PARTNER – at Pavia, January 2012
LET and Fractionation
Bleddyn JonesUniversity of Oxford
1. Gray Institute for Radiation Oncology & Biology2. 21 Century School Particle Therapy Cancer Research
Institute, Oxford Physics.
LH Gray •studied neutron effects in biological systems.•thought that neutrons were a good tool for research, but not suitable for cancer therapy.•was opposed by a medical doctor, Constance Wood.
She dismissed Gray from the post of Director of Physics at Hammersmith Hospital.•Dr Wood had used her family fortune (from brewing beer) to develop first European clinical linear accelerator, produced by the Vickers Company (who built aeroplanes, submarines, radar equipment etc.)
From Fowler, Adams and Denekamp : Cancer Treat. Reviews 1976, 3, 227-256
‘‘Megamouse expt’ at Northwood Gray Lab, Megamouse expt’ at Northwood Gray Lab, Fowler, Sheldon, Denekamp, Field (IJROBP, 1, Fowler, Sheldon, Denekamp, Field (IJROBP, 1,
579-92, 1976)579-92, 1976)
% Tumour control for same level of skin reaction in mice
Overall time in days (also related to number of fractions)
Improvement due to cell cycle progression, reoxygenation
Deterioration due to repopulation
Improvement at short times with metronidazole or neutrons (compensating for hypoxia)
Adding a repopulation correction factor to Adding a repopulation correction factor to LQ modelLQ model
Surviving fraction describes a Surviving fraction describes a reduction in viable cell numbers reduction in viable cell numbers but is opposed by repopulationbut is opposed by repopulation
If there are c cells at start of If there are c cells at start of radiation there will be c.SF radiation there will be c.SF after radiation.after radiation.
The clonal expansion during The clonal expansion during radiotherapy is represented by radiotherapy is represented by NNtt=N=Nooee-kg.t-kg.t, [eq 1], [eq 1]
where t is the elapsed time where t is the elapsed time when Nwhen Noo cells become N cells become Ntt cells cells and kand kgg is the growth rate is the growth rate constantconstant
When NWhen Ntt/N/Noo=2 the population =2 the population will have doubled, so that the will have doubled, so that the time is then the doubling time time is then the doubling time of cells……..that isof cells……..that is
2=e2=e-kgTp-kgTp…….so that ln2=-kK…….so that ln2=-kKgg.T.Tp p
[eq 2] and so k[eq 2] and so kgg can be replaced can be replaced by ln2/Tby ln2/Tp p in eq 1 abovein eq 1 above
RCFeN
N pT
t
t .693.0
0
So, fractional increase in number of cells is obtained from equation 1 and 2
Let this ratio be the repopulation correction factor (RCF) as it opposes cell kill;
Net number of cells after treatment over a time t becomes
= c. SF x RCF
Full LQ equation with allowance Full LQ equation with allowance for repopulationfor repopulation
pp T
tddn
T
t
ddn eeeSF.693.0.693.0 2
2
The net surviving fraction is
This is a powerful equation with many applications ….the lowest surviving fraction will be obtained with highest dose and highest radiosensitivities and longest doubling times and shortest overall time
See Fowler 1988 Progress in Fractionated Radiotherapy, Brit J RadiologyFowler showed that different fractionation schedules could have similar tumour control rates when overall time and repopulation included .
Some general principlesSome general principlesAs T increasesAs T increases……
more time for more time for normal tissue normal tissue
repair and repair and repopulation…repopulation…less severe acute less severe acute reactionsreactions
tumour tumour repopulation, so repopulation, so cure rate may fall cure rate may fall if fast cellular if fast cellular doubling timesdoubling times
Re-oxygenation of Re-oxygenation of hypoxic tumourshypoxic tumours
As f (inter-fraction interval) reduces
•time to repair radiation damage…more incomplete repair present at next treatment …enhanced effects in late reacting normal tissues
•opportunity for tumour cell repopulation
As n increases
More opportunities for repair between fractions
T then increases unless f is reduced in which case treatment is accelerated
If d increases, D(=n.d) must be reduced to preserve iso-effect/ tissue tolerance
Ionising Radiation and DNA
+ microdosimetric theories
Sparsely ionising radiation (low-LET)e.g. -rays, -particles
Low concentrationof ionisation events
Densely ionising radiation (high-LET)
e.g. -particlesC6+ ions
High concentrationof ionisation events
DNA
electron tracks
Dr Mark Hill, Gray Institute, Oxford
RBE depends on ……..RBE depends on …….. Particle,Particle, Energy & DepthEnergy & Depth Target Target VolumeVolume DoseDose per treatment ..RBE varies per treatment ..RBE varies
inversely with dose. A treatment plan inversely with dose. A treatment plan contains many dose levels.contains many dose levels.
Facility: neutron & Facility: neutron & -ray -ray contaminationcontamination
Cell & Tissue type : slow growing Cell & Tissue type : slow growing cells have highest RBEs.cells have highest RBEs.
Use of single value RBE was Use of single value RBE was mistakemistake
Paravertebral Epithelioid Paravertebral Epithelioid SarcomaSarcoma
Intensity Modulated Protons Intensity Modulated Protons (IMPT) vs. (IMPT) vs.
Intensity Modulated Photons Intensity Modulated Photons (IMRT) 7 (field)(IMRT) 7 (field)
IMPTIMPT IMXTIMXT
Esophageal radiotherapy Esophageal radiotherapy dose distributions – dose distributions – Protons vs. IMRTProtons vs. IMRT
Track structure on the nuclear/cellular scale
l µm Chromosome domains
-particle
H2AX
Very non-homogeneous
High-LET (e.g. -particles)
~20-40 DSB(~70% complex)
3 lethal chromosome breaks
l µm
Low-LET (e.g. -rays)
Relatively homogeneous
H2AX
~2 alpha tracks~1000 electron tracks
1 Gy corresponds to:
~20-40 DSB (~20% complex)
1 lethal chromosome break
Biological effects More cell kill per unit
dose. Enhanced Biological
effects Need single dose
RBE (x-ray dose/neutron dose for equal bio-effect ) to estimate required neutron dose to give same effect as x-rays or -ray Cobalt beam.
RBE – components in a RBE – components in a ratioratio
][
][
HighLET
LowLET
Dose
DoseRBE
Changes with dose per fraction and cell cycling in repair proficient cells
Little or no changes in required dose with dose per fraction and cell cycling in repair proficient cells; but this dose follows the numerator and reduces sharply because of tending to Rmax
Reduced repair capacity Reduced repair capacity at high LETat high LET
α parameter increases by more than α parameter increases by more than the increase in the increase in ββ [ e.g. 2.5-3 [ e.g. 2.5-3 compared with 1.3 for fast neutrons]compared with 1.3 for fast neutrons]
Then, α/Then, α/ββ increases with LET and so increases with LET and so “fractionation sensitivity” reduces“fractionation sensitivity” reduces
α –related damage is less repairable α –related damage is less repairable than than ββ related damage. related damage.
RBE depends on Cell Type and its RBE depends on Cell Type and its // ratio which reflects repair ratio which reflects repair
capacitycapacityCarbon ions
Radioresistant cells with greatest curvature (higher DNA repair capacity) show higher RBEs (GSI, Weyreuther et al)
X-rays
Recovery ratio – the ratio of Recovery ratio – the ratio of surviving fractions for one and two surviving fractions for one and two
fractions to same total dose.fractions to same total dose.
2
2
]2[
]2[
)(2)(2]2[
)2()2(]2[
2log
;
.
2
222
2
dRR
eSF
SFRR
eeeSF
eSF
e
d
d
d
ddddddd
ddd
For low LET radiations
RR for high LET RR for high LET radiationsradiations
2min2
min
].2.2.
]2[
]2[
)(2.)(2.]2[
)2()2(]2[
.2.,2.log
,
.
22
22min
22min
22minmax
22minmax
22minmax
22minmax
LHe
dRBERdR
d
d
dRdRdRdRdRdRd
dRdRd
dRBERordRRR
eoreSF
SFRR
eeeSF
eSF
LH
HHHHHH
HH
So, the capacity for So, the capacity for repair with standard x-repair with standard x-
rays is higher by a factor rays is higher by a factor of: of:
1.
2.
22
min
22
2min
2
2min
2
][
][
2
R
RBEd
R
d
dR
d
RR
RR
HL
H
L
highLET
lowLET
Now RBE>1 and RBE>Rmin, dH>1So RR of low LET radiation always exceeds that of high LET
For iso-effect
Another methodAnother methodConsider the change in the number of fractions N for the same effect when dose per fraction is changed; assume N is continuous variable.
22
minmax2
2minmax
2min
max
2min
max
.
.2..
dRRkd
RdRkkBED
dd
dN
kdR
Rd
BEDN
k
dRRNdBED
Numerator term in parentheses is smaller than denominator squared term in parentheses for increasing Rmax and Rmin compared with unity for low LET [for equal k, d and BED]
Where α/β=k
LOW LET change in total dose with number of fractions (or dose per fraction)
LOW LET: change in total dose with number of fractions (or dose per fraction)
The medical prescriptionCobalt Gray equivalent (coGyeq) or X-
ray equivalent Gray (eqGy) Intended dose (i.e. x-ray dose) is divided
by the RBE (relative biological effect).Traditionally, RBE is a constant factor,
e.g. 3 for neutrons, 1.1 for protons, 2.5 for C ions….to all tissues & at all doses in body….and - independent of α/β ratio
45 Gy in 15# 45/3=15 coGyeq neutrons
Experiments: assumption not true for neutrons (& C ions), but what about protons?
Neutron TherapyNeutron Therapy Prescription of radiation using fixed RBE of 3 at tumour Prescription of radiation using fixed RBE of 3 at tumour depth and assumed to be the case at all other points depth and assumed to be the case at all other points within a patient (all tissues, all doses). within a patient (all tissues, all doses). The pseudo exponential dose fall-off with depth beyond a The pseudo exponential dose fall-off with depth beyond a tumour will be compensated for by increase in RBE.tumour will be compensated for by increase in RBE.
RBE=2.5
RBE=3
RBE=4-6
Using more fields will only make matters worse
BED - how do we get BED - how do we get there?there?
By definition of the “Log By definition of the “Log cell kill”=Ecell kill”=E
)()ln(
,
,
2
)( 2
2
ddNESF
eSF
eSF
N
ddNN
dd
BED - The ConceptBED - The Concept Represents total dose if given in Represents total dose if given in
smallest fraction sizesmallest fraction size
/1
E dndBED
)( 2ddnE
ndE
ndE
ndndd
2,0
How can we picture BED for high LET radiations?
DOSE (Gy)
Surviving Fraction
Imagine the dose to be given in infinitely small fractions with no curvature to slope
BED
Single fraction
Dose for same effect in single fraction
Dose for same effect in four fractions
All have same Effect/
High LET shifts all curves to left, but effect defined by same low LET BED
BED - some implicationsBED - some implications
/1
/1 2
221
11
ddn
ddn
Fowler`s ‘FE’ – fractionation effect Fowler`s ‘FE’ – fractionation effect plotplot
E=n(E=n(d+d+dd22)) E=D(E=D(++d)d) Divide throughout Divide throughout
by E and by D, soby E and by D, so
dEED
1
y = c + mx
1/D
d
/E
tan=/E
= - /
/=intercept/slope
Use of BEDUse of BED Refers to points/small volumes of interest; can be extended to Refers to points/small volumes of interest; can be extended to
volumes as in EUD.volumes as in EUD. Comparisons are for individualsComparisons are for individuals Iso-effect calculations, ranking of BEDs for comparisons of Iso-effect calculations, ranking of BEDs for comparisons of
different techniques/schedules.different techniques/schedules. Compensation for errors in dose delivery and unscheduled Compensation for errors in dose delivery and unscheduled
treatment extensionstreatment extensions Dose rate effectsDose rate effects Generic comparisons of different fractionation schedules in Generic comparisons of different fractionation schedules in
radiotherapy – including high and low LET radiationsradiotherapy – including high and low LET radiationsReference: Jones B, Dale RG, Deehan C, Hopkins KI, Morgan Reference: Jones B, Dale RG, Deehan C, Hopkins KI, Morgan
DAL. The role of biologically effective dose (BED) in DAL. The role of biologically effective dose (BED) in Clinical Oncology. Clinical Oncology 2001;13:71-81.Clinical Oncology. Clinical Oncology 2001;13:71-81.
Jones B and Dale RG. Radiobiological compensation of Jones B and Dale RG. Radiobiological compensation of treatment errors in radiotherapy. Brit J Radiology, 81, treatment errors in radiotherapy. Brit J Radiology, 81, 323-326, 2008.323-326, 2008.
Dale RG, Hendry JH, Jones B, Deehan C et al. Dale RG, Hendry JH, Jones B, Deehan C et al. Practical Practical methods for compensating for missed treatment days in methods for compensating for missed treatment days in radiotherapy, with particular reference to head & neck radiotherapy, with particular reference to head & neck schedules. Clinical Oncology, 14, 382-393, 2002.schedules. Clinical Oncology, 14, 382-393, 2002.
The fractionated isoeffect The fractionated isoeffect equationequation
22HHHHHLLLLL ddNddN
Obtaining BED:•Divide throughout by αL to give BED on LHS.•It follows that RHS, also divided by αL, represents the for the high LET radiation.•Note if NL=NH, roots are simpler, and RBE is then the ratio of doses per fraction.
Useful equations for high LET Useful equations for high LET radiations radiations
L
HMINH
L
HMAXH
LLLLHHHH
RBEd
RBEd
ddddE
,
,0
22
= the RBE at low dose
= the RBE at high dose
Jones, Carabe and Dale BJR 2006 – adapted for treatment interruption calculations
RBE is defined as dL/dH
The RBE between RBEmax and RBEmin is given by solving the first equation for dL, and then divide by dH, so that
H
HH
d
RBEdkRBEdkkRBE
2
44 min2
max2
Where k is the low LET / ratio
)()/(
minmax
)/(
minmax
.
,
;
)(
2
2
2
2
2
KLL
HH
L
HH
HLMIN
L
HMIN
L
HMAX
L
HH
L
HH
L
HHHH
TTKdRBE
RBEndBED
dRBERBEndBED
Thence
RBE
RBE
RBE
ddn
EBED
ddNE
Biological Effective Doses for High LET radiation • the low LET /
ratio is used
• RBEs act as multipliers of the low LET α/β
• RBE values will be between RBEmax and RBEmin depending on the precise dose per fraction
• KL is daily low LET BED required to compensate for repopulation KH/RBEmax
Note:•RBEmax is intercept on y axis, •RBEmin is asymptote at high dose•A fixed RBE, of say 3, would intersect all curves
ApplicationsConverting a specific low LET BED to that for high LET, when the low LET α/β ratio is known……use
For isoeffect calculations in the case of two high LET schedules – need (α/β)H value
.
=
=
- KHT1H= - KHT2H
Then, for N1H(αHd1H+βHd1H2)=
N2H(αHd2H+βHd2H2)
Divide throughout by αH
And so,
2min
max
RBE
RBERC whe
re
Some important caveats – slide 1
•Use same α/β ratio across isoeffect equations to preserve units• Changing fractionation numbers between low and high LET radiation introduces a complication. RBE should be specific for the dose per fraction used.
•If fraction numbers differ, work out equivalent low LET dose/# for same # Number as the proposed high LET schedule and then convert, or use the equations with RBEmax and RBEmin and fraction numbers (NL and NH).•Beware of “fractionated RBEs” based on total doses when NLNH
(suggested by Dasu & Dasu) – Suggest always use single dose RBE and then compensate for fractionation
Some important caveats – slide 2
Question: Estimate the dose/# required for a 10 fraction high LET schedule equivalent to 30# of 2 Gy [low LET] for CNS tissue α/β=2 Gy for RBEmax=6 and RBEmin=1.25.First, find equivalent of 30# schedule in 10 #:-30(1+2/2)=10dL(1+dL/2); dL=4 GyThen find dH in: 10*dH(6+1.252*dH/2) =10*4 (1+4/2) dH=1.69 Gy. Note the RBE per fraction is then 4/1.69=2.37Alternatively we could calculate dH direct from 10*dH(6+1.252*dH/2) =30(1+2/2) dH=1.69 Gy. But the RBE is not 2/1.69=1.18Use RBE on dose per fraction basis for equal No of #.
Q2: A tumour boost of 3 Gy-eq dose per fraction for 6 fractions delivers, incorrectly, 4 Gy-eq for the first two fractions. What dose should be given in the remaining fractions to maintain same tumour control (assuming α/β=9 Gy and late CNS isoeffect α/β=2 Gy, and RBE of 3 for the Gy-eq calculation.For CNS, intended low LET BED = 6*3(1+3/2) =45 Gy2.Delivered BED=2*4(1+4/2)=24 Gy2.Deficit = 45-24=21 Gy2
In 4 remaining fractions, need 4*d(1+d/2)=21;d= 2.39 Gy-eq. [or 2.39/3= 0.8 Gy high LET]For tumour control, solve same steps for α/β=9 Gy , giving d=2.45 Gy-eq; a higher dose. So, to maintain same tumour control need to exceed CNS BED…..!
BUT …Previous slide presumes RBE does not vary with dose per fraction! If the actual doses of high LET given were intended: 3/3=1 Gy/# and in first two fractions was actually 4/3=1.33 Gy/#Then, if RBEmax=6, RBEmin=1.25 in CNSIntended BED=6*1 (6+1*1.252/2)=40.69 Gy2.Delivered BED= 2*1.33(6+1.33*1.252/2)=18.17 Gy2
Deficit BED= 40.69-18.17=22.52 Gy2
The dose, dH, then required in remaining 4 # is found by solving:4 dH(6+dH*1.252/2)=22.52dH=0.86 Gy of high LET; NOTE this is a different result to the previous page [dH=0.8 Gy] due to RBE changing with dose per# …..WE MUST IMPROVE SYSTEM!
Worked example of a time Worked example of a time delaydelay
Schedule: megavoltage X-ray of 45 Gy in Schedule: megavoltage X-ray of 45 Gy in 25 fractions, then ‘boost’ of 6 Gy 25 fractions, then ‘boost’ of 6 Gy [physical dose] in 2 fractions using a [physical dose] in 2 fractions using a high-LET radiation with RBEmin = 1.3 high-LET radiation with RBEmin = 1.3 and RBEmax =8. and RBEmax =8.
There is a delay of one week in delivery of There is a delay of one week in delivery of boost, due to patient illness. boost, due to patient illness.
Assume tumour daily repopulation Assume tumour daily repopulation equivalent of 0.6 Gy per day after a lag equivalent of 0.6 Gy per day after a lag interval of 25 days during megavoltage x-interval of 25 days during megavoltage x-ray treatment; normal tissue ray treatment; normal tissue // =2 Gy, =2 Gy, tumour tumour // = 10 Gy. = 10 Gy.
Worked example -IIWorked example -II The intended BED to normal tissue The intended BED to normal tissue
from x-rays = 45 from x-rays = 45 (1+1.8/2)= 85.5 (1+1.8/2)= 85.5 GyGy22
The intended BED to any marginal The intended BED to any marginal normal tissue that receives the added normal tissue that receives the added high-LET boost of 2 fractions of 3 Gy high-LET boost of 2 fractions of 3 Gy = 6 = 6 (8+1.3 (8+1.3223/2)= 63.2 Gy3/2)= 63.2 Gy22
total intended maximum BED to total intended maximum BED to same volume of normal tissue = 85.5 same volume of normal tissue = 85.5 + 63.2 = 148.7Gy+ 63.2 = 148.7Gy22
Worked example -IIIWorked example -III The intended BED to tumour by x-rays = The intended BED to tumour by x-rays =
45 45 (1+1.8/10)=53.1 Gy (1+1.8/10)=53.1 Gy1010
the intended BED to tumour by high LET = the intended BED to tumour by high LET = 6 6 (8+1.3 (8+1.322 3/10)=51.04 Gy 3/10)=51.04 Gy1010
So, total tumour BED is So, total tumour BED is 53.1+52.04=104.14 Gy53.1+52.04=104.14 Gy1010 before allowing before allowing for repopulationfor repopulation
The additional seven days of repopulation The additional seven days of repopulation must be allowed for because of the must be allowed for because of the treatment interruption in providing the treatment interruption in providing the boost, which is equivalent to 0.6 boost, which is equivalent to 0.6 7=4.2 7=4.2 GyGy1010..
Worked example - IVWorked example - IV The boost must accommodate the original high-LET The boost must accommodate the original high-LET
BED plus 4.2 Gy, i.e. 51.04 + 4.2 = 55.24 GyBED plus 4.2 Gy, i.e. 51.04 + 4.2 = 55.24 Gy1010
As this is to be given in two fractions, then :As this is to be given in two fractions, then :
22dd (8+1.3 (8+1.322d/10)=55.24, d/10)=55.24,
d = 3.23 Gy/fraction - instead of the original 3 Gy d = 3.23 Gy/fraction - instead of the original 3 Gy per fraction.per fraction.
BUTBUT Normal tissue BED is : 2 Normal tissue BED is : 23.233.23(8+1.3(8+1.3223.23/2) 3.23/2) = 69.31Gy= 69.31Gy22. .
Total (low plus high-LET) normal tissue BED Total (low plus high-LET) normal tissue BED increases by 69.31 - 63.2 = 6.11Gyincreases by 69.31 - 63.2 = 6.11Gy22, ( 4.1% increase) , ( 4.1% increase) in order to maintain the same tumour BED. This in order to maintain the same tumour BED. This might increase tissue side effects.might increase tissue side effects.
A compromise solution e.g. 3.15 Gy instead of 3.23 A compromise solution e.g. 3.15 Gy instead of 3.23 Gy might be used. This would lead to 67.17 GyGy might be used. This would lead to 67.17 Gy22 maximum high-LET BED to the normal tissues and maximum high-LET BED to the normal tissues and 53.75 Gy53.75 Gy10 10 to the tumour.to the tumour.
Summary :RBE is likely to be related to low LET(control) α/β ratio in two ways :
•Inversely at lower doses where RBEmax dominates
•Directly at high doses where RBEmin dominates
L
L
L
LH
H QRBERBE
2min
max .
L
L
H
HL
L SRBE
RBE
max
min .
L
L
ACRBE
max
L
LBKRBE
min
From previous definitions of RBEmax and RBEmin
Then impose boundary conditions on lower limit of each RBE ( the RBE due to change in beam physics alone)
L=Low LET, H=High LET
RBEMAX = αH/αL
RBEMIN =(βH/βL)
RBEMAX = A+B/(α/β)L
RBEMIN = C+K(α/β)L
Fast neutron data Hammersmith and Clatterbridge data. Then replace the two RBE limits in: BED[highLET] =DH(RMAX+RMIN
2dH/(α/β)L)BED[lowLET] =DL(1+dL /(α/β)L)
We can then replace RBEmax and We can then replace RBEmax and RBEmin with functions of RBEmin with functions of αα//ββ in in
L
H
L
L
H
LLH
BKdA
Cdd
RBE
.445.0 22
And then solve roots to obtain ‘flexible’ RBE as:
SKIN
Oesophagus..acute
Kidney
Lung
Four examples from Hammersmith animal neutron experiments – (Carabe-Fernandez et al IJRB 2007)
RBE
RBE
Low LET / ratio (Gy)
RBE variation mainly found at low dose per fraction, with greater range in late-reacting tissues (low / ratio).
Note: most RBE assays done using low / ratio endpoints (respond like brown and green lines).
We need this relationship for We need this relationship for protons & ionsprotons & ions
At Clatterbridge, we obtained RBEmax of ~1.4 in At Clatterbridge, we obtained RBEmax of ~1.4 in two cell lines: bovine endothelium, + human two cell lines: bovine endothelium, + human Bladder (MGH)Bladder (MGH)
Boston review of proton RBE studies: Paganetti et al IJROBP 2002
In vitro ? shows trend to higher RBE at low dose
In vivo and in vitro results are consistent with high / ratio endpoints, as expected from log phase CHO-V79 cells and acute small intestine crypt assay
If relationship scaled down for protons as:
RBEmax=1.0+1.2/(RBEmax=1.0+1.2/(αα//ββ))LL RBEmin=1.0+Sqrt[0.0005 /(RBEmin=1.0+Sqrt[0.0005 /(αα//ββ))LL]]
20 30 40 50 60 70 80 90TOTAL DOSECo Eq Gy
20
40
60
80
100PERCENTAGE CURES
1# 4# 9# 18#
UK Modelling Carbon ions for early lung cancer (Japan): using Monte Carlo computer simulation of hypoxic and oxic (repopulating) with re-oxygenation flux, reduced oxygen dependency of ion cell kill and typical RBE.
Model accounts for single fraction deviation from Japanese model
Jones B & Dale RG. Estimation of optimum dose Jones B & Dale RG. Estimation of optimum dose per fraction for high LET radiations IJROBP, 48, per fraction for high LET radiations IJROBP, 48,
1549-1557, 20001549-1557, 2000
T T ff (n-1), where (n-1), where ff is average inter-fraction is average inter-fraction interval;interval;
TKdRdRnE Max .22min
/1
;/
1d
d
BEDn
dndBED
Eliminate n and T in
Then differentiate and solve (dE/dT)=0 to give max cell kill for constant level of normal tissue side effect defined by the BED. Also for more sparing forms of radiation d = g z, where z is dose to tumour and d to normal tissue
0)/(.2)/(
)/( 2
fKzfgKzg
dt
dzLATE
TUM
LATE
The solution when plotted shows that z’ (the optimum dose per fraction for the same NT isoeffect) :
• Increases as g is reduced, as with a better dose distribution
• Reduces as f is shortened, • Increases with K (for rapidly growing
tumours)• Increases as / of cancer approaches that
of the normal late reacting tissues [OAR].
With an increase in RBE, z falls, but all above features the same
High LET optimum dose per High LET optimum dose per fraction using calculus methodfraction using calculus method
Even for protons, treatments might be accelerated;
Germany 19#
Japan 16, 10, 4, 1 #
Preliminary dataPreliminary data
0 1 2 3 4 5 6 7 810-3
10-2
10-1
100
24 MeVprotons
2.7MeV protons4.5MeV protons
rays
3.3MeV particles
(121 keV/m)
Sur
vivi
ng fr
actio
n
Dose (Gy)0 1 2 3 4 5 6
0.01
0.1
1
control PI3-kinase inhibitor
Sur
vivi
ng fr
actio
n
Dose (Gy)
3.3MeValpha-particles
Proton survival data Radio-sensitizers and high-LET
radiation
RBE & SER reduced but sensitisation remains
100
60
10
Medulloblstoma in a child
X-rays
Proton particles
X-rays
Proton particles
What is reasonable & simple to apply to What is reasonable & simple to apply to structures only in PTV? For protons…..structures only in PTV? For protons…..
•Prescription RBE: 1.1, or RBEmax1.2, RBEmin1.01 ?
•Late-reacting NT RBE: 1.15, or RBEmax1.3, RBEmin 1.02 ?
•CNS RBE 1.2, or RBEmax 1.4, RBEmin 1.03 ?
•Fast growing tumours –
RBE 1.05, or RBEmax 1.1, RBEmin 1.01 ?These are conservative values, aimed to ensure better normal tissue protection & preserve tumour control.Note: for slow growing tumours a 1.1 RBE probably underestimates the true RBE.
Total isoeffective doses to 50 Gy/25 Total isoeffective doses to 50 Gy/25 # (x-rays) & for 25 fractions of # (x-rays) & for 25 fractions of
protons & suggested RBEsprotons & suggested RBEsProton dose for CNS late isoeffect(α/β = 2 Gy)
Proton dose for fast-growing tumour isoeffect(α/β = 7 Gy)
RBE=1.1 (fixed)45.45 Gy
RBE=1.1 (fixed)45.45 Gy
Rmax=1.4, Rmin=1.0343.18 Gy
Rmax= 1.1, Rmin=1.0146.82 Gy
RBE=1.2 (fixed)41.67 Gy
RBE=1.05(fixed)47.69 Gy
Extra constraints in treatment Extra constraints in treatment planning – inclusion of RBE planning – inclusion of RBE uncertaintiesuncertainties
errorRBE
errorRBE
P
PS
CA
NT
L
H
1
1.
P is physical dose sparing for low (L) and high (H) LET cases
2.
3..3
2
2.
3..
2.01
2.01.
CA
NT
L
H
CA
NT
L
H
CA
NT
L
H
RBE
RBE
P
PS
RBE
RBE
P
P
RBE
RBE
P
PS
So, physical sparing (H) must be improved by ~33% a (1/3) in NT dose to account for worse case scenario.Brit J Radiol, [Jones, Underwood & Dale] accepted
in press 2011
Local Effect Model & Local Effect Model & RBERBE
1.1. LEM underestimates RBE by ~10 -LEM underestimates RBE by ~10 -25%; 25%;
2.2. Most work done in CHO-V79 cells with Most work done in CHO-V79 cells with relatively high relatively high // ratio. ratio.
Implication 1Implication 1: in slowly growing tumour : in slowly growing tumour - if - if αα//ββ lower and lower and RBE higher & high RBE higher & high dose confined to tumour…expect better dose confined to tumour…expect better tumour controltumour control
Implication 2:Implication 2: in faster growing tumour in faster growing tumour - if - if αα//ββ higher and tumour RBE lower & higher and tumour RBE lower & tumour tumour notnot dose-escalated, expect worse dose-escalated, expect worse tumour control tumour control
Local Effect Model & Local Effect Model & RBERBE
if RBE higher in critical late reacting if RBE higher in critical late reacting normal tissue (since low normal tissue (since low αα//ββ), dose ), dose planning constraints need to be more planning constraints need to be more demanding……achievable with Cdemanding……achievable with C6+6+ & & protons in spot scanning mode?protons in spot scanning mode?
At dose per fraction > in vitro assay At dose per fraction > in vitro assay (e.g. doses (e.g. doses SF of 10 SF of 10-8 -8 -10-10-10-10 for for single fractions), the predicted RBE single fractions), the predicted RBE may be far lower (as in Japanese lung may be far lower (as in Japanese lung experience of 16 experience of 16 1# )1# )
Consequences of not Consequences of not using RBE to full using RBE to full
advantage?advantage? Null hypothesis will be favoured in a Null hypothesis will be favoured in a
clinical trial if tumour RBE exceeds or clinical trial if tumour RBE exceeds or is less than ‘fixed’ prescription RBEis less than ‘fixed’ prescription RBE
Results in pragmatic studies will not Results in pragmatic studies will not be as good as expectedbe as good as expected
If RBE in critical late reacting NT If RBE in critical late reacting NT exceeds that of fixed prescription exceeds that of fixed prescription RBE, then any ‘dose sparing’ of these RBE, then any ‘dose sparing’ of these NT will be less effective. NT will be less effective.
Proton Therapy – what can Proton Therapy – what can we expect?we expect?
Z1=GTV
Z3=remainder of body outside PTVZ2 =PTV
OAR
OAR
Dose Status TCP
[Z1+Z2]
Z2 side
effects
Z3 side
effects
Z1,Z2, Z3 better worse* better
Z1,Z2=, Z3 better equal** better
Z1=,Z2=, Z3 equal** equal ** better
Z1=,Z2, Z3 worse better better
Dose Status Tumour Control (in Z1 and Z2) Z2 side effects Z3 side effects
Z1, Z2, Z3 much better
if RBEC>RBERx
better or equal or worse (depending on dose ) if RBEC≤RBERx
better only if
RBENT<RBERx and
depending on dose Worse if RBENT≥RBERx
Better if dose reduction sufficient to overcome any disadvantage in RBE
Z1, Z2=, Z3 better
if RBEC>RBERx
better, equal or worse depending on dose in Z1, equality of α/β or extent
of RBEC<RBERx
Better if RBENT<RBERx
Equal if RBENT=RBERx
Worse if RBENT>RBERx
Better if dose reduction sufficient to overcome any disadvantage in RBE
Z1=, Z2=, Z3 Better – only if RBEC>RBERx
Same if RBEC=RBERx
worse depending on extent of
RBEC<RBERx
Better if RBENT<RBERx
equal - only if
RBENT=RBERx
Worse if RBENT>RBERx
Better if dose reduction sufficient to overcome any disadvantage in RBE
Z1=, Z2, Z3 Worse, unless if RBEC>RBERx Better if RBENT≤RBERx
Could be equal if
RBENT>RBERx depending
on dose
Better if dose reduction sufficient to overcome any disadvantage in RBE
Carcinogenesis ‘turnover Carcinogenesis ‘turnover points’.points’.
Small animal evidence, Small animal evidence, mice etc is well mice etc is well establishedestablished
Clinical distributions: Clinical distributions: cancers more in cancers more in penumbra and exit penumbra and exit dose regions; sarcomas dose regions; sarcomas sometimes in high dose sometimes in high dose regions…..? Related regions…..? Related therefore to intrinsic therefore to intrinsic radiosensitivity?radiosensitivity?
Combination of Combination of induction process and induction process and cell killing produces cell killing produces ‘TOP.’‘TOP.’
Chapters on fractionation, repair, repopulation, oxygen modelling, high LET etc.
Published by British Institute of Radiology, London
www.bir.org.uk
Benefits of improved particle therapy Reduced fear of therapy Improved patient experience Reduced side effects Better quality of life More cost effective
Barber Institute of Art
University of Birmingham
In the long term
The Bethe Bloch equation
Energy deposition cm-
1=K.charge2/velocity2 Mass influences velocity
energy loss, slowing down ( velocity), probability of electronic interactions,
leading to Bragg peak, & little or no dose beyond it.
Most interactions occur when particle velocity that of electrons in atoms along path.
