1. Quantities and Measurements - 2 Dosimetric Quantities
Kerma, Dose, LET and more
Day 2 – Lecture 8

2. Objective
To know about dosimetric quantities, associated terminology and underlying concepts
We will learn about kerma (rate), exposure (rate), absorbed dose (rate), linear energy transfer (LET), lineal energy transfer, and organ dose
Additional underlying terms and concepts will be discussed, as shown on the next slide.

3. Content Kerma (rate) Mass energy absorption coefficient Air Kerma
Exposure (rate)
Absorbed dose (rate)
Energy imparted
Linear energy transfer (LET)
Lineal energy transfer
Organ dose
To fully develop the concepts of kerma, exposure, and absorbed dose, we need to discuss and understand concepts such as mass energy absorption coefficient and energy imparted.

4. Kerma Kerma (Kinetic Energy Released per unit Mass)
Kerma is defined as:
K =
where
dEtr is the sum of the initial kinetic energies of all the charged particles liberated by uncharged particles in a mass dm
dEtr dm
Kerma is a concept useful primarily for photons and neutrons in any medium. It includes all of the energy transferred to charged particles by the incoming radiation, even if some of that energy is not deposited locally.
Kerma represents the transference of energy from photons or other primary incident radiation (e.g. neutrons) to directly ionizing particles (e.g. electrons).

5. Kerma The unit of kerma is the J kg-1
The special name for the unit of kerma is gray (Gy)
One of the main values of the concept of kerma is in clarifying the steps involved in energy deposition.

6. Kerma Rate .
The kerma rate, K, is the quotient of dK by dt, where dK is the increment of kerma in the time interval dt, thus:
K =
The unit is J kg-1 s-1 and the special name for the unit of kerma rate is gray per second
(Gy s-1) . dK dt
Kerma rate is simply energy transferred to charged particles per unit time.

7. Exposure
Exposure is:
A quantity used to indicate the amount of ionization in air produced by x- or gamma-ray radiation
The SI unit of exposure is the coulomb per kilogram (C/kg)
One R = 2.58 x 10-4 C/kg. R stands for the unit of roentgen, an old unit which is still used in some applications.
Note that exposure applies only to electromagnetic radiation and only in air. Thus, it has definite limitations but we still need to understand the concept since many portable health physics instruments still read out in units of roentgens or multiples thereof.
Also, for example, in the United States the roentgen is still allowed to be used by licensees of the USNRC on radiation survey records (but not on official dose records).

8. Exposure
The exposure, X, in units of C kg-1, is related to the air kerma as follows:
X =
where “W” is the average energy spent by an electron to produce an ion pair and “e” is the electronic charge W
Ka (1 – g) e
For fast electrons in dry air, W/e has the average value of ± 0.05 J C-1.
Note that the old unit for exposure, which was the roentgen, R, is related to the SI unit as follows:
1 R = x C kg-1
Many radiation protection portable survey instruments are still calibrated in units of roentgen and multiples thereof, so it is still necessary to understand and use the roentgen.
where g is the fraction of initial secondary electron energy that is radiated as bremsstrahlung

9. Exposure
Exposure is measured under conditions of electronic equilibrium
Electronic equilibrium is discussed in more detail in another session, but basically, when the same number of electrons are set in motion in a given volume by the primary radiation as come to rest in that same volume, we say that “electronic equilibrium” has been attained. For electronic equilibrium to exist, the attenuation of the primary radiation beam must be negligible in a distance equal to the mean range of the electrons.

10. Exposure Rate X = The unit is C kg-1 s-1.
The exposure rate, X, is the quotient of dX by dt, where dX is the increment of exposure in the time interval dt, thus:
X =
The unit is C kg-1 s-1 . dX dt
Exposure rate is simply the production of ionization in air per unit time.

11. Absorbed Dose The absorbed dose, D, is given by: D = de/dm
Where de is the mean energy imparted to matter of mass dm _
Energy imparted is the energy incident minus the energy leaving the mass; minus the energy released in nuclear transformations ( to keep the dose from becoming negative when the mass contains a radioactive source).
The medium should always be specified.
Kerma represents the transference of energy from the photons (or neutrons) to the directly ionizing particles. The subsequent transference of energy from these directly ionizing particles to the medium (e.g. air or tissue) is represented by the absorbed dose.
In the region of electronic equilibrium, the kerma and absorbed dose are equal.

12. Absorbed Dose The unit of absorbed dose is J kg-1
The special name for the unit of absorbed dose is gray (Gy)
Note that kerma and absorbed dose have the same units and in fact are equal in the region of electronic equilibrium.

13. Energy Imparted Energy imparted is the energy incident minus
the energy leaving the mass (excluding the energy released in nuclear transformations to keep the dose from becoming negative when the mass contains a radioactive source)
Energy imparted is basically the energy that is absorbed locally by the medium. The energy imparted determines the dose.

14. Absorbed Dose Rate .
The absorbed dose rate, D, is the quotient of dD by dt, where dD is the increment of absorbed dose in the time interval dt, thus:
D =
The unit is J kg-1 s-1 and the special name for the unit of absorbed dose rate is gray per second (Gy s-1) . dD dt
The absorbed dose rate is simply the absorbed dose delivered per unit time period.

15. Lineal Energy Transfer
Lineal energy transfer is the energy transferred from a particle to the medium traversed per unit length
The magnitude is expressed in kilo-electron volts per micrometer (keV/µm)
Given the wide range of values for energy deposition for the same dose, the biological effect will vary according to the type of radiation. For example, comparing the effects of alpha and gamma rays is rather like comparing the effect on a target of a cannonball with that of buckshot.
The energy transferred may be the same, but the kind of damage inflicted will be different.

16. Lineal Energy Transfer
Expresses the level of energy transferred at a microscopic scale
For alpha particles, as the dose decreases the number of hit cells decreases, but not the degree of impact on those cells, whereas for gamma rays the quantity of energy deposited per cell goes down, but not the number of cells hit.
This difference makes alpha particles more damaging relative to gamma rays and thus they have a higher radiation weighting factor relative to gamma rays.
The lineal energy transfer is the microdosimetric analogue of the linear energy transfer (LET).

17. Linear Energy Transfer
Linear energy transfer (LET), is defined generally as:
L = [ ]
where dE is the energy lost in traversing distance dl dE dl
Measurement of the number of ionizations which radiation causes per unit distance as it traverses the living cell or tissue is called the linear energy transfer of the radiation. The concept involves lateral damage along the path, in contrast to path length or penetration capability. Medical X-rays and most natural background radiation are low LET radiation, while alpha particles have high LET. On the average, fission fragments have high LET.
In order to have a quantitative sense of the frequency of the different cell effects caused by radiation exposure, imagine a colony of 1,000 living cells exposed to a 1 cGy X-ray (about the dose for one X-ray spinal examination). There would be two or three cell deaths, two or three mutations or irreparable changes in cell DNA and about 100,000 ionizations in the whole colony of cells -- ranging from 11 to 460 ionisations per cell.

18. Linear Energy Transfer
A measure of how, as a function of distance, energy is transferred from radiation to the exposed matter
A high value of LET indicates that energy is deposited within a small distance
While cells can repair some damage, no one claims that there is perfect repair even after only one such X-ray. A comparable 1 cGy exposure to neutrons which have higher linear energy transfer (LET) would be expected to cause more cell deaths and more mutations. The ionizations caused would range from 145 to 1,100 per cell.
Alpha particles which occur naturally would cause roughly 10 times as many cell deaths and mutations, and 3,700 to 4,500 ionizations per cell. Alpha particles have high linear energy transfer.
The average number of cell deaths and mutations caused by fresh fission particles (i.e. those present soon after detonation of a nuclear bomb) would be even greater, with the ionizations as frequent as 130,000 per cell.

19. Organ Dose
Organ doses can arise from both external and internal radiation (i.e. intakes of radioactive material)
Measurement/calculation of organ dose from external radiation is usually more straightforward than for intakes of radioactive material
Therefore, the next slides focus on organ doses from internal radiation

20. Organ Dose
Following an intake into the body of a radioactive material, there is a period during which the material gives rise to equivalent doses delivered in the organs or tissues of the body at varying rates
The time integral of the equivalent-dose rate is called the committed equivalent dose.
 is usually taken to be 50 years for adults and 70 years for children.
Depending on the half lives of the radionuclides, there will be effects over time from radiation doses. To account for the continuing irradiation of organs and tissues after intake, there is the committed dose concept.
The committed equivalent dose is the time integral of the equivalent dose-rate in a specific tissue following intake of a radionuclide into the body. Unless specified otherwise, an integration time of 50 y after intake is recommended for the occupational dose, and 70 y for members of the public.

21. Specific Organs for Which Doses Are Calculated
Gonads
Bone marrow (red)
Bladder
Breast
Thyroid
Skin
Remainder
Colon
Lung
Stomach
Liver
Oesophagus
Bone surface
There is a specific list (shown in this slide) of organs and tissues for which radiation doses are typically calculated. There are 12 specific organs/tissues plus remainder. The specific remainder organs are shown in the next slide.

22. Remainder Organs Adrenals Upper large intestine Small intestine Kidney
pancreas
Brain
Spleen
Thymus
Uterus
muscle
The remainder consists of the tissues and organs shown in this slide. The list includes organs which are likely to be selectively irradiated.
In those exceptional cases in which a single one of the remainder tissues or organs receives an equivalent dose in excess of the highest dose in any of the twelve organs for which a weighting factor is specified, a weighting factor of should be applied to that tissue or organ and a weighting factor of to the average dose in the rest of the remainder as defined in this slide.

23. Phantom for Organ Dose Calculation
To calculate organ doses over various organs and tissues in a human body, an anthropomorphic phantom, a mathematical representation of a human body, is usually employed. The particular phantom shown in this slide was developed by Cristy and Eckerman (1987). This phantom is a hermaphroditic phantom that has a trunk and most internal organs of an adult male, but also has breasts, ovaries and a uterus which are representative of an adult female.
This phantom consists of three major sections: (i) the trunk and arms represented by elliptical cylinder, (ii) the legs and feet represented by two truncated circular cones, and (iii) the head and neck represented by an elliptical cylinder capped by half an ellipsoid. Within these sections, well over 150 organs and structures were modeled geometrically and assigned one of three tissue types: skeletal, lung or soft tissue. In this phantom, the organs and exterior shape of the phantom are defined by simple mathematical equations, such as cylinders, ellipsoids, cones, or their combinations. In this model, four coordinate systems were used in addition to the main coordinate system to model some organs, which cannot be easily modeled in the main coordinate system (i.e., adrenals, gall bladder and heart).

24. Organ Dose
X-ray beam striking the duodenum during a fluoroscopy procedure. Radiation will often selectively irradiate a particular organ or part of the body, depending on beam size and orientation.
Scattered radiation can also irradiate other organs and tissues, as portrayed in the slide.

25. Summary
Dosimetric quantities and associated terminology were discussed
Students learned about kerma, exposure, absorbed dose, linear energy transfer, lineal energy transfer and organ dose

26. Where to Get More Information
Knoll, G.T., Radiation Detection and Measurement, 3rd Edition, Wiley, New York (2000)
Attix, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986)
International Atomic Energy Agency, Determination of Absorbed Dose in Photon and Electron Beams, 2nd Edition, Technical Reports Series No. 277, IAEA, Vienna (1997)

27. Where to Get More Information
International Commission on Radiation Units and Measurements, Quantities and Units in Radiation Protection Dosimetry, Report No. 51, ICRU, Bethesda (1993)
International Commission on Radiation Units and Measurements, Fundamental Quantities and Units for Ionizing Radiation, Report No. 60, ICRU, Bethesda (1998)
Hine, G. J. and Brownell, G. L., (Ed. ), Radiation Dosimetry, Academic Press (New York, 1956)

28. Where to Get More Information
Bevelacqua, Joseph J., Contemporary Health Physics, John Wiley & Sons, Inc. (New York, 1995)
International Commission on Radiological Protection, Data for Protection Against Ionizing Radiation from External Sources: Supplement to ICRP Publication 15. A Report of ICRP Committee 3, ICRP Publication 21, Pergamon Press (Oxford, 1973)