Radiation Interactions with Biological Matter - Radiobiology PDF

Radiation Interactions with Biological Matter - Radiobiology BME 229 Fall 2024 1  Radiobiology Radiobiology is the study of the action of ionizing radiations on living things. Prerequisites: (1) Radiation physics...

Radiation Interactions with Biological Matter - Radiobiology BME 229 Fall 2024 1  Radiobiology Radiobiology is the study of the action of ionizing radiations on living things. Prerequisites: (1) Radiation physics (2) Biology History of Radiology: Discovery of X-rays by the German physicist Wilhelm Conrad Rontgen in 1895. The science of diagnostic radiology was born in the late 18’th century. The French physicist Antoine-Henri Becquerel discovered radioactivity emitted by uranium compounds in 1896 and a few years later the science of radiotherapy was born. 2 Interaction of Radiation with Matter - General  f = c = 3108 m/s 3  The Photon Energy Formula 1: E [J] = h. f [Hz] h = Planck’s constant = 6.6261×10-34 m2.kg/s Formula 2: E [keV] = 12.4 /  [A] 1 eV = 1.6022 × 10-19 J 1 Angstrom (A) = 10-10 m 4  Electromagnetic Radiation In the EM spectrum, wavelengths vary from ~tens of km for radio waves Electromagnetic spectrum to ~10-10 m for x- and -rays. The energy in a beam of x- or -rays is quantized into large individual packets, each of which is big enough to break a chemical bond and initiate a biological change. The critical difference between nonionizing and ionizing radiations is the size of individual energy packets (i.e. the energy of each photon), not the total energy involved. 5  Ionizing Radiations The absorption of energy from radiation in a biologic material may lead to one of the following phenomena: (1) Excitation of the material The raising of an electron in an atom or molecule of the material to a higher energy level without actual ejection of the electron. It happens when the radiation energy is not high. (2) Ionization of the material The ejection of one or more orbital electrons from the atom or molecule of the material. It happens when the radiation energy is above certain limit. This type of radiation is called “Ionizing Radiation”. NOTE: The energy dissipated per ionizing event is usually high enough to break chemical bonds in the biologic material. This may lead to biological effects! 6  Types of Ionizing Radiations Two types of ionizing radiations: (1) Electromagnetic Radiations (2) Particulate Radiations Electromagnetic Radiations: Two most widely used: x-rays and -rays X-rays are produced extranuclearly, e.g. using an electronic device to accelerate electrons and stop them abruptly in a target -rays are produced intranuclearly from radioactive decays Two ways to treat x- and -rays: (1) As an electromagnetic wave with given frequency and wavelength  f = c = 3108 m/s (2) As an stream of photons or packets of energy. Each energy packet contains an amount of energy equal to h f , where h is the Planck’s constant. h = Planck’s constant = 6.6261×10-34 m2.kg/s 7  Ionizing Photon Energy An empirical result: Electromagnetic radiations are usually considered ionizing if they have a photon energy in excess of 124 eV, which corresponds to a wavelength shorter than about 10-8 m. This falls within wavelengths shorter than ultraviolet radiation in the EM spectrum. 8  Units of Radiation Quantity of radiation is expressed in 3 different units: Rontgen (R), Rad, or Gray (Gy). Rontgen is the unit of exposure and is related to the ability of x- or -rays to ionize air. 1 Rontgen is the amount of radiation required to liberate positive and/or negative charges of 1 electrostatic unit of charge (esu) in 1 cm3 of air at standard temperature and pressure (STP). 1 esu ≈ 3.33564×10−10 C STP: temperature = 25 ºC, and pressure = 1 atm. 9  Units of Radiation Rad is the unit of absorbed dose and corresponds to an energy absorption of 100 erg/g. For the x- and -rays, an exposure of 1 R results in an absorbed dose in water or soft tissue roughly equal to 1 Rad. 1 erg = 10-7 J (The unit of energy in the CGS system) Gray is the newer unit for the absorbed dose (in the SI system), which corresponds to an energy absorption of 1 J/kg. 1 Gy = 100 Rad 1 cGy = 1 Rad 10  Particulate Radiations Particulate radiation originates from particles like: electrons, positrons, protons, -particles, neutrons, and heavy charged ions. Electrons: Small negatively-charged particles that can be accelerated to high energy to a speed close to the speed of light by means of devices like betatron or linear accelerator. Electric charge of an electron e = -1.602176 ×10-19 C Positrons: Identical to electrons with the exception of the charge polarity. Electric charge of a positron +e = +1.602176 ×10-19 C Protons: Positively charged particles having a charge equal to that of an electron and a mass almost 2000 times greater than that of an electron. They are accelerated to useful energies by means of devices such as cyclotron. 11  Particulate Radiations -particles: Nuclei of helium atoms that consists of two protons and two neutrons. They have a net positive charge and can be accelerated similar to protons. -particles also are emitted during decay of heavy naturally occurring radionuclides such as uranium and radium. Neutrons: Particles with a mass similar to that of protons, but with no electrical charge. Because they are electrically neutral, they can not be accelerated in an electrical device. They are produced if a charged particle is accelerated to high energy and then made to impinge on a suitable target material. Neutrons are also emitted as a by-product if heavy radioactive atoms undergo fission, that is, split to form two smaller atoms. Heavy charged particle: Nuclei of elements such as carbon, neon, argon, or iron that are positively charged because some or all of the orbital electrons have been stripped from them. To be useful for radiation therapy, they must be accelerated to high energies. 12  Ionization of Biologic Materials Ionization of biologic materials caused by radiation can be classified into two categories: (1) Direct ionization It is caused by particulate radiation, provided the individual particles have sufficient kinetic energy to directly disrupt the atomic structure of the biologic material they pass through and to produce chemical and biological changes. (2) Indirect ionization It is caused by electromagnetic radiations (x- and -rays). They do not produce chemical and biologic damage themselves, but when they are absorbed in the medium, they give up their energy to produce fast- moving charged particles (mostly electrons) and free radicals that in turn are able to produce damage. 13  Interaction of Radiation with Matter Ionizing Radiation Non-Ionizing Radiation X-rays (indirectly) Lasers -rays (indirectly) Ultra-violet Electron beams (directly) Infra-red Protons (directly) Ultrasound -particles (directly) MRI b-particles (directly) Neutrons (indirectly) Ionization = The process whereby a neutral atom acquires a positive or negative charge. 14  Interactions of Radiation with Matter X-ray and -rays are photons. Photons are individual packets of electromagnetic energy have no mass have no charge have wave-like + particle-like properties travel at the speed of light, c have Energy, E = h f X-rays and -rays are indirectly ionising radiation. That is: 1. They transfer energy to the medium (Kerma) 2. They produce high-speed electrons and free radicals Electrons deposit energy in the medium through excitation and ionisation along their tracks The deposition of energy in this way is what gives rise to radiation dose (Absorbed dose) (Exposure: ability of X- and -rays to ionize air). 15  Interactions of Radiation with Matter Photons interact with matter through five major processes: 1. Elastic scattering (e/r) 2. Photoelectric effect (t/r) Are important 3. Compton effect (s/r) in radiobiology! 4. Pair production (k/r) 5. Photonuclear interactions (z/r) The probability of a particular process taking place is represented by its own attenuation coefficient (given in brackets above) (a.k.a. mass absorption coefficient) The total attenuation coefficient represents the probability that photons will interact with the medium  e t s k z X = + + + + r r r r r r X 16  Elastic Scattering Outgoing photon Incoming photon No loss of photon energy hnin = hnout 17  Elastic Scattering Elastic scattering is also known as called “Coherent” or “Rayleigh” scattering Occurs mainly at low energies Large Z materials Contributes nothing to KERMA or dose, no energy transferred, no ionisation, no excitation No real importance in radiobiology 18  The Photoelectric Effect Incoming photon Outgoing electron Ee = hn - W Ee: maximum kinetic energy of the outgoing electron W: energy needed to remove electron (binding energy) 19 The Photoelectric Effect Photoelectric absorption process This is a dominating process at low energies which is a characteristic of diagnostic radiology systems. 20  The Compton Effect Compton absorption process This is a dominating process at high energies which is a characteristic of radiation therapy systems. 21  The Compton Effect Outgoing Incoming electron photon f q Outgoing photon 22  The Compton Effect Interaction of photon with unbound atomic electrons Scatter + partial absorption of photon energy Scattered electron + scattered photon Change in photon wavelength depends on angle of scattered photon out- in = constant×(1- Cosq) in: wavelength of the incoming photon, out: wavelength of the outgoing photon If photon makes a direct hit: 1. Electron will be scattered straight on with maximum energy 2. Photon will be scattered backwards i.e. q = 180o with minimum energy 3. Scattered photon energy 23  The Compton Effect Dominating process at high energies which is a characteristic of radiation therapy systems Depends on electron density (re) Independent of Z s/r  re / hn 24 Difference between Compton and Photoelectric Absorption Processes - Physics Compton process deals with high-energy photons whereas Photoelectric process deals with low-energy photons. In the Compton process only a small fraction of the photons energy is transferred to the orbital electrons. In the Photoelectric process a major portion of the photons energy is transferred to the orbital electrons. The difference between the Photoelectric Effect and Compton Effect are the nature of the interaction of incident photons with electrons. In the Photoelectric Effect kinetic energy is the main player in which the kinetic energy of a photon excites an electron. In the Compton Effect, the important aspect is the scattering effect that depends on the angle of the photon and its momentum. 25 Difference between Compton and Photoelectric Absorption Processes - Biophysics The mass absorption coefficient for the Compton process is independent of the atomic number of the absorbing material. Mass absorption coefficient = The linear absorption coefficient divided by the density of the absorber. The mass absorption coefficient for the Photoelectric process is a cubic function of the atomic number of the absorbing material (Z3). Bone has higher atomic number comparing to soft tissue (due to its Calcium content). This is why X-rays are absorbed to a greater extent in bones and create contrast in radiology images. 26  Pair Production – Type 1 Outgoing Electron, E- Incoming Photon, hn Outgoing Positron, E+ 27  Pair production –Type 2 Outgoing Electron, E2- Original Electron, E1- Incoming Photon Outgoing Positron, E+ hn > 2.04 MeV Otherwise called Triplet Production Incident photon interacts with Coulomb field of atomic electrons and is absorbed Incident photon transfers energy to Host e- and e-/e+ pair produced 28  Summary Process Symbol Type of Variation with Interaction Z Elastic e/r Bound  Z2 electrons Photoelectric t/r Bound  Z3 electrons Compton s/r Nearly free Indep. of Z electrons Pair Production k/r Heavy nuclei Z Table from: P. Dendy & B. Heaton, Physics for Diagnostic Radiology, 2nd Edition  Photonuclear Interactions High energy photon interacts with atomic nucleus resulting in emission of a proton (p) or a neutron (n) Occurs for incident photons with energy > few MeV Not significant in radiobiology 30  Direct and Indirect Actions of Radiation Important: The biologic effects of radiation results mainly from damage to DNA! Two mechanisms of actions (or indeed interaction) of ionizing radiation with DNA: (1) Direct action It happens when the radiation interacts directly with the DNA and its atoms in the cell. As a result, the atoms of the DNA may be ionized or excited, thus initiating a chain of events that leads to biologic changes. (2) Indirect action It happens when the radiation interacts with other atoms or molecules in the cell (particularly water which comprises about 80% of a cell) to produce free radicals that are able to diffuse far enough to reach and 31 damage DNA.  Free Radical A free radical is an atom or molecule carrying an unpaired orbital electrons in the outer shell (odd number of electrons). Free radicals have high degree of chemical reactivity. Interaction of radiation with water molecule: H 2 O → H 2 O + + e- H2O+ is an ion radical, i.e. it is both an ion and a free radical. H2O+ + H2O → H3O+ + OH OH is called Hydroxyl radical which is a highly reactive free radical. It is estimated that about 2/3 of the X-ray damage to DNA in mammalian cells is caused by the Hydroxyl Radical. Free radicals break the DNA bonds which leads to chemical and then biologic effects in cells. 32 Chain of Events Leading to Biologic Effects 33  Absorption of Neutrons Neutrons are uncharged particles. For this reason, they are highly penetrating compared with charged particles of the same mass and energy. Difference between neutrons and x-rays is in the mode of their interaction with tissue: X-ray photons interact with the orbital electrons of atoms of the absorbing material by the Compton or Photoelectric processes. Neutrons interact with the nuclei of atoms of the absorbing material and set in motion fast recoil protons, α-particles, and heavier nuclear fragments. In soft tissue, interaction between incident neutrons and hydrogen nuclei is the dominant process of energy transfer, because hydrogen is the most abundant atom in tissue. 34  Absorption of Neutrons At low to moderate energies (6 MeV), the interaction of neutrons with nuclei is primarily an inelastic scattering process. Two types of scattering in particle physics: - Elastic scattering: Energy of the incident photon or particle (electron, positron, or neutron) is conserved. - Inelastic scattering: Energy of the incident photon or particle is not conserved (reduced or increased). 35 Interaction of Neutrons with Hydrogen Nucleus Generation of recoil protons 36 Interaction of Neutrons with Carbon or Oxygen Nuclei (Spallation) Generation of α-particles 37 Differences Between Photons and Neutrons X- and -rays are indirectly ionizing and give rise to fast-moving secondary electrons or free radicals. Fast neutrons are both indirectly or directly ionizing (depending on their energy), but give rise to recoil protons, -particles, and heavier nuclear fragments. Protons, -particles, and heavier nuclear fragments are all significantly heavier than electrons (protons are 2000 times, -particles are 8000 times, and nuclear fragments are an order of magnitude (at least 10 times) larger/heavier than electrons). For X- and -rays indirect biologic effect is a dominant process, but for heavy particles set in motion by neutrons, direct actions have greater importance in biologic effects. 38 Differences Between Photons and Neutrons – cont. Indirect effects caused by X- and -rays are most easily modified by chemical means that inhibit creation of free radicals (various radio- protective compounds have been developed for this purpose). These compounds, however, have little use for neutron-based radiations because the biologic effects are caused through direct actions. 39 Paradigm of Radiation Biological Damage 40 Radiation Damage to DNA DNA Strand Breaks and Chromosomal Aberrations 41  Mammalian Cell M = Molarity (unit of concentration). It is the number of moles of solute per litre of solution. 42 Cellular Scale 43  DNA and RNA Main biologic effects of radiation include: Cell killing, and cell mutation (Carcinogenesis and Hereditary effects) There are strong evidences that DNA is the primary target and route cause for the biologic effects of radiation! DNA (DeoxiriboNucleic Acid) is a molecule inside the nucleus of cells that carries genetic information. DNA is a large molecule with a well-known double-helix structure. It consists of two strands, held together by hydrogen bonds between the bases. RNA (RiboNucleic Acid) is the chemical cousin of the DNA and is responsible for translating the genetic code of DNA into proteins. DNA → Double stranded RNA → Single stranded 44  DNA The backbone of each strand consists of alternating sugar and phosphate groups. Attached to this backbone are four bases, the sequence of which specifies the genetic code. The four bases are divided into two groups: Single-ring groups (Pyrimidines) These are Thymine and Cytosine. Double-ring groups (Purines) These are Adenine and Guanine. The bases on opposite strands must be complementary: Adenine pairs with Thymine Guanine pairs with Cytosine DNA has negative charge. 45  DNA and Chromosome Chromosomes are long pieces of DNA contained in the nucleus of cells. Chromosomes are the structures that hold our genes. Chromosomes come in pairs. For most people each cell in their body has 23 pairs of chromosomes (for a total of 46). Histone is a type of protein found in chromosomes. Histones bind to DNA, help give chromosomes their shape, and help control the activity of genes. 46  DNA Strand Breaks Breaks in DNA strands is the route cause of various biologic effects. Single-strand Breaks (SSBs) (Fig. B) Breaks in only one strand of the DNA. They are usually repaired readily using the opposite strand as a template. They are therefore of little biologic consequence as far as cell killing is concerned. Double-strand Break (DSB) (Figs. C and D) Breaks in both strands that are opposite one another or separated by only a few base pairs. The interaction of two double- strand breaks, if not repaired, may result in cell killing or cell mutation. 47  Measuring DNA Strand Breaks There are various techniques to measure both single-strand and double-strand DNA breaks. Most current techniques are based on the Electrophoresis technique. Electrophoresis: The use of an external electric field to separate large biomolecules such as DNAs or DNA fragments on the basis of their electric charge by running them through acrylamide or agarose gels. Smaller pieces of DNA move faster and farther than larger pieces, and thus can be separated and counted. Two most widely used electrophoresis methods: ▪ Pulsed-Field Gel Electrophoresis (PFGE) It is used to detect double-strand breaks induction and repair. ▪ Single-cell Electrophoresis (Comet Assay) It is used to detect both double- and single-strand breaks induction and repair (a more sensitive method) NOTE: From DNA single- and double-strand breaks, the latter, i.e. double- strand breaks, have the most significant role in cell killing and other biologic 48 effects of radiation.  Chromosomes and Telomeres What is Chromosome?! Thread-like structures consist of DNA and proteins found in all cell nucleus (except red blood cells). Each chromosome contains hundreds to thousands of genes that carry our genetic information. Chromosomes come in pairs and humans have 23 pairs of chromosomes (each parent contributes one chromosome in each pair), containing a total of 50,000 to 100,000 genes from each parent. What is Chromatid?! One of two identical strands into which a chromosome splits during mitosis What is Telomere?! A small segment at the end of DNA that becomes shorter with every replication of the DNA. DNA will no longer replicate beyond a certain point of telomere reduction. So telomeres provide a mechanism to control the replication of the DNA. Chromosome division is a precursor to cell division (mitosis). 49 Cell Cycle 50 Cell Mitosis 51 Radiation-induced Chromosome Aberrations If the radiation dose would be enough, double-strand breaks are produced in the chromosomes. Once breaks are produced, different fragments may behave in a variety of ways: 1. The breaks may rejoin in their original configuration → Next mitosis remains intact! 2. The breaks may fail to rejoin and give rise to an aberration → Scored as a deletion at the next mitosis. 3. Broken ends may rejoin other broken ends from other chromosomes → Give rise to chromosomes that appear to be grossly distorted. Aberrations seen at metaphase: 1. Chromosome aberrations: It happens if a cell is irradiated early in interphase , before the chromosome material has been duplicated. 2. Chromatid aberrations: It happens if the dose of radiation is given later in interphase, after the chromosome material has been duplicated and the chromosomes consists of two strands of chromatin. 52 Breakage + Misjoining → Chromosome Aberrations 53 Radiation-induced Chromosomal Aberrations Many types of chromosomal aberrations and rearrangements are possible. In general, chromosomal aberrations can be divided into two classes: 1- Asymmetric aberrations 2- Symmetric aberrations 54  Radiation-induced Asymmetric Chromosomal Aberrations – Lethal Aberrations Lethal aberrations are those involve interchanges between two separate chromosomes which lead to a gross changes in chromosomal structure and resulting chromosomes with asymmetries and/or some fragments! Cells with chromosomes with asymmetric aberration will die during subsequent mitosis. These aberrations are also called “Unstable” aberrations. 55 Examples of Asymmetric Chromosomal Aberrations A. Dicentric aberration B. Ring aberration C. Anaphase bridge 56 Radiation-induced Symmetric Chromosomal Aberrations - Carcinogenetic Aberrations Two types of chromosomal aberrations that are carcinogenic to cells: 1- Symmetric translocation 2- Small interstitial deletion In these aberrations, the changes are not significant to kill cells but they are significant enough to induce carcinogenesis or hereditary effects in cells. These aberration usually lead to symmetric chromosomes that survive subsequent mitosis. They are therefore called “Stable” aberrations. 57 Radiation-induced DNA Damage - Summary Ionizing Radiation DNA Damage Single-strand Break Double-strand Break Repaired Chromosomal Aberrations No Biologic Effects! Asymmetric (Unstable) Symmetric (Stable) Cell Death Cell Mutation Tissue/Organ Cancer Hereditary Malfunction/Death Effects 58  Radiation Biology – A Complicated Field of Study 30-100 Trillion Cells at Risk Radiation Bioeffects Depend on: Different Cell Types Different Cell Cycles Different Types and Dosage of Radiation 59  Linear Energy Transfer (LET) Relative Biologic Effectiveness (RBE) Radiation Equivalent Dose 60  The Deposition of Radiant Energy If radiation is absorbed in biologic material, ionization and excitation occur that are not distributed at random but tend to be localized along the tracks of individual charged particles in a pattern that depends on the type of radiation. The spatial distribution of the ionizing events produced by different particles varies enormously. X- and -rays are sparsely ionizing because along the tracks of the photons the primary ionizing events are well separated in space. -particles and neutrons are densely ionizing because their tracks consist of dense columns of ionizing events. 61  Ionizing Radiation - Reminder Ionizing radiation is radiation that has sufficient energy to ionize an atom or molecule. , b and  radiation emitted during radioactive decays have energies of several MeV; Therefore, a single particle can ionize thousands of atoms and molecules. 62  Radiation Exposure ⚫ Exposure measures the ionization produced in air by X- or  rays at standard pressure and Am I exposed temperature (25 oC and 1atm). to some kind of radiation? ⚫ Exposure E is the total charge produced per unit mass of air Q Radiation E= Source m Exposure is measured in Roentgens (R): 1 R = 2.58 ×10-4 C/kg air Exposure does not tell us anything about the radiation damage of the living tissue! 63  Absorbed Dose ⚫ Absorbed dose D is the If I am energy absorbed per unit mass exposed to radiation, of absorbing material: what is my Energy dose? D= m Absorbed dose is measured in Grays (Gy): Eenter Eexit 1 Gy = 1 J/kg The old unit for the absorbed dose is rad (radiation absorbed dose) 1 rad = 0.01 Gy or 1 Gy = 100 rad Absorbed dose still does not tell us Eabsorbed = Eenter − Eexit anything about the biological damage of the absorbing material 64 or tissue! Problem: A film badge worn by a radiologist indicates that she has received an absorbed dose of 2.5×10-5 Gy. The mass of the radiologist is 65 kg. How much energy has she absorbed? Answer: The absorbed dose (D) is given by Energy absorbed D= Mass of absorbing material Energy absorbed is: E = D  Mass = (2.5  10-5 Gy)(65 kg) E = 1.6×10-3 J 65  Linear Energy Transfer (LET) Linear Energy Transfer (LET) is the energy transferred per unit length of the track. The unit of LET is [E]/[L] such as keV/m LET = dE / dl For typical irradiations, the energy per unit length of track varies over a wide range of values. Therefore, the average LET is usually used in practice. Typical values of LET (average) for various irradiations: Around 0.2 keV/m for cobalt-60 -rays Around 2 keV/m for 250-kV X-rays Around 1000 keV/m for heavy charged particles encountered in space 66  Average LET It is possible to calculate the average LET in various ways. Two methods to define average: - Track Average (the most commonly used method) - Energy Average Track Average LET is obtained by dividing the track into equal lengths, calculating the energy deposited into each length, and finding the mean. Energy Average LET is obtained by dividing the track into equal energy increments and averaging the length of track over which these energy increments are deposited. 67  Average LET A simplified exponentially-depositing energy For most irradiations, the biologic effects correlated well will the Track Average LET. 68  Relative Biologic Effectiveness The amount of absorbed radiation is expressed in terms of the Absorbed Dose. Absorbed dose is a measure of the energy absorbed per unit mass of medium. The unit of absorbed dose is Gray (Gy) or rad. Equal doses of different types of radiation do not produce equal biologic effects! The relative biologic effectiveness (RBE) of a radiation is defined to account for the variations in biologic effects of various radiations with equal doses. The RBE of a test radiation (r) is defined as the ratio D250/Dr, in which D250 and Dr are the doses of 250-keV X-rays and the test radiation respectively, required to produce equal biologic effects. The 250-keV X-rays is used as a standard radiation in definition of the RBE. 69  RBE and Fractionated Doses For a given radiation, an RBE value of n means that a dose equal to 1/n of the 250-keV X-rays produces the same biologic effect as the 250-keV x-rays. The RBE is a function of biologic endpoint and dose. The RBE varies largely for different types of cells and tissues. The inter-tissue variations of the RBE reduces by increasing the energy of the irradiation. 70  RBE as a Function of LET For most mammalian cells of human origin, RBE increases with LET to a maximum at about 100 keV/µm, thereafter decreasing with higher LET. 71  The Optimal LET LET = 100 keV/µm is an optimum value for most human cells in terms of producing biologic effects. At this density of ionization, the average separation between ionizing events just about coincides with the diameter of the DNA double helix (~2 nm). Radiation with this density of ionization has the highest probability of causing a double-strand DNA break by the passage of a single charged particle. 72  Factors that Determine RBE RBE depends on the following parameters: Radiation density (LET) Radiation dose (energy) Number of dose fractions Dose rate Type of biologic cell or tissue Biologic end point 73  Equivalent Dose RBE is a rather complicated parameter to interpret because it depends on various factors including the tissue type and the biologic end point. To simplify this parameter, the ICRP (International Commission on Radiological Protection) introduced a simpler but rather subjective parameter called “Equivalent Dose”. The equivalent dose is defined as the multiplication of the absorbed dose by a factor called “Radiation Weighting Factor (WR)”. Units of the equivalent dose: - Sievert (Sv) when the absorbed dose is expressed in Gray - Rem (Rad equivalent man) when the absorbed dose in expressed in Rad - 1 Sv = 100 Rem 74  Values of WR The value for WR varies from 1 for all low-LET radiations (X- and -rays) to a maximum of 20 for high-energy neutrons and α particles. (varies from 5 to 20) 75  Equivalent Dose – Example 1 Example: Calculate the equivalent dose if a tissue were exposed to 0.15 Gy of cobalt-60 -rays plus 0.02 Gy of 1-MeV neutrons. Answer: ED = (0.15  1) + (0.02  20) = 0.55 Sv, or 55 rem 76  Equivalent Dose – Example 2 Example: A beam of neutron particles is incident at a 15-g tumor. There are 1.6 ×1010 particles per second reaching the tumor, and the energy of each particle is 4 MeV. The WR for the radiation is 14. Find the biological equivalent dose (in rem) given to the tumor in 25 s. Solution: The absorbed dose (AD) is equal to the energy absorbed by the tumor divided by its mass:  1.60  10 –19 J  ( 25 s ) (1.6  10 10 s –1 )( 6 ) 4.0  10 eV   AD = Energy absorbed =  1 eV  Mass 0.015 kg = 17 Gy = 1700 rad The biologically equivalent dose is equal to the product of the absorbed dose (AD) and the WR coefficient: Equivalent Dose = AD  WR = (1700 rad)(14) = 2.4 ×104 rem 77