5-Tillegg (Fra Kildefil 3) Dosimetri

7/30/2019 5-Tillegg (Fra Kildefil 3) Dosimetri

1/14

Supplement 5

1 Dosimetry of ionizing radiation

1.1 Definition of dose

Definition: D limV0

V

, [ Jkg

= Gy]

If a beam of ionizing radiation is directed towards a material, the dose is defined as the mean energydeposited per unit mass of the material. By defining the interaction volume where deposited energyis measured to be vanishingly small, a dose definition is obtained that will be valid for each point inthe irradiated material.

1.2 Dose from charged particles (i.e. directly ionizing radiation)

Dose: D =

Scol

This expression is valid only for a fluence of particles of defined particle energy E, since the stoppingpower S is energy dependent. Please note that dose is defined based on collision stopping power.

Radiative stopping power leads to photon emission, thus representing radiation which is not locallyabsorbed and therefore not included in the dose at this point in the material. Stot = Scol + Srad,where Srad is due to bremsstrahlung. The above expression is valid only for a thin section ofthe material, since the energy of charged particles will continuously decrease as the particles passthrough the material, thus the energy distribution of the particles in the beam will no longer berepresented by the well-defined energy E. The dose must then be expressed as an integral over theenergy spectrum of the product of the fluence distribution and the corresponding values of collisionstopping power.

1.3 Dose from photons (i.e. indirectly ionizing radiation)

The dose is deposited by secondary charged particles, which arise in the material after discrete inter-actions of photons with the material. Our starting point is the total linear attenuation coefficient: = + + , [m1]

Where ,, represent respectively photo electric effect, Compton ef-

fect, and pair production.

1


2/14

A fraction of the photon energy fluence interacts within the material, and is therefore removedfrom the collimated primary radiation beam. How large is the energy deposition in the material,

due to these interactions?

1.4 Energy transferred to charged particles

The fraction of energy transferred to charged particles (i.e. secondary electrons) and being presentas kinetic energy of these particles, is expressed by the energy transfer coefficient:

tr = (1

h) + (1 h

h) + (1 2mc

2

h)

For each interaction process, the fraction that does not represent energy transferred to chargedparticles, is subtracted. For photo-electric interactions, this represents the fraction of energy subse-quently being emitted as characteristic X-rays due to the vacancy created in one of the electronic

orbitals of the atom (Auger electron emission will, however, be included in the dose, since theirenergy subsequently will be locally deposited). For Compton interactions the fraction of energyrepresented by the escaping Compton photons is subtracted, and for pair production, the energy ofthe two annihilation photons is subtracted. The mass-energy transfer coefficient ( tr

) is a tabulated

quantity, and can be found for different photon energies and different materials.

1.5 Corrections due to bremsstrahlung for charged particles

Some of the kinetic energy of secondary electrons will be converted into photon energy throughthe generation of bremsstrahlung, and thus be lost as locally deposited energy. By subtracting this

fraction, the mass energy absorption coefficient is obtained.Mass energy-absorption coefficient: en

= ( tr

)(1 g),

1

mkg

m3

= [ m

2

kg]

g is the fraction of energy which escapes as bremsstrahlung.

2


3/14

From the table, one sees that the difference between

and tr

is largest for photon energiesaround 0.1MeV. This is because of a strong contribution from Compton scattering. Substantialbremsstrahlung contributions are only found for high energies, especially in dense materials, such as

lead, thus causing the mass energy absorption coefficient to be significantly smaller than the energytransfer coefficient.

3


4/14

This figure shows how Compton scattering leads to en

<

for photon energies around 0.1MeV.

Compton attenuation coefficients are divided into contributions from scattering (s = compton h

h)

and energy-transfer (tr = compton Teh

). Attenuation due to Rayleigh-scattering(r)(i.e. coherentscattering) is also plotted in the figure above, but not included in our equations since it does not

lead to energy absorption.

1.6 CPE (Charged particle equilibrium)

Dose can now be defined based on the mass energy absorption coefficient:

Dose: DCP E

=

en

,

Jkg

= [Gy]

is here the energy fluence of photons, i.e. = h, where is the particle fluence of photons.Due to conservation of linear momentum during the interactions, the track of each secondary electron

will on average be in the forward direction, and the field of secondary charged particles thereforehas a net forward direction. Close to the surface of the material the density of tracks in a materialslice of thickness dx will therefore be less than in a slice further into the material. Charge particleequilibrium (here: electron equilibrium) can be illustrated to exist from a certain depth x in thematerial if equally many tracks that originate at lower x-values are found in the slice at depth xas those that exit from this slice into larger depths of the material. The figure below is meant toillustrate this. Actually, it is the dose contributions from those electron tracks gained and lost atdepth x that must be equal for CPE to exist at depth x.

4


5/14

1.7 KERMA (Kinetic energy released per mass)

KERMA: K tr , Jkg = [Gy]Collision KERMA: Kc

en

= K(1 g)

DCP E

= KC

The two Kerma quantities defined above are theoretical concepts that are useful for discussingdose close to the interface between two different materials.

1.8 Interface dosimetry

Chosen:

en

1

Sc

2

In this case, Sc has to represent the mean value of the true Sc for the field of secondary particles.The photon field is homogeneous, i.e it is assumed that the attenuation is negligible throughoutboth media. Together with the indication of the mass energy absorption coefficient being lower in

5


6/14

medium 1 than in medium 2, this leads to the step function in collision Kerma at the interface. Thefield of secondary charged particles is continuous over the interface, and if mass stopping power islarger in medium 1 than in medium 2, this leads to the discontinuity in dose at the interface betweenthe two materials. Close to the interface in material 1 the dose is increasing due to some backscatterof secondary electrons from material 2, where the release of secondary electrons is more pronounceddue to the larger (en/). Note that CPE does not exist in an interval close to the interface, i.e.where D differs from KC.

1.9 Including attenuation

If the attenuation of the beam is not negligible, a graph of dose and Kerma quantities would be asin the figure shown below, where a photon beam in air enters a material from the left. The ordinateaxis is logarithmic, leading to a linear decrease of Kerma as a function of depth. There is a build-upof dose close to the surface, due to lack of electron equilibrium close to the surface. In this case we seethat the value of collision Kerma at a certain depth equals the dose at a certain distance x farther

away in the beam direction. This distance x may be considered as the average forward range ofsecondary electrons, remembering that charged particles deposit most of their energy towards theend of their tracks.

6


7/14

1.10 Bragg-Gray cavity theory (for a gas ionization chamber)

Measuring the dose (in the form of ionization) is easiest in gases, due to the requirements of exact

registration of all the ions formed. Measurements taken inside the gas shall represent the dose in agiven medium.

Bragg-Gray cavity: This is a gas cavity so small compared to the range of the secondaryelectrons, that the net ionization is due to the field of secondary electrons formed inside thewall. The Bragg-Gray cavity does not affect the field of secondary electrons. The fluence of sec-ondary particles, is assumed to be continuous over the boundary between the wall and the gas:

DwallDgas

=Sc

wall

Sc

gas

Again, Sc is the mean value for the spectrum of secondary electrons. The

wall has to be thick enough for CPE to be established within the wall. Based on the interfacedosimetry presented in section 1.8 the following relationships can be derived:

DmediumDwall

=

en

medium

en

wall

Dmedium =

en

medium

en

wall

Sc

wall

Sc

gas

Dgas

Special case:

1.) Homogeneous dosimeter:

Sc

wall

=

Sc

gas

for all energies

This cancels the requirement of a small gas-cavity. This situation is obtained by having equiva-lent atomic composition in the gas and the wall.

7


8/14

2.) Tissue equivalent wall:

en

medium

=

en

wall

This is obtained by having the same atomic composition in the wall as in the medium. cancelsthe requirement on the thickness of the wall (CPE requirement).

1.11 Use of gas-cavity dosimeter for micro dosimetry

We want the measurements of stochastic energy depositions in a small volume of gas to representstochastic energy depositions in a microscopic volume of a given medium.

Specific energy deposited: z = V

Notice that D =limV0 z

We want to represent a typical biological volume such as the nucleus of a cell, by a small gasdetector in the same type of medium. The aim is that pulse measurements of energy depositionin this detector will represent energy deposition in the biological volume of interest. This leads tothe requirement: Same stochastic energy deposition in the two volumes from a secondary particletraversing the volume:

gas = dE

dx

gas

lgas = medium = dE

dx

medium

lmedium

lgas =

Sc

medium

mediumSc

gas

gas

lmedium

8


9/14

Example: lgas 10mm, f or lmedium 10m

z = m

= 1m

= 1

l3 l

dE

dx

l l2 =

Sc

zmedium =

Sc

medium

Sc

gas

zgas

The dimension of the gas detector is the result of medium/gas being approximately equal to 1000,and mass stopping powers of medium and gas being approximately equal. Thus, measurementsof energy deposition in the detector can be used to determine energy deposition in the biologicalvolume of interest.

The two figures on the following page show measurements of specific energy by a micro-dosimetricdetector in a situation where the exposure is gradually decreased so that very low values of dose willbe given. Low doses are achieved by decreasing the exposure time and/or increasing the distance

between the detector and the point source giving off the radiation. At low doses the stochasticnature of energy deposition will become apparent, and eventually the dose will be so low that notall exposure events result in an energy deposit in the detector. In the figure panels, the left ordinateshows specific energy z, the right ordinate shows the probability (in per cent) of an exposure causingan energy deposit in the detector (from secondary electron(s) passing through the detector).

Notice that as long as this probability p is 100 per cent, specific energy z equals dose D, as in-dicated by the diagonal segment of the graph. For lower doses, specific energy reaches a constantplateau, whereas the probability of a hit (i.e. an energy deposit in the detector) decreases.

Notice that for the whole dose range: D = p z

The main conclusion from these two panels is that each type of radiation has a characteristic valuefor its single-hit energy deposition in a small volume like the nucleus of a biological cell. For Co-60photons this value is indicated as 1 mGy, whereas for neutrons which have protons as their secondarycharged particles, this value is 50 mGy, i.e. 50 times larger.

9


10/14


11/14

1.12 External dosimetry for radiation protection purposes ( radiation)

Dosimetric characteristics for each radioactive nuclide has been determined for radiation protection

purposes. For external irradiation, it is assumed that only emitted photon radiation contributes tothe dose (far enough from the source). The characteristic quantity is then the specific gamma rayconstant , which gives the collision Kerma rate in air per Becquerel of a point source at a distanceof 1 m.

Radiation from a point source of activity A hits a material:

Kc,air =Ar2 air

In the material (at CPE): DmCP E

= Kc,air

en

m

en

air

Kc,air =

en

air

= A4r2

,i kiE,i

en

air,E,i

air =1

4

,i kiE,i

en

air,E,i

,

Gym2

sBq

= [Gy m2]

In the above equations ki is the yield of gamma photons of energy E, i.e. how many photons of

this energy is emitted per disintegration of the source. Multiplication with values of the mass energyabsorption coefficient in air is taken at the appropriate energies, and summation is over all gammaemissions of the source. For calculating the dose rate in the medium from the upper equation, theratio of mass energy absorption coefficients between the medium and air needs to be taken as anappropriate average value for the radiation emitted by the nuclide in question.

is sometimes given relative to the exposition rate [ Cs1

kg] instead of the dose rate.

exp.rate =doserate

We

,

Cm2

kg

Where We

is the amount of energy required to generate an ion-pair in air, which is about 34eV.

11


12/14

1.13 Internal dosimetry for radiation protection purposes (,, )

Internal dosimetry i used to determine the dose from radioactive substances introduced into thebody, usually through inhalation or ingestion. For internal dosimetry all types of radiation ( , , )must be taken into account. In general, the radioactive source(s) will be distributed in a source

organ S, and average dose is to be determined for one or more target organs T. The quantity whichwill characterize this dose delivery, is the specific effective energy SEE.

Dose rate: DT =

s AsSEE(T S)

Specific effectiveenergy: SEE(T S) = 1

mT

i kiEii(T S)

Here represents the absorbed fraction, Ei is the mean particle energy, ki is the amount of emittedradiation of type i per disintegration, and mT is the mass of the target organ T. Notice that forgamma radiation, E is the photon energy, but for beta radiation E is the average energy of theemitted beta particles , i.e. around Emax/3 for electron emissions.

Absorbed fractions depend on the type of radiation. If the source organ is the same as the tar-get organ, and emissions are assumed to deposit all their energy in the target organ, but noneif the source organ is different from the target organ. For (and neutron) irradiation, the absorbedfraction needs to be determined for each gamma energy and each geometry relating source and targetorgans.

i(T S) =

1,ifS T , 0,ifS T , i, if , neutrons

Dose is obtained by integrating dose rate over time: D =

s As SEE(T S), A =t0

A()d

12


13/14

13


14/14

1.14 Biokinetic models

To be able to determine the dose in internal dosimetry, it is necessary to know how the activity in

the target organ A(t) varies with time. For this purpose, biokinetic models are used for internaldosimetry in biological organisms.

The example below illustrates a two-compartment model, where the intake of radioactivity is incompartment 1. Through physiological processes this radioactivity is transported to compartment2, characterized by the bio-physiological rate constant 1. Finally the radioactivity is excretedfrom compartment 2 (e.g. through urine), characterized by rate constant 2. Note that these bio-physiological transfer rates out of compartments 1 and 2 come in parallel to radiological decay of theactivity in each of these compartments. Thus, the effective transition rate is the sum of radiologicaland bio-physiological transition rates

Activity: dA1dt

= (R + 1)A1 A1(t) = A0eeff t

Effective transition rate: eff = R + B

Effective half-life: T12,eff =

T12RT1

2B

T12B+T1

2R

If either the radiological or the bio-physiological half-life is short, the effective half-life of the nuclidein that compartment will be short. If both the radiological and the bio-physiological half-life arelong, the effective half-life of the nuclide in that compartment will be long.

14

Documents

5-Tillegg (Fra Kildefil 3) Dosimetri