2 Brachytherapy Physics-Sources and Dosimetry

Brachytherapy Physics: Sources and Dosimetry

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THE GEC ESTRO HANDBOOK OF BRACHYTHERAPY | Part I: The basics of Brachytherapy Version 1 - 01/12/2014

of the source or in the capsule, the yield of emitted photons is significantly lower than what is emitted by the bare source mate- rial). This can be overcome by adding an extra but simplified step in the calculation of the dose at each arbitrary point in which the radiation to that point is assumed to pass the source capsule obliquely. From the geometry and by using the absorption co- efficient of the wall material and the thickness of the wall, the reduction of the dose can be taken into account. However, this approach does not include complex scattering effects and is only valid in a first approximation. Sometimes instead of K . ref , only the apparent activity, A a , is known. The apparent activity is defined as the activity of an un- screened point source of the same radionuclide, which would give rise to the same air kerma rate as the actual encapsulated source under defined conditions. If A a is known, then K . ref can be calculated using: in which Γ δ is the air kerma rate constant specific of the radionu- clide (for values see Table 2.1, last column). It should be noted that vendors of sources usually specify their source strength on a certificate in several different units, to comply with the demands of different treatment planning systems. For that, they use pub- lished conversion factors between the units. 5.2 The TG-43 approach to dose calculation Based on the assumption that brachytherapy sources show dose distributions that are cylindrically-symmetric, the TG-43 brachytherapy dosimetry formalism (35, 44, 45) utilizes a polar coordinate system along the source long-axis (z-axis) with the coordinate system origin located at the centre of the source, as shown in Fig. 2.9. The source is placed in a spherical water phan- tom with a diameter of 40 cm to obtain a full scatter situation in the vicinity of the source. Dose distributions at point P( r,θ ) near the source are obtained with radial distance r and polar angle θ expressed relative to the origin and source long-axis, respective- ly. A special reference point P( r 0 , θ 0 ) is positioned at r 0 = 1 cm and θ 0 = 90º in the transverse-plane of the source. For Fig. 2.9, the angle β = θ 2 – θ 1 , and t is the capsule thickness in the trans- verse-plane direction. Either the 1-D or 2-D equations used to calculate dose rate are used in modern treatment planning systems as shown in the fol- lowing equations with dosimetry parameters defined below. ref . K (nuclide) a δ A Γ• = (2.14)

tissue) (in tissue . D

.

(2.11)

•

D

=

air) (in tissue

r

)ϕ(

In summary we can write:

tissue

µ

. K

.

1

en

•

•

•

(2.12)

)ϕ(r

D

=

tissue

ref

2

r

air

with:

tissue

µ

. K

.

1

en

•

•

•

)ϕ(r

D

=

: Reference Air Kerma Rate (RAKR)

tissue

ref

2

r

air

tissue

µ

. K

.

1

en

: ratio of the mean mass energy absorption coefficients for tissue and for air )ϕ(r • 2 r

•

•

D

=

tissue

ref

air

tissue

µ

1

en

: distance factor (inverse square law) )ϕ(r •

•

2

r

tissue

air

1

•

•

: effective transmission through tissue )ϕ(r

2

r

air

The effective transmission, ϕ(r) , was studied by Meisberger et al . (34) who published a summary of published data for distances from 0 up to 10 cm, and modelled these data in a polynomial function. The Meisberger data have been used widely, and the polynomial parameters have been published in many textbooks. The use of the K . ref for the specification of the strength of a brachytherapy source has the following advantages: • source strength is directly traceable to a national standard; • dose rate in a tissue is closely related to the K . ref as can be seen for a point source (see the equations above); • it is easy to make a first estimate of the exposure hazards around a patient/an application (see chapter 3 on Radiation Protection in Brachytherapy). Many of the sources used in brachytherapy are not point sourc- es but have certain dimensions, e.g. wire sources. The dose rate from sources of a particularly geometry can be calculated by considering the source to be made of many point sources. In this way the geometry of the source is taken into account. For linear sources such as radioactive wires, the length, l , can be divided into n pieces of wire each with a length Δl . The linear reference air kerma rate, k . ref , for a segment Δl is then

.

.

l Δl

In the 1-D approach:

ref K k •

=

ref

(2.13)

n l

2

Δl

=

r

.

0

( ) D r S Λ = K

( ) g r ϕ r ( ) an P

(2.15)

r

The total dose at point P can then be obtained by summation of the contribution of each of the n point sources, into which the wire or linear source has been subdivided. The conventional methodology of dose calculation often relies on the derivation of the reference air kerma rate from the ra- dioactive contents of the source (the real and the effective , as- sumed , or apparent activity; due to self-absorption in the core

In the 2-D approach:

G r

( ) , θ

L

(2.16)

( D r θ ,

S

( ) ( g r F r

θ

Λ

=

,

)

)

K

L

( G r L

,

θ

)

0 0