Radiotherapy physics

1. Radiation Therapy Physics
Dr. J. M. Eltabib
Radiation Oncology
Tripoli Medical Center
M.R.C.P medicine UK, L.B.M. S Radiotherapy

2. Radioactive Decay
Formalism: Decay Schemes:
• Radioactive decay may be described by a reaction scheme, such as:
• These schemes allow us to track mass, charge, and energy
• Decay energy is shared between the decay products, depending on the
mode of decay:
 In α-decay, almost all of the energy goes into the α-particle
 In γ-decay, all of the energy goes into the photon or an internal
conversion electron
 In β-decay, energy is shared between a beta particle and a neutrino or
an antineutrino

3. Radioactive Decay
Alpha (α) Decay:
• Nuclei emit alpha particles (2n& 2p) instead of single protons or neutrons
• Occurs in very heavy nuclei z˃52 X A>190
• Decay energy is split between the daughter nucleus and the α-particle, but
almost all of it goes to the α-particle
• Typical alpha energies range from 2 to 8 MeV
• Alpha particles are monoenergetic
• Limited range (<10cm in air; 60μm in tissue)
• Easily shielded (e.g., paper, skin)
• Strongly interact with e- of the matter causing heavy damage → internal
radiation hazard

4. Radioactive Decay
Beta (β) Decay
• Occurs in nuclei that need to gain or lose protons
• β-decay is always isobaric, meaning there is no change in mass number
• There are three different beta decay modes:
 Beta-minus and beta-plus actually produce beta radiation
 Electron capture is a “beta” process but produces gamma radiation
• Beta particles are polyenergetic:
• Average energy ~ 1/3 of the maximum energy
• Neutrinos and antineutrinos do not really interact with regular matter,
so they do not contribute to radiation dose
• Range approx. 12m/MV in air, a few mm in tissue
• 1ry an internal hazard, but high beta can be an external hazard to skin
• Aluminum and other light materials are used for shielding

5. Radioactive Decay
Beta (β-) Decay or Negatron emission:
• One of the neutrons is able to turn into a proton
• In doing so, the nucleus spits out an electron (negatron) & an antineutrino
Beta (β+) Decay or Positron emission:
• One of the protons turns into a neutron
• In doing so, the nucleus spits out an anti-electron (positron) & a neutrino
• When the positron meets a regular electron, it annihilates!
• This releases the electron and positron’s mass as energy → two identical
0.511 MeV photons are emitted in opposite directions (PET scans)

6. Radioactive Decay
Beta (β-) Decay or Negatron emission:

7. Radioactive Decay
Electron Capture (EC):
• One of the protons turns into a neutron
• Nucleus does not have an excess of 1.02 MeV, the nucleus eats one of its
electrons → it emits a neutrino, but most of the decay energy remains in
the daughter nucleus
• Because there is a vacancy in one of the inner electron shells, one of the
outer shell electrons will fall into this vacancy and produce characteristic
X-rays (gamma ray) or Auger electrons (internal conversion electrons)
• NB. More energetic nuclei can decay by either beta-plus or EC

8. Radioactive Decay
Decay processes from an excited nucleus:
• When a nucleus is in an excited or metastable state (usually from a
previous nuclear reaction like beta emission) → it get rid of that extra
energy by two main mechanisms:
1. Gamma emission:
• The excess energy is simply released as a photon (gamma ray) with the exact
amount of energy needed to become stable
2. Internal conversion:
• The excess energy is transferred to a low energy orbital e- and it is ejected
from the atom
• The vacancy in one of the inner e- shells → one of the outer shell electrons
will fall into this vacancy and produce characteristic x-rays or auger electrons

9. Radioactive Decay
Gamma Emission:
• Is always isomeric (no change in atomic mass or atomic number)
• Most gamma emission occurs during or after alpha or beta decay
• 60Co decays to an excited 60Ni which immediately releases the excess
energy as γ-rays
• The β-rays are negligible (they do not escape the machine head)
• 60Co is a  emitter with 2 energies of 1.17& 1.33 MeV (average 1.25 MeV)
• Metastable nuclear isomers such as 99mTc can exist in an excited state and
emit gammas more gradually

10. Radioactive Decay
Internal conversion:
• The nucleus transfers energy to an inner shell electron and kicks it out
• This produces a vacancy in an inner electron shell
• Outer shell electrons will fill the vacancy, producing characteristic X-rays
or Auger electrons
• Internal conversion results in a spectrum of energies
• The useful radiation from 125I brachytherapy seed is actually characteristic
X-rays

11. Radioactive Decay

12. Radioactive Decay
Decay processes from an excited nucleus:

13. Radioactive Decay
Mathematics of Radioactive Decay:
• 1 Curie (Ci)=3.7x1010 disintegrations per second
• 1 Becquerel (Bq)= 1 disintegration per second (SI unite)
• 3 ways of quantifying radioactivity: mCi, ; mg-Ra (obsolete);
air-kerma strength (the current standard)
Exponential Decay:
• Activity (A) is proportional to number of atoms present (N), multiplied by the
decay constant λ. The decay constant is unique to each radionuclide
A = -λN
A(t) = A0e-λt
Half-Life time:
• How long it takes to decay to half the original activity:
• Nuclides with a long half-life have a low activity, and vice versa

14. Radioactive Decay
Mathematics of Radioactive Decay:
Mean Life time:
• Defined quite simply as 1/λ
• This is equal to the hypothetical amount of time it would take a source to
completely decay
• Mean life is useful for calculating dose and dose rate of permanent
brachytherapy implants
Effective half-life:
• When an isotope is being excreted from the body, its half-life is shorter
than its physical half-life
• Then teff is the effective half-life
Specific activity (Ci/gm):
• It is the activity per unit mass of a radioactive material
• Co60 = ~200 Ci/gm; Co60 has a higher specific activity ~ 200 times of Ra

15. Radioactive Decay
Radioactive Equilibrium:
• If multiple radioactive species in
sequence is placed in a sealed
container (each with its own t1/2 →
these may reach “equilibrium” over
time
• The 1st nuclide in the decay chain is
called the parent while the 2nd
nuclide is the daughter
• Types of equilibrium:
1. Secular equilibrium
2. Transient equilibrium
3. No equilibrium

16. Radioactive Decay
Secular equilibrium:
• When daughter t1/2 is much shorter
than the parent t1/2
• The daughter activity builds up over
time, until it is roughly equal to the
parent activity
• After the buildup period, the
apparent activity and half-life of the
daughter are basically the same as
the parent
• Examples:
• 226Ra (t1/2 =1,620yrs), 222Rn (4.8 days)
• 90Sr (t1/2 = 29.12yrs), 90Y (64 h)

17. Radioactive Decay
Transient equilibrium:
• When daughter t1/2 is only a little
shorter than the parent t1/2
• The daughter activity builds up as
the parent activity decays
• Eventually the daughter activity
slightly exceeds the parent activity,
and both curves decay together
• During transient equilibrium, the
daughter nuclide appears to have
slightly more activity and the same
t1/2 as the parent
• Examples:
• 99Mo (t1/2 66 h), 99mTc (6 h)

18. Radioactive Decay
No equilibrium:
• When daughter half-life is longer than parent half-life
• All of the parent nuclide decays into daughter, and there is no equilibrium
• Ex: 131Te (30 h), 131I (192 h)
Daughter Elution:
• When the daughter nuclide is extracted from a parent for use (ie, 99mTc,
90Y) it is called “daughter elution” or “milking the cow”
• This is useful for tabletop production of a short half-life nuclide
• Parent nuclide produces daughter nuclide until they reach either secular
or transient equilibrium

19. Radioactive Decay
Naturally Occurring Radioisotopes:
• These are mostly atomic numbers 81–92 in 4 series plus some weird ones
1. Thorium series
2. Neptunium series
3. Uranium Series (most important) – starts with 238U and includes 226Ra
and 222Rn
4. Actinium series
• Oddballs (not part of a well defined decay series):
• 3H, 14C (carbon dating), 40K (bananas), 50 V, 87Rb, 115In, 130Te, 138La,
142Ce, 144Nd, 147Sm, 176Lu, 187Re, 192Pt

20. Radioactive Decay
Man-Made Radioisotopes:
• Stable nuclei may be bombarded with protons, neutrons or other particles
to get new radioactive species
Neutron bombardment:
4 types:
1. (n,γ) – most common – nucleus absorbs a neutron, gets excited, and releases a
gamma ray
eg: 1H+n →2H (hydrogen bombarded with a neutron becomes deuterium)
2. (n,α) – neutron goes in, alpha particle breaks off from nucleus
eg: 10B+n → 7Li+4He (this reaction is the basis for neutron detection)
3. (n,p) – neutron goes in, proton is kicked out (No neutron to proton
transformations)
eg: 32S+n →32P+1H (this is how you make 32P for craniopharyngioma treatments)
4. Fission!!! – see below.

21. Radioactive Decay
Charged Particle Bombardment:
Protons Bombardment:
• Throwing protons at something will often create positron emitters (like
18F used in PET scans) but can also cause other reactions noted below:
• (p,γ) – proton goes in, excite nucleus and gamma rays come out
• (p,n) – proton goes in, neutron gets kicked out
• (p,d) – proton goes in, deuteron (2H) gets kicked out
Heavier particles Bombardment:
• alpha particles (4He nuclei) and deuterons (2H nuclei)
• Both are capable of being incorporated into the nucleus with the end
result being the expulsion of a proton or a neutron

22. Radioactive Decay
Fission:
• 235U splitting into 92Kr and 141Ba with 3 neutrons and 200 MeV
• 238U makes up 99.2 % of natural uranium, is less likely to undergo fission
• Uranium enrichment increases the percentage of 235U to increase the
ability to sustain fission
• Low enriched (3–4 % 235U) is used for power plants, and some can even
use un-enriched uranium
• Nuclear weapons require at least 20 % 235U with special engineering
• Nuclear reactors are used to make MANY of our sources: 90Sr, 90Y, 131I (NOT
125I or 123I), 89Sr, 192Ir, 60Co, 137Cs

23. Radioactive Decay
Nuclear fusion:
• Is the reverse of nuclear fission—lighter nuclei are fused together
into heavier ones. Again, a large amount of energy is released in the
process
• Fusion of hydrogen nuclei into helium nuclei is the source of our
sun’s energy

24. Thank you for your attention
Any Questions?