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
A=
ΔN
= −λ N
Δt
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.
N = N0 e − λ t
A = A0 e− λ t
➠
Half-Life T½: The time period in which the
activity decays to one half of the original value.
T1/ 2
0.693
=
λ
➠
A = A0 e
⎛ 0.693 ⎞
⎟t
− ⎜⎜
⎟
⎝ T1 2 ⎠
Some common isotopes
Isotope
226Ra
T1/2
1622 y
Eavg(MeV)
0.83
60Co
5.26 y
1.25
137Cs
30 y
0.662
192Ir
74.1 d
0.38
125I
60.2 d
0.03
198Au
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
Exposure Rate (R/hr)
➠
X = Γ isotope A 1
226Ra
60Co
137Cs
d2
Γ (R.cm2/hr.mCi)
8.25
13.07
125I
3.226
4.57
1.089
198Au
2.327
192Ir
Equivalent mass of radium
⎡ Γ isotope ⎤
mg-Ra-eq = ⎡⎣ A isotope (mCi) ⎤⎦ ⎢
⎥
⎣ Γ Ra ⎦
Air-kerma strength
 2 .k. W
Sk = X.d
e
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
Source Designs
137Cs
Source Designs
125I
Source Designs
226Ra
Source Designs
226Ra
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
X = Γ isotope A 1
d2
[0.305 mR/hr]/{[4.57 R.cm2/hr.mCi]x(1/15cm)2}
= 15.02 mCi
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.
 2 .k. W
Sk = X.d
e
X = Γ isotope A 1
d2
Sk = (8.25 R/hr) x (1 cm)2 x (0.876 cGy/R)
Sk = 7.23 cGy cm2/hr
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:
ΓA
X = 2
r
 ftis
dD = X.
ftis converts the exposure in air to absorbed dose in
tissue.
Sievert Integral
Γ ρ dx e − µ d / cos θ
dD =
ftis
r2
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.
Sievert Integral
Γ ρ dx e − µ d / cos θ
(1)
dD =
ftis
r2
D is a function of r and θ.
Expression can be
integrated over dx to give:
D=
Γρ
ftis
h
∫
θ2
θ1
e − µ d / cos θ dθ
This 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
Distance along the source axis (cm from center)
Perpendicular
distance from
source (cm)
0.0
0.25
0.50
0.75
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
1.5
2.0
2.5
3.0
50.67 43.75 11.94 3.34
0.5
1.0
1.48
0.81
0.50
3.5
4.0
4.5
-
-
-
5.0
20.26 16.95 8.18
3.38
1.70
1.00
0.64
0.44
0.31
0.23
0.18
10.84 9.29
5.67
2.99
1.67
1.03
0.69
0.48
0.35
0.27
0.21
6.67
5.89
4.10
2.52
1.55
1.01
0.69
0.50
0.37
0.28
0.22
3.20
2.96
2.38
1.74
1.24
0.89
0.65
0.48
0.37
0.29
0.23
1.85
1.76
1.52
1.23
0.96
0.74
0.57
0.45
0.35
0.28
0.23
1.20
1.15
1.04
0.89
0.74
0.60
0.49
0.40
0.32
0.26
0.22
0.83
0.81
0.75
0.67
0.58
0.49
0.41
0.34
0.29
0.24
0.21
0.61
0.60
0.57
0.52
0.46
0.40
0.35
0.30
0.26
0.22
0.19
0.47
0.46
0.44
0.41
0.37
0.33
0.29
0.26
0.23
0.20
0.17
0.37
0.36
0.35
0.33
0.30
0.28
0.25
0.22
0.20
0.18
0.16
0.30
0.29
0.28
0.27
0.25
0.23
0.21
0.19
0.17
0.16
0.14
-
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
Transverse distance from center of source (cm)
Distance along the
length of source
(cm from center)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.0
21.052 6.808
3.241
1.866
1.204
0.837
0.614
0.468
0.368
0.296
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
17.445 5.997
2.996
1.773
1.162
0.816
0.602
0.461
0.364
0.293
8.404
4.177
2.409
1.536
1.051
0.758
0.569
0.441
0.351
0.285
3.663
2.597
1.777
1.245
0.902
0.676
0.521
0.411
0.331
0.271
1.943
1.639
1.275
0.975
0.750
0.585
0.464
0.375
0.307
0.255
1.187
1.093
0.925
0.757
0.613
0.498
0.407
0.336
0.280
0.236
0.794
0.768
0.686
0.591
0.500
0.420
0.353
0.298
0.253
0.216
0.566
0.564
0.522
0.466
0.408
0.353
0.304
0.262
0.226
0.196
0.422
0.429
0.407
0.374
0.336
0.298
0.262
0.230
0.202
0.177
0.326
0.335
0.325
0.304
0.279
0.252
0.226
0.201
0.179
0.159
0.258
0.268
0.263
0.250
0.233
0.214
0.195
0.177
0.159
0.143
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