Recombination factor dependancy of high and low dose...

Giuseppe FeliciSordina IORT Technologies S.p.A.

Recombination factordependancy of high and low dose

pulsed accelerators for electron beam energies

XIV Ulusual Medikal Fizik Kongresi

Talk Overview

2

• Dose per pulse what is the so called “ high dose per pulse” ? Where does it comes from ?Why IORT Linacs have a higher dose per pulse ?

• Dosimetric formalism and framework : IAEA TRS 398The physics modelization of ion recombinationA different modelization for ksCalculus and examples


Low and high dose per pulse

3

pcGyHzPRF

GyDRd

HzHz

Gy

p 05.060][

]min[)(pulseperDose

]400,200[(PRF)Frequency RepetitionPulse

min10(DR) RateDose

≈⋅

≡

∈

≈

]pcGy5,pcGy0.4[)(pulseperDose

]40,5[(PRF)Frequency RepetitionPulse

]min20,min4[(DR) RateDose

∈

∈

∈

pd

HzHz

GyGy

EBRT LINAC

IORT LINAC

The dose per pulse generated by IORT linacs is up to 100 times higher respect to the standard


Where does the difference come from ?

4

EBRT LINAC

IORT LINAC


LIAC e-beam transport system is realized with low Z material

5 XIV Ulusual Medikal Fizik Kongresi

6XIV Ulusual Medikal FizikKongresi

Beam Optic Transfer efficiency is higher for IORT linacs

Transfer efficiency variesbetween50 % @ 12 MeV and 8% @ 6 MeV

IORT Linacs design specs

1. Electron ONLY linac2. Maximum mobility, able to move inside standard hospital space

(elevators, doors…);3. Not isocentric but capable of performing easily and safely docking

process;4. As small and light as possible;5. Different energies, giving the possibility of irradiating a PTV with

thickness ranging up to 3.5 cm inside the 90% isodse;6. It has to produce the minimum X rays possible, for radioprotection

issues;

Low strayradiation

High dose per pulse


Absorbed Dose to water according to IAEA TRS 398 formalism

8

00 ,,, QQQDQQw kNMDw

⋅⋅=

spolHPTi

iQ kkkkMkMM ⋅⋅⋅⋅=⋅= ∏ ,''

sk

Absorbed dose to water at the reference depth zref in water for a reference beam of quality Q0

M’ measured signal

Factor to correct for the difference between the response of anionization chamber in the reference beam quality Qo used forcalibrating the chamber and in the actual user beam quality, Q.

Factor to correct the response of an ionization chamber for the lackof complete charge collection (due to ion recombination).

0,QQk


ks modelization : from the definition of the problem tothe solution

9

2005

2006

The saturation loss for plane parallel ionization chambers at high dose-per-pulse valueA. Piermattei, S. Delle Canne, L. Azario, A. Russo, A. Fidanzio, R. Miceli, A. Soriani, A. Orvieto, and M. Fantini

2000

2006


10

Laitano’s paper allows TVA (Two VoltageAnalysis) for determining ks, eliminating the needof an external chemical dosimeter and greatlysimplifying the dosimetric characterization

Chemical dosimeter can be used for externalaudit

Dw = ΔA Nw Πki


ks the standard approach according to IAEA TRS 398

21

)1(ln1 u

uks +≈

+≈

11

( )uu

f += 1ln1V

rdu2µ

=

•d(m) distance between chamber plates•μ (mV/C) a constant depending on the gas in the cavity chamber• r (C/m3) the charge liberated in air per unit volume and per pulse • V (Volt) the voltage supply of the chamber.

This model is applicable only if the fraction of electrons escapingattachment to oxygen molecules and reaching the collecting electrodes isnegligible.The high-energy pulsed electron beams of interest in clinical dosimetryhave usually a dose-per-pulse value of about 0.05 cGy/ pulse. This meansthat r and, consequently, u are small for the usually employed plane-parallel ionization chambers. Thus can be expanded to first order, giving

fks

1=


If ks < 1.03

This model fails for high dose per pulse !


ks: Laitano’s theory

p−−= 11λ

13

−++=

−

λλ

λλ 11ln1''')1( ue

uf

−=

−ττ w

d

ed

wp 1•d interelectrodic distance•w free electrons migration velocity inside the air cavity•τ electron mean life before recombination•w ,τ can be calculated vs electric field intensity

Free electron fraction is independent from the dose per pulse and is always different from zero. Its effect becomes relevant when the dose per pulse is high, that means when u is increasing.

( )uu

f += 1ln1

Vrdu

2µ= p is the free electron fraction

ffu

=+→

'''lim0

Boag, 1987


w electron drift velocity

14

( )

−−

+−−+=−−

−

cnenec

ndebaw

cEnEcE 11

w(E)

0,0E+00

5,0E+05

1,0E+06

1,5E+06

2,0E+06

2,5E+06

3,0E+06

3,5E+06

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

V/cm

cm/s

parametres mu d (cm) V1 (V) E (V/cm) w (cm/s)a 5,83535E+04cm/s 0,1 300 3000,0 2,36E+06b 2,41820E+07cm/s V2 (V) c 1,56809E-04cm/V 100 1000,0 1,33E+06d 3,86396E-03cm/Ve 1,03039E-03cm/Vn 4,89435E-03cm/V

Hochhauser et al, 1997


National Medical Physics Conference15

Electron Mean lifetime before attachment

parametres mu d (cm) V1 (V) E (V/cm) tau (s)a 6,26950E-08 s 0,1 300 3000 5,35E-08b 1,82679E-04 cm/V V2 (V) c 6,44401E-08 s 100 1000,0 2,11E-08d 1,8111E-04 cm/V

tau(E)

0,E+00

1,E-08

2,E-08

3,E-08

4,E-08

5,E-08

6,E-08

7,E-08

8,E-08

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

V/cm

s

( ) ( )dEbE ecea −− −+−= 11τ Hochhauser et al, 1997

TVA :ks determination

16

After w, tau have been determined p can be calculated ; now it is possible tocalculate ks experimentally using TVA technique

( )( )( )

−++

−++

=−

−

111ln

111ln

''

12

1212

111

1

21

212

1

111

2

1

uVV

u

eVVu

eu

QQ

λλ

λλ

λλ

λλ

2

112 uu

VV

=( )

=

2

112

11

2

1

u,

,''

VVpf

upfQQ

( )11 ),(1

upfksat λ

=

Vrdu

2µ=

2

1

2

1

''

ff

QQ

=

It is resolved numerically respect to u1

Once u1 is determined f is calculatedwith the corresponding voltage V1


17

A specific calculus software has been developed bySordina


ks : numerical examples

18

1

1,02

1,04

1,06

1,08

1,1

1,12

1,14

0 1 2 3 4 5 6

Advanced Markus@ 400 V

ROOS @ 200 V

PPC 05 @ 300 V

chamber type interelectrodic spacing (cm) polarization (V)

PTW Roos 0,2 200PTW Adv. Markus 0,1 400

IBA PPC 05 0,06 300

0>∂∂

p

s

dk

Vrdu

2µ=


PPC05Adv. MarkusROO

S

dp(cGy/p)

Cylindical ionization chambers


( )2/1

2)/ln(

⋅

−+

−=ba

bababadcyl

b internal radius (mm)

a external radius (mm)

dcyl equivalent electrode separation (mm)

It is possible to calculate ks also for cylindrical chambers using the Boagformula

Semiflex Pin Point

20

Thanks !


Recombination factor dependancy of high and low dose...

Documents

Transcript of Recombination factor dependancy of high and low dose...