A prototype calorimeter for HDR 192Ir brachytherapy sources

Thorsten Sander, Hugo Palmans, Simon Duane

National Physical Laboratory, Teddington, UK

LNE-LNHB / BIPM Workshop on “Absorbed Dose and Air Kerma Primary Standards”, Paris, 9 - 11 May 2007

Overview

• Absorbed dose measurements for brachytherapy • MC calculations for calorimeter design

parameters• MC calculated correction factors• Heat transfer simulations• Conclusions• Future work

Proposed measurement method:calorimetry

• Objective: investigate feasibility of calorimetry for brachytherapy

• Alternative method to current air kerma based approach (using reference air kerma rate (RAKR), dose rate constant Λ and TG-43 to derive absorbed dose)

• Direct measurement of absorbed dose

Tcm

ED prad Δ==point P

Problems in brachytherapy dosimetry

• High dose gradient over clinically relevant range (0.5 cm to 5 cm from source centre) resulting in heat flow down temperature gradients

• Self-heating of radioactive source

• Huge variety of brachytherapy source designs

Schematic drawing of prototype calorimeter(RZ-geometry)

R = 10 cm

Z =

14 c

mZ

R

1 mm vacuum gap

Absorber:Graphite ring, 2 mm x 5 mm, R = 2.5 cm

EGSnrc Monte Carlo simulations

• Various aspects of calorimeter modelled with DOSRZnrc

• Source (Nucletron microSelectron Classic):– Bare 192Ir spectrum used for 192Ir cylinder– AISI 316L stainless steel encapsulation

5.0 mm

3.50 mm

1.10 mm0.60 mm

Stainless steel cableAISI 316

Stainless steel plugAISI 316L

Stainless steel capsuleAISI 316L Active Iridium-192 core

0.40 mm

Build-up curves in water and graphite

Nucletron microSelectron Classic Ir-192 source in water and graphite

4.0E-145.0E-146.0E-147.0E-148.0E-149.0E-141.0E-131.1E-131.2E-131.3E-131.4E-13

0 1 2 3 4 5 6 7 8 9 10

Water equivalent radial distance R, cm

D x

r2 p

er e

mitt

ed p

hoto

n, G

y cm

2

(x m

uen_

w,g

for g

raph

ite)

WaterGraphite

• (μen/ρ)wg = 1.11 for mean 192Ir energy

• Energy dependent calculate fluence spectrum

5 cm4 cm3 cm2 cm

Scatter build-up along R-axis

ROI = 1 mm x 1 mm 1 cm

0 cm 20 cm

20 cm

Scatter build-up in graphite

Min. R required at ROI to get 99.9% and 99.5% of Dfull scatter

y = 4.0377x

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6

Radial distance of ROI from source centre, cm

min

. R, c

m 99.9% of max.99.5% of max.Linear (99.9% of max.)Linear (99.5% of max.)

Variation of Daverage with core height

Daverage(core height) / Dfull scatter at various ROIs

97.0%

97.5%

98.0%

98.5%

99.0%

99.5%

100.0%

00.

10.

20.

30.

40.

50.

60.

70.

80.

9 11.

11.

21.

31.

41.

51.

61.

71.

81.

9 2

Core height, cm

Perc

enta

ge o

f Dav

erag

e /

Dfu

ll sc

atte

r

ROI: 0.5 cmROI: 1 cmROI: 2 cmROI: 3 cmROI: 4 cmPoly. (ROI: 4 cm)Poly. (ROI: 3 cm)Poly. (ROI: 2 cm)Poly. (ROI: 1 cm)

Summary of MC simulations

Source to core, cm (graphite)

Build-up

Min. R, cm

Min. Z/2, cm

Max. core height, cm

Dose gradient over 2 mm, %

1 X X

0.5

2.5 10.1 6.8 0.6 18.5 1.60E-02 2.69E-03

0.75

1.05

9.99E-02 1.68E-02

2 ( ) 8.1 5.4

X

23

15

11

2.52E-02 4.24E-03

3 12.1 8.1 1.12E-02 1.88E-03

4 16.2 10.9 6.21E-03 1.04E-03

X

Dose rate from 370 GBq source, Gy/s

ΔT in 120 s, K

5 X X X

Calorimeter correction factors

gap vacuumgraphite core,

graphite core,gap

+

=D

Dk

metalairgraphite core,

graphite core,inh

++

=D

Dk

0033.1core

pointvol ==

DD

k

‘point’ = 0.1 mm x 0.1 mm core = 2 mm x 5 mm Z

R

Inhomogeneity correction due to aluminium tube

Percentage change of dose to core due to absorption and scatter in aluminium tube

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Thickness of aluminium tube, cm

Perc

enta

ge c

hang

e of

abs

orbe

d do

se, %

Inhomogeneity correction due to stainless steel tube

Percentage change of dose to core due to absorption and scatter in stainless steel tube

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06

Thickness of stainless steel tube, cm

Perc

enta

ge c

hang

e of

abs

orbe

d do

se, %

Gap correction factor

Percentage change of dose to core due to vacuum gap

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.5 1 1.5Thickness of vacuum gap, mm

Perc

enta

ge c

hang

e of

ab

sorb

ed d

ose,

%

Displacement correction factor, Z-axis

0002.10.25mmZ displaced,

centralZdisp, ==

=DDk

Absorbed dose to core with respect to source position

1.795E-14

1.800E-14

1.805E-14

1.810E-14

1.815E-14

1.820E-14

1.825E-14

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Source position relative to centre, cm

Abs

orbe

d do

se, G

y

Series1Poly. (Series1)

Displacement correction factor, R-axis

θε cosd=

d

r r + εθ

21)(r

rD ∝

)( ε+rD

∫∫ + )cos( θθ drdrDd

Taylor expansion

≈symmetric

displaced

DD

2

2

231

rd

+

0.1%With r = 25 mm

d = 0.64 mm

Self-heating of Nucletron microSelectron 192Ir source

• Maximum source activity = 550 GBq• Self-heating due to gamma radiation = 1.04E-2 W• Self-heating due to electrons = 1.59E-2 W• Total self-heating power = 2.63E-2 W

Stainless steel cable

Stainless steel plug

Stainless steel capsuleActive Iridium-192 core

Heat transfer simulations

• Main modes of heat transfer:• Conduction• Thermal

radiation• Heat equation:

solved by finite element modelling

• Stationary and transient solutions

Example: heat conduction from self-heating and radiative heating

Self-heating,Tinit= 10 KTinit= 0 K

Radiative heating

Self-heating and radiative heating, Tinit= 10 K

No conduction

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

3.5E-03

4.0E-03

4.5E-03

5.0E-03

0 200 400 600 800 1000

Time, s

Cha

nge

of c

ore

tem

pera

ture

, K

Control of self-heating effect, stationary solution, thermostatic mode

Thermistor 1+2:

-45.55 W m-2

Modes of operation

• Adiabatic mode• Measurement of

temperature difference

• Thermostatic mode• Electrical substitution

method• Advantage: rapid repetition

of calorimeter runs is possible

Power

Prad

Ptr

Pelec

Time

Power of heat transfer to core = constant

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

-200 -150 -100 -50 0 50 100 150 200

Time, s

Tem

pera

ture

cha

nge,

K

ΔT

Conclusions + future work

• Prototype calorimeter for HDR brachytherapy sources:– Suitable dimensions and materials derived from MC simulations– Vacuum gap around core to control self-heating effect of

radioactive source– Heat transfer simulations used to find optimum position for

thermistors and maximum heating power required per component

• Future work:– Build, test and characterise calorimeter + refine correction

factors for final design– Work out conversion from absorbed dose to graphite water– Measure absorbed dose and compare with RAKR approach and

TG43

Acknowledgements

• University supervisors: Ivan Rosenberg and Robert Speller

• UCLH: Derek D’Souza• NPL staff: Hugo Palmans, Simon Duane, Mark Bailey,

David Shipley, Nigel Lee, Chris Thomas, Gary Mapp, Edmund Kirby, Peter Bird, Keith Burgon, Geoff Stammers, Pravin Patel