Radiation  is the transmission of energy via waves or particles.

Radiation may be the result of natural sources (Uranium-223 decay, solar emissions, cosmic rays, etc.) or may be man-made (an X-ray machine, linear accelerators, an LED bulb, etc.).

Because of the variety of radiation sources and properties, they are often categorized by energy (ionizing vs non-ionizing), type (electromagnetic vs. particle) or charge (charged or uncharged).

Ionizing radiation is radiation that carries sufficient energy to detach electron from atoms or molecules.

• Ionizing radiation is potentially hazardous because of its ability to damage DNA.
• The energy threshold to be considered ionizing radiation is between 10eV and 33eV for photons.
• This is in the ultraviolet region and explains why sun exposure causes sunburn (erythema)!

Key Point: When people (especially medical physicists) are discussing radiation, they are usually discussing highly energetic ionizing forms of radiation.

Unit (Symbol)DefinitionUnits
Exposure (X) Amount of ionization per mass of air due to X-rays and gamma rays.Roentgen (R) Absorbed Dose (D) Amount of energy imparted by radiation per unit mass.SI: Gray (Gy) Kerma (K) Kinetic Energy Released per unit MAss
Kinetic energy transferred to charged particles per unit mass.
SI: Gray (Gy) Equivalent Dose (HT) A measure of absorbed dose weighted for the biological effectiveness
of the types(s) of radiation (relative to the low LET photons and electrons)
to produce stochastic health effects in humans.
SI: Sievert (Sv) 1 rem = 0.01Sv
Dose Equivalent (H) A measure of absorbed dose weighted for the biological effectiveness of
the types of radiation (relative to low LET photons and electrons) to
produce stochastic health effects in humans.
Sievert (Sv) 1 rem = 0.01Sv
Effective Dose (E) A measure of equivalent dose, weighted for the biological sensitivity of
the exposed tissues and organs (relative to whole body exposure) to
stochastic health effects in humans.
Sievert (Sv) 1 rem = 0.01Sv
Effective Dose
Equivalent (HE) A measure of equivalent dose, weighted for the biological sensitivity of
the exposed tissues and organs (relative to whole body exposure) to
stochastic health effects in humans.
Sievert (Sv) 1 rem = 0.01Sv

#### Exposure

Exposure (X) is defined by ICRU as the quotient of dQ by dm where dQ is the absolute value of the total charge of the ions of one sign produced in air when all electrons liberated by photons in air of mass dm are completely stopped in air. Exposure is only defined up to about 3MeV because of the size of a free air ionization chamber required for higher energy measurements. #### Fluence/Flux

Fluence (Φ) is a measure of the total number of quanta which enter an area.

Flux (φ) is a measure of the rate at which quanta enter an area per unit time. That means that flux is the time derivative of fluence.

#### Linear Attenuation Coefficient

Linear attenuation coefficient (μ) is the fraction of a photon beam which is attenuated per unit path length (units: cm-1).

• I(x) is the intensity exciting the material
• I(0) is the incident intensity #### Absorbed Dose (D)

Absorbed dose is the energy deposited per unit mass to a medium by radiation. ##### Dose to matter

Dose to air (Dair) may be found directly from exposure (X) and the roentgen-to-cGy conversion factor fair as in the below equation. Dose to medium (Dmed) may be found directly using the below equation where fmed is the f-factor and A is a transmission factor. In reality, dose is often measured in a gas filled ionization chamber which requires Cavity Theory to convert Dair to Dmed. Key Point: Ion chambers placed in medium collect charge in air which is then converted, through application of Cavity Theory, to the dose to the medium.

#### KERMA (K)

KERMA, which stands for Kinetic Energy Released per unit MAss, is the quotient of the initial kinetic energies of all charge ionizing particles liberated by uncharged particles (photons) per mass of material. KERMA is divided into two components:

• Collision KERMA (Kcoll) is the amount of energy released in collision type interactions.
• Under conditions of Charged Particle Equilibrium (CPE), KColl = Absorbed Dose.
• In practice, because of scattering and attenuation, CPE is never established but Transient Charged Particle Equilibrium is established.
• Under TCPE: KColl ∝ Absorbed Dose ##### TERMA

Total Energy Released per unit MAss, TEMRA, is similar to KERMA but includes energy losses due to Coherent (Rayleigh) scattering. For MV beams, Coherent scattering is negligible, so KERMA = TERMA.

#### Equivalent Dose (H)

Equivalent dose represents the stochastic health effects of low levels of ionizing radiation to the human body. X-rays, gamma rays, electrons and muons1
Neutrons
• <10keV: 5
• 10-100keV: 10
• 100keV - 2MeV: 20
• 2MeV-20MeV: 10
• >20Mev: 5
Protons > 2MeV2
Alpha particles, fission fragments and non-relativistic heavy nuclei20
Source: ICRP 60

Key Point: Although neutrons are indirectly ionizing, they have a high radiation weighting factor. This is because they transfer their energy to protons which have a high LET due to their charge and large mass.

#### Effective Dose (E)

Effective dose uses tissue weighting factors to compare the risk of stochastic effects from a specific distribution of doses to organs with the risk of stochastic effects of a uniform whole body dose. This is achieved by multiplying equivalent dose (HT) to a tissue with a tissue weighting factor (wTand summing for all tissues. Because the tissue weighting factors (wT) were developed based on stochastic risks for a generic population of diversified age and gender, values of effective dose represent stochastic risk to a generic population rather than to any individual. Further, because these values are somewhat subjective, tissue weighting factors vary between the reports of different agencies.

##### Tissue Weighting Factors (WT)

OrganWT
Red bone marrow
Colon
Lung
Stomach
0.12
Breast
Liver
Esophagus
Thyroid
0.05
Skin
Bone surface
0.1
Remainder0.05
Total1.0
Data from Table 1.1 of NCRP 116

#### X-rays

X-rays are photons with an energy between about 10eV and 100keV. They may be produced naturally as electrons transition from high to low energy orbitals (characteristic X-ray emission) or as a result of a Bremsstrahlung interaction between an electron and a nucleus.

Classification

• Uncharged
• Electromagnetic
• Ionizing

#### Gamma Rays

Gamma (γ) rays are highly penetrating electromagnetic radiation arising from the decay of radioactive atomic nuclei. The term “gamma ray” may be used to refer to any photon with an energy about 100keV, including those generated in a linear accelerator.

Classification

• Uncharged
• Electromagnetic
• Ionizing

Electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the speed of light in that medium. As a result of the high speed, the particle is forced to rapidly decelerate releasing a photon. Cherenkov radiation is responsible for the characteristic blue glow of an underwater nuclear reactor. While seriously cool, Cherenkov radiation is generally non-ionizing and is not used for clinical treatments.

Classification

• Uncharged
• Electromagnetic
• Non-ionizing

#### Alpha Particles

Alpha particles consist of a helium-4 nucleus (two protons and two neutrons). Alpha particles are produced primarily through alpha decay of heavy elements. They are charged (2+) ionizing radiation. Because of their large charge and mass, they are considered a high LET form of radiation. This increases their biologically effective dose by a factor of 10-20 relative to photons or electrons.

Classification

• Charged
• Particle (Helium ions)
• Ionizing

• Typical energy: 5MeV
• At this energy, alphas are non-relativistic traveling at only about 0.05c.
• Range in air of about 4cm
• Range in tissue 40-90um
• RBE: 10-20
• LET: 100keV/um (High)
• Charge: 2+

#### Beta Particles

Beta particles are energetic electrons or positrons (anti-matter electrons with a positive charge) that are emitted by radioactive decay of an atomic nucleus. Electron beams may also be generated using a heated cathode (a process known as “boiling off”) and accelerated via an electric field, as in a linear accelerator.

Classification

• Charged
• Particle (Electrons)
• Ionizing

• Naturally occurring beta particles have continuous energy distribution due to beta decay neutrino.
• Charge: 1- (electrons), 1+ (positrons)
• RBE: 1

#### Delta Particles

Delta (δ) particles are secondary electrons liberated from a medium by interaction with a primary electron.
Delta rays which are created by a delta ray may be referred to as an "epsilon ray," although this notation is not in common use in medical physics.

Classification

• Charged
• Particle (Electrons)
• Ionizing

Protons are the heavy, positively charged constituent of an atoms nucleus. Although proton radiation is a byproduct of several nuclear reactions (e.g. 14N + α 17O + p) and even lightning strikes, it is also routinely produced via cyclotrons and used in proton therapy and particle physics. Although more expensive to produce clinically than electron or photon beams, they have a sharp Bragg peak and are able to deposit large doses locally while sparing surrounding tissues. This makes proton therapy a good choice for several situations including pediatric radiation therapy.

Classification

• Charged
• Particle (Protons)
• Ionizing

• Charge: 1+
• RBE: 1.1

Neutron radiation consists of energetic free neutrons. Neutrons are released as the result of neutron fission or fusion or from radioactive decay. Interestingly, free neutrons are unstable (mean life = 887s) and will decay into a proton, an electron, and an anti-electron-neutrino. Because neutrons have no charge, they cannot interact with matter through electric fields and thus have a significantly longer range than charged particles. Neutrons are typically divided into “fast” and “thermal” (slow) categories because of differences in their properties at these ranges. Fast neutrons are best attenuated by kinetic impact with hydrogen-rich materials such as plastics. Due to conservation of energy and momentum, hydrogen's mass (which is near that of a neutron) allows it to absorb the maximum amount of energy in a collision with a neutron.

Once the neutron has energy of less than about 0.025eV, it is considered a thermal neutron (so named because this is the energy range of kinetic energy in most materials). The neutron absorption cross-section is increased greatly at thermal energies in certain elements such as Boron-10. Hence Boron’s use in high energy linear accelerator shielding.

Classification

• Uncharged
• Particle (Neutron)
• Ionizing

• Charge: 0
• RBE immediate radiation injury: 1
• RBE cataracts, leukemia, and genetic changes: 4-10

### Photon Interactions

There are 4 main interactions between photons (X-rays and gamma rays) and matter. These are coherent scattering, photoelectric absorption, Compton scattering, and pair production.

Several factors impact the probability that a photon will undergo an interaction with matter including the energy of the photon and the properties of the atoms making up the material, largely driven by the atomic number (Z) of the absorber.

#### Coherent Scattering

Coherent scattering occurs when a photon undergoes an elastic scattering event with a material. Because the scattering is elastic no energy is lost by the photon during the interaction.

Important Points

• Primarily for low energy photons
• Two types of coherent scattering
• Rayleigh Scattering
• Elastic scattering of light by all electrons in the atom
• Thomson scattering
• Elastic scattering of light by a single electron in the atom

Probability of Coherent Scattering #### Photoelectric Absorption

The photoelectric effect occurs when a photon is absorbed by an inner shell electron causing the electron to gain sufficient energy to be ejected from the atom.

After ejection of the inner shell electron, the missing electron must be replaced by an outer shell (higher energy) electron. For this to happen, the outer shell electrons must loose energy by emission of a characteristic X-ray and/or an Auger Electron.

Requirements

• Energy threshold (minimum required energy) equal to the binding energy of the orbital electron

Energy After Interaction Probability of Photoelectric Absorption Resonance: The photoelectric effect exhibits a resonance phenomenon in which photons with energy close to the binding energy of an electron greatly increase the probability of interaction.

• Resonance peaks are named for their electron shells (i.e. k-edge)
• These peaks are exploited for use in imaging contrast in CT.
##### Characteristic X-rays

Characteristic X-rays are emitted as atomic outer-shell electron decay to a lower energy state.

Called “characteristic” because their energy is tied to the quantized energy levels between atomic orbitals causing the X-ray spectrum to be unique to a given element. ##### Auger Electrons

Auger electron emission is a competing means by which an atomic orbital may lose energy to fill a lower energy electron hole with a higher energy electron via the emission of another electron.

Auger electron emission may be thought of as a two-step process:

1. A higher energy electron emits a characteristic X-ray, thereby losing sufficient energy to fill the hole.
2. The characteristic X-ray is absorbed by another electron which is then ejected from the atom. This is the Auger electron. • EAuger Electron is the kinetic energy of the Auger electron
• ΔEAtomic State is the difference in energy between the initial and final atomic state
• EBinding is the binding energy of the Auger Electron prior to ejection

#### Compton Scattering

Compton scattering is an inelastic scattering event in which the incident photon interacts with a single electron. Because the interaction is inelastic, the photon transfers some of its energy to the electron during the interaction. This causes the electron to be ejected from its orbital.

Compton scattering is the most probable photon interaction in water for photons in the range of about 30keV to 30MeV.

Key Point: Because the Compton dominant range in soft tissue extends from 30keV to 30MeV, Compton scattering is a very important interaction of medical applications both in imaging and for radiation therapy!

Probability of Compton Scattering Because Compton scattering involves interaction of a photon with a singular photon, the electron density (number of electrons per unit mass) is the most important material property for Compton scattering interaction cross section.

Hydrogen has no neutrons and, therefore, about double the electron density of other atoms. This means that hydrogen has about double the Compton interactions per unit mass than any other low mass element.

For light elements other than hydrogen, the electron density is roughly constant. As a result, the probability of Compton scattering is nearly independent of effective atomic number.

 Element/Material Density (g/cc) Effective Atomic Number Electrons per gram Hydrogen 0.0009 1 6 × 1023 Carbon 2.25 6 3.01 × 1023 Lead 11.3 82 2.38 × 1023 Air 0.00129 7.64 3.01 × 1023 Water 1.0 7.42 3.34 × 1023 Fat 0.92 5.92 3.48 × 1023 Muscle 1.0 7.42 3.36 × 1023 Bone 1.85 13.8 3.00 × 1023
##### Compton Scattering Angle

Scatter angle and energy change are dictated by conservation of energy and momentum. After scattering, the energy is shared between the electron and the scattered photon minus the binding energy of the photon.

Note: the binding energy is often taken to be “0” because the electron is weakly bound and said to be “free.” • E’ is the energy of photon after interaction in MeV
• E0 is the energy of the photon before interaction in MeV
• Φ is the scattering angle of the photon
• 0.511 – rest mass of electron in MeV
• Eelectron is the electron energy after scatter
• Ebinding is the electron binding energy before scatter. Typically taken to be 0.

Key Point: Compton Scattering Angle

• As photon energy increases, the angular scatter distribution becomes more forward peaked.
• Reference angles:
• Forward scatter (0º scatters): The photon retains all of its energy (no interaction)
• Side scatter (90º scatters): The photon retains 0.511 MeV
• Back scatter (180º scatters): The photon retains 0.255 MeV

#### Pair Production

In pair production, a photon transitions to an electron/positron pair. The presence of a massive particle is required. This allows for conservation of energy and momentum as the massive particle is able to absorb some recoil energy.

Pair production typically occurs via interaction of a photon and an atomic nucleus.

Triplet production is a special type of pair production which occurs when the massive particle is an electron. Triplet production is less common and requires more energy than pair production.

Requirements

• Energy threshold
• Pair production: 2 × me = 1.022 MeV
• Twice the rest mass of an electron plus a small (typically neglected) additional energy to be transferred to the nucleus.
• Triplet production: 2×me + (3 × 2/3)me = 4me = 2.044 MeV
• Energy to create the rest mass of the electron and positron PLUS each of the three particles must acquire a kinetic energy of about 2/3MeV!
• Occurs near a particle with mass, usually an atomic nucleus
• This is required as the particle must absorb some recoil energy for conservation of both momentum and energy.

Probability of Pair Production Key Point: Although the threshold energy for pair production is only 1.022 MeV, it does not become a significant concern in clinical radiation therapy for beams under 10MV.

#### Photodisintegration

During photodisintegration an atomic nucleus absorbs a high-energy photon, causing the nucleus to decay into its constituent particles.

Decay products commonly include protons, neutrons, alpha particles and other more massive nuclides.

Energy Threshold

Because photodisintegration breaks nuclear bonds, the required minimum energy is in the range of 8-10MeV.

### Charged Particle Interactions

PropertyElectronsProtons
PathMany high angle scatters due to low massTravels in straighter path due to increased mass
Bragg PeakNot clinically present due to range stragglingUsed clinically, requires energy selection or bolus to target desired depth
Clinical Energy Range6MeV - 22MeV6MeV - 230MeV

#### General Concepts

Owing to their electric charge, most charge particle interactions are dominated by Coulomb's law. As a result, energy loss occurs continuously, rather than discretely, based on the magnitude of the particles charge and its interaction time (velocity). • C is the particles charge
• Thus, alpha particles (charge = 2+) interact much more strongly for the same velocity than do protons or electrons (charge = 1 or 1- respectively).
• v is the particles speed
• Particles with greater speed have less time to interact and thus are able to transfer less energy.
• Changes in energy for relativistic particles changes their mass more than their velocity. Thus while a charged particle is relativistic, its rate of energy loss is roughly independent of velocity.
• This leads to a “Bragg Peak” in which the charged particle gives up most of its energy near the end of its path.

Coulomb's Law • ke: Coulomb's constant (9 × 109 N·m2/C2)
• qn: charge n
• r: distance between charges 1 and 2

#### Stopping Power

Stopping power S(E) refers to the energy loss by charged particles per unit path length of a material.

Equation: Mass Stopping Power (S/ρ): Stopping power is commonly presented as mass stopping power which is the ratio of stopping power to the material density.

##### Factors impacting stopping power

Stopping power is a property of the material that the charged particles are passing through.

Energy Dependence:

Stopping power is proportional to the square of the particles charge and inversely proportional the square of the particle's velocity. Stopping power tends to vary slowly with energy for relativistic particle energies because of its proportionality to velocity. At lower energies, where velocity varies directly with energy, stopping power varies significantly with energy giving rise to a Bragg peak.

#### Charged Particle Range

Range (R) is related to stopping power as: ##### Continuous Slowing Down Approximation (CSDA)

The range of a charged particle is often computed assuming a continuous set of Coulomb interactions with the medium. This range, referred to as the CSDA range, is based on the average energy loss per unit path length in a given medium.

##### Impact of Charged Particle Mass

Scatter angle in tissue is greatly impacted by the mass of the charged particles. The mass of a proton is approximately 1,835 times that of an electron (mp = 938MeV, me = 0.511MeV). As a result, protons tend to travel in straighter paths than electrons.

#### Bragg Peak

Because energy loss by Coulomb interaction is proportional to 1/v2, a large portion of a charged particles energy is lost near the end of its path. This phenomenon results in a significant increase in deposited dose near end of a charged particle's path. This increased dose deposition is known as a Bragg Peak.

Important Points

• Bragg peaks are exploited in proton therapy to improve dose distributions.
• Range straggling and energy straggling reduce the sharpness of a clinical Bragg peak. This is why Bragg peaks are not present in clinical electron beams.

Bremsstrahlung radiation is electromagnetic radiation produced as a charged particle slows and scatters during interaction with an atomic nucleus.

Bremsstrahlung energy efficiency is the ratio of the output energy emitted as X-rays to input energy deposited by electrons in a linac target. Bremsstrahlung energy efficiency may be approximated as in the below equation where Z is the target atomic number and E is the accelerating energy in volts. Note: The above efficiency relationship holds only in the low MV region (<12MV). Source: Khan, F. M. (2010). Physics of X-ray Production. In The Physics of Radiation Therapy (p. 31). Baltimore, MA: Lippincott Williams & Wilkins. Bremsstrahlung is used to generate kV imaging X-ray beams as well as high energy MV beams in linear accelerators. This is an extremely inefficient process with only about 1% efficiency for kV (imaging) beams but improves markedly in the MV region with clinical linear accelerators achieving between 30% and 95% efficiency.

Key Point: Bremsstrahlung photons are emitted in a continuous energy spectrum.

• Maximum energy is equal to the incident electron energy.
• Average energy is 1/3 to 1/2 of the maximum energy.

### Neutron Interactions

##### Recoil Interactions
• A neutron hits a nucleus and transfers some energy to it. The charged nucleus then produces further ionizations through Coulomb interactions.
• Maximum energy transfer is limited by conservation of charge and momentum.
• Interaction of a hydrogen nucleus (a proton) allows for maximum energy transfer because of their similar masses.
• Interactions with heavy elements result in little energy transfer (think of a ball hitting a wall).
##### Nuclear Activation
• Neutrons, especially low energy “thermal” neutrons, may also be absorbed by the nucleus. This may produce a spontaneous decay of the nucleus or it could yield a new isotope which may undergo decay at a later time.
• Neutron activation is the process of creating a radioactive isotope through neutron interactions.
• Due to its high hydrogen content, neutron dose to fat is about 20% higher than dose to muscle for the same fluence and energy.

## Knowledge Test

1. What is the minimum kinetic energy per beta particle in triplet production?

Question 1 of 3

2. A 117 keV photon undergoes a photoelectric interaction. The liberated electron has an energy of  84keV. Select all true statements regarding this interaction.

Question 2 of 3

3. An 8.6 MeV photon undergoes pair production. Assuming the electron has 50% more energy than the positron, how much energy does the electron have?

Question 3 of 3
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