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.

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 From Fowler, Adams and Denekamp : Cancer Treat. Reviews 1976, 3, 227-256

% Tumour control for same level of skin reaction in mice ‘Megamouse expt’ at Northwood Gray Lab, Fowler, Sheldon, Denekamp, Field (IJROBP, 1, 579-92, 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)

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

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 .

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

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

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

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

Esophageal radiotherapy dose distributions – Protons vs. IMRT

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

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 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

Reduced repair capacity at high LET α parameter increases by more than the increase in β [ e.g. 2.5-3 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.

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

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

RR for high LET radiations

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

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]

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 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?

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

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

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

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

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

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 = - /

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, 323-326, 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, 382-393, 2002.

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.

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

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

Applications Converting 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 . And so, = where Then, for N1H(αHd1H+βHd1H2)= N2H(αHd2H+βHd2H2) Divide throughout by αH = - KHT1H= - KHT2H

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.

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

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(6+1.252*dH/2) =10*4 (1+4/2) dH=1.69 Gy. Note the RBE per fraction is then 4/1.69=2.37 Alternatively we could calculate dH direct from 10*dH(6+1.252*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 #.

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 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= 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)=22.52 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!

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.

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 = 85.5 + 63.2 = 148.7Gy2

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  (8+1.32 3/10)=51.04 Gy10 So, total tumour BED is 53.1+52.04=104.14 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.

Worked example - IV The boost must accommodate the original high-LET BED plus 4.2 Gy, i.e. 51.04 + 4.2 = 55.24 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 69.31 - 63.2 = 6.11Gy2, ( 4.1% increase) in order to maintain the same tumour BED. This might increase tissue side effects. A compromise solution e.g. 3.15 Gy instead of 3.23 Gy might be used. This would lead to 67.17 Gy2 maximum high-LET BED to the normal tissues and 53.75 Gy10 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

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)

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)

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

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

At Clatterbridge, we obtained RBEmax of ~1 At Clatterbridge, we obtained RBEmax of ~1.4 in two cell lines: bovine endothelium, + human 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 If relationship scaled down for protons as: RBEmax=1.0+1.2/(α/β)L RBEmin=1.0+Sqrt[0.0005 /(α/β)L]

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 per fraction for high LET radiations IJROBP, 48, 1549-1557, 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

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 fraction using calculus method Even for protons, treatments might be accelerated; Germany 19# Japan 16, 10, 4, 1 #

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

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

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.

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 43.18 Gy Rmax= 1.1, Rmin=1.01 46.82 Gy RBE=1.2 (fixed) 41.67 Gy RBE=1.05(fixed) 47.69 Gy

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

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

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 10-8 -10-10 for single fractions), the predicted RBE may be far lower (as in Japanese lung experience of 16 1# )

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.

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

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

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

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.’

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 In the long term Barber Institute of Art University of Birmingham 75

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.