Physics of Radiotherapy - Phy428-528

Physics of Radiotherapy

Lecture II: Interaction of Ionizing Radiation With Matter

Charge Particle Interaction

Energetic charged particles interact with matter by electrical forces and lose kinetic energy via:

• Excitation

• Ionization

• Radiative losses (Bremsstrahlung Production)

~ 70% of charged particle energy deposition leads to non-ionizing excitation

Specific Ionization

• Number of primary and secondary ion pairs produced per unit length of charged particle’s path is called specific ionization

• Expressed in ion pairs (IP)/mm

Increases with electrical charge of particle (more for alpha as compare to electron)

Decreases with incident particle velocity

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

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)

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).

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

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)

The energy loss by incident electron through inelastic collisions is described by the total linear stopping power Stot which represents the kinetic energy EK loss by the electron per unit path length x:

Stot =dEK/dx MeV/cm

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

Electrons traversing an absorber lose their kinetic energy through ionization collisionsand radiation collisions.

The rate of energy loss per gram and per cm2 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.

Photon Interactions

Probability• “chance” of event happening

can be mathematically expressed

example:

The probability of a woman experiencing breast cancer in her lifetime is 1:9

• x-ray interactions are chance events

relative predictions can be made • energy of the photons

• type of matter the x rays are passing through

cannot predict how one photon will interact

Photon Interactions

Probability of photon interaction depends on

• Energy of Incident Photon

• The type of traversing matter

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

Classical Scattering

(Coherent or Elastic) Occurs at low energy (< 10 keV)

Atom first excited by photon

Then releases (radiates) photon of same keV &

New photon travels in different direction from original photon but usually forward (small scatter angle)

Coherent Scattering is further classified as Rayleigh Scattering

• If interaction occurs with whole atom

Thompson Scattering

• If interaction occurs with shell e-

Photoelectric Effect (Complete

absorption)

The orbital electron is ejected from the atom with kinetic energy

EK=hν-EB

• where EB 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 EB of the absorber atom, the photoelectric effect is most likely to occur with a K-shell electron in comparison with higher shell electrons.

Photoelectric Effect

Electrons in higher energy shells cascade down to fill energy void of inner shell

Characteristic radiation

Photoelectric interaction probability• inversely proportional to cube of photon

energy low energy event

• proportional to cube of atomic number

P.E ~ Z3/E3

More likely with inner (higher) shells• tightly bound electrons

Interaction much more likely for• low energy photons

• high atomic number elements

Photon Energy Threshold

• binding energy of orbital electron

binding energy depends on

• atomic number

higher for increasing atomic number

• shell

lower for higher (outer) shells

most likely to occur when photon energy & electron binding energy are nearly the same

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 shell

shell offers new candidate target electrons

Causes step increases in interaction probability as photon energy exceeds shell binding energies

Photon Energy

InteractionProbability

K-shell interactions

possible

L-shell interactions

possible

L-shell binding energy

K-shell binding energy

Compton Scattering

Source of virtually all scattered radiation

Process

• incident photon (relatively high energy) interacts with free (loosely bound) electron

• some energy transferred to recoil electron

electron liberated from atom (ionization)

• emerging photon has

less energy than incident

new directionElectron out(recoil electron)

Photon inPhoton out

-

What is a “free” electron?

• low binding energy

outer shells for high Z materials

all shells for low Z materials

Electron out(recoil electron)

Photon in Photon out

-

Incident photon energy split between electron & emerging photon

Fraction of energy carried by emerging photon depends on

• incident photon energy

• angle of deflection

similar principle tobilliard ball collision

higher incident energy = less photon deflection

high energy (1MeV) photons primarily scatter forward

diagnostic energy photons scatter fairly uniformly

• forward & backward

at diagnostic energy photons lose very little energy during Compton Scattering

At therapy energy level, photons lose most of energy through Compton scattering

• higher deflection = less energy retained

Electron out(recoil electron)

Photon in Photon out

deflectionangle

-

' 1 cose

h

m c

λ’ is wavelength of scattered photon and λis the wavelength of incident photon

max

2

1 2eE hf

(Ee)Max is maximum energy transfer torecoil electron and α=hf/mec

2 (rest massenergy of electron

Interaction Probability is

• independent of atomic number (except for hydrogen)

• Proportional to electron density (electrons/gram)

• fairly equal for all elements except hydrogen (~ double)

Interaction Probability

• decreases with increasing photon energy

decrease much less pronounced than for photoelectric effect

Photon Energy

InteractionProbability Compton

Photoelectric

Pair Production (Complete absorption)

Exist at high photon energy

• Ei > 1.022 MeV

(e- rest mass energy = .511 MeV)

Photon interacts with nuclear force field

• uses 1.022 MeV to produce pair of electron like particles

e+ (positron) & e- (negatron)

Photon ceases to exist

E = 1.022 MeV + Ee+KE + Ee-KE

Photon Interaction Probabilities

Photoelectric Pair Production

COMPTON

Z

10

100

Energy (MeV)

0.01 0.1 1.0 10 100

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.)

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

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%.

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

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