Manual Medical Radiation Dosimetry: Theory of Charged Particle Collision Energy Loss

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The Coulomb interaction slows the velocity of protons before Bragg peak. Where N is the target density, Z 2 ,, m e , v , Z 1 , and L are referred as target atomic number, the electron the mass, the velocity, the charge and the stopping function. As the energy lowers, the velocity lowers to 0, causing a peak the Bragg peak to occur. The width of peak depends on range straggling in medium and initial energy spectrum while the peak to plateau ratio depends on the width of energy spectrum.

Usually, the values of stopping powers are obtained from experiments and simulations and are similar to cross-sections in the sense that they are natural properties of the materials [ 9 ]. The stopping powers for various materials are given in International Commission on Radiation Units and Measurements report 49 [ 10 ]. Therefore, the low atomic number Z materials have the greater mass stopping power than high-Z materials. For example, the stopping power for a 1 MeV proton is High Z materials scatter the proton at a larger angle without much energy loss so that those materials are used to spread out the beam.

Non-elastic interactions with protons occur at higher energies and produce secondary particles which usually stop in the vicinity of the interaction and have a relatively high biological effectiveness. Primary protons are lost in non-elastic nuclear interactions.


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These secondary products are absorbed locally. These non-charged particles can pass a relatively longer ranged to be absorbed by surroundings Fig. Numerous neutrons are produced by nuclear interaction of protons, thus the neutron induced interactions should be examined in detail for the actual proton therapy.

The endpoint processes transfer electrons mainly through ionization collisions to generate many ions and radicals. As the proton slows down, it causes increased interaction with orbital electrons to make maximum interaction at the end of range. Finally, at the end of interactions, the energy is lowered below the proton's stopping power so that they exchange electrons with hydrogen atoms of the target.

This is called charge-changing process [ 12 , 13 ]. The ions and radicals induce biological damage in the bio-cells effectively despite of the slight dose contribution [ 14 ]. These electrons can move only a few micrometers at the most, which is almost the same scale as a chromosome in the cell nucleus [ 14 ].

The advantage of low energy proton beams are from the spatial distribution of ions and radicals which may form clusters and attack bio-molecules such as DNA [ 15 ].

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Thus, the RBE increases in a depth beyond the endpoint of the Bragg peak [ 16 ]. According to the radiation weighting factors defined in the International Commission on Radiological Protection ICRP recommendation [ 17 ], these factors for electrons, protons, and alpha particles are 1, 2, and 20, respectively. This result suggests that the proton dosimetry beyond the Bragg peak is difficult to evaluate accurately. Though the charged particles are still losing their energy by the interactions with atomic electrons at the entry region, the angular and energy straggling is much lower than protons as the heavy particles have much larger mass [ 18 ].

In the energy interval of therapeutic interest, heavy charged particles show diverse interactions from pure fragmentation at high energy levels to Rutherford scattering and inelastic scattering interactions in low energy levels depending on the nuclear structure of target matter Fig. Except at low velocities, the heavy charged particles lose a negligible amount of energy in nuclear collisions.

Thus, the heavy particles have much larger relative dose in the Bragg peak and small lateral scattering than protons and they offer an improved dose conformation as compared with photon and proton beam. Another characteristic of heavy charged particle beam is that by the lower-charge fragments, they produce considerable dose tails after the Bragg peak. Carbon hits oxygen and both atoms are fragmented into boron and nitrogen generating delta radiation.

The delta radiations decay to emit gamma radiation which can be used as the source of PET-CT in treatment field. Due to locally absorbed radiation around and after the Bragg peak, relative biological effectiveness RBE increases abruptly. Nuclear interactions of heavy particles are occurred by either gazing or head-on collisions. Unlike gazing collisions, the head-on collisions occurs less frequently but these interactions transfer large energy to cause projectile breaks into many small pieces, and no high-velocity fragment survives.

Heavy ions having gazing interactions with nuclei may result in fragmentation of the incident ions or target nucleus. The resultant charged fragments of the target nuclei that interpenetrate undergo significant interactions. In the interaction, evaporated nucleons changing the characteristics of the nucleons and light clusters are produced. The importance of the fragments depends upon how it affects the absorbed dose distribution in linear energy transfer LET which in turn depends upon the nature of the medium, ion type and its energy [ 20 ].

Further, these effects increase as a function of the beam energy. The interactions may serve advantages for the therapy verification with the similar mechanisms as positron emission tomography PET imaging. Verification of dose delivery to the tumor is possible by taking advantage of the property of positrons in producing keV annihilation gamma photons [ 22 , 23 ]. These isotopes travel almost the same velocity as the main beam and stop in almost the same place and they emit gamma rays to be detected in a conventional PET scanner.

As a consequence the location of the spread out Bragg peak and therefore the high dose treatment volume is visualized [ 24 ]. The secondary positron emission is exploited for visualizing the dose distribution during irradiation in hadron therapy and consequently allowing a safer irradiation of the tumor volume by supplying sufficient quality for monitoring in head and neck cancer treatments [ 26 ]. While the fragments lighter than 12 C, such as for example 11 B, are mainly produced by projectile and target fragmentation, the occurrence of fragments heavier than 12 C is also very significant because they are found in a considerable amount with rather low energies which may contribute to the increase of the RBE of the carbon beam Fig.

As a result, many radioactive and stable isotopes may be produced in interaction between heavy ion beam and the elements of soft tissues [ 27 ]. In a calculation model for the carbon therapy, the 12 C interact with the elements 16 O, 12 C, 14 N and 1 H, which are the most abundant nucleus in fat and muscle tissue, produce isotopes such as: The 18 F and 24 Na have a half-life of minutes and 15 hours respectively. Thus it is inferred that after carbon ion therapy the patient must be quarantined [ 27 ]. Still, thorough studies of the nuclear interactions of the heavy particles in the therapeutic energy range are needed before their clinical applications.

The low LET radiation generates radicals to cause single strand break while the high LET radiation causes multiple lesions to cause double strand break. During the heavy particle interactions, the fragmentation of elements atoms occur resulting isotopes e. It is similar to the stopping power except that it does not include the effects of radiative energy loss i.

When Zirkle and Tobias [ 28 ] introduced the term LET, it was regarded to be a universal parameter for radiobiological effects. The relative RBE, which is the dose of a reference radiation to achieve the same biological effect of photon, shows dependency on LET. Of the note, the LET is a macroscopic physical parameter that cannot be directly translated to the biological effectiveness. In a recent report, RBE for charged particles has calculated utilizing initial slopes of V79 Chinese hamster cell line survival curves.

The results indicate that the amount of energy deposited in biological entities is not appropriate measure of the effectiveness of charged particle especially at lower dose region. Protons are regarded as having slightly higher relative biological effectiveness RBE than photons. The generic RBE of proton in current radiation therapy is 1. Further, the generic RBE is not considering various physical and biological properties such as energy, fractional dose or particular tissues. As mentioned above, the RBE is certainly higher than 1.

In this part of the depth-dose curve, the average proton energy decreases rapidly, leading to an increased LET. Recently, Grassberger et al. This suggests that if a critical structure is located distal to target, the generic LET of proton is not apt to be applicable making the dosimetric optimization become very complicated. As the principal concern of radiation oncologists to use RBEs is that to benefit from the large pool of clinical results obtained from photon beams, the large variations of LET in proton beam distal to the Bragg peak cause a lot of stresses to the physicians.

Thus, it has been suggested that the proton therapy planning needs a more accurate way of acquiring an electron density on images or proton stopping power on images. The proton CT pCT is a potential candidate for accomplishing this [ 36 , 37 ]. Moreover, the issues concerned about secondary cancers, especially in pediatrics are discussed.

Paganetti [ 16 ] reported that the biological effect downstream of the target caused by neutrons was analysed using a radiation quality factor of Even though the biological dose was found to be below 0. The contribution of neutron to the effective dose which is produced by proton beams when treated with 72 Gy by passive beam modulator was reported about mSv [ 38 ].

For a cured patient who underwent treatment at age 60, this corresponds to an estimated lifetime cancer risk of about 0. In another study to predict risks of second malignant neoplasm incidence and mortality due to secondary neutrons in a girl and boy receiving proton craniospinal irradiation showed that the risks of a fatal SMN were 5. Hall [ 41 ] pointed out that many proton facilities use passive method to produce a field of sufficient size, but the use of a scattering foil produces neutrons, which results in an effective dose to the patient higher than that of IMRT.

Therefore the benefit of protons is only achieved if a scanning beam is used in which the doses are 10 times lower than with IMRT. In reply to Gottschalk's comments [ 42 ] that "However, neutron dose is rarely, if ever, the main concern," E. Hall again emphasized that "just how uncertain our knowledge really is of the cancer risks from low doses of neutrons". This measurable increase in LET over the terminal few mm of the SOBP results in an extension of the biologically effective range [ 31 ]. The avoidable lifetime cancer risks may be lower in actively scanning method rather than passive method [ 43 ].

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Medical radiation dosimetry—theory of charged particle collision energy loss by Brain McParland

The heavy charged particle beams show very diverse RBEs as they travel through the matter. While the protons are producing relatively localized biological damage according to the dose, the heavy particles are producing many ion tracks around the path so that they cause locally multiplied damages [ 44 ]. Thus simple dose scaling or plotting of dose from a reference depth dose is not appropriate. To understand the models of heavy charged particles, it is needed to understand ion track and track structures.

Introduction

Actually, it is the track structure rather than LET which implicate radiobiologic effect for the heavy particle beams. The expression 'track structure' refers to an 'event-by-event' description of the physical processes following irradiation, represented as a matrix Sn i ,X, E , where i is the interaction type, X is its position, and E is the deposited energy [ 44 ]. In comparison with the photon beam, which is sparsely ionizing radiation, the particle beams produce dense ionization tracks with more 'clustered damage' [ 45 ].

The mechanism of producing clustered damage is that the particle beams have very complex track structures characterized by energy depositions along with the primary particle path and radially projecting secondary beams so called 'delta-rays'. A delta ray is characterized by very fast electrons produced in quantity by alpha particles or other fast energetic charged particles knocking orbiting electrons out of atoms.

Collectively, these electrons are defined as delta radiation when they have sufficient energy to ionize further atoms through subsequent interactions on their own. Delta rays appear as branches in the main track.


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  7. These branches will appear nearer the start of the track of a heavy charged particle, where more energy is imparted to the ionized electrons. For this purpose, a local effect model LEM has been suggested which showed that the predictions of the LEM are in good agreement with clinical data [ 46 , 47 ]. The biological damages such as DNA double strand break DSB or fragmentation are significantly related with beam quality. DSB are mostly formed in the central area, while the single strand break tends to spread to the surrounding area.

    In a recent report, the prediction of whole-genome simple chromosome exchanges dicentric plus reciprocal translocations was possible with the PARTRAC code based on ion track structure model [ 44 ]. In this report, Ballarini et al.

    Basics of particle therapy I: physics

    Qualitatively, the dose response was basically linear both for fragments smaller than 1 kbp, which is critical to a higher RBE value. This reflects the role of radiation track-structure, which for high-LET radiation is particularly effective at producing clustered energy depositions and thus very small DNA fragments. Thus the statistical difference of the DSB induction among the low LET and high LET radiation may important contributions with the aim of performing reliable predictions of the consequences of heavy-ion irradiation.

    With the development of new technologies, including beam application and treatment planning, there will likely be a broader implementation of particle beam therapies within a very recent future. As we have only one proton center, the Korean radiation oncology society is not paying their attentions on the particle beams. The authors hope this contribution may provoke some interests for the Korean radiation oncologists' society on the particle therapies and may help them to prepare the tsunami of paradigm shift in radiation therapy.

    No potential conflict of interest relevant to this article was reported. National Center for Biotechnology Information , U.

    Journal List Radiation Oncol J v. Published online Sep Find articles by Seo Hyun Park. Find articles by Jin Oh Kang. Author information Article notes Copyright and License information Disclaimer. Abstract With the advance of modern radiation therapy technique, radiation dose conformation and dose distribution have improved dramatically. Proton, Neutron, Carbon ion, Particle therapy. Introduction The modern radiation therapy has evolved to the state-of-the-art with the advances in imaging and dose conformation techniques.

    Basic Particles in Therapy The term radiation applies to the emission and propagation of energy through space or a material medium, whereas the particle radiation means the energy propagated by traveling corpuscles that have a definite rest mass and a definite momentum [ 4 ]. Open in a separate window. Interactions of Particles with Matter Particles can only interact if the total charges and quantum numbers are conserved.

    Interactions of neutron The neutron has a mass of 1. Interactions of proton The proton has a mass of 1. It depends on the charge and velocity of the projectile charged particles and the atomic number and electron density of the target material according to the simplified Bethe formula: Interactions of heavy charged particles 1 Electron collision: Proton Protons are regarded as having slightly higher relative biological effectiveness RBE than photons.

    Heavy charged particles The heavy charged particle beams show very diverse RBEs as they travel through the matter. Outlook With the development of new technologies, including beam application and treatment planning, there will likely be a broader implementation of particle beam therapies within a very recent future.

    Footnotes No potential conflict of interest relevant to this article was reported. Heavy ion synchrotron for medical use: Particle Therapy Co-operative Group. Particle Therapy Co-operative Group; Particle therapy facilities in a planning stage or under construction [Internet] Available from: Patient statistics per end of Hadron therapy patient statistics.

    Particle Therapy Co-Operative Group; The physics of radiation therapy. Goitein M, Jermann M. The relative costs of proton and X-ray radiation therapy. Clin Oncol R Coll Radiol ; National Institute of Standards and Technology. National Institute of Standards and Technology; Stopping power and range tables for protons [Internet] Available from: Calculations of electronic stopping cross sections for lowenergy protons in water.

    Inelastic-collision cross sections of liquid water for interactions of energetic protons. Nuclear collision processes around the Bragg peak in proton therapy. Nikjoo H, Goodhead DT. Track structure analysis illustrating the prominent role of low-energy electrons in radiobiological effects of low-LET radiations. Nuclear interactions in proton therapy: Studies in penetration of charged particles in matter.

    Nuclear science series report Protocol for heavy charged-particle therapy beam dosimetry: Aspects of fast-ion dosimetry. Nucleus-nucleus interaction modelling and applications in ion therapy treatment planning. Limited-angle 3D reconstruction of PET images for dose localization in light ion tumour therapy.

    If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser. This is a preview of a remote PDF: More from Journal of Radiation Oncology Concurrent whole brain radiotherapy and short-course chloroquine in patients Bread of Life Unified numerical model of collisional depolarization and broadening rates Alternatively, you can download the file locally and open with any standalone PDF reader: Medical radiation dosimetry—theory of charged particle collision energy loss by Brain McParland Richard James Crilly 0 Oregon Health and Science University , Portland, OR, USA - In the daily grind of clinical physics, we are often confronted with the need to make intelligent decisions on the accuracy of our computer-generated calculations.

    To do so, we fall back on a standard list of assumptions to justify our tack. If pressed, we review a plethora old papers and notes to justify our actions. In this book, Dr. McParland authors a detailed, clear development of charge particle energy deposition. In the foreword, the author posits that for purposes of medical applications, the study of radiative losses is insignificant, though he does concede that this may not be true for high energy electrons.

    Given the current work done to improve dosimetric accuracy by fractions of a percent, I am not certain I entirely agree with this line of argument. Nonetheless, I agree on the primary importance of understanding the theory underlying charged particle energy loss. The majority of the book is clearly meant for the physicist and has little to offer anyone without a clear understanding of basic quantum physics, electromagnetic theory, and higher order mathematics. A clear exception to this assertion would be is the extensive introduction which is a wonderful essay summarizing earlier models.

    It is in the form of a historical narrative that allows us to envision not only the series of incremental steps that lead to the modern theory but also the numerous miss-steps and near misses that are the hall mark of scientific advancement. The actual development of physics theory starts with the second section that entails a review of quantum scattering theory.

    Thankfully, for this reviewer, the text does not assume the readers last quantum class was a number of weeks ago and eases into the subject carefully outlining each assumption and approximation made along the way. This section lays the ground work for the second part of the book wherein the topics of elastic Coulomb scatter are covered in great detail from simple classical solutions to multiple elastic Coulomb scatter including Fermi-Eyges theory. Part three covers the development of collisional energy concepts including collisional stopping power, charged particle range, and the continuous slowing down approximation.