Impact of variable RBE on proton fractionationAlexandru Dasua)
Department of Radiation Physics UHL, County Council of Östergötland, 581 85 Linköping, Sweden andRadiation Physics, Department of Medical and Health Sciences, Faculty of Health Sciences, LinköpingUniversity, 581 83 Linköping, Sweden
Iuliana Toma-DasuMedical Radiation Physics, Stockholm University and Karolinska Institute, 171 76 Stockholm, Sweden
(Received 17 May 2012; revised 18 October 2012; accepted for publication 9 November 2012;published 13 December 2012)
There is a growing interest in proton radiation therapy re-flected by the increasing number of patients treated withthis radiation modality, which at present stands at more than60 000 worldwide.1 This comes primarily from the improveddose distributions that could be achieved with protons in com-parison to photons beams. Thus, the finite range of protons intissue and the steep dose fall-off at the distal edge of the rangecould be used to limit the irradiation of the normal tissuesaround the target.
Protons are generally low linear energy transfer (LET) ra-diation, rather similar to photons and electrons and thereforea generic value of 1.1 was proposed for the relative effective-ness of protons2 and many clinical schedules have been basedon this recommendation.1 Nevertheless, experimental studieshave shown that the relative biological effectiveness (RBE) ofprotons varies with tissue type, dose, and energy of the pro-tons. Indeed, analyses of experimental data showed that at thesame LET, the RBE for slowly growing cells and tissues ishigher than that for fast growing ones.3–5 This is in line with
earlier clinical and experimental observations from neutronsand other particles showing higher effects in late reacting tis-sues than in acutely reacting tissues and might reflect the in-crease in the fraction of irreparable damage with high LETwhich affects more late reacting tissues. Furthermore, for aparticular type of cells, the RBE increases with increasingLET of the protons. This latter aspect is particularly importantfor the distal end of the proton range that exhibits an increasein LET. The impact of some of these aspects has been studiedtheoretically. Thus, Tilly et al.4 and more recently Frese et al.6
studied the impact of variable RBE for clinical planning ofhead and neck (H&N) cancers. Other studies investigated theimplications of variable RBE on the biological range of pro-tons in tissues.5, 7, 8 A general radiobiological analysis of pro-tons versus carbon ions taking into account variations in RBEwas also recently performed by Suit et al.1 This study adds tothese investigations and presents an exploration of the impactof dose fractionation in the light of variable proton RBE forclinically relevant situations that may employ proton beams.This is an important aspect for clinical radiotherapy given therekindled interest for varying fractionation for a number of
011705-2 A. Dasu and I. Toma-Dasu: Impact of variable RBE on proton fractionation 011705-2
tumors. Hypofractionation issues could also be brought intodiscussion for protons since the favorable dose distributionsthat may be achieved with this radiation modality might en-courage the use of shorter schedules employing larger dosesper fractions.
II. METHODS AND MATERIALS
The fractionation effects for variable RBE have been stud-ied with the linear-quadratic (LQ) model9–12 that works quitewell for clinical schedules employing low LET radiation.13
Thus, the survival after nlow doses dlow of photons (or simi-larly low LET radiation) is given by Eq. (1):
SFlow = exp⌊nlow
(−αdlow − βd2low
)⌋, (1)
where α and β are parameters of the model relevant for photonirradiation. Equation (1) can be rewritten as in Eq. (2):
Effectlow=nlow(αdlow + βd2
low
). (2)
The effect of protons or higher LET radiation could be de-scribed with similar equations by applying dose-modifyingfactors (DMF) to the parameters describing the response tolow LET radiation:14
Effectprot = nprot(αDMFαdprot + βDMFβd2
prot
), (3)
where dprot is the physical proton dose and DMFα and DMFβ
are the dose-modifying factors relevant for protons.Equations (2) and (3) could then be used to determine the
RBE of protons [Eq. (4)]:
RBE = α
β
−1 +√
1 + 4α / β
(DMFαdprot + DMFβd2
prot
α / β
)
2dprot. (4)
The relative effectiveness of various fractionated schedulescould also be determined with the help of Eqs. (2) and (3).Thus, the photon isoeffective or equivalent dose (EQD) withfractional dose dlow (usually 2 Gy) from a given fractionatedproton dose could be calculated with Eq. (5):
EQDlow = nprotdprot
(DMFα + DMFβdprot
α / β
)(
1 + dlowα / β
) . (5)
Equations (4) and (5) represent the most general expres-sions for evaluating the effectiveness of proton schedules andcould also be used for radiobiological calculations for higherLET radiation. Theoretical work and experimental findingssuggested that the DMFβ term for protons and even higherLET radiation is close to unity4–6, 15–20 and has been assumedas such in the present study.
The general expression for the variation of DMFα with α/βand LET for protons is given by Eq. (6) and has been derivedfrom analyses of experimental data:4, 5, 20
DMFα = 1 + qL
α / β, (6)
where L is the LET of the radiation and q is a constant around0.4 Gy nm/eV as shown in analyses of experimental data.5, 20
The LET dependence in Eq. (6) is in agreement with theproposals of Kellerer and Rossi21 for a nonlinear dependencewhich in the limit for low LET values that are relevant for pro-tons transforms into a linear dependence with LET. Further-more, it also reflects the inverse relationship between DMFα
and α/β proposed by the theoretical work by Hawkins.15, 16
Theoretical calculations of clinical proton beams haveshown a rather broad range of relevant LET values.22–24 Thus,the LET in the target is approximately 3 eV/nm with smallvariations depending on the technique used to cover it. Out-side the target there is a broader LET range depending onwhether the irradiation comes from the entrance plateau orthe distal part of the Bragg peak. In these regions LET val-ues higher than 5 and even 10 eV/nm could be encountered.Consequently, three LET values (3, 5, and 10 eV/nm) wereconsidered for point calculations of isoeffects.
In contrast to the formalism above, one could assume thatthe RBE of protons is described by a generic value of 1.1 asrecommended by ICRU,2 irrespective of the tissue type or theLET of the protons. The equivalent photon dose under thisassumption (EQD1.1) would be given by Eq. (7):
EQD1.1 = 1.1 · nprotdprot
(1 + 1.1·dprot
α / β
)(
1 + dlowα / β
) , (7)
where dlow is the dose-per-fraction of the reference photonschedule (usually 2 Gy).
The impact of assuming a variable DMFα versus a genericRBE of 1.1 could be quantified by the ratio of equivalent pho-ton doses predicted by Eqs. (5) and (7). This approach allowsthe separation of fractionation effects and DMF-related ef-fects and leads to an easy quantification of the relative de-viation in predicted effectiveness [Eq. (8)]. It should be notedthat this approach also removes the need for a particular pho-ton fractionation to be used as reference:
Relative deviation =(
DMFα + dprot
α / β
)
1.1 ·(
1 + 1.1·dprot
α / β
) . (8)
The equations above could also be expanded to include theeffects of overall treatment time,12 but this aspect has not beenaccounted for in point analyses for the sake of simplicity. Theformalisms described above have been used for clinicallyrelevant calculations for different fractionation sensitivitiescovering a broad range of tumors and normal tissues. Thus,α/β = 10 Gy may be considered relevant for the fractionationsensitivity of fast growing tumors and for acute reactions ofnormal tissues, while α/β = 3 Gy would be relevant for latereacting normal tissues as well as for some slow growingtumors. Even lower values of α/β = 1.5 Gy have been takeninto consideration for slowly growing tumors and normaltissues with very high fractionation sensitivity. Specificanalyses were performed for combinations of fractionationsensitivities that may be encountered at the irradiation ofH&N and prostate tumors. Calculations were based on theassumption that late reacting normal tissues may be presentnear the tumor and could therefore get into the planning
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treatment volume (PTV) receiving full prescribed dose. Thissituation cannot be excluded for either H&N tumors or forprostate tumors and could thus be regarded as a situation thatmight be clinically encountered. Isoeffect calculations werealso compared with reported clinical results.
III. RESULTS
Figure 1 shows the variation of RBE [Eq. (4)] with protondose-per-fraction and LET for the tissue types considered inthis study. It can be seen that the generic value of 1.1 appearsto be a reasonable estimate for the proton RBE for rapidlygrowing tissues (α/β = 10 Gy) irradiated with low LET radia-tion (LET = 3 eV/nm). Indeed, in this case the differences arewithin about 5% which is comparable with current clinicaldosimetric precision. However, for slower growing tissueslike late reacting tissues or prostate tumors (α/β = 1.5–3 Gy),the generic value provides an underestimate for low fractionaldoses. The problem becomes progressively worse for higherLET that could be found outside the target volume and atlower fractional doses. This is particularly important for latereacting normal tissues (α/β = 1.5–3 Gy) situated outsidethe target volume, which receive lower fractional doses thanthe tumor. Acutely reacting tissues (α/β = 10 Gy) outside
0 2 4 6 8 100.5
1.0
1.5
2.0
2.5LET=10 eV/nm
α/β=1.5 Gyα/β=3 Gyα/β=10 Gy
Proton dose per fraction (Gy)
0 2 4 6 8 100.5
1.0
1.5
2.0
2.5LET=5 eV/nm
α/β=1.5 Gyα/β=3 Gyα/β=10 Gy
RB
E
0 2 4 6 8 100.5
1.0
1.5
2.0
2.5LET=3 eV/nm
α/β=1.5 Gyα/β=3 Gyα/β=10 Gy
FIG. 1. Variation of the RBE with proton dose-per-fraction for tissues withvarious fractionation sensitivities.
the target appear to be less affected by this increase ineffectiveness, at least for LET values up to about 5 eV/nm.
The clinical implications of assuming a constant RBE ir-respective of fraction size could also be assessed with a dif-ferent approach. Thus, given the generally low LET of theprotons for most of their range, a natural approach of chang-ing the fractionation patterns would be to use the photon ex-perience at matching the complication levels in late reactingnormal tissues (α/β = 3 Gy). Figure 2 shows the relationshipbetween the proton dose-per-fraction and the number of frac-tions for isoeffective treatments calculated with Eq. (7) fordlow = 2 Gy to give an EQD1.1 = 70 Gy for α/β = 3 Gy—this dose is considered relevant for the treatment of both H&Ntumors and prostate carcinomas. Thus, under this assumption,35 proton fractions of 1.82 Gy would be equivalent to 70 frac-tions of 1.08 Gy or 20 fractions of 2.68 Gy. However, underthe assumption of variable RBE, the isoeffective photon doseswould be different depending on the fractionation sensitivityof the tumors and normal tissues in each individual site.
Figure 3 illustrates the differences between equivalent pho-ton doses in 2 Gy per fraction in the target volume calcu-lated with Eqs. (5) or (7) for late reacting normal tissues(α/β = 3 Gy). Thus, it appears that the use of a variableDMFα leads to increased predictions from hyperfractionatedschedules and lower predictions from highly hypofractionatedschedules. This is in contrast with the case of H&N tumors(or other fast growing tumors, α/β = 10 Gy) where the use ofa variable DMFα will lead to consistently lower predictionsthan the generic RBE = 1.1 (Fig. 4). Furthermore, comparingthe predicted isoeffective photon doses for a variable DMFα
it appears that a higher overall effect is expected for late re-actions than for fast growing tumors over the whole rangeof fractional doses. This indicates that photon approaches forchanging fractionation may not work for fast growing tumorsand that a loss of tumor response or an increase in late com-plications might be expected.
This contrasts with the situation in Fig. 5 illustrating thecase of prostate tumors (α/β = 1.5 Gy). In this case, the useof a variable DMFα versus the generic RBE = 1.1 will leadto even higher tumor effect predictions for hyperfractionatedschedules and lower for hypofractionated schedules than fornormal tissues (Fig. 3). Furthermore, analyzing the predic-tions for overall effects, expected tumor response is consis-tently above normal tissue predictions indicating the presenceof a therapeutic window over a broad range of fractionaldoses. Nevertheless, caution is advised against using too lowdoses per fraction as for these a variable DMFα predicts anincrease in effectiveness in comparison to a constant RBE= 1.1. It should be mentioned that in Fig. 5 the tumor EQD forvariable RBE is not strictly constant and that its appearanceis strictly the result of a chance combination of parameters.
The results in Figs. 3–5 refer to cases where late react-ing tissues are near the tumor and represent the limiting fac-tor for the prescribed dose. The importance of this approachmight decrease for highly conformal and stereotactic treat-ments where the aim is to limit the “red shell,” the volumeof tissue receiving therapeutic doses.25 In this case, the pres-ence of late reacting tissues in regions with high LET outside
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0 10 20 30 40 50 60 70 800
2
4
6
8
10
Dos
e pe
r fr
actio
n (G
y)
Number of fractions
FIG. 2. Proton doses per fraction and the number of fractions for isoeffective treatments calculated to give an EQD1.1 = 70 Gy for α/β = 3 Gy [Eq. (7)].
the target will make the issue of fractional doses even moreimportant. This is illustrated by the analysis in Fig. 6, show-ing that the use of a variable DMFα will lead to higher re-sponse predictions than the generic RBE = 1.1 especially fortissues with high fractionation sensitivities (low α/β) receiv-ing very small fractional doses. This indicates the importanceof taking into account the variation of the equivalent photondose with α/β when analyzing particular combinations of lo-
cal dose, LET, and fractionation sensitivity in relation to tol-erance levels for individual cases.
These results suggest that changing fractional doses inclinical protocols for protons may lead to deviations from therelatively well known pattern from photons. An importantquestion in this context concerns the existence of clinicalevidence to support the use of a variable DMFα for responsepredictions from proton treatments. Clinical studies on the
0 1 2 3 4 5 6 7 8 9 1040
50
60
70
80
90
100
110
Equ
ival
ent p
hoto
n do
se in
2 G
y fr
actio
ns (
Gy)
Proton dose per fraction (Gy)
Normal tissues (α/β=3 Gy)
FIG. 3. Equivalent photon doses in 2 Gy per fraction calculated for late reacting tissues (α/β = 3 Gy) and LET = 3 eV/nm for the treatments in Fig. 2 usingEqs. (5) (solid line) or (7) (dashed line).
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0 1 2 3 4 5 6 7 8 9 1040
50
60
70
80
90
100
110
Equ
ival
ent p
hoto
n do
se in
2 G
y fr
actio
ns (
Gy)
Proton dose per fraction (Gy)
Tumor (α/β=10 Gy)
FIG. 4. Equivalent photon doses in 2 Gy per fraction calculated for rapidly growing tumors (α/β = 10 Gy) and LET = 3 eV/nm for the treatments in Fig. 2using Eqs. (5) (solid line) or (7) (dashed line).
irradiation of prostate tumors are the best candidates sincethe high fractionation sensitivity of these tumors leads torather large differences in the predicted isoeffective photondose. Results from two major clinical studies are availablefor such an evaluation. Thus, Slater et al.26 presented theresults from 1255 patients treated with protons at LomaLinda University. The patients received either protons in 37
fractions of 1.82 Gy or a mixture of 25 fractions of 1.8 Gyphotons plus 15 fractions of 1.82 Gy protons. The two sched-ules were deemed equivalent to 74 GyE for α/β = 10 Gy.The overall biochemical disease-free-survival rate at 5 yrusing the ASTRO definition was 75%. Zietman et al.27
presented the results of another study with 393 patientstreated with a combined photon and proton schedule with
0 1 2 3 4 5 6 7 8 9 1040
50
60
70
80
90
100
110
Equ
ival
ent p
hoto
n do
se in
2 G
y fr
actio
ns (
Gy)
Proton dose per fraction (Gy)
Tumor (α/β=1.5 Gy)
FIG. 5. Equivalent photon doses in 2 Gy per fraction calculated for slowly growing tumors (α/β = 1.5 Gy) and LET = 3 eV/nm for the treatments in Fig.2using Eqs. (5) (solid line) or (7) (dashed line).
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12
34
56
78
910
1.0
1.2
1.4
1.6
1.8
2.0
12
34
56
78
910
Rel
ativ
ede
viat
ion
Proton dose per fraction (Gy)alpha/beta (Gy)
LET=3 eV/nm(a)
12
34
56
78
910
1.0
1.2
1.4
1.6
1.8
2.0
12
34
56
78
910
Rel
ativ
ede
viat
ion
Proton dose per fraction (Gy)alpha/beta (Gy)
LET=5 eV/nm(b)
12
34
56
78
910
1.0
1.2
1.4
1.6
1.8
2.0
12
34
56
78
910
Rel
ativ
ede
viat
ion
Proton dose per fraction (Gy)alpha/beta (Gy)
LET=10 eV/nm(c)
FIG. 6. Relative deviation of predictions from a variable DMFα versus thegeneric RBE = 1.1 [Eq. (8)] for combinations of doses, LET, and fractiona-tion sensitivities (α/β) that may be encountered outside the target.
28 photon fractions of 1.8 Gy plus either 11 or 16 protonfractions of 1.82 Gy. Their clinically observed biochemicalcontrol rates at 5 yr according to the ASTRO criteria were61% in the low-dose arm and 80% in the high-dose arm. Thevariations in treatment schedules and fractionation in thesestudies provide an interesting diversity for comparisons withdose response curves for photons that might provide valuableinsight into the clinically relevant RBE approach. Thus, eitherthe generic RBE [Eq. (7)] or the variable RBE approach[Eqs. (5) and (6) for LET = 3 eV/nm] could be used tocalculate the equivalent photon dose from the prostate studiesabove and the results could then be used with dose responseparameters for prostate patients treated with photons to pre-dict the expected response and compare it to clinical results.Recent findings regarding the dose response parametersfor photons have been used for calculations.28, 29 Thus, thefractionation sensitivity of prostate tumors has been assumedto be in the range 1–2 Gy.29–31 The logit dose-responseparameters used to predict the biochemical failure at 5 yraccording to the ASTRO criteria in patient populations withmixed risks were D50 = 59.0 Gy and γ = 1.04.29 The resultsof this analysis are presented in Table I showing the rangeof results that could be obtained for various assumptionsregarding the α/β value for prostate tumors. It can be seenthat assuming a variable RBE for protons leads to predictionsfor biochemical control that are closer to clinically observedresults than the assumption of a generic RBE, which leads tolower predictions. Unfortunately, a similar analysis for latereacting normal tissue response is hampered by the lack ofinformation regarding the dose distributions in normal tissuesoutside the target as well as by the low clinically observedcomplication rates from prostate treatments as recentlyreviewed by Suit et al.1 Nevertheless, the tumor controlresults support the use of a variable RBE when changingfractionation in proton therapy as well as for analyzingclinical results from particle therapy.
IV. DISCUSSION
This study explored the impact of variable RBE on chang-ing fractionation for proton therapy and highlighted the dif-ficulties that may be encountered in extrapolating the resultsfrom photon therapy to protons or even higher LET radiationand devising isoeffective treatments in terms of normal tissuecomplications or tumor response for particle therapy. The re-sults of this study therefore come to complement other stud-ies investigating the clinical impact of the variable RBE fortherapeutically used particles in dose planning studies4, 6 or interms of the predicted biological range of particles.5, 7, 8
Altered fractionation schedules are currently employedfor photon radiotherapy and given the perception of protonsas low LET radiation might also be tried for this radiationmodality in the attempt to maximize the differential inresponse between tumors and normal tissues. Indeed, the im-proved dose distributions that may be achieved with protonsmight provide an incentive to use this radiation modality forschedules employing higher doses per fraction. Furthermore,hyperfractionation for photons had led to improved results
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TABLE I. Predictions for biochemical tumor control probabilities (bTCP) for proton treatments for prostate cancer.
Dose per Observed EQD Predicted EQD1.1 Predictedfraction No of bTCP α/β (Gy) bTCP (Gy) bTCP
aNote: Predicted bTCP was calculated with dose response parameters reported by Dasu and Toma-Dasu (Ref. 29) for the ASTRO criteria for biochemical failure in patientpopulations with mixed risks (D50 = 59.0 Gy and γ = 1.04).
for rapidly proliferating tumors and could therefore beconsidered for protons given their perception as low-LETradiation. The results in this study however indicate that itis important that such endeavors account for the variationof RBE with proton LET and tissue type when calculatingisoeffective schedules or when analyzing the results fromparticle therapy and comparing them to those from photontherapy. Thus, hyperfractionation might be associated witha risk of increased complications in late-reacting tissue asthe α/β dependence of DMFα amplifies the fractionationeffects in this dose range. Furthermore, hyperfractionationcould be a disadvantage for rapidly growing tumors since theα/β dependence of DMFα might counteract the fractionationdifferential with late reacting tissues. This is in line with theclinical neutron experience where treatments for rapidly pro-liferating tumors have usually led to increased complicationrates. There is also the risk that hypofractionation may leadto lower response than expected from a generic RBE value,although the impact of α/β is reduced for large doses and thedifferential trends known from photons are restored.
An important question in relation to these observationsconcerns the magnitude of the predicted differences, becauseit is unlikely that any differences might be noticed as long
as they are comparable to uncertainties originating fromother causes, e.g., dosimetric uncertainty. The model usedfor analysis in the present study has been derived fromexperimental data and reflects dependences proposed bothby the microdosimetric theory of dual radiation action21 andthe microdosimetric kinetic theory15, 16 in the LET range thatis relevant for therapeutic protons. It is interesting to notethat the microdosimetric kinetic theory16 suggested that the qparameter in Eq. (6) may be related to the size of the micro-dosimetric domains that are relevant for cell inactivation. Itshould also be mentioned that cell survival data that was usedto derive Eq. (6) has generally been derived from protons withhigher LET than are relevant for clinical radiation therapyand therefore a question may be raised regarding the accuracyof the extrapolation of the relationship. Indeed, Hawkins16
and Carabe et al.5 suggested that the extrapolation of DMFα
for LET = 0 may be below one, although the results of We-denberg et al.20 suggest that this may not be the case. In thiscontext it should be recognized that at present radiobiologicaluncertainties are larger than dosimetric uncertainties and thismakes difficult to discriminate between the predictions ofdifferent models. From this perspective, the use of a pointanalysis as in the present study is to be preferred for exploring
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the impact of the variable RBE on response predictions whenchanging the fractionation pattern, while relative comparisonsmight be suited for analyses of the response predictions inindividual cases of dose and LET distributions. Nevertheless,the results in Table I suggest that a relationship betweenthe biological effectiveness of protons, LET, and tissuefractionation sensitivity may exist and that further investi-gations are warranted. It is interesting to note that a lineardependence of the α parameter with clinically relevantLETs has also been found for heavier ions as shown, forexample, by Koike et al.32 on fibrosarcoma cells irradiatedwith carbon-ions. This is in line with the initial proposalsby Kellerer and Rossi21 and indicates that the findings ofthe present study may also be applicable for other particles.Nevertheless, these particles may have a broader clinicallyrelevant LET range where the linear approximation may nolonger be valid and therefore one would have to account forthe full LET dependence of the parameters.21, 33–35 However,the clinical experience with neutrons showing higher RBEvalues for late responding normal tissues1, 36 supports the re-lationship between clinical RBE and fractionation sensitivitypredicted in this study.
As mentioned before, calculations in this study werebased on the assumption that late reacting normal tissuesmay be present in the PTV, receiving full prescribed dose.This is a reasonable assumption that could be used for pointcomparisons of the effectiveness of various schedules.12
Nevertheless, as the extent of overlap between PTV andnormal tissues at risk depends on the morphology of thepatients and the margins used, individual calculations couldalso be performed to account for the rather complex variationof dose-per-fraction and LET in the PTV and the surroundingtissues which influences the relative deviation in predictedeffectiveness as illustrated in Fig. 6. Leaving aside theradiobiological uncertainties mentioned earlier, it must bementioned that the dose and LET distributions in the targetand the surrounding tissues may differ depending on the irra-diation technique used22, 23 and this will ultimately influencethe loss or gain in effects in comparison to predictions from ageneric RBE. This stresses the need for accurate calculationsof LET and dose distributions in tissues from clinical protonbeams and the importance of accurate determination of tissuecomposition as it will determine the interaction properties ineach individual case. For mixed LET fields, dose-averagedLET calculations would probably be the most relevant forprotons since relatively large numbers of interaction eventsare required for these particles to deposit therapeutic dosesin subcellular structures and few of these lead to LETcomponents for which the linearity in Eq. (6) may no longerbe valid. This is in contrast to higher LET particles that mayrequire substantially fewer events leading to substantial doseheterogeneities in subcellular structures. Track-averagedLET calculations together with dose heterogeneity analyses37
might be required in this case. However, the exploration ofthese issues is beyond the purpose of the present study.
Irrespective of the uncertainties listed above, it must beconcluded that the increased radiobiological sensitivity toparticles of tissues with low α/β values amplifies their high
fractionation sensitivity making them susceptible to higherresponse changes when varying the fractionation pattern thantissues with low fractionation sensitivity. As has been shownin this study this may lead to changes of the response patternsknown from photons and therefore the transfer of the photonknowledge to protons and other ions should be pursued withcaution. Further investigations on the clinical implicationsof fraction size for therapy with protons and other ions aretherefore warranted.
V. CONCLUSIONS
The results of this study have shown that the dependenceof the RBE on the fractionation sensitivity of the tissue quan-tified as α/β has a strong impact on the predicted effectivenessof fractionated proton radiotherapy. The largest changes are tobe expected from hyperfractionated schedules where the useof a variable DMFα may lead to a reversal of the effectivenessthat may be expected from the use of a generic RBE. Whileuncertainties may exist with respect to the absolute magni-tude of these effects, the results indicate that care should beemployed for changing the clinical fractionation patterns forparticles or when analyzing results from clinical studies em-ploying this type of radiation.
ACKNOWLEDGMENTS
The authors would like to thank Professor Jack Fowler forstimulating discussions on fractionation in particle therapyand comments on this paper. The authors report no conflictsof interest in conducting the research.
a)Author to whom correspondence should be addressed. Electronic mail:[email protected]; Telephone: +46-10-1032658.
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