1. PARTNER – at Pavia, January 2012 LET and Fractionation
Bleddyn Jones
University of Oxford
Gray Institute for Radiation Oncology & Biology
21 Century School Particle Therapy Cancer Research Institute, Oxford Physics.

2. 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.)

3. From Fowler, Adams and Denekamp : Cancer Treat
From Fowler, Adams and Denekamp : Cancer Treat. Reviews 1976, 3,

4. % Tumour control for same level of skin reaction in mice
‘Megamouse expt’ at Northwood Gray Lab, Fowler, Sheldon, Denekamp, Field (IJROBP, 1, , 1976)
Deterioration due to repopulation
% Tumour control for same level of skin reaction in mice
Improvement at short times with metronidazole or neutrons (compensating for hypoxia)
Improvement due to cell cycle progression, reoxygenation
Overall time in days (also related to number of fractions)

5. Adding a repopulation correction factor to LQ model
Surviving fraction describes a reduction in viable cell numbers but is opposed by repopulation
If there are c cells at start of radiation there will be c.SF after radiation.
The clonal expansion during radiotherapy is represented by Nt=Noe-kg.t, [eq 1]
where t is the elapsed time when No cells become Nt cells and kg is the growth rate constant
When Nt/No=2 the population will have doubled, so that the time is then the doubling time of cells……..that is
2=e-kgTp…….so that ln2=-kKg.Tp [eq 2] and so kg can be replaced by ln2/Tp in eq 1 above
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

6. Full LQ equation with allowance for repopulation
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 Radiology
Fowler showed that different fractionation schedules could have similar tumour control rates when overall time and repopulation included .

7. Some general principles
As T increases…more time for
normal tissue repair and repopulation…less severe acute reactions
tumour repopulation, so cure rate may fall if fast cellular doubling times
Re-oxygenation of hypoxic 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

8. Ionising Radiation and DNA + microdosimetric theories
Sparsely ionising radiation (low-LET)
e.g. -rays, -particles
Low concentration
of ionisation events
electron tracks
Densely ionising radiation (high-LET)
e.g. -particles
C6+ ions
High concentration
of ionisation events
Dr Mark Hill, Gray Institute, Oxford
DNA 8

9. Particle, Energy & Depth Target Volume
RBE depends on ……..
Particle, Energy & Depth
Target Volume
Dose per treatment ..RBE varies inversely with dose. A treatment plan contains many dose levels.
Facility: neutron & -ray contamination
Cell & Tissue type : slow growing cells have highest RBEs.
Use of single value RBE was mistake

10. Paravertebral Epithelioid Sarcoma Intensity Modulated Protons (IMPT) vs. Intensity Modulated Photons (IMRT) 7 (field)
IMPT IMXT

11. Esophageal radiotherapy dose distributions – Protons vs. IMRT

12. Track structure on the nuclear/cellular scale
Low-LET (e.g. -rays)
High-LET (e.g. -particles)
Chromosome domains
H2AX
-particle
H2AX
1 Gy corresponds to:
~1000 electron tracks
~2 alpha tracks
~20-40 DSB
(~20% complex)
1 lethal chromosome break
~20-40 DSB
(~70% complex)
3 lethal chromosome breaks
Relatively homogeneous
Very non-homogeneous

13. 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.

14. RBE – components in a ratio
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

15. Reduced repair capacity at high LET
α parameter increases by more than the increase in β [ e.g compared with 1.3 for fast neutrons]
Then, α/β increases with LET and so “fractionation sensitivity” reduces
α –related damage is less repairable than β related damage.

16. RBE depends on Cell Type and its / ratio which reflects repair capacity
Radioresistant cells with greatest curvature (higher DNA repair capacity)
show higher RBEs (GSI, Weyreuther et al)
X-rays
Carbon ions

17. Recovery ratio – the ratio of surviving fractions for one and two fractions to same total dose.
For low LET radiations

18. RR for high LET radiations

19. So, the capacity for repair with standard x-rays is higher by a factor of:
For iso-effect
Now RBE>1 and RBE>Rmin, dH>1
So RR of low LET radiation always exceeds that of high LET

20. Another method
Consider the change in the number of fractions N for the same effect when dose per fraction is changed; assume N is continuous variable.
Where α/β=k
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]

21. LOW LET change in total dose with number of fractions (or dose per fraction)

22. LOW LET: change in total dose with number of fractions (or dose per fraction)

23. The medical prescription
Cobalt 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?

24. Neutron Therapy Prescription of radiation using fixed RBE of 3 at tumour depth and assumed to be the case at all other points within a patient (all tissues, all doses). The pseudo exponential dose fall-off with depth beyond a tumour will be compensated for by increase in RBE.
RBE=2.5
RBE=4-6
RBE=3
Using more fields will only make matters worse

25. BED - how do we get there? By definition of the “Log cell kill”=E

26. BED - The Concept
Represents total dose if given in smallest fraction size

27. How can we picture BED for high LET radiations?
Dose for same effect in four fractions
Dose for same effect in single fraction
DOSE (Gy)
BED
Surviving Fraction
All have same Effect/
Single fraction
Imagine the dose to be given in infinitely small fractions with no curvature to slope
High LET shifts all curves to left, but effect defined by same low LET BED

28. BED - some implications
Any two schedules can either be compared or equated
An exact solution can only be obtained for a specific / value
Solving for d when / changes will give a different answer
BED values must be qualified by the / ratio used

29. Fowler`s ‘FE’ – fractionation effect plot
E=n(d+d2)
E=D(+d)
Divide throughout by E and by D, so
/=intercept/slope
1/D
tan=/E
/E
y = c + mx d
= - /

30. Use of BED
Refers to points/small volumes of interest; can be extended to volumes as in EUD.
Comparisons are for individuals
Iso-effect calculations, ranking of BEDs for comparisons of different techniques/schedules.
Compensation for errors in dose delivery and unscheduled treatment extensions
Dose rate effects
Generic comparisons of different fractionation schedules in radiotherapy – including high and low LET radiations
Reference: Jones B, Dale RG, Deehan C, Hopkins KI, Morgan DAL The role of biologically effective dose (BED) in Clinical Oncology. Clinical Oncology 2001;13:71-81.
Jones B and Dale RG. Radiobiological compensation of treatment errors in radiotherapy. Brit J Radiology, 81, , 2008.
Dale RG, Hendry JH, Jones B, Deehan C et al. Practical methods for compensating for missed treatment days in radiotherapy, with particular reference to head & neck schedules. Clinical Oncology, 14, , 2002.

31. The fractionated isoeffect equation
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.

32. Useful equations for high LET radiations
RBE is defined as dL/dH
= the RBE at low dose
= the RBE at high dose
The RBE between RBEmax and RBEmin is given by solving the first equation for dL, and then divide by dH, so that
Where k is the low LET / ratio
Jones, Carabe and Dale BJR 2006 – adapted for treatment interruption calculations

33. 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

34. Note:
RBEmax is intercept on y axis,
RBEmin is asymptote at high dose
A fixed RBE, of say 3, would intersect all curves

35. Applications
Converting a specific low LET BED to that for high LET, when the low LET α/β ratio is known……use

36. For isoeffect calculations in the case of two high LET schedules – need (α/β)H value.
And so, =
where
Then, for N1H(αHd1H+βHd1H2)= N2H(αHd2H+βHd2H2)
Divide throughout by αH =
- KHT1H=
- KHT2H

37. 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.

38. Some important caveats – slide 2
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 NLNH (suggested by Dasu & Dasu) – Suggest always use single dose RBE and then compensate for fractionation

39. 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 Gy
Then find dH in: 10*dH( *dH/2) =10*4 (1+4/2)
dH=1.69 Gy.
Note the RBE per fraction is then 4/1.69=2.37
Alternatively we could calculate dH direct from
10*dH( *dH/2) =30(1+2/2)
But the RBE is not 2/1.69=1.18
Use RBE on dose per fraction basis for equal No of #.

40. 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…..!

41. BUT …Previous slide presumes RBE does not vary with dose per fraction
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 CNS
Intended 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= =22.52 Gy2
The dose, dH, then required in remaining 4 # is found by solving:
4 dH(6+dH*1.252/2)=22.52
dH=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!

42. Worked example of a time delay
Schedule: megavoltage X-ray of 45 Gy in 25 fractions, then ‘boost’ of 6 Gy [physical dose] in 2 fractions using a high-LET radiation with RBEmin = 1.3 and RBEmax =8.
There is a delay of one week in delivery of boost, due to patient illness.
Assume tumour daily repopulation equivalent of 0.6 Gy per day after a lag interval of 25 days during megavoltage x-ray treatment; normal tissue / =2 Gy, tumour / = 10 Gy.

43. Worked example -II
The intended BED to normal tissue from x-rays = 45  (1+1.8/2)= 85.5 Gy2
The intended BED to any marginal normal tissue that receives the added high-LET boost of 2 fractions of 3 Gy = 6  (8+1.323/2)= 63.2 Gy2
 total intended maximum BED to same volume of normal tissue = = 148.7Gy2

44. Worked example -III
The intended BED to tumour by x-rays = 45  (1+1.8/10)=53.1 Gy10
the intended BED to tumour by high LET = 6  ( /10)=51.04 Gy10
So, total tumour BED is = Gy10 before allowing for repopulation
The additional seven days of repopulation must be allowed for because of the treatment interruption in providing the boost, which is equivalent to 0.6  7=4.2 Gy10.

45. Worked example - IV
The boost must accommodate the original high-LET BED plus 4.2 Gy, i.e = Gy10
As this is to be given in two fractions, then :
2d (8+1.32d/10)=55.24,
d = 3.23 Gy/fraction - instead of the original 3 Gy per fraction.
BUT Normal tissue BED is : 23.23(8+1.323.23/2) = 69.31Gy2.
Total (low plus high-LET) normal tissue BED increases by = 6.11Gy2, ( 4.1% increase) in order to maintain the same tumour BED. This might increase tissue side effects.
A compromise solution e.g Gy instead of 3.23 Gy might be used. This would lead to Gy2 maximum high-LET BED to the normal tissues and Gy10 to the tumour.

46. 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

47. 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)

48. RBEMAX = αH/αL RBEMIN =(βH/βL) RBEMAX = A+B/(α/β)L
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+RMIN2dH/(α/β)L)
BED[lowLET] =DL(1+dL /(α/β)L)

49. We can then replace RBEmax and RBEmin with functions of α/β in
And then solve roots to obtain ‘flexible’ RBE as:

50. Four examples from Hammersmith animal neutron experiments – (Carabe-Fernandez et al IJRB 2007)
Kidney
Oesophagus..acute
RBE
SKIN
Lung
RBE

51. 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).

52. We need this relationship for protons & ions

53. At Clatterbridge, we obtained RBEmax of ~1
At Clatterbridge, we obtained RBEmax of ~1.4 in two cell lines: bovine endothelium, + human Bladder (MGH)

54. 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

55. If relationship scaled down for protons as: RBEmax=1. 0+1
If relationship scaled down for protons as: RBEmax= /(α/β)L RBEmin=1.0+Sqrt[ /(α/β)L]

57. 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

58. Jones B & Dale RG. Estimation of optimum dose per fraction for high LET radiations IJROBP, 48, , 2000
T  f (n-1), where f is average inter-fraction interval;
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

59. 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

61. High LET optimum dose per fraction using calculus method
Even for protons, treatments might be accelerated;
Germany 19#
Japan 16, 10, 4, 1 #

62. Radio-sensitizers and high-LET radiation
Preliminary data
Radio-sensitizers and high-LET radiation
Proton survival data
RBE & SER reduced but sensitisation remains

63. Medulloblstoma in a child
X-rays
X-rays
100 60 10
Proton particles
Proton particles

64. What is reasonable & simple to apply to structures only in PTV
What is reasonable & simple to apply to 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.

65. Total isoeffective doses to 50 Gy/25 # (x-rays) & for 25 fractions of protons & suggested RBEs
Proton 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
Rmax=1.4, Rmin=1.03 Gy
Rmax= 1.1, Rmin=1.01
46.82 Gy
RBE=1.2 (fixed)
41.67 Gy
RBE=1.05(fixed)
47.69 Gy

66. Extra constraints in treatment planning – inclusion of RBE uncertainties
P is physical dose sparing for low (L) and high (H) LET cases
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

67. Local Effect Model & RBE
LEM underestimates RBE by ~10 -25%;
Most work done in CHO-V79 cells with relatively high / ratio.
Implication 1: in slowly growing tumour if α/β lower and RBE higher & high dose confined to tumour…expect better tumour control
Implication 2: in faster growing tumour if α/β higher and tumour RBE lower & tumour not dose-escalated, expect worse tumour control

68. Local Effect Model & RBE
if RBE higher in critical late reacting normal tissue (since low α/β), dose planning constraints need to be more demanding……achievable with C6+ & protons in spot scanning mode?
At dose per fraction > in vitro assay (e.g. doses  SF of for single fractions), the predicted RBE may be far lower (as in Japanese lung experience of 16 1# )

69. Consequences of not using RBE to full advantage?
Null hypothesis will be favoured in a clinical trial if tumour RBE exceeds or is less than ‘fixed’ prescription RBE
Results in pragmatic studies will not be as good as expected
If RBE in critical late reacting NT exceeds that of fixed prescription RBE, then any ‘dose sparing’ of these NT will be less effective.

70. Proton Therapy – what can we expect?
OAR
Z3=remainder of body outside PTV
Z1=GTV
Z2 =PTV
OAR

71. Dose Status
TCP
[Z1+Z2]
Z2 side effects
Z3 side effects
Z1,Z2, Z3
better
worse*
Z1,Z2=, Z3
equal**
Z1=,Z2=, Z3
equal **
Z1=,Z2, Z3
worse

72. Tumour Control (in Z1 and Z2) Z2 side effects Z3 side effects
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
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
Z1=, Z2=, Z3
Better – only if RBEC>RBERx
Same if RBEC=RBERx
worse depending on extent of RBEC<RBERx
equal - only if RBENT=RBERx
Z1=, Z2, Z3
Worse, unless if RBEC>RBERx
Better if RBENT≤RBERx
Could be equal if
RBENT>RBERx depending on dose

73. Carcinogenesis ‘turnover points’.
Small animal evidence, mice etc is well established
Clinical distributions: cancers more in penumbra and exit dose regions; sarcomas sometimes in high dose regions…..? Related therefore to intrinsic radiosensitivity?
Combination of induction process and cell killing produces ‘TOP.’

74. Chapters on fractionation, repair, repopulation, oxygen modelling, high LET etc.
Published by British Institute of Radiology, London

75. Benefits of improved particle therapy
Reduced fear of therapy
Improved patient experience
Reduced side effects
Better quality of life
More cost effective
In the long term
Barber Institute of Art
University of Birmingham 75

76. 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.