Radiotherapy & Radiation physics

Ionising radiation properties

Contains enough energy to remove electrons from atoms creating ions.

• Interacts strongly with tissues.

• Damages cells/DNA

• Detected for imaging

Main types of ionizing radiation & their properties

Alpha particles: heavy, positively charged, don’t travel far & are stopped by paper / skin.

• Not commonly used in imaging as they don’t penetrate far enough.

Beta particles: high speed electrons or positrons (positively charged electrons), lighter & travel further than alpha, stopped by aluminium.

X-rays & Gamma rays: high energy electromagnetic waves with no mass & no charge, are attenuated by bone/lead.

• Important in imaging as they can be picked up by detectors outside the body.

Neutrons: Indirectly ionizing via collision / activation & are stopped by low-z elements.

• Not commonly used in imaging

Ionizing radiation sources

• Radioactive decay of radionuclides

• X-ray tube (is a form of particle accelerator)

• Nuclear reactors

• Particle accelerators

• Nuclear fusion

• Cosmic rays

Process & effect of radioactive decay of radionuclides

• Ionising radiation produced when unstable radionuclide release energy/particles to achieve a more stable state.

• Particles emitted knock electrons off atoms in surrounding matter causing ionisation.

Process of creating ionizing radiation with an X-ray tube & nuclear reactors

X-ray tube:

• Electrons accelerated towards a metal target.

• Sudden deceleration when they hit target releases X-rays.

Nuclear reactors:

• Nuclear fission causes heavy nuclei to split & release energy, neutrons, gamma radiation.

Particle accelerator uses

• Charged particle beams (used in radiotherapy) - directly treat cancer by firing high energy particles at tumour, which gets damaged by energy deposited.

• Form radionuclides via nuclear reaction - produce radioactive isotopes used in imaging/therapy.

  • Fire high-energy particles at target nucleus causing nuclear reaction & target becomes radionuclide.

  • Produces radioactive isotopes used in imaging/therapy.

Process of creating ionizing radiation with Nuclear fusion & Cosmic rays

Nuclear fusion - light nuclei combine to form heavier nucleus releasing energy.

Cosmic rays - high energy particles from space interact with atmosphere producing ionising radiation.

Characteristic X-rays production & its difference to gamma

Gamma ray emission comes from nucleus & X ray comes from electron cloud.

Atomic electrons transitions produce characteristic X-rays.

• Each element has it own electron energy levels & its corresponding characteristic X-ray energy.

Binding energy definition & X-ray production process

1. Electrons in atoms sit in shells (K, L, M) each with a specific binding energy.

2. If inner shell electron is removed the outer electron can fall down to fill the gap.

3. Atom emits X-ray with energy equal to difference between energy levels.

Binding energy (negative wrt unbound state) - energy required to remove electron from atom.

X-ray fluorescence (XRF)

• Analytical technique where a material gets bombarded with high energy X-rays/ Gamma rays to become excited.

• A characteristic x-ray gets emitted & used to identify the material.

Nuclear structure components definitions (Z, A, N, Isotopes, Isobars, Isotones)

• Z: number of protons = atomic number.

• A: total number of nucleons = mass number.

  • A (protons + neutrons) ≈ atomic weight.

• N: number of neutrons = A-Z.

• Isotopes: nuclides with same Z.

• Isobars: nuclides with same A.

• Isotones: nuclides with same N.

Forces in nucleus

Coulomb force (repulsive) – protons push each other apart.

Nuclear force (attractive) – holds nucleons together.

Stability – balance between coulomb & nuclear force.

Nuclear shell model definitions & energy state types

Nuclear shell model – nucleus has energy levels & nucleons occupy specific energy states.

• Ground state – lowest nucleus energy state.

• Excited state (doesn’t last long) – nucleus has extra energy.

• Metastable state – excited state that last unusually long.

What occurs to unstable nuclei?

• Radioactive decay – particles/photons emitted to achieve more stable state (higher binding energy per nucleon).

• Higher binding energy ≈ lower value on total energy level diagram.

Define light & heavy nuclei

• Light nuclei (N=Z): equal number of protons & neutrons.

• Heavy nuclei: more neutrons than protons.

• Protons repel each other (coulomb force) & extra neutrons help stabilise the nucleus.

• Unstable nucleus (not in stability band) decays to move back to stability.

Decay types

• Beta plus decay: neutron deficient nuclides.

• Beta minus decay: neutron has excess nuclides.

Beta minus emission properties

Beta minus emission (too many neutrons) - neutron in nucleus changes into a proton, electron & a neutrino,

• Neutron in nucleus changes into a proton, an electron & a neutrino.

• Z increases by 1 & A stays the same.

Beta minus decay

• Continuous spectrum of electron energies (up to Emax) - energy shared between electron & neutrino.

• Average energy E = 1/3*Emax

Beta minus & gamma decay properties and define isometric transition

• Daughter nucleus is still excited after beta minus decay & emits a gamma ray immediately after.

• Can emit multiple gamma - have well defined energies characteristic of radionuclide.

• Example: 131-Iodine

• Isometric transition - delayed gamma emission when daughter left in a long-lived metastable state

Electron capture

Proton in nucleus captures an orbital electron from K or L shell & becomes a neutron.

• Z decreases by 1 & A stays the same.

• Captured inner-shell electron means atom has an electron vacancy.

• Outer electron that fill the gap cause the atom to emit: characteristic X-rays/Auger electron/ Gamma emission (if nucleus is left excited).

Positron (Beta plus) decay properties

Proton changes into a neutron, a positron & a neutrino.

• Z decreases by 1 & A stays the same

• Positron annihilates with atomic electron.

  • Mass is converted into energy: 2 gamma photons (each with 511keV energy) that travel in opposite directions.

Annihilation coincidence detection process & line of response

1. Radionuclide decays.

2. Positron is emitted.

3. Positron annihilates with an electron.

4. 2 551keV photons are detected by a ring of detectors around the patient.

Line of response - allows PET to localise where tracer is in body.

• 2 detectors detect photons at similar times.

• System assumes annihilation occurred along line between them.

Beta plus vs Electron capture decay

Beta plus & EC decays are alternate decay routes to same nucleus.

• Can reduce proton in proton rich nucleus by either: emitting a positron/ capturing an electron.

• Low-Z : mostly beta-plus.

• High-Z : mostly EC.

Define Becquerels, Branching ratio and the equation for radioactivity amount & half life.

Radioactivity measure in Becquerels

• 1decay per second = 1 Becquerel.

• Each decay can lead to several/ no emission.

Branching ratio (%) - fraction of decays that can lead to a particular emission.

Radioactivity amount: A(t) = A₀e^-𝜆t

Half-life (time for activity to fall to ½ its original value): T_1/2=0.693 / λ

Radiation types & interaction mechanism determine

• Charged particle: alpha & beta particles.

• Electromagnetic radiation: x-rays & gamma rays.

Interaction mechanisms determine: radiation detection, shielding, dosimetry

Collisional losses definition & causes

Charged particles interact with electrons & nuclei & slow down (lose energy) as they travel.

Causes:

• Ionization

• Excitation

• Bremsstrahlung

Ionization process and results & effects.

Incident charged particle gives enough energy to knock electron completely out of atom from outer shell.

• Can create secondary electrons: delta (𝛿) – rays.

Result: atom is ionized, free electron is produced that can go on to cause more ionization.

Effects:

• Damage to tissue

• Produces electrical signals in detectors

• Deposits dose in matter

Excitation process & effect

Charged particle gives energy to atom/molecule to raise electron to higher energy state.

• Atom is disturbed not ionised – no electron fully removed.

• Energy stored temporarily (can be released later).

Bremsstrahlung process & what its good for

Radiative energy loss mechanism - incident charged particles interact with nucleus, changes direction & emits a photon.

• Produces a continuous spectrum - energy can vary continuously from 0 up to max energy.

Good for: High Z absorber materials, high incident energy, small particle mass.

Charged particle tracks

Gradually slows down & loses energy – passes through material, leaving a trail of ionized atoms.

• Heavy particles (proton alpha) – straight tracks, densely ionizing.

• Electrons (𝑒^-,𝑒⁺) – convoluted path, less dense ionization.

Ionization volume (measured by radiation detectors) - detect particles in radiation detector.

Path length & range definition

Path length - total distance travelled.

Range - net penetration distance.

• Path length > range for beta particles.

• Twisted electrons path travel long distances but not deep.

Indirect ionisation properties and interaction types

High energy photon interaction are indirectly ionising: X-rays, Gamma rays, annihilation photons, bremsstrahlung.

• Photons have no charge.

• Produce secondary charged particles (ejected electrons, electron-positron pairs) during interaction.

• Charged particles then cause ionisation.

Interaction types: photoelectric effect, Compton scattering, pair production, Rayleigh scattering.

Photoelectric effect process

• Incident gamma is absorbed by atom

• Photoelectron is ejected (usually from inner shell if enough energy is available).

  • E_pe= E_incident - E_binding

• Inner shell vacancy leads to X-rays/Augers being emitted when electrons from other shells fall down to fill the gap.

• Photoelectron causes an ionization train.

Compton scattering properties

• Incident gamma is scattered

• Outer-shell electron is ejected as recoil electron: E_recoil = E_incident - E_scattered

• Scattered photon has lower energy than the incident photon: E_{min_scattered} < E_scattered < E_incident

• Forward peaked - scattering probability determined by Klein Nishina distribution

Problems of scattered photons in Compton scattering

• Go in wrong direction

• Still reach detector sometimes

• Reduce image contrast

• Add noise & mispositioned count

Pair Production properties

• Photon disappear & β⁺, β^- pair created.

• Minimum photon energy for pair production: 2×511keV = 1.022MeV

• Beta particles go on to cause ionization

• β⁺ creates 511keV annihilation photons.

Pair production process

1. High energy photon comes near nucleus.

2. Photon disappears.

3. Energy becomes mass + kinetic energy of: 1 electron, 1 positron.

Label the photon interaction chart

1. Photoelectric effect - used when Z is high (bione, iodine) & energy is low.

2. Compton scattering

3. Pair production - only occurs at high energies.

What are definitions and equations for attenuation, linear attenuation, mass attenuation, transmitted beam intensity & half value layer

• Attenuation - photons are absorbed/ scattered out of beam as they pass through a material.

• Linear attenuation coefficient 𝜇_l (units cm^-1).

• Mass attenuation coefficient: 𝜇_m(Z,E) = 𝜇_l /𝜌.

• Transmitted beam intensity: e^-𝜇lx

• Half value layer (50% intensity decrease) - large HVL (weaker attenuation, need more material for shielding), small HVL (strong attenuation, need less material for shielding).

Radiation detectors purpose and types

Radiation detectors - convert incident radiation to detectible form (light/ charge).

Convert radiation to measurable electrical signal: directly ( charge created in detector volume), indirectly (use light signal).

Main detector types:

• Scintillation detectors (indirect).

• Gas-filled detectors (direct)

• Semi-conductor detectors (direct)

Quantum efficiency definition & properties that affect it

Quantum efficiency (%) - probability that radiation (usually gamma) reaching detector is absorbed & detected.

• Varies with radiation & energy type.

• Depends on attenuation coefficient (𝜇 cm^-1) or radiation length (1/𝜇).

• Affected by: detector material thickness & radiation energy.

Sensitivity definition & properties

Sensitivity (%) - how accurate detector can tell where radiation came from.

• Depends on efficiency & detector size (solid angle).

• Is a property of whole system.

• High sensitivity: large area (compensates for low QE), better image quality (less noise).

Energy resolution definition

Energy resolution (ΔE %) - detector’s ability to distinguish between different photon energies.

• Characterised by full width at half maximum (FWHM).

• Smaller FWHM has better energy resolution.

• ΔE = f (no. electrons/ photon collected).

• More charge carriers means better statistical accuracy & resolution

Requirements of good energy resolution

• Radiation energy identification.

• Energy discrimination/ scatter rejection - removes low energy scattered photons.

• Positioning schemes - some detectors use energy information.

• Enables advances/ novel imaging techniques.

Spatial resolution definition

Spatial resolution (essential for imaging) - detector’s ability to determines analogue/ digital position of incoming radiation.

• Measure by FWHM (mm) - better spatial resolution & sharper image when smaller.

• Use many small detectors.

• Minimises/ simplifies amount of electronic readout needed.

• Ideally robust, cheap.

Temporal resolution definition

Temporal resolution - detector’s ability to measure time of radiation event accurately.

• Determines when particle/ photon is detected.

• Need fast & accurate (high statistics signal).

• Essential for coincidence detection accuracy.

• Important in PET (time of flight: 10ps).

Count rate capability/ dead time definition

Count rate capability/ dead time - detector’s ability to accurately record events at high count rates:

• Dead time - period after detection when detector can’t record another event.

  • Lose data at high count rates.

• Readout of each detected pulse takes too long - pulses overlap.

Gas filled detectors set up and situations where they are ineffective

• Gas contained between 2 electrodes.

• Ionisation collected & small current flows.

• Low QE & low sensitivity for X-rays & gamma-rays - gasses aren’t dense so photons are less likely to interact with it.

Process of how gas filled detectors function

1. Radiation enters gas & ionises the gas atoms.

2. Free electron & positive ions are produced.

3. Electric field moves them to electrodes.

4. Produces a small current/pulse.

Different types of gas filled detectors

Survey Meter (radiation safety monitor)

• Calibrated in mSv/hr

• Protective cap removed for alpha, beta & very-low energy (<10 keV) photons.

Dose calibrator - measures amount of radioactive tracer in syringe/vial before patient administration.

• Calibrated in Bq.

• Response depends on energy so calibration factors required.

Properties of gas filled detectors in terms of quantum efficiency, sensitivity, energy resolution, temporal resolution, count rate capability, spatial resolution.

Survey meter:

• Quantum efficiency: low (gas)

• Sensitivity: very low (doesn’t matter as count rate is high).

• Energy/ temporal/spatial resolution: none

• Count rate capability: moderate

Dose calibrator:

• Quantum efficiency: low (gas)

• Sensitivity: low (improved by large volume, large activities measured so doesn’t matter).

• Energy/ temporal/spatial resolution: none

• Count rate capability: moderate

Scintillation detectors

Scintillation detector - convert energy from ionisation & excitation into visible light.

• Use inorganic crystals / organic substances dissolved in liquid solution.

• Amount of light is proportional to energy deposited.

• Original experiments counted scintillation on zinc sulphide screen - now use highly sensitive photodetectors.

Process of scintillation detector

1. Radiation enters scintillator & deposits energy.

2. Scintillator emits visible light

3. Photodetector converts light to electric signal.

Scintillator components

Most are impurity activated.

Nal(Ti) crystal - detector of choice for most routine apps.

• Dense, high energy (Z), cheap, high light yield.

• Hygroscopic (need Aluminium jacket/ optical window) - absorbs moisture from air so must be sealed.

• Some with thin aluminium or Be entrance window for low energy radiations.

Photocathode (QE: 10-30%) - converts light to electrons.

Photomultiplier tube: gain 10⁶ at each dynode.

• Voltage must be very stable - multiplication factor very sensitive to voltage changes.

Process for photomultiplier tube

1. Receive flash from scintillator.

2. Convert light to electrons at photocathode

3. Multiply electrons through dynodes & output strong electric pulse.

Scintillation detector examples & their properties in terms of quantum efficiency, sensitivity, energy resolution, temporal resolution, count rate capability & spatial resolution.

Well counter - quantifies small activities (e.g. blood samples).

• Very high (>50%): quantum efficiency (very large Nal detector >5cm diameter), sensitivity.

• Good energy resolution.

• No temporal / spatial resolution.

• Poor count rate capability (not required as only measuring small activities).

Contamination monitor:

• High : quantum efficiency

• Low: sensitivity (small detector volume)

• Good: Energy resolution

• Moderate: count rate capability

• No temporal/ spatial resolution

Gamma Camera:

• Very high (thick Nal crystal): quantum efficiency

• High: sensitivity (large area detectors).

• Good: energy resolution (~50% must reject scattered radiation), Count rate capability, temporal resolution (not needed for SPECT)

• 3mm FWHM spatial resolution.

Semi conductor detectors properties

Semi-conductor detectors provide direct radiation detection.

• Solid state version of gas-filled detector.

• High density (>x2000) & high sensitivity.

• Need cooling using liquid nitrogen to remain at 77 kelvin: high purity germanium HPGe, Ge(Li) & Si(Li) operated & stored at low temperatures.

• Room temp SCs (CdZnT) are becoming available.

HPGe Detector properties

• Standard choice for gamma spectroscopy.

• Operate at 77 kelvin.

• Energy resolution 1keV for 122 keV gamma ray.

• 10cm*10cm cylinders available.

• Drift (charge collection) times up to 100nS.

CdTe & CZT properties

Starting to be used in imaging system.

• Can be operated at room temperature without excessive electronic noise.

• Worse energy resolution than HPGe.

• High atomic number (>Ge) - relatively thin detectors have good stopping efficiency for detecting gamma rays.

Gamma ray spectroscopy properties in terms of quantum efficiency, sensitivity, energy resolution, temporal resolution, count rate capability & spatial resolution.

Best for energy accuracy but not fast timing.

• Good: quantum efficiency, sensitivity (depends on configuration).

• Excellent: energy resolution

• No temporal resolution (not usually needed but poor for PET) & poor count rate capability.

• Spatial resolution (can be used for imaging).

Film spectroscopy properties in terms of quantum efficiency, sensitivity, energy resolution, temporal resolution, count rate capability & spatial resolution.

• Very low: quantum efficiency (used in combination with phosphor/scintillator).

• Moderate sensitivity (used in with phosphor/scintillator).

• No energy/temporal resolution

• Poor count rate capability (film is easily overexposed).

• Excellent spatial resolution