, electron transport, and energy deposition in both water and nanomaterials. Monte Carlo approach is used to follow each X-ray photon and then electron. The enhancement is defined as the ratio of energy deposition in water with nanomaterials to without nanomaterials, which gives relative enhance- ment. Relative enhancement is then subtracted by 1 to obtain absolute enhancement. In this simulation package, enhancement factor is the numerical value of the dose incurred in water with nanomaterials when irradiated with the flux of X-rays that deposit 1 Gy of X-rays in pure water. The units of enhancement are dose enhance- ment units (DEU). Energy loss of electrons in nanomaterials is modeled after the Bethe formula [5], which does not produce more electrons as electrons traverse in materials but simply reduces the energy of the electrons of interest as they traverse the nanomaterials. If transport does not occur in the volume of interest such as in type 1 or 2 physical enhancement regions, then the deposition is not recorded. This means energy deposition events in nanomaterials are not recorded. If the deposition occurs in water, then the amount of energy deposition is recorded for enhancement determination. Figure A.1 shows the overall flowchart. The Monte Carlo method, which has built-in Geant4 and NOREC, is interfaced with the homemade C++ program along with the nanomaterial shape features as a code in Mathematica and is linked to the C Appendix A A Monte Carlo Program Package... 467 Fig. A.1 Overall flowchart. The simulation begins at X-ray absorption and creation of electrons. These electrons are then traverse nanomaterials and water. Energy deposited in water is recorded. Shapes of nanomaterials are embedded in the program. The number of electrons used in the simulation is specified at the beginning. Each electron is followed until its energy is below 7.4 eV. Enhancement value is then computed using the normalized energy deposited in water volume of interest 468 Appendix A A Monte Carlo Program Package... ++ program. An executable file is then built. All implementation and visualization is carried out in Mathematica by calling the C++ generated executable. Figure A.2 shows the production of electrons from nanomaterials upon X-ray absorption. Two processes are investigated. The first is photoelectron emission. This is handled by the code G4CrossSectionHandler/EPDL97. Once a vacancy is created, the filling of the vacancy is simulated using the Geant4 G4AtomicDeexcitation/ EADL code, which examines all the vacancies until they are pushed to the continuum. Figure A.3 shows the flowchart for electron transport in the medium such as water. The flowchart shows the routine that is used to perform the electron transport e– Emission Photoe– Auger e– Begin Auger Cascade Submit E γ (G4AtomicDeexcitation: EADL) Decide a shell of Ebind to ionize (G4CrossSectionHandler : Decide a shell to move 1st vacancy to EPDL97) Decide energy release path Pop/push the old/new vacancy Push Vacancy – Auger no Push e with Eγ – E bind ? yes Decide a shell to release e– from Push the emitted e– Push the new vacancy no All Vacancies in Continuum? yes Begin Next Iteration Fig. A.2 Flowchart of the algorithm that tracks the relaxation history of electrons emitted from X-ray absorbing atoms with a distribution of photoelectrons carrying different energies resulting from absorption of an X-ray photon (of energy Eγ) by an atom. Low-energy electromagnetic package from Geant4 Collaboration (G4CrossSectionHandler and G4AtomicDeexciation) available online from CERN is employed in the simulation. (Adopted from Guo et al. [2]. Copyright (2012) American Chemical Society) Appendix A A Monte Carlo Program Package... 469 Fig. A.3 Flowchart of the algorithm that tracks the transport of electrons in Au or other nanomaterials and in water. A geometry is defined first, which is given in the Mathematica program. Then a number of electrons are emitted from a randomly selected gold atom in the gold nanostruc- ture. These electrons then traverse through the nanostructure and then water until their energy is lower than 7.4 eV. Bethe formula is used to calculate energy loss in the gold nanostructure or nanostructures of other compositions, and NOREC is used to calculate energy loss in water. (Adopted from Guo et al. [2]. Copyright (2012) American Chemical Society) simulation. This routine is repeated with a fixed geometry and at different initial electron energies Ee to obtain the average energy deposition. The initial electron is placed in a chosen starting material (e.g., Au) at a random position and direction. The electron then enters the electron queue, and the transport begins. The NIST Electron Inelastic-Mean-Free-Path Database and Electron Elastic-Scattering Cross-Section Database are used in the simulation of transport in Au, and the energy 470 Appendix A A Monte Carlo Program Package... lost in each step Δl is computed using a continuous energy loss formula. Once the electron moves out of Au and reaches water, NOREC is used to simulate the transport of both primary and secondary electrons in water. These electrons are tested for boundary crossing, and the electrons that enter a material (e.g., Au) are again placed in the electron queue with the positions (xi, yi, zi) and the energy Ei (i represents the ith electron) at the time of crossing. The electrons are transported individually until the electron queue is empty. Each electron is removed from the queue when the energy goes below Emin (7.4 eV) either in water or in other materials. Algorithm The program integrates Geant4 modules, NIST database, and NOREC with home- made codes in C++ and Mathematica to calculate X-ray absorption, electron gener- ation, electron transport, and electron energy loss in nanomaterials and water with different types and shapes of material. The compiled C++ programs and header files are placed in folders together with the required codes from Geant4 and NOREC as well as the homemade Monte Carlo code that includes geometrical shapes. In the following subsections, steps taken to build the executable are described.
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