Commissioning a Monte-Carlo Design of a Visible Radiation Photon Emission - Assignment Example

Commissioning a Monte-Carlo model of external radiotherapy photon beam (10Mv) for the new varian linear accelerator Name Institution Subject Instructor Date Introduction Monte Carlo techniques have previously been used in the medical physics for over 50 years as noted by Rogers (2006). They have played a wide role in the correction in the attenuation process as well as the scatter of the ions that are exhibited in the chambers as stipulated Cygler, Daskalov, Chan & Ding (2004). Radiotherapy has proved to be an excellent method for cancer treatment by eradicating the tumor cell using ionization radiation (Fix, M. K., Keall, Dawson & Siebers, 2004). In its application, it is recommended that an efficient quality assurance procedure is applied to ensure that the right amounts of doses are administered to the tumor volumes and ensure that chances of affecting normal tissues are reduced significantly. Essentially, the tumor that controls and compilation probability of the perfect tissues sigmoidally depends on the radiation dose as noted by Flock, Patterson, Wilson & Wyman (1989). It is prudent to know the accurate dose to patients in relation to the characteristic steep gradient curves of doses for control of cancerous tumors compilation. Any mistake on the dose administered may render the patient being given an under dosage or the normal tissues being compiled. The accepted level of uncertainty recommended in the administration of radiotherapy is a 5% level. There a variation in the slopes about the effects of dosage to patients but it has been reported that an increase of 1% in accurate dosage will result to an increase in cure rate at a rate of about 2% for tumors at the initial stages. Besides the strive to offer quality treatment to persons, any attempt to up the knowledge about the effect of doses calls based on epidemiology will call for a significant reduction on the levels of uncertainties on doses delivered during radiotherapy. The level of uncertainty required in dose administration is needed to be at 1 standard deviation or 2% which is envisaged to reach a 1% level of uncertainty in the future (Boone & Scihert,1988). These uncertainties are attributable to the ionization chamber dosimetry and the available data. Presently, we have other radiation techniques using small fields thus sparing the organs at risk. An example of such method is the stereotactic radiotherapy which has proved to provide good tumor volume conformity. The IMRT (Intensity modulated radiation therapy) uses non-uniform fields composed of numerous minute fields and the dose to the patient is administered through these small fields as noted by Heath, Scuntjens & Sheikh-Bagheri (2004). It is the application of these advanced means of radiotherapy which has challenged the existing dosimetry protocols in order to achieve higher levels of precision. Physics and ionization radiation In the event that some charged particles pass through a medium, an interaction occurs with the absorber atoms through Coulomb interaction with the nuclei of the atom and orbital of the electrons, this collision can either be elastic or inelastic with the former meaning that only a change of direction occurs and the later meaning that more energy is transferred (Fippel, Haryanto, Dohm, Nusslin, & Kriesen, 2003). The interactions can be either in form of: Interaction between the electrons and orbital in which there is ionization with removal of the orbital –electron and excitation of the absorber atoms. These ejected electrons are called knock on electrons and they posses sufficient energy enabling them travel a certain distance away from the point of interaction. The ionized atom then returns back to its initial point with an emission characteristic of the x-rays. There is also an interaction between the electron nucleus and the electron orbital which is radiative. In this, there is scattering followed by the loss of energy and production of Bremsstrahlung radiative photons. Stopping powers, S=dE/dx describes the energy loss per unit length of a material. The most frequently used is the mass stopping S/p with p being density. This stopping power is a combination of all the radiative and collisional dissipations (Poone & Verhaegen, 2005). These radiative photons usually travel long distances before they are absorbed. There exists a direct proportion relationship between the absorbed dose and the collision part of the stopping power s. Scol/p=u 1/Z/A ln (E/I)2 + ln(1+/2)+F+_(- With r being the radius of the electron, m is its mass, c light’s velocity, A is the atomic weight, u is the mass of atom, Z is the atomic number, E represents the atoms kinetic energy of the electron, F represents the auxiliary fn of the electron and d is the density effect correction. The Electrons Range There exists a stochastic variation in the range of electrons which is dependent on the individual interactions occurring. The continuous Slowing Down approximation (CSDA) is one of the commonest analytical concepts used to estimate ranges (Shi, Zhou, Zhen, Lu & Zhang, 2010). In this R is the integral of stopping power reciprocal. i.e. RCSDA= (P/S) dE The range is found to be smaller owing to the creation of secondary particles with the particles. Also the depth of penetration is reduced due to the scattering of electrons in the medium and their curved trajectories. Interaction of photons The photons may undergo scattering coherently (Rayleigh), undergo photoelectric absorption, or undergo an incoherent scattering (Compton),or produce an electron/positron pair of atoms in the electromagnetic field (Reynaert, Van Der Marck, Schaart, Van Der Zee, Van Vliet-Vroegindeweij, Tomsej, & De Wagter, 2007). In this, the number of photons ton pass through a medium decreases exponentially according to the interactions. There is no transfer of energy between the electrons bound in the orbital and the initial photons in the Reighleigh scattering but still has a significant contribution to the photon beam attenuation. The interaction between a photon and a free electron results into Compton effect. In this, a part of the photon’s energy is lost and from the atom shell, a recoil electron is ejected. In case the energy exceeds four times the mass of rest, a pair production occurs in the orbital electrons resulting into what is called triplet production. At the energies above 10MeV, we might experience photo nuclear reactions. This is due to the absorption of the high energy photon by the nucleus of the atom hence resulting in emission of photons or neutrons. The differential cross section governs the probability of having the occurrence of a single process and directional change of the created particles and change of energy of the incident photons (Verhaegen & Seuntjens, 2003). They are dependent on the medium, the atomic number and photon energy based on theoretical and semi-empirical values. The Monte Carlo Simulation of Radiation Transport This requires thorough understanding of the nature of the interaction of microscopic particles and their probability distributions. It employs sampling and probability distributions of the particles by the use of randomly distributed numbers ( 0,1) to depict the trajectories followed by the particles. Differential cross sections are used for the probability distributions to get the interaction mechanisms (Xu, Walsh, Telivala, Meek,& Y ang, 2009). In this, many particles of higher orders may result from a primary particle thus resulting in a history or shower. To calculate the macroscopic distribution of a dose, we require knowing the number of particles. i.e. set them at large numbers like N.THE Gaussian distribution is followed by Monte Carlo integration and the resulting estimated mean is within the range of  and is inversely related to the sampling size. The uncertainity of the mean can be found using the formula below. Therefore it means we should have an appropriate sample size N to get results within the necessary confidence level. This remains the best method to calculate the patient dose since it’s more accurate and is able to cope with heterogeneous densities where other methods would seem to fail. The convolution or the superposition algorithm is the most commonly used ,these describe dose distribution around the photon interaction site. It is also used when doing X-ray examinations for diagnosis works to either offer image processing, the evaluation of dose to patients and correction purposes. Variance Reduction Techniques (VRTs) The random nature of the Monte Carlo is its main drawback as a stochastic technique. According to the Monte Carlo, an increase in the samples results in a reduced uncertainty but it makes it hard to compute. The Monte Carlo’s simulation measure for efficiency can be expressed as: The variance of the simulation is denoted by 2 and the CPU simulation time T. The CPU simulation time is directly proportional to the simulated particles number N. the VRT, is an idea made to increase the efficiency.tis technique not only reduces the variance but it also lowers the time required to attain a certain uncertainty. In addition to this method of increasing efficiency, we have other two classes which serve the same purpose. In the first method, the efficiency is increased by transport simulation estimation. In it the threshold is increased thus reducing the time of simulation, but it also introduces a bias. The other efficiency increasing method is the ‘true’ VRT since there is no bias introduced. The ideas opposing this are the ‘splitting’ and the ‘Russian Roulette’. splitting is considered to cause N particles reduce to 1/N but the disposition dose is increased as a result of increase in the spitted particles number. On the other hand, the Roulette reduced the stimulated particles number but reduce the stimulation time hence its transportation time. Linear Accelerators Simulation To investigate the ionization chambers in t needs a realistic model of the source of radiation. In it the particles emanating from the linac ; the therapeutic external sources are characterized by a phase space which can simply be expressed as a multidirectional distribution and a function of f( E, x,u….).however measuring the phase is almost impossible. The linacs to start using photons have a general construction mode. In it the accelerated electrons to charges of MeVs will exit a vacuum window, closes the flight tube which is vacuum filled with electrons to cause acceleration and an arrangement of some bended magnets. We have some energy in the electrons and distribution either spatial or angular. Forward moving Bremsstrahlungs photons are produced once the electrons reach the target. Finally x and y fields are shaped by a colliminating system. Simulations using Monte Carlo allow us give the general phase spaces of the models and they also help calculate the dose distributions. However, we realize a lot of time is spent if we us linac head to calculate the photon transport (Chetty, Curran, Cygler, Demarco, Ezzell, Faddegon, Siebers, 2007).. This is because only a minimal amount of kinetic energy will produce the Bremsstrahlungs photons. To help calculate qualities related to photons like dose or fluence at the bottom of linac, we employ modern Monte Carlo algorithms enabled by special VRTs. In the BEAMnrc code, the DBS (Directional Bremsstrahlungs Splitting) is introduced. In this, when a radiation event happens either through the production of Bremsstrahlung photons, emission of characteristic X-rays or annihilation, then it is split into NBRSPL times with a 1/NBRSL weight being carried by the resultant photons. We can ensure an increased computation time for split photons transport lesser than the increase in dose and fluence efficiency at the bottom of the linac if the correct splitting number is selected. The 4D Monte Carlo simulation methods This is a method which continuous stimulates a beam and a patient motion by utilizing EGSnrc code. This method usually links the gantry and collimator settings to a patient on a particle-particle basis. (Rogers, Faddegon, Ding, Ma, We, & Mackie, 1995) To achieve synchronization, two novel particle sources are used in order to map it onto defDOSXYZnrc Monte Carlo code which in turn will compute the dose to the patient geometry. The delivery of dose by RapidArc plan is stimulated by the use of RPM and linac files. We can understand the effect of interplay existing between the beam and the phantom motions by performing simulations using and not using the motion synchronization. Clinical Radiation Dosimetry Inorder to esttimate the required dose to administer to a cancer patient, a number of steps need to be followed.in the clinics, we use a calibrated ionization chamber whose calibration is traceable to the national standard Labs. In the event of external beam radiotheraphy, we appply linacs( linear accelerators) for treatment and it is required that the outputs are well known to ensure that the right dose is delivered in reference points per monitor unit.the pprocedures for dosimetry are outlined in the national dosimetry protocols or the codes of practice in dosimetry (Seco, Adams, Bidmead, Partridge, & Verhaegen, 2005). The distribution of individual doses to patients is based on models of calculation for the treatment planning systems.the commisioning of any palnning system in linac radiotheraphy is based upon throughh measurement of dose distributions under a number of conditions. The absolute and relative dosimetry methods are applied in the admistartion of doses to patients.absolute dosimetry . relative dosimetry gives the steps needed to be followed inorder to come up with the absolute dose interms of water dose Dw under a defined reference condition.in this method, ionization chambers which is calibrated at secondary standard laboratory mainly the manufacturing company.the dosimetry protocols provide the appropriate data to ensure correct beam quality correction factor Kq required since the quality of the user’s beam is different from the calibration beam.the Monte Carlo simulations provide the data for correction factors Kq based on dose possibility and its measurement. The relative dosimetry technique is needed for treatment machine characterisation as a source of radiation.the two techniques;absolute and relative make use of results to provide calculations for the right dose to patients based on either direct Monte Carlo calculations or analytical techniques. Modeling of linear accelerator of photon beam `This remains the initial stage of the Monte Carlo based Treatment Planning systems. To ensure we attain a sure calculated dose rate, this will depend on the precise and accurate description of the linear accelerator head. The second part of the process in the patient dose calculation makes use of the Monte Carlo dose engine codes like the 53,31,6,19,5,9,60 or other codes which are committed to radiotherapy only (47, 20, 62, 79, 61, 20, 32).these committed codes are more suitable in radiotherapy application for they can be used in therapeutic applications between 25-50MeV ranges and can also be applied in biological applications like lungs and bones. To perform photon beam linear accelerator based on MC, considerable time is spent on beam modeling. This modeling is intended to describe individual beam properties by the linear accelerator (Verhaegen & Seuntjens, 2003). a MC based deseplan is usually made to improve efficiency and avoid time consuming step wise methods which have to be employed for each accelerator head every time. The photon beam model is employed to model the beam properties like the energy, the direction, the statistical weights and the point of origin a method known as Phase Space. A BEAMnrc Model of an accelerator head-6 MV and 15MV beams The BEAMnrc is an MC program for radiation simulation built on an EGSnrc MC code for transport of electrons and photons. The program is able to model all linear accelerators by utilizing the component module programs. Every accelerator’s part is referred as a distinct component and can be made up of different elements which are defined by their compositions and geometrical information from manufacturers. All the assemblies combine to form the accelerator’s head geometrical model, these are the primary collimator, the jaws, the multi-leaf collimators and the flattening filters. The MLC is composed of forty leaf pairs with a width of 1cm. the geometrical model has an X-ray target, a 6MV (one) or 15MV (two) flattening filters, a mirror, an ionization chamber and the X and Y jaws. Patient Dose modeling The heterogeneity corrections This correction is rare and it’s applied in breast or prostate patients but can also be applied in chest complications where a large lung volume is to be irradiated or the lung tissues covering a tumor. The heterogeneity correction method ensures that the dose is arrived at with more accuracy. In the heterogeneous dose calculation method, the most important part is the radiological depth along the ray line up to the calculation point is recognized that electronic disequilibrium effects occurring due to extent of lateral field are pronounced in the low density parts like lungs (Verhaegen, F., & Seuntjens, 2003). The CF is expressed by: CF= (heterogeneous medium dose/homogeneous dose at the same point.) By the use of more conventional methods, the correction factor can be found by CF=TPR (deff,rd)/TPR (d,rd) The RTAR method calculates the primary beam with much accuracy but the scatter method is found to be incorrect since factors like the shape, location and size of the heterogeneous medium are excluded from the scatter. The RTAR method operates on the assumption of infinity of the heterogeneous medium. The Monte Carlo Dose Engine For radiation treatment purpose, incoming photons and electrons form interactions with matter and form the dose distribution. To calculate the dose distribution, we utilize the dose engine utilizing a virtual phantom to represent the geometry of the patient. The techniques applied in the dose engine are the KERMA approximation method and summation of the energy deposited. The KERMA method rides on the assumption that amount carried out by a volume of electrons is equivalent to that carried by energy carried in hence not taking effect of secondary electrons and is not commonly used (Heath, Scuntjens & Sheikh-Bagheri, 2004).. The summation of energy on the other hand, needs one to know the amount of energy entered and left for each particle in a voxel. The ionization chamber Dosimetry The direct or indirect effect caused by ionization in a medium is used to find out the absorbed dose. The effects in the medium can be confirmed by some chemical changes occurring in the medium, photographic film blackening, light emission or ionization of the solids and gases (Jiang, Boyer, & Ma, 2001). Another method is calorimetry which connects increase of heat from absorption of radiation energy to the dose absorbed .this method is very efficient and precise but it calls for strictly controlled conditions of measurement. The mostly used detectors in clinical dosimetry are ionization chambers filled with air. This is usually cheap and provides an easy means of reading and reproducibility and precise measurement of the absorbed dose. During the interaction of the radiation and the air molecules, there is transfer of energy inside the chamber resulting in ion pairs quantifiable in terms of electric current measured by electrometer. The high voltage electrode leads to an increased electric field and current. Parallel and cylindrical designs are employed to form the electrodes. The Dosimetry Protocols The present protocols give the procedures to be followed to establish the absorbed dose to water using graduated ionization chambers for external radiation therapy (Petousii-Henss, Zankl, Fill, & Regulla, 2002). These ionization chambers are then placed under a water-filled phantom and the users beam is used to irradiate it. This method applies calibrated ionization chambers instead of direct use of the cavity theory since the exact volume of air cavity is not exactly specified by various manufacturers. The calibration coefficient can be introduced as Dw.Qo=ND,w.Qo. .the coefficient of calibration is traceable to primary standard lab and is related to the reading on the Dosimeter, which is formed in the electrometer and the ionization chamber under the reference conditions regarding measurements, depths, temperatures, phantom sizes, and pressure of the air, the electric field size and the quality of incident beam (Ma, Li, Deng, & Fan, 2008). In this, corrections in charge measurements since they also cause effects apart from the deviations in the beam quality and density. These include correction for temperature –pressure in varying densities and humidity of air, correction for changes in polarity,. The users beam dose to water as measured by the ionization dosimeter can be given as Dw,Q=Mc.ND,w,c060.kQ , Where the Mc gives the reading of the corrected water dosage, the Co60 is the factor of calibration, the beam quality correction factor is represented by kQ. The dosimetry protocols are helpful to the users since they provide them with the correct data of Kq for the correct beam qualities and the different ionization chambers for maintenance of the geometrical reference conditions. It is not possible to carry out a direct measurement since there exists no ideal cavity and there is simultaneous occurrence of the individual perturbation factors. The IAEA and the German DIN 6800-2 define the beam quality Q as the ratio of 10 cm dose reading and a 20 cm depth in a phantom of water. Also, the TG-51 explains the beam quality as a percentage value of the relative doses in depth without the presence of contaminating electrons. Charged Particle Disequilibrium (CPD) The fields possessing smaller sizes less than the charged particle’s lateral range may sometimes exhibit a degree of disequilibrium of the charged particles (CPD).The perturbations remain unknown but they vary according to the space within fields ,the penumbra and the boundaries of the fields (Reynaert et al., 2007). The electron spectra change within the field range is very rigorous hence making it very difficult to determine the dose with the ionization chamber and the regions of the CBD thus leading to uncertainties to a high level of more than 5%. The overall effect of this is the spatial resolution loss in measurement of dose. However, this can be corrected by the use of a perturbation correction factor, which caters for changes in fluence by inserting finite volumes in relation to the required dose to water. The problems for SFD are categorized into three: Radiation source size effects: this leads to only a section of the source being viewed from the detectors view attributed to collimation finite size and the source. Loss of CPE and the electron ranges: it is realized that electrons posses a lateral range at the boundary of field. However, this can be prolonged extensively by air’s low density. Measurement: it makes it impossible to make corrections for the reference dosimetry caused by the collapse of the Spencer –Attix cavity. Never the less, we have other advanced methods applied to help alleviate the CPD related problems by using the Monte Carlo simulations; these are referred to as the c factors in small IMRT fields (Heath & Seuntjens, 2003). Conclusion and recommendation In conclusion, the techniques of Monte Carlo in the simulation of radiation have a great importance in the medical physics. The use of EGSnrc tools aid in measuring the NaI detector that emerges from the spectra of the radiotherapy. The increase in the computing power has also enabled the utilization of Monte Carlo techniques that have aided in the commercial treatment plans such as the use of beam radiotherapy. This has also been possible it he application of the photon transportation study that is applied in photon therapy. It is recommended that more advanced software are developed that would enhance the accuracy of the results. This is vital as the when the correction factors are calculated, one needs to consider the calculation of the overall chamber as well as the response calculation. References Boone, J. M., & Scihert, J. A. (1988). Monte Carlo Simulation of the Scattered Radiation Distribution in Diagnostic Radiology. Medical Physics, 15, 713-720. Chetty, I. J., Curran, B., Cygler, J. E., Demarco, J. J., Ezzell, G., Faddegon, B. A., ...............& Siebers, J. V. (2007). Report of the AAPM Task Group No. 105: Issues Associated with Clinical Implementation of Monte Carlo-based Photon and ElectronExternal Beam Treatment Planning. New York: American Association of Physicists in Medicine. Cygler, J. E., Daskalov, G. M., Chan, G. H., & Ding, G. X. (2004). Evaluation of the First Commercial Monte Carlo Dose Calculation Eninge for Electron Beam Treatment Planning. Medical Physics, 31, 142-153. Fippel, M., Haryanto, F., Dohm, O., Nusslin, F., & Kriesen, S. (2003). A Virtual Photon Energy Fluence Model for Monte Carlo Dose Calculation. Medical Physics, 30, 301-311. Fix, M. K., Keall, P. J., Dawson, K., & Siebers, J. V. (2004). Monte Carlo Source Model for Photon Beam Radiotherapy: Photon Source Characteristics. Medical Physics, 3106-3121. Flock, S. T., Patterson, M. S., Wilson, B. C., & Wyman, D. R. (1989). Monte Carlo Modelling of Light Propagation in Highly Scattering Tissues: Model Prediction and Comparison with Diffusion Theory. IEEE Trans. Biomed. Eng., 36, 1162-1168. Heath, E., & Seuntjens, J. (2003). Development and Validation of a BEAMnrc Component Module for Accurate Monte Carlo Modelling of the Varian Dynamic Millenium Multileaf Collimator. Phys Med Biol, 48(24), 4045-4063. Heath, E., Scuntjens, J., & Sheikh-Bagheri, D. (2004). Dosimetric Evaluation of the Clinical Implementation of the First Commercial IMRT Monte Carlo Treatment Planning System at 6 MV. Medical Physics, 31, 2771-2779. Jiang, S. B., Boyer, A. L., & Ma, C. M. (2001). Modelling the Extrafocal Radiation and Monitor Chamber Backerscatter for Photon Beam Dose Calcualtion. Medical Physics, 28, 55-66. Ma, C. M., Li, J. S., Deng, J., & Fan, J. (2008). Implementing of Monte Carlo Dose Calculation for CyberKnife Treatment Planning. Journal of Physics, 102(1), 1-10. Petousii-Henss, N., Zankl, M., Fill, U., & Regulla, D. (2002). The GSF Family of Voxel Phantoms. Physics in Medicine and Biology, 47, 89-106. Poone, E., & Verhaegen, F. (2005). Accuracy of the Photon and Electron Physics in GEANT4 for Radiotherapy Applications. Medical Physics, 32, 1696-1711. Reynaert, N., Van Der Marck, S. C., Schaart, D. R., Van Der Zee, W., Van Vliet-Vroegindeweij, N., Tomsej, M.,.............. & De Wagter, C. (2007). Monte Carlo Treatment Planning for Photon and Electron Beams. Radiation Physics and Chemistry, 76, 643-686. Rogers, D. W. (2006). Fifty Years of Monte Carlo Simulations for Medical Physics. Physics in Medicine and Biology, 51(13), R287-R301. Rogers, D. W. O., Faddegon, B. A., Ding, G, X., Ma, C. M., We, J., & Mackie, T. R. (1995). Beam- a Monte-Carlo Code to Simulate Radiotherapy Treatment Units. Medical Physics, 22, 503-524. Seco, J., Adams, E., Bidmead, M., Partridge, M., & Verhaegen, F. (2005). Head-and-neck IMRT Treatments Assessed with a Monte Carlo Dose Calculation Engine. Physics in Medicine and Biology, 50, 817-830. Shi, Y., Zhou, L. H., Zhen, X., Lu, W., & Zhang, S. (2010). The Simulation of Linear Accelerator Using BEAMnrc with DOSXYCnrc. Bioinformatics and Biomedical Engineering (iCBBE), 2010 4th International Conference (pp. 1-4). Guangzhou: IEEE. Verhaegen, F., & Seuntjens, J. (2003). Monte Carlo Modelling of External Radiotherapy Photon Beams. Physics in Medicine and Biology, 48, R107-R164. Xu, Z., Walsh. S. E., Telivala, T. P., Meek, A. G., & Yang, G. (2009). Evaluation of the Eclipse Electron Monte Carlo Dose Calculation for Small Fields. Journal of Applied Clinical Medical Physics, 10(3), 75-85 Read More

It is the application of these advanced means of radiotherapy which has challenged the existing dosimetry protocols in order to achieve higher levels of precision. Physics and ionization radiation In the event that some charged particles pass through a medium, an interaction occurs with the absorber atoms through Coulomb interaction with the nuclei of the atom and orbital of the electrons, this collision can either be elastic or inelastic with the former meaning that only a change of direction occurs and the later meaning that more energy is transferred (Fippel, Haryanto, Dohm, Nusslin, & Kriesen, 2003).

The interactions can be either in form of: Interaction between the electrons and orbital in which there is ionization with removal of the orbital –electron and excitation of the absorber atoms. These ejected electrons are called knock on electrons and they posses sufficient energy enabling them travel a certain distance away from the point of interaction. The ionized atom then returns back to its initial point with an emission characteristic of the x-rays. There is also an interaction between the electron nucleus and the electron orbital which is radiative.

In this, there is scattering followed by the loss of energy and production of Bremsstrahlung radiative photons. Stopping powers, S=dE/dx describes the energy loss per unit length of a material. The most frequently used is the mass stopping S/p with p being density. This stopping power is a combination of all the radiative and collisional dissipations (Poone & Verhaegen, 2005). These radiative photons usually travel long distances before they are absorbed. There exists a direct proportion relationship between the absorbed dose and the collision part of the stopping power s.

Scol/p=u 1/Z/A ln (E/I)2 + ln(1+/2)+F+_(- With r being the radius of the electron, m is its mass, c light’s velocity, A is the atomic weight, u is the mass of atom, Z is the atomic number, E represents the atoms kinetic energy of the electron, F represents the auxiliary fn of the electron and d is the density effect correction. The Electrons Range There exists a stochastic variation in the range of electrons which is dependent on the individual interactions occurring. The continuous Slowing Down approximation (CSDA) is one of the commonest analytical concepts used to estimate ranges (Shi, Zhou, Zhen, Lu & Zhang, 2010).

In this R is the integral of stopping power reciprocal. i.e. RCSDA= (P/S) dE The range is found to be smaller owing to the creation of secondary particles with the particles. Also the depth of penetration is reduced due to the scattering of electrons in the medium and their curved trajectories. Interaction of photons The photons may undergo scattering coherently (Rayleigh), undergo photoelectric absorption, or undergo an incoherent scattering (Compton),or produce an electron/positron pair of atoms in the electromagnetic field (Reynaert, Van Der Marck, Schaart, Van Der Zee, Van Vliet-Vroegindeweij, Tomsej, & De Wagter, 2007).

In this, the number of photons ton pass through a medium decreases exponentially according to the interactions. There is no transfer of energy between the electrons bound in the orbital and the initial photons in the Reighleigh scattering but still has a significant contribution to the photon beam attenuation. The interaction between a photon and a free electron results into Compton effect. In this, a part of the photon’s energy is lost and from the atom shell, a recoil electron is ejected.

In case the energy exceeds four times the mass of rest, a pair production occurs in the orbital electrons resulting into what is called triplet production. At the energies above 10MeV, we might experience photo nuclear reactions. This is due to the absorption of the high energy photon by the nucleus of the atom hence resulting in emission of photons or neutrons. The differential cross section governs the probability of having the occurrence of a single process and directional change of the created particles and change of energy of the incident photons (Verhaegen & Seuntjens, 2003).

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