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

some drawbacks are associated with this new approach as well. Where TG-43 follows the lines of a parametrization of the radi- ation dose deposition around a given source design, the conven- tional method follows the path of the radiation emitted from a source and its physical interaction with matter. Both calculation methods and their limitations are discussed in the next few sec- tions. The last section 5.6 of this chapter addresses the possible future developments in brachytherapy dose calculation. 5.1 The conventional dose calculation methodology The dose rate at a point near a given radioactive γ-source de- pends on several parameters. These include the distance to the source, the reference (linear) kerma rate of the source, the source shape, the composition and thickness of its metallic sheath, and the composition of the medium between the source and the point. The following formulas show how the dose rate to D . tissue at a point P, can be deduced from the reference air kerma rate K . ref when point P is surrounded by tissue and is at a distance r in tissue from a point source (see Fig. 2.8c). As mentioned before, the source strength is given as the K . ref , i.e., as the air kerma rate in air at a distance of 1 m. For the kerma rate to air at point P, surrounded by air and at a distance r (in m) we can write according to the inverse square law (see Fig. 2.8a):

air

air

P

distance r

point source

a

air

tissue

P

distance r

point source

b

tissue

tissue P

distance r

i t source

point source

c

Fig. 2.8The different steps in the calculation of the dose to tissue at a point P at a distance r from a point source with a reference air kerma strength of K . ref , at 1 meter, expressed in μGy.h -1 . a: point P in air surrounded by air,

b: point P in tissue surrounded by air, and c: point P in tissue surrounded by tissue.

.

.

1

(2.6)

K

K

air) (in air

=

•

ref

2

r

For the tissue kerma rate in a small volume (mass) of tissue at point P, we can write:

tissue

Fig. 2.9 The source and its capsule in a polar coordinate system. The reference point at ( r 0 , θ 0 ) at 1cm and 90º is in the transverse-plane of the source (35, 44, 45). (Courtesy: D. Baltas)

µ

air) (in tissue . K

.

tr

(2.7)

K

air) (in air

=

•

air

tissue

therefore the mean mass energy absorption coefficient equals in close approximation the mean mass energy transfer coefficient:

µ

.

tr

in which air) (in air •

K

ir)

=

air

µ

µ

(2.9)

tr =

en

is the ratio of the mean mass energy transfer coefficients in tissue and in air (see Fig. 2.8b). This ratio is almost identical for γ- and X-rays emitted by iridium-192 and cesium-137 and a value close to 1.10 is appropriate. Then, under conditions of electronic equilibrium, the air kerma rate to air can be converted to a dose rate to air

All the energy that is transferred to tissue is absorbed locally in tissue and therefore the dose to a small volume of tissue that is surrounded by air equals the kerma to that small volume of tis- sue.

We can now write:

(1 air) (in tissue . K •

. D

(2.8)

g

air) (in tissue

=

)

tissue

µ

.

. D

1

en

(2.10)

K

air) (in tissue

=

•

•

ref

2

r

In this formula, g represents the fraction of the energy of the electrons that is lost due to the generation of bremsstrahlung in the mass (this quantity g should not to be confused with the g(r) function defined in the next section as the radial dose function). This radiation is not absorbed locally. This equation actually demonstrates the differences between the quantities dose (en- ergy absorbed ) and kerma (energy transferred ). For the energies of γ-rays used in brachytherapy, the fraction g can be neglected, which means that the bremsstrahlung losses are small and that

air

If we now surround both the small volume of tissue at point P and the source by tissue (see Fig. 2.8c), then we have to account for attenuation (absorption and scatter) in tissue. The attenuation correction factor ϕ(r) has been introduced to take this effect into account (34).