1. Linear Energy Transfer and Relative Biological Effectiveness
Radiobiology for the Radiologist, chapter 7, pg
Linear Energy Transfer and Relative Biological Effectiveness

2. The Deposition of Radiant Energy

3. The Deposition of Radiant Energy
Radiation Absorption of Biologic material
Occurrence
Ionization
Excitation
Not distributed at random
Localized along the tracks of individual charged particle
Depends on the types of radiation involved

4. The Deposition of Radiant Energy
Examples
Photons of x-rays
Give rise to fast electrons
Particle carrying unit of charge
having very small mass
Neutrons
Give rise to recoil protons
Mass: x of electrons
α-particle
Particle carrying 2 electric charge
Mass: 4 x of protons, 8000 x of electrons

5. The background : electron micrograph of human cell
The white dot : computer simulate ionizing events
Intermediated in ionization density
Densely ionizing
Sparsely ionizing
Sparsely ionizing
Variation of ionization density associated with different types of radiation

6. The Deposition of Radiant Energy
The spatial distribution of ionizing events produced by different particles varies enormously
Radiation
Sparsely ionizing
Ionizing events are well separated in space
Densely ionizing
Produce dense column of ionization
Energy ↓, Density of ionization ↑

7. Linear Energy Transfer

8. Linear Energy Transfer
Definition of linear energy transfer (LET)
Energy transfer per unit length of the track
L = dE / dL
Unit : keV/μm
can be only an average quanitities
The energy per unit length of track varies over such a wide range

9. Linear Energy Transfer
Method of calculation
Track average
Dividing the track into equal lengths and averaging the energy deposited in each length
Energy average
Dividing the track into equal energy intervals and averaging the lengths of the tracks that contain this amount of energy

10. But the track average and energy average are different for neutrons
Table 7.1. Typical Linear Energy Transfer Values
Radiation
Linear Energy Transfer, keV/μm
Cobalt-60 γrays
250-kV x-rays
10-MeV protons
150-MeV protons
14 MeV neutrons
2.5-MeV αparticles
2-GeV Fe ions
0.2
2.0
4.7
0.5
Track Avg Energy Avg.
166
1,000
The method of averaging makes little difference for x-rays or for monoenergetic charged particles
But the track average and energy average are different for neutrons
It is useful as a simple and naive way to indicate the quality of different types of radiation
Energy ↑, LET↓, Biological effectiveness ↓

11. Relative Biologic Effectiveness

12. Relative Biologic Effectiveness
Equal doses of different types of radiation do not produce equal biologic effects
e.g. Biologic effect : 1 Gy of neutron > 1 Gy of x-rays
Formal definition
The RBE of some test radiation (r) compared with x-rays is defined by the ratio D250/Dr where D250 and Dr are, respectively, the doses of x-rays and the test radiation required for equal biological effect
Example for measuring the RBE of some radiation test
Test system : lethality of plant seedlings
e.g. LD50 of the plant seedlings:
X-rays: 6 Gy, Neutrons: 4 Gy
RBE = 6: 4 or 1.5

13. Relative Biologic Effectiveness
Typical survival curves for
mammalian cells exposed to
x-rays and fast neutrons
At survival fraction of 0.01,
RBE is 1.5
At survival fraction of 0.6,
RBE is 3.0
Because the survival curves
have different shapes, the
RBE does not have a unique
value but varies with dose
Size of the dose ↓, RBE ↑

14. Relative Biologic Effectiveness and Fractionated Doses

15. Relative Biologic Effectiveness and Fractionated Doses
The effect of giving doses of x-rays or fast neutrons in 4 equal fractions
At surviving fraction 0.01,
RBE is 2.6
Dose fraction ↑, RBE ↑
The survival curve is reexpressed
after each dose fraction
The shoulder is larger for x-rays
than for neutrons
Result in an enlarged RBE for
fractionated treatment 10
Surviving fraction
1.0
10-1
10-2
10-3

16. Relative Biologic Effectiveness and Fractionated Doses
Conclusion
The net result is that neutrons become progressively more efficient than x-rays as
the dose per fractions ↓
The number of fractions ↑

17. Relative Biologic Effectiveness for Different Cells and Tissues

18. Mouse crypt cells (most resistant)
Markedly less variation
in radiosensitivity
among different cell lines
Mouse bone marrow (most sensitive)
Survival curves for various types of clonogenic mammalian cell irradiated with 300-kV x-rays or 15-MeV neutrons

19. Relative Biologic Effectiveness for Different Cells and Tissues
The variation in radiosensitivity among different cell lines is markedly less for neutrons than for x-rays
Reasons
X-rays : survival curve have large and variable initial shoulders
Accumulate and repair a large amount of sublethal radiation damage
Large RBEs for neutrons
Neutrons : shoulder region is smaller and less variable
Small neutron RBE values

20. Relative Biologic Effectiveness (RBE) as a function of Linear Energy Transfer (LET)

21. Relative Biologic Effectiveness (RBE) as a function of Linear Energy Transfer (LET)
X-rays : 2 keV/μm
α-rays : 150 KeV/μm
If LET ↑
Curve is steeper
Shoulder of the curve ↓
Survival curves for cultured cells of human origin exposed to 250-kVp x-rays, 15-MeV neutrons, and 4-MeV α-particles

22. Peak of RBE at LET 100 keV/μm
RBE falls again
LET between 10 – 100 keV/μm
RBE ↑rapidly
LET < 10 keV/μm
RBE ↑slowly
The LET at which the RBE reaches a peak is much the same for wide range of mammalian cells
Variation of relative biologic effectiveness (RBE) with linear energy transfer (LET) for survival of mammalian cells of human origin

23. The Optimal Linear Energy Transfer

24. The Optimal Linear Energy Transfer
LET at 100 keV/μm
The average separation between
ionization events coincides with
the diameter of the DNA helix
(i.e., about 20 nm)
Highest probability of causing a
double-strand break by the
passage of a single charged
particle
Diagram illustrating why radiation with a linear energy transfer of 100 keV/μm has the greatest relative biological effectiveness for cell killing, mutagenesis, or oncogenic transformation

25. The Optimal Linear Energy Transfer
X-rays
Sparsely ionization
Probability of a single track
causing a double-strand break is low
LET > 200 keV/μm
Readily produces d-s break
Energy “wasted” because the
ionizing events are too close together
RBE is a ratio of doses producing
equal biologic effect
RBE : densely ionizing radiation <
optimal LET radiation
More effective per track, less
effective per unit dose

26. The Optimal Linear Energy Transfer
Summary
The most biologically effective LET is that at which there is a coincidence between the diameter of the DNA helix and the average separation of ionizing events
Radiation having this optimal LET
Neutrons of a few hundred keV
Low-energy protons
α-particle

27. Factors that Determine Relative Biologic Effectiveness

28. Factors that Determine Relative Biologic Effectiveness
Radiation quality
Type of radiation
Energy of the radiation
Electromagnetic or particular
Charged or uncharged
Radiation dose
Number of dose fractions
The shape of the dose-response relationship varies for radiations that differ substantially in their LET
Dose rate
sparsely ionizing radiations varies critically
Densely ionizing radiations depends little
Biologic system or endpoint
Marked influence on the RBE
High RBE : accumulate and repair a great deal of sublethal damage

29. The Oxygen Effect and Linear Energy Transfer

30. For 250 kVp x-rays
Low LET
high OER (2.5)
Survival curves for cultured cells of human origin determined for four different types of radiation

31. For 4-MeV α-particles
Slight less densely
ionizing
LET 110 keV/μm
OER = 1.3
For 15-MeV neutrons
Intermeidated
ionizing
OER = 1.6
For 2.5 MeV α-particles
Densely ionizing
LET = 166 keV /μm
OER = 1

32. Oxygen enhancement ratio as a function of linear energy transfer.
LET < 60 keV/μm
OER fall slowly
LET > 60 keV /μm
OER falls rapidly
LET reached about 200 keV /μm
OER reaches unity
Oxygen enhancement ratio as a function of linear energy transfer.
Measurements were made with cultured cells of human origin.

33. Variation of the oxygen enhancement ratio (OER) and the relative
biologic effectiveness (RBE) as a function of the linear energy
transfer (LET) of the radiation involved.
The two curves are virtually mirror images of one another
Rapid increase of RBE and the rapid fall of OER occur at about the same
LET, 100 keV /μm

34. Radiation Weighting Factor

35. Radiation Weighting Factor
The purpose
Radiation differ in their biologic effectiveness per unit of absorbed dose
The complexities of RBE are too difficult to apply in specifying dose limits in every day radiation protection
Equivalent dose
Absorbed dose × weighting factor
Unit : sievert (Sv) where dose is expressed in grays
Rad equivalent man (rem) where dose is
expressed in rads
Discussed later in chapter 15

36. The End
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