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Physics of Radiotherapy Lecture II: Interaction of Ionizing Radiation With Matter

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Charge Particle Interaction Energetic charged particles interact with matter by electrical forces and lose kinetic energy via: Energetic charged particles interact with matter by electrical forces and lose kinetic energy via: ExcitationExcitation IonizationIonization Radiative losses (Bremsstrahlung Production)Radiative losses (Bremsstrahlung Production) ~ 70% of charged particle energy deposition leads to non-ionizing excitation ~ 70% of charged particle energy deposition leads to non-ionizing excitation

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Specific Ionization Specific Ionization Number of primary and secondary ion pairs produced per unit length of charged particle’s path is called specific ionizationNumber of primary and secondary ion pairs produced per unit length of charged particle’s path is called specific ionization Expressed in ion pairs (IP)/mmExpressed in ion pairs (IP)/mm Increases with electrical charge of particle (more for alpha as compare to electron) Increases with electrical charge of particle (more for alpha as compare to electron) Decreases with incident particle velocity Decreases with incident particle velocity

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Linear Energy Transfer (Stopping Power of The Medium) Amount of energy deposited per unit path length (eV/cm) is called the linear energy transfer (LET) and is also known as stopping power of the medium Amount of energy deposited per unit path length (eV/cm) is called the linear energy transfer (LET) and is also known as stopping power of the medium LET of a charged particle is proportional to the square of the charge and inversely proportional to its kinetic energy LET of a charged particle is proportional to the square of the charge and inversely proportional to its kinetic energy High LET radiations (alpha particles, protons, etc.) are more damaging to tissue than low LET radiations (electrons, gamma and x-rays) High LET radiations (alpha particles, protons, etc.) are more damaging to tissue than low LET radiations (electrons, gamma and x-rays)

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Electron Interaction As an energetic electron traverses matter, it undergoes Coulomb interactions with absorber atoms, i.e., with: Atomic orbital electrons Atomic nuclei Through these collisions the electrons may: Lose their kinetic energy (collision and radiation loss). Change direction of motion (scattering).

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Energy losses are described by stopping power (LET). Scattering is described by angular scattering power. Collision between the incident electron and an absorber atom may be: Elastic Inelastic

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In elastic collision the incident electron is deflected from its original path but no energy loss occurs. In an inelastic collision with orbital electron the incident electron is deflected from its original path and loses part of its kinetic energy (collisional loss). In an inelastic collision with nucleus the incident electron is deflected from its original path and loses part of its kinetic energy in the form of bremsstrahlung (radiative loss)

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The energy loss by incident electron through inelastic collisions is described by the total linear stopping power S tot which represents the kinetic energy E K loss by the electron per unit path length x: S tot =dE K /dx MeV/cm

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Mass Stopping Power Total mass stopping power is defined as the linear stopping power divided by the density of the absorbing medium. It has two parts, collisional and radiative

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Electrons traversing an absorber lose their kinetic energy through ionization collisions and radiation collisions. The rate of energy loss per gram and per cm 2 is called the mass stopping power and it is a sum of two components: Mass collision stopping power Mass radiation stopping power The rate of energy loss for a therapy electron beam in water and water-like tissues, averaged over the electron’s range, is about 2 MeV/cm.

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Photon Interactions Probability Probability “chance” of event happening“chance” of event happening can be mathematically expressed can be mathematically expressed example: example: The probability of a woman experiencing breast cancer in her lifetime is 1:9 The probability of a woman experiencing breast cancer in her lifetime is 1:9 x-ray interactions are chance eventsx-ray interactions are chance events relative predictions can be made relative predictions can be made energy of the photonsenergy of the photons type of matter the x rays are passing throughtype of matter the x rays are passing through cannot predict how one photon will interact cannot predict how one photon will interact

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Photon Interactions Probability of photon interaction depends on Probability of photon interaction depends on Energy of Incident PhotonEnergy of Incident Photon The type of traversing matterThe type of traversing matter

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Photon Interactions Transmitted through matter (unchanged) Change direction with no energy loss 1.Classical Scattering (Coherent Scattering) Change direction and lose energy 2.Compton Scattering Deposit all energy in the matter 3.Photoelectric Effect 4.Pair Production 5.Photodisintegration

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Classical Scattering (Coherent or Elastic) Occurs at low energy (< 10 keV) Occurs at low energy (< 10 keV) Atom first excited by photon Atom first excited by photon Then releases (radiates) photon of same keV & Then releases (radiates) photon of same keV & New photon travels in different direction from original photon but usually forward (small scatter angle) New photon travels in different direction from original photon but usually forward (small scatter angle) Coherent Scattering is further classified as Coherent Scattering is further classified as Rayleigh Scattering Rayleigh Scattering If interaction occurs with whole atomIf interaction occurs with whole atom Thompson Scattering Thompson Scattering If interaction occurs with shell e -If interaction occurs with shell e -

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Photoelectric Effect (Complete absorption) The orbital electron is ejected from the atom with kinetic energy E K =hν-E B where E B is the binding energy of the orbital electron. The ejected orbital electron is called a photoelectron. When the photon energy hν exceeds the K-shell binding energy E B of the absorber atom, the photoelectric effect is most likely to occur with a K-shell electron in comparison with higher shell electrons.

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Photoelectric Effect Electrons in higher energy shells cascade down to fill energy void of inner shell Electrons in higher energy shells cascade down to fill energy void of inner shell Characteristic radiation Characteristic radiation

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Photoelectric interaction probability Photoelectric interaction probability inversely proportional to cube of photon energyinversely proportional to cube of photon energy low energy event low energy event proportional to cube of atomic numberproportional to cube of atomic number P.E ~ Z 3 /E 3 P.E ~ Z 3 /E 3 More likely with inner (higher) shells More likely with inner (higher) shells tightly bound electronstightly bound electrons Interaction much more likely for Interaction much more likely for low energy photonslow energy photons high atomic number elementshigh atomic number elements

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Photon Energy Threshold Photon Energy Threshold binding energy of orbital electronbinding energy of orbital electron binding energy depends on binding energy depends on atomic numberatomic number higher for increasing atomic number higher for increasing atomic number shellshell lower for higher (outer) shells lower for higher (outer) shells most likely to occur when photon energy & electron binding energy are nearly the same most likely to occur when photon energy & electron binding energy are nearly the same

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Photoelectric interactions decrease with increasing photon energy BUT Photoelectric interactions decrease with increasing photon energy BUT When photon energies just reaches binding energy of next (inner) shell, photoelectric interaction now possible with that shellWhen photon energies just reaches binding energy of next (inner) shell, photoelectric interaction now possible with that shell shell offers new candidate target electrons shell offers new candidate target electrons Causes step increases in interaction probability as photon energy exceeds shell binding energies Causes step increases in interaction probability as photon energy exceeds shell binding energies

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Photon Energy Interaction Probability K-shell interactions possible L-shell interactions possible L-shell binding energy K-shell binding energy

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Compton Scattering Source of virtually all scattered radiation Source of virtually all scattered radiation Process Process incident photon (relatively high energy) interacts with free (loosely bound) electronincident photon (relatively high energy) interacts with free (loosely bound) electron some energy transferred to recoil electronsome energy transferred to recoil electron electron liberated from atom (ionization) electron liberated from atom (ionization) emerging photon hasemerging photon has less energy than incident less energy than incident new direction new direction Electron out (recoil electron) Photon in Photon out -

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What is a “free” electron? What is a “free” electron? low binding energylow binding energy outer shells for high Z materials outer shells for high Z materials all shells for low Z materials all shells for low Z materials Electron out (recoil electron) Photon in Photon out -

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Incident photon energy split between electron & emerging photon Incident photon energy split between electron & emerging photon Fraction of energy carried by emerging photon depends on Fraction of energy carried by emerging photon depends on incident photon energyincident photon energy angle of deflectionangle of deflection similar principle to billiard ball collision similar principle to billiard ball collision

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higher incident energy = less photon deflection higher incident energy = less photon deflection high energy (1MeV) photons primarily scatter forward high energy (1MeV) photons primarily scatter forward diagnostic energy photons scatter fairly uniformly diagnostic energy photons scatter fairly uniformly forward & backwardforward & backward at diagnostic energy photons lose very little energy during Compton Scattering at diagnostic energy photons lose very little energy during Compton Scattering At therapy energy level, photons lose most of energy through Compton scattering At therapy energy level, photons lose most of energy through Compton scattering higher deflection = less energy retainedhigher deflection = less energy retained Electron out (recoil electron) Photon in Photon out deflection angle -

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λ’ is wavelength of scattered photon and λ is the wavelength of incident photon (E e ) Max is maximum energy transfer to recoil electron and α=hf/m e c 2 (rest mass energy of electron

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Interaction Probability is Interaction Probability is independent of atomic number (except for hydrogen)independent of atomic number (except for hydrogen) Proportional to electron density (electrons/gram)Proportional to electron density (electrons/gram) fairly equal for all elements except hydrogen (~ double)fairly equal for all elements except hydrogen (~ double)

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Interaction Probability Interaction Probability decreases with increasing photon energydecreases with increasing photon energy decrease much less pronounced than for photoelectric effect decrease much less pronounced than for photoelectric effect Photon Energy Interaction Probability Compton Photoelectric

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Pair Production (Complete absorption) Exist at high photon energy Exist at high photon energy Ei > 1.022 MeVEi > 1.022 MeV (e- rest mass energy =.511 MeV) (e- rest mass energy =.511 MeV) Photon interacts with nuclear force field Photon interacts with nuclear force field uses 1.022 MeV to produce pair of electron like particlesuses 1.022 MeV to produce pair of electron like particles e+ (positron) & e- (negatron) e+ (positron) & e- (negatron) Photon ceases to exist Photon ceases to exist E = 1.022 MeV + E e+KE + E e-KE E = 1.022 MeV + E e+KE + E e-KE

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Photon Interaction Probabilities Photoelectric Pair Production COMPTON Z 10 100 Energy (MeV) 0.01 0.1 1.0 10 100

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Linear Attenuation Coefficient The most important parameter used for characterization of x-ray or gamma ray penetration into absorbing media is the linear attenuation coefficient μ The linear attenuation coefficient depends upon: Energy of the photon beam Atomic number Z of the absorber The linear attenuation coefficient may be described as the probability per unit path length that a photon will have an interaction with the absorber This interaction may be any one of the interactions discussed so for (PE,CS PP etc.)

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For collimated beam of mono- energetic photons, the intensity of photon beam after passing through thickness x of some homogenous medium is For collimated beam of mono- energetic photons, the intensity of photon beam after passing through thickness x of some homogenous medium is

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Several thicknesses of special interest are defined as parameters for mono-energetic photon beam characterization in narrow beam geometry: Half-value layer (HVL1 or x1/2) Absorber thickness that attenuates the original intensity to 50%. Mean free path (MFP ) Absorber thickness which attenuates the beam intensity to 1/e = 36.8%. Tenth-value layer (TVL or x1/10) Absorber thickness which attenuates the beam intensity to 10%.

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In medical physics photon interactions fall into four groups: Interactions of major importance Photoelectric effect Compton scattering by free electron Pair production (including triplet production) Interactions of moderate importance Rayleigh scattering Thomson scattering by free electron Interactions of minor importance Photonuclear reactions Negligible interactions Thomson and Compton scattering by the nucleus

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For a given hν and Z: Linear attenuation coefficient μ is sum of all interaction probabilities, mostly μ = PE Cross-section + Scattering Cross- section + PP Cross-section

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