Recombination factor dependancy of high and low dose...
Transcript of 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
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Talk Overview
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• 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
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Low and high dose per pulse
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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
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Where does the difference come from ?
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EBRT LINAC
IORT LINAC
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LIAC e-beam transport system is realized with low Z material
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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
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Absorbed Dose to water according to IAEA TRS 398 formalism
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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
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ks modelization : from the definition of the problem tothe solution
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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
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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
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ks the standard approach according to IAEA TRS 398
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)1(ln1 u
uks +≈
+≈
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( )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=
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If ks < 1.03
This model fails for high dose per pulse !
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ks: Laitano’s theory
p−−= 11λ
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−++=
−
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
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w electron drift velocity
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( )
−−
+−−+=−−
−
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
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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
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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
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
=
It is resolved numerically respect to u1
Once u1 is determined f is calculatedwith the corresponding voltage V1
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A specific calculus software has been developed bySordina
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ks : numerical examples
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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=
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PPC05Adv. MarkusROO
S
dp(cGy/p)
Cylindical ionization chambers
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( )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
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Thanks !
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