Brachytherapy

Introduction

Brachy : short

Brachytherapy: Therapy at a short distance

Brachytherapy refers to radiation therapy that involves the application of radioactive material directly into or immediately adjacent to the tumor.

Types of applications

Interstitial: Placement of radioactive sources directly into tumor or tumor bed (head and neck, breast and soft tissue sarcomas)

Types of applications

Intracavitary: Places radioactive sources within a body cavity (cervical cancer)

Types of applications

Intraluminal: Places the source of radiation within body “tubes” such as esophagus, trachea, bronchus and rectum.

Types of applications

Topical: Places the radioactive sources on top of the area to be treated (choroidal melanoma)

A custom-made radiation plaque. On the left is the inside of a plaque with the radiation seeds. On the right is the gold coating on the outside of the plaque.

Units

1 Ci (curie): 3.7x1010 disintegration/sec

1 Bq (becquerel): 1 disintegration/sec

1 Ci = 37 GBq

1 mg-Ra-eq = 0.98 mCi (mg-Ra-eq is the mass of radium required to produce the same exposure rate at 1cm from the substitute source)

Radioactive Decay

Activity A: is the rate of decay of a radioactive material or the change in the number of atoms in a certain amount of time.

Half-Life T½: The time period in which the activity decays to one half of the original value.

A = ΔNΔt

= −λN

N = N0e−λ t

➠ A = A0e−λ t

T1/ 2 =0.693λ ➠

A = A0e− 0.693T1 2

⎛

⎝⎜⎜

⎞

⎠⎟⎟t

Some common isotopes

Isotope T1/2 Eavg(MeV)226Ra 1622 y 0.8360Co 5.26 y 1.25137Cs 30 y 0.662192Ir 74.1 d 0.38125I 60.2 d 0.03198Au 2.7 d 0.41

Exposure rate constant Γ

Γ: the exposure rate (R/hr) at 1m from a 1 Ci source (or 1cm from a 1mCi source) ➠ R.m2/hr.Ci (R.cm2/hr.mCi)

Isotope Γ (R.cm2/hr.mCi)226Ra 8.2560Co 13.07137Cs 3.226192Ir 4.57125I 1.089198Au 2.327

X = Γ isotopeA 1d 2

Exposure Rate (R/hr)➠

Equivalent mass of radium

mg-Ra-eq = Aisotope (mCi)⎡⎣ ⎤⎦ Γ isotopeΓ Ra

⎡

⎣⎢

⎤

⎦⎥

Air-kerma strength

Sk: is the air-kerma rate measured at 1m. It expressed in units µGy.m2/hr (cGy.cm2/hr).

k.W/e has a value of 0.876 cGy/R

Sk = X.d

2 .k.W e

Source Designs

137Cs

Source Designs

125I

Source Designs226Ra

Source Designs226Ra

Examples

A 10 mg radium source is left inadvertently in an unshielded drawer for 7 hrs. Estimate the exposure received by a worker who remained 20 cm from the source for this time.

1mg @ 20 cm = 8.25 x (1/20)2=0.0206 R/hr

10 mg => 0.206 R/hr

exposure for 7 hrs = 7 hr x 0.206 R/hr = 1.44 R

Alternatively,

0.825R.m2/hr.Ci x 10 x10-3Ci/(0.2m)2 x 7hr=1.44R

Examples

Calculate the exposure rate @ 10 cm from a 10 mCi Cs137 source.

Ẋ= 3.226 R.cm2/hr.mCi x 10 mCi x (10 cm)-2 = 322.6 mR/hr

Examples

At 15 cm the exposure rate from an 192Ir source is 305 mR/hr. What is the activity of the source?

Γ = 4.57R .cm2/hr.mCi

[0.305 mR/hr]/{[4.57 R.cm2/hr.mCi]x(1/15cm)2} = 15.02 mCi

X = Γ isotopeA 1d 2

Examples

What is the radium equivalence of 25 mCi source of 137Cs?

mg-Ra-eq= (25mCi) x (3.226/8.25) =9.776 mgRaeq

Examples

What is the activity of a 137Cs in mCi if it is described as a 20 mgRaeq?

A (mCi) = 20 mgRaeq x (8.25/3.226)= 50.3 mCi

Examples

What is the air-kerma strength at 1 cm of a 226Ra point source having an activity of 1 mg.

Sk = (8.25 R/hr) x (1 cm)2 x (0.876 cGy/R)

Sk = 7.23 cGy cm2/hr

Sk = X.d

2 .k.W e X = Γ isotopeA 1d 2

Sievert Integral

Consider a Ra source with linear source density ρ and filtration d of platinum. The absorbed dose rate at point P may be calculated as:

dD = X. ftis

X = ΓAr 2

ftis converts the exposure in air to absorbed dose in tissue.

Sievert Integral

Γρdx is the exposure rate in R/hr, 1 cm from the source of strength ρdx mg.

r2 corrects for the exposure rate by the inverse square law.

e-μd/cosθ gives the attenuation produced by d/cosθ cm of platinum sheath with linear absorption coefficient μ.

dD = Γ ρ dx e−µd / cosθ

r 2ftis

Sievert Integral

dD = Γ ρ dx e−µd / cosθ

r 2ftis

D is a function of r and θ.

Expression can be integrated over dx to give:

(1)

D = Γ ρ h

ftis e−µd / cosθ

θ1

θ 2

∫ dθThis integral can not be evaluated analytically, but has been determined using numerical integration by Sievert.

Application of Sievert integral

Shalek and Stovall used the Sievert integral with corrections for attenuation and scatter in soft tissue around the source to compute a dose rate table for linear radium sources (1969)

Shalek - Stovall table

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.250.500.751.01.52.02.53.03.54.04.55.0

50.67 43.75 11.94 3.34 1.48 0.81 0.50 - - - -20.26 16.95 8.18 3.38 1.70 1.00 0.64 0.44 0.31 0.23 0.1810.84 9.29 5.67 2.99 1.67 1.03 0.69 0.48 0.35 0.27 0.216.67 5.89 4.10 2.52 1.55 1.01 0.69 0.50 0.37 0.28 0.223.20 2.96 2.38 1.74 1.24 0.89 0.65 0.48 0.37 0.29 0.231.85 1.76 1.52 1.23 0.96 0.74 0.57 0.45 0.35 0.28 0.231.20 1.15 1.04 0.89 0.74 0.60 0.49 0.40 0.32 0.26 0.220.83 0.81 0.75 0.67 0.58 0.49 0.41 0.34 0.29 0.24 0.210.61 0.60 0.57 0.52 0.46 0.40 0.35 0.30 0.26 0.22 0.190.47 0.46 0.44 0.41 0.37 0.33 0.29 0.26 0.23 0.20 0.170.37 0.36 0.35 0.33 0.30 0.28 0.25 0.22 0.20 0.18 0.160.30 0.29 0.28 0.27 0.25 0.23 0.21 0.19 0.17 0.16 0.14

Distance along the source axis (cm from center)

Perp

endi

cula

r di

stan

ce fr

om

sour

ce (c

m)

Dose (cGy) per mg.hr in tissue delivered at various distances by Linear Radium source (0.5 mm Pt filtration, active length 1.5 cm)

Example

What is the dose-rate at point P (x = 2cm, y = 2 cm)? The source is a 10-mg radium tube with an active length of 1.5 cm and 0.5 mm Pt. (the midpoint of the source is at the origin)

from the table for “along” and “away” of 2 cm:

Ḋ = 0.96 cGy/mg.hr x 10 mg = 9.6 cGy/hr

Krishnaswamy table for 137Cs

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

21.052 6.808 3.241 1.866 1.204 0.837 0.614 0.468 0.368 0.29617.445 5.997 2.996 1.773 1.162 0.816 0.602 0.461 0.364 0.2938.404 4.177 2.409 1.536 1.051 0.758 0.569 0.441 0.351 0.2853.663 2.597 1.777 1.245 0.902 0.676 0.521 0.411 0.331 0.2711.943 1.639 1.275 0.975 0.750 0.585 0.464 0.375 0.307 0.2551.187 1.093 0.925 0.757 0.613 0.498 0.407 0.336 0.280 0.2360.794 0.768 0.686 0.591 0.500 0.420 0.353 0.298 0.253 0.2160.566 0.564 0.522 0.466 0.408 0.353 0.304 0.262 0.226 0.1960.422 0.429 0.407 0.374 0.336 0.298 0.262 0.230 0.202 0.1770.326 0.335 0.325 0.304 0.279 0.252 0.226 0.201 0.179 0.1590.258 0.268 0.263 0.250 0.233 0.214 0.195 0.177 0.159 0.143

Transverse distance from center of source (cm)

Dis

tanc

e al

ong

the

leng

th o

f so

urce

(c

m fr

om c

ente

r)

Dose (cGy) per mg.hr in tissue delivered at various distances by Linear 137Cs source (1 mm stainless steel , active length 1.4 cm)

Example

What is the dose at point P (previous example) if the source is a 137Cs tube of 10 mg-Ra-eq, with an active length of 1.4 cm and filtration of 1 mm stainless steel?

from the table for “along” and “away” of 2 cm:

Ḋ = 0.975 cGy/mg-Ra-eq.hr x 10 mg-Ra-eq = 9.75 cGy/hr