Ahmed S.N. Physics and Engineering of Radiation Detection

Подождите немного. Документ загружается.

606 Chapter 11. Dosimetry and Radiation Protection

particular type of radiation and the location of its source, that is

T,R

= w

·D

T,R

, (11.2.1)

where H

T,R

is the equivalent dose due to radiation type R, D

T,R

is the mean ab-

sorbed dose delivered by radiation R,andw

is the radiation weighting factor. The

radiation weighting factor is given by

= Q

·N

, (11.2.2)

where Q

and N

are the quality and modiﬁed factors for the radiation type R

respectively. For external sources of radiation, N

is taken to be unity. For internal

sources, N

is assigned a value by some relevant authority. In most cases a value of

= 1 can be taken and the knowledge of the quality factor is suﬃcient to calculate

the weighting factor. The quality factors for diﬀerent radiation types are listed in

Table 11.2.1

Note that the above formula is valid for only one type of radiation. In case

of mixed ﬁeld, the total equivalent dose can be obtained by simply summing the

contribution due to individual types of radiation, that is



· D

T,R

. (11.2.3)

Since the weighting factor is a dimensionless quantity, the equivalent dose is also

measured in units of J/kg. However now the speciﬁc name given to the unit is sievert

represented by the symbol Sv. There is also an older unit called rad equivalent for

man or rem, which is still in limited use. The conversion from Sv to rm is fairly

simple with

1 Sv ≡ 100 rem.

Example:

In a mixed radiation environment, a person receives 20 mGy of γ-ray dose

and 2 mGy of slow neutron dose. Calculate the total equivalent dose received

by the person.

Solution:

As the source is external, we can take N

= 1 and the weighting factors for

the two radiation types as given in Table 11.2.1 are

=1 and w

=5.

In table-11.2.1 as well as in earlier sections the particle energies have been given in electron volt units

(keV , MeV ) instead of the conventional SI units of Joules. This convenient unit of energy is deﬁned as the

energy attained by an electron when it is made to accelerate by an electric potential diﬀerence of 1 volt.

E = qV =(1.6 × 10

−19

C)(1

)

This gives

1eV =1.6 × 10

−19

11.2. Quantities Related to Dosimetry 607

Table 11.2.1: Quality Factors for Diﬀerent Types of Particles.

Type of Radiation Quality Factor (Q

)

x-rays, γ-rays 1

Electrons, Muons 1

α-Particles 20

Fission Fragments 20

Heavy Nuclei 20

Protons 5-10

Neutrons with E < 10 keV 5

10-100 keV 10

>100 keV up to 2 MeV 20

2-20 MeV 10

> 20 MeV 5

The equivalent doses due to γ-rays and neutrons are given by

T,γ

= w

· D

T,γ

= (1)(20)

=20mSv

T,n

= w

·D

T,n

= (5)(2)

=10mSv

The total dose received by the person is then sum of these individual doses,

that is

= H

T,γ

+ H

T,n

=20+10

=30mSv

A.4 Eﬀective Dose

The equivalent dose as described above can be used for one tissue type only as it

does not address the sensitiveness of tissue types to the same type of radiation.

Thequestionis,howwecandeterminethewholebodyequivalentdosetoestimate

the risk associated with a certain type of radiation environment. Or how one can

estimate the whole body dose if the dose received by a particular organ is known.

This is done by using the quantity eﬀective dose, deﬁned through the relation

E = w

· H

, (11.2.4)

608 Chapter 11. Dosimetry and Radiation Protection

where w

is the tissue weighting factor and H

is the equivalent dose in the tissue

T . The rational behind weighting the equivalent dose with w

is that, as explained

earlier, each tissue or organ responds diﬀerently to radiation. As with equivalent

dose, the eﬀective dose is also measured in units of sievert. The w

for diﬀerent

tissues and organs are given in Table 11.2.2. The reader should note that these

numbers are based on the ICRP recommendations at the time of writing this book.

For the most up to date factors the reader is encouraged to refer to the most recent

ICRP publications.

Table 11.2.2: Tissue weighting factors w

according to 1990 recommendations of

ICRP(26).

Tissue or Organ w

Gonads 0.20

Bone marrow (red), Colon, Lung, Stomach 0.12

Bladder, Breast, Liver, Oesophagus, Thyroid 0.05

Skin, Bone surface 0.01

Remainder 0.05

The eﬀective dose as computed from the above relation is good for any single

tissue or organ and only one type of radiation. In case of mixed radiation exposure

to more than one tissues and organs, the total eﬀective dose can simply by obtained

by adding the respective contributions together, that is

total



T,i

, (11.2.5)

where the subscript i refers to each organ. H

T,i

is the total equivalent dose for each

organ i as calculated from equation 11.2.3.

Example:

During a CT scan of the stomach, that had to be repeated several times, a

patient receives a total absorbed dose of 0.3 Gy. Compute the total eﬀective

dose received by the patient.

Solution:

Since CT scan is performed with x-rays therefore the radiation weighting factor

= 1. The equivalent dose received by the patient’s stomach is

T,R

= w

·D

T,R

= (1)(0.3)

=0.3 Sv.

11.2. Quantities Related to Dosimetry 609

The tissue weighting factor for stomach is w

=0.12 as given in Table 11.2.2.

The eﬀective dose is then give by

E = w

·H

T,R

=(0.12)(0.3)

=0.036 Sv =36mSv.

The usual eﬀective dose received during a typical CT scan of abdomen is

around 10 mSv, which means that this patient received more than three times

the usual dose.

11.2.B Flux or Fluence Rate

We know that the ionizing power of radiation is directly related to the energy it car-

ries. This can be understood by noting that in most gases the number of charge pairs

produced per unit of absorbed energy is almost independent of the type of radiation

(see chapter on gas ﬁlled detectors). In case of solids, although this independence

is not guaranteed, still the ionization caused by radiation depends to a large extent

to the energy it delivers. In dosimetry therefore one is interested in determining the

amount of radiation carried by the radiation. Energy ﬂux is a measure that can be

used to characterize this quantity. Another quantity closely related to energy ﬂux

is the particle ﬂux.

In order to deﬁne particle and energy ﬂuxes, Let us ﬁrst assume that we have

a mono-energetic beam of particles incident on a material having a cross sectional

area da. IfwecountthenumberofparticlesdN incident on this area in a time dt,

then the particle ﬂux can be calculated from

dtda

. (11.2.6)

This shows that the particle ﬂux simply represents the number of particles incident

on a surface per unit area per unit time. In the ﬁeld of dosimetry this quantity is

also known as particle ﬂuence rate. Now, since we have a mono-energetic beam of

particles therefore we can use the above relation to compute the energy ﬂux as

dtda

, (11.2.7)

where E

is the energy carried by a single particle. The energy ﬂux is a measure of

the total energy incident on a surface per unit area per unit time. Another term used

for this quantity, specially in dosimetry, is the energy ﬂuence rate. Energy ﬂuence

rate is actually the preferred terminology adopted widely in the ﬁeld of dosimetry.

In fact, the usage of ﬂux is discouraged in this ﬁeld. It is evident that the energy

ﬂuence rate and particle ﬂuence rate are directly related through the relation

= E

Φ. (11.2.8)

Up until now we have considered the radiation beam to be absolutely mono-

energetic, that is, all the particles had same energy. This is certainly not true since

an absolute mono-energetic beam of particles is impossible to create. A realistic

610 Chapter 11. Dosimetry and Radiation Protection

beam has an energy spectrum with a range that could be very narrow or very wide.

If the energy spectrum is well deﬁned, in most instances we can assign an average

energy

to all the particles and still use the above formulas to compute the energy

ﬂux. However a better thing to do would be to compute the energy ﬂux spectrum

through the relation

dΨ

dtda

, (11.2.9)

where dΨ represents the energy ﬂux at the energy E

. A practical but very basic

way to do this would be to increment the discriminator windows in a single channel

analyzer in small steps and counting the particles for a certain time. This procedure

when carried out for the whole range of particle energies would yield the energy

ﬂux spectrum. Of course a better way would be to use a multi channel analyzer,

which generates the spectrum without the need to change the discriminator level

repeatedly.

11.2.C Integrated Flux or Fluence

Sometimes it is desired to compute the ﬂux and ﬂuence rates integrated over a

certain time period. This could, for example, be required to determine the radiation

dose received by a patient undergoing radiation therapy.

The ﬂux integrated over a period of time is called integrated ﬂux or ﬂuence.

Mathematically, it is given by

Φ=

, (11.2.10)

where, dN represents the number of particles passing through the area da.Since

this relation does not explicitly contain time, it can also be interpreted to represent

the number of particles incident on a surface area da at any instant. However this

deﬁnition is somewhat misleading, since practically speaking, it is unmeasurable. We

have repeatedly seen in the previous chapters that performing a counting experiment

always involves time during which the counting is performed. This time can be

made very small but its width is still limited by the timing resolution of the readout

circuitry. It is therefore preferable to see the particle ﬂuence as representing the

particle ﬂux integrated over a time period.

Just like the particle ﬂuence we can also deﬁne the energy ﬂuence or integrated

energy ﬂux as the amount of energy incident on a surface area within a certain time

period. Mathematically speaking, this can be written as

Ψ=

, (11.2.11)

where, as before,

represents the average particle energy.

Example:

1.5 × 10

photons having an average wavelength of 0.12 nm pass through a

surface of area 1.8 cm

per second. Determine the energy ﬂuence rate and

the integrated particle ﬂux for 1 second of irradiation.

11.2. Quantities Related to Dosimetry 611

Solution:

The energy ﬂuence rate for photons is given by

dtda

where

λ is the average wavelength of the photons. Substituting the given

values in this equation gives



6.63 × 10

−34



2.99 × 10



0.12 × 10

−9

1.5 × 10

(1) (1.8 × 10

−4

)

=1.37 × 10

−7

−2

−1

The integrated ﬂux can be computed as follows.

Φ=

1.5 × 10

1.8 × 10

−4

=8.33 × 10

−2

=8.33 × 10

−2

11.2.D Exposure and Absorbed Dose - Mathematical Deﬁnitions

We have already deﬁned the terms exposure and absorbed dose. Here we will look

at their proper mathematical deﬁnitions.

Exposure X is deﬁned as the charge dQ produced by heavy charged particles

(ions) per unit mass dM of dry air when all the electrons liberated by the incident

photons are completely stopped. Mathematically we can write this as

X =

. (11.2.12)

This deﬁnition of exposure has a fundamental problem that it is valid only for

photons in dry air. Of course the intention for deﬁning it in this way was to stan-

dardize the quantity and to make available a yardstick for comparison. However

since the ways photons interact with target materials are very diﬀerent from other

particles, such as neutrons or α-particles, therefore exposure has not been found to

be very useful in characterizing damage due to other types of radiation.

Example:

Estimate how much energy deposition of photons per unit mass of dry air is

equivalent to 1 R.

612 Chapter 11. Dosimetry and Radiation Protection

Solution:

We know that

1 R =2.58 × 10

−4

C/kg.

To determine the number of charge pairs per kg corresponding to 1 R,we

simply divide the right hand side of the above equivalence by the unit electrical

charge, that is

N =

2.58 × 10

−4

1.602 × 10

−19

=1.61 × 10

charge pairs per kg. (11.2.13)

The production of charge pairs is related directly to the energy deposited E

and the energy needed to produce a charge pair, through the relation

N =

The W -value for most gases including air is approximately 34 eV .Usingthis

and the value of N as calculated above we can determine the required energy

equivalent to 1 R as follows.

E = NW



1.61 × 10



(34)

=5.47 × 10

eV kg

−1

=5.47 × 10

MeV g

−1

In laboratory environments it is often desired to estimate the exposure expected

from a known radioactive source. Intuitively thinking we can say that the exposure

from a radioisotope is proportional to the following quantities.

 Source Activity: The more the activity the larger number of decays and

hence higher exposure. Source activity is given by λ

N with λ

and N being

the sample’s decay constant and the number of radioactive atoms in the sample

respectively.

 Inverse of Distance Squared: Exposure decreases with increasing distance

from the source. According to the inverse square law, the ﬂux of radiation

varies by inverse of the square of the distance from a point source. Since

exposure is directly related to ﬂux, it will also be inversely proportional to r

the distance between the source and the point of measurement. A point worth

mentioning here is that a source can be considered a point source if the point

of measurement is much larger than its mean radius.

 Exposure Time: Radiation exposure increases with increasing exposure time.

11.2. Quantities Related to Dosimetry 613

Combining all of the above, we can reach at the following relation for the exposure

from a radiation source.

X ∝

=Γ

, (11.2.14)

where t is the exposure time and Γ is generally known as the gamma constant.

Gamma constant is speciﬁc to the type of radioisotope and its values for most

isotopes are available in literature (see Table 11.2.3). The usual quoted units of Γ

are Rcm

/MBqh and Rcm

/mCih.

Table 11.2.3: Gamma constants and predominant decay modes other than γ-decays

of some radioisotopes (4). All values are given in Rcm

mCi

−1

Isotope (mode) Γ Isotope (mode) Γ Isotope (mode) Γ

227

Ac (β) 2.2

198

Au (β) 2.3

228

Ra (β) 5.1

124

Sb (β) 9.8

181

Hf (β) 3.1

106

Ru (β) 1.7

As (γ,e

) 10.1

124

I (EC) 7.2

Sc (β)) 10.9

140

Ba (β) 12.4

130

I (β) 12.2

Se (EC) 2.0

Be (EC) 0.3

132

I (β) 11.8

110

Ag (EC,β) 14.3

Ca (β) 5.7

192

Ir (β) 4.8

Na (EC) 12.0

C (EC) 5.9

Fe (β) 6.4

Na (β) 18.4

134

Cs (EC,β) 8.7

140

La (β) 11.3

Sr (EC) 3.0

137

Cs (β) 3.3

Mg (β) 15.7

182

Ta (β) 6.8

Cl (β) 8.8

Mn (EC) 18.6

121

Te (EC) 3.3

Co (EC) 0.9

Ni (β) 3.1

187

W (β) 3.0

Co (β) 13.2

Nb (β) 4.2

Y (EC) 14.1

154

Eu (EC,β) 6.2

K (β) 1.4

Zn (EC) 2.7

Ga (β) 11.6

226

Ra (α) 8.25

Zr (β) 4.1

614 Chapter 11. Dosimetry and Radiation Protection

Example:

Calculate the exposure received in 2 hours at a distance of 3 cm from a 10

mCi cobalt-60 source.

Solution:

The gamma constant for cobalt-60 is 13.2 Rcm

mCi

−1

. To calculate the

exposure we substitute this and the given values in equation 11.2.14.

X =Γ

=13.2

(10)(2)

=29.3 R (11.2.15)

Note that since λ

N corresponds to the activity of the material therefore we

did not need individual values of λ

and N .

Since exposure can not be used for particles other than photons therefore another

quantity called absorbed dose has been introduced. It is deﬁned as the average energy

E absorbed in an inﬁnitesimal volume element dV per unit density ρ of the medium.

D =

lim

V →0

(11.2.16)

Note that this deﬁnition has less parameters than the deﬁnition of exposure and

therefore is much easier to measure and compare. The parameter that needs a bit

of attention here is the volume element, which according to the deﬁnition should be

inﬁnitesimally small. The question is how small is inﬁnitesimally small. The answer

lies in the physical limit of signal to noise ratio set by the statistics of charge pair

production. We know that the production of charge pairs is a statistical process with

the standard deviation given by

√

N for the production of N charge pairs. Now,

the production of charge pairs is, among other things, dependent on the availability

of molecules and therefore to the volume element itself. Hence the volume element

should not be too small to cause high ﬂuctuations in the charge pair production. Of

course the ﬂuctuations also depend on the energy ﬂux of the radiation and therefore

one can not generally say how big the volume element should be for all cases.

Whatever the volume is, one can in general express the absorbed dose in terms

of energy absorbed per unit mass, that is

D =

, (11.2.17)

where dM = Vρ is the mass of the sample. From this deﬁnition it is evident that

the SI units for absorbed dose are J/kg. This is generally known as a gray and

represented by the symbol Gy.

Radiation quantities and conversion factors relating to dosimetry are listed in

Table 11.2.4.

11.2. Quantities Related to Dosimetry 615

Table 11.2.4: New and old units of quantities related to radiation dose and their

conversion factors.

Old Unit New Unit Conversion

Name Symbol Name Symbol Factor

Radiation Absorbed Dose rad Gray Gy 1Gy = 100rad

Rad Equivalent for Man rem Sievert Sv 1Sv = 100rem

Curie Ci Bacquerel Bq 1Bq =2.7 ×10

−11

11.2.E Kerma, Cema, and Terma

In this section we will describe three quantities, Kerma, Cema, and Terma, that are

in common use in the ﬁeld of dosimetry due to their eﬀectiveness in characterizing

the macroscopic eﬀects of radiation.

E.1 Kerma

Kerma is an acronym of kinetic energy released in a medium per unit mass. It is

deﬁned as the total kinetic energy of all the charged particles liberated by uncharged

particles per unit mass of the target material. Mathematically, it is written as the

quotient of the charged particle’s kinetic energy E

kin

and the mass of the material

dm,thatis

K =

kin

. (11.2.18)

Kerma is generally measured in the same units that are used for absorbed dose,

that is, J/kg or Gray.NotethatheredE

kin

is the kinetic energy of the charges

produces as a result of radiation interaction. This energy is not necessarily equal to

the energy transferred by the incident radiation since some of the energy can also

go into other processes, such as radiative and radiationless transitions. The other

point to note here is that the mass element dm should be very small.

The above deﬁnition of Kerma is actually a simpliﬁed form of the actual micro-

scopic deﬁnition, which takes the form

K = lim

V →0

E

kin

ρV

. (11.2.19)

A point worth noting here is that the condition of the volume element shrinking to

zero ensures that the deposition of energy by radiative transfers gets ignored. In

this way Kerma is actually an approximation of absorbed dose.

Kerma is not independent of the type of the target material and therefore must

always be deﬁned with respect to the medium. For example, the energy released in

air per unit mass of air should be written as air Kerma.

The energy lost by the incident radiation has two main components: collisional

loss and radiative loss. K can therefore be divided into K

col

and K

rad

corresponding