The potential impact of relative biological effectiveness uncertainty on charged particle treatment prescriptions.
ABSTRACT There continues to be uncertainty regarding the relative biological effectiveness (RBE) values that should be used in charged particle radiotherapy (CPT) prescriptions using protons and heavier ions. This uncertainty could potentially offset the physical dose advantage gained by exploiting the Bragg peak effect and it needs to be clearly understood by clinicians and physicists. This paper introduces a combined radiobiological and physical sparing factor (S). This factor includes the ratio of the most relevant physical doses in tumour and normal tissues in combination with their respective RBE values and can be extended to contain the uncertainties in RBE. S factors can be used to study, in a simplified way for tentative modelling, those clinical situations in which highlinear energy transfer (LET) irradiations are likely to prove preferable over their lowLET counterparts for a matched tumour isoeffect. In cases where CPT achieves an excellent degree of normal tissue sparing, the radiobiological factors become less important and any uncertainties in the tumour and healthy tissue RBE values are correspondingly less problematic. When less normal tissue sparing can be achieved, however, the RBE uncertainties assume greater relevance and will affect the reliability of the doseprescription methodology. More research is required to provide accurate RBE estimation, focusing attention on the associated statistical uncertainties and potential differences in RBE between different tissue types.

Article: Particle therapy.
[Show abstract] [Hide abstract]
ABSTRACT: Particle therapy has a long history. The experimentation with particles for their therapeutic application got started soon after they were produced in the laboratory. Physicists played a major role in proposing the potential applications in radiotherapy as well as in the development of particle therapy. A brief review of the current status of particle radiotherapy with some historical perspective is presented and specific contributions made by physicists will be pointed out wherever appropriate. The rationale of using particles in cancer treatment is to reduce the treatment volume to the target volume by using precise dose distributions in three dimensions by using particles such as protons and to improve the differential effects on tumors compared to normal tissues by using highLET radiations such as neutrons. Pions and heavy ions combine the above two characteristics.The British journal of radiology 12/2011; 84 Spec No 1:S13. · 2.11 Impact Factor  SourceAvailable from: Pankaj ChaudharyPankaj Chaudhary, Thomas I Marshall, Francesca M Perozziello, Lorenzo Manti, Frederick J Currell, Fiona Hanton, Msci, Stephen J Mcmahon, Joy N Kavanagh, Giuseppe Antonio, Pablo Cirrone, Francesco Romano, Kevin M Prise, Giuseppe Schettino, P Chaudhary, T Marshall[Show abstract] [Hide abstract]
ABSTRACT: The biological optimization of proton therapy can be achieved only through a detailed evaluation of relative biological effectiveness (RBE) variations along the full range of the Bragg curve. The clinically used RBE value of 1.1 represents a broad average, which disregards the steep rise of linear energy transfer (LET) at the distal end of the spreadout Bragg peak (SOBP). With particular attention to the key endpoint of cell survival, our work presents a comparative investigation of cell killing RBE variations along monoenergetic (pristine) and modulated (SOBP) beams using human normal and radioresistant cells with the aim to investigate the RBE dependence on LET and intrinsic radiosensitvity.International journal of radiation oncology, biology, physics. 06/2014;  SourceAvailable from: Marco DuranteRebecca Grün, Thomas Friedrich, Michael Krämer, Klemens Zink, Marco Durante, Rita EngenhartCabillic, Michael Scholz[Show abstract] [Hide abstract]
ABSTRACT: Purpose: Proton radiotherapy is rapidly becoming a standard treatment option for cancer. However, even though experimental data show an increase of the relative biological effectiveness (RBE) with depth, particularly at the distal end of the treatment field, a generic RBE of 1.1 is currently used in proton radiotherapy. This discrepancy might affect the effective penetration depth of the proton beam and thus the dose to the surrounding tissue and organs at risk. The purpose of this study was thus to analyze the impact of a tissue and dose dependent RBE of protons on the effective range of the proton beam in comparison to the range based on a generic RBE of 1.1.Methods: Factors influencing the biologically effective proton range were systematically analyzed by means of treatment planning studies using the Local Effect Model (LEM IV) and the treatment planning software TRiP98. Special emphasis was put on the comparison of passive and active range modulation techniques.Results: Beam energy, tissue type, and dose level significantly affected the biological extension of the treatment field at the distal edge. Up to 4 mm increased penetration depth as compared to the depth based on a constant RBE of 1.1. The extension of the biologically effective range strongly depends on the initial proton energy used for the most distal layer of the field and correlates with the width of the distal penumbra. Thus, the range extension, in general, was more pronounced for passive as compared to active range modulation systems, whereas the maximum RBE was higher for active systems.Conclusions: The analysis showed that the physical characteristics of the proton beam in terms of the width of the distal penumbra have a great impact on the RBE gradient and thus also the biologically effective penetration depth of the beam.Medical Physics 11/2013; 40(11):111716. · 2.91 Impact Factor
Page 1
The potential impact of relative biological effectiveness
uncertainty on charged particle treatment prescriptions
1B JONES, MSc, MD,1T S A UNDERWOOD, MPhys and2R G DALE, PhD, FlnstP
1Gray Institute for Radiation Oncology and Biology, University of Oxford, Headington, Oxford, UK, and2Department of
Radiation Physics and Radiobiology, Imperial College Healthcare NHS Trust, London, UK
ABSTRACT. There continues to be uncertainty regarding the relative biological
effectiveness (RBE) values that should be used in charged particle radiotherapy (CPT)
prescriptions using protons and heavier ions. This uncertainty could potentially offset
the physical dose advantage gained by exploiting the Bragg peak effect and it needs to
be clearly understood by clinicians and physicists. This paper introduces a combined
radiobiological and physical sparing factor (S). This factor includes the ratio of the most
relevant physical doses in tumour and normal tissues in combination with their
respective RBE values and can be extended to contain the uncertainties in RBE. S factors
can be used to study, in a simplified way for tentative modelling, those clinical
situations in which highlinear energy transfer (LET) irradiations are likely to prove
preferable over their lowLET counterparts for a matched tumour isoeffect. In cases
where CPT achieves an excellent degree of normal tissue sparing, the radiobiological
factors become less important and any uncertainties in the tumour and healthy tissue
RBE values are correspondingly less problematic. When less normal tissue sparing can
be achieved, however, the RBE uncertainties assume greater relevance and will affect
the reliability of the doseprescription methodology. More research is required to
provide accurate RBE estimation, focusing attention on the associated statistical
uncertainties and potential differences in RBE between different tissue types.
Received 24 August 2010
Revised 18 November 2010
Accepted 25 November
2010
DOI: 10.1259/bjr/36792876
’ 2011 The British Institute of
Radiology
Conventional megavoltage Xray therapy almost in
variably makes use of physical dose planning to identify
the best achievable dose distributions. For any given
physical dose plan, manipulation of the treatment frac
tionation (total dose, fraction size, overall time etc.) may
then be used to secure further improvements in the
therapeutic index. Fractionation allows sublethal radia
tion damage in all irradiated tissues to be repaired be
tween fractions, with the overall repair capacity varying
between tissues and tumour types. As lateresponding
normal tissues usually possess more repair capacity than
do tumours, the use of small or modestsized fractions,
rather than larger fractions, is more likely to spare such
tissues preferentially. This consideration is particularly
important when treatment volumes are large, or if they
extend significantly into critical normal tissues such as
the spinal cord, lung, kidney, bowel etc.
In contrast to conventional Xray therapy, charged
particle therapy (CPT) using hadrons (such as protons)
or heavier ions (such as helium or carbon) entails the use
of Bragg peaks to deposit dose far more selectively in
tumours, with a potentially large reduction in normal
tissue dose. CPT dose prescriptions must take account of
the changed relative biological effectiveness (RBE) as,
compared with Xrays, less physical dose is required to
produce a given biological effect. RBEs vary from around
an average of 1.1 for protons to 1.4–5.0 or more for
helium or carbon ions [1, 2]. These high RBEs are a
consequence of raised linear energy transfer (LET),
which in simple terms represents the local intensity of
energy transfer by ionisation on a microscopic scale,
normally expressed in units of kiloelectronvolts per
micrometre. Owing to the enhanced complexity of
deoxyribonucleic acid (DNA) damage that occurs with
increased LET, however, cellular DNA repair mechan
isms are less effective for radiation with higher RBE
values. This means that treatment dose plans involving
highLET radiation are less fractionsizedependent than
those for megavoltage Xray therapy. Nevertheless, some
residual fractionation effect will remain in most clinical
applications of highLET radiotherapy because CPT
inherently involves a mixture of low and highLET
radiation present before the Bragg peak and highLET
radiation present within the Bragg peak.
The analysis used here makes use of the linear
quadratic (LQ) formulation for low and highLET
radiations, and allows for the systematic change in RBE
that occurs with changing dose per fraction. This follows
from including two fundamental RBE parameters within
biological effective dose (BED) equations: the maximum
RBE value (RBEmax) at near zero fraction dose and the
lower limit of RBE (RBEmin) at very high fraction dose
[3, 4]. These RBE parameters are shown within the
BED equation in Appendix A as Equation A1. These two
parameters can be used to calculate a ‘‘working’’ RBE at
a specified dose per fraction. The classical definition of
RBE is the ratio of doses for the two forms of radiation
Address correspondence to: Professor Bleddyn Jones, Gray Institute
for Radiation Oncology and Biology, University of Oxford, Old
Road Research Campus, Headington, Oxford OX3 7DQ, UK. Email:
Bleddyn.Jones@rob.ox.ac.uk
The British Journal of Radiology, 84 (2011), S61–S69
The British Journal of Radiology, Special Issue 2011 S61
Page 2
when given as a single fraction or in equal numbers of
fractions. In the case of multiple fractions, the ratio of iso
effect total doses can be used to express a different
‘‘fractionated RBE’’. However, use of the BED method
allows calculation of both dose per fraction and fraction
numbers required for high and lowLET isoeffects.
We intend that this article should be understood by
both clinical physicists and medical personnel and hence
we have used a necessarily simplified approach, but one
which expresses ideas with potential clinical relevance.
This approach has similarities to the US and Japanese
practical guidelines for proton and ion beam therapy,
where constraints are defined routinely at welldefined
tissue points, such as the spinal cord surface, midspinal
cord or optic chiasm, or using the maximum allowable
skin dose. The use of volumerelated models to predict
normal tissue complication probabilities are not used in
this article because of their requirement for many addi
tional assumptions and their lack of validation in clinical
practice.
Methods
TheterminologybelowusessuffixesofL andH forlow
and highLET, respectively. Let the tumour dose per
fraction at the prescription point be zHfor highLET and
zLfor lowLET radiations. As RBE is the ratio of the low
to highLET single doses (or dose per fraction) necessary
for a given biological isoeffect, then the required value of
zHin the highLET case may be calculated from the RBE
specific to the tumour volume (RBEtum) by:
zH~
zL
RBEtum
ð1Þ
Equation 1 represents the isoeffective dose conversion
required when the fraction number is the same for both
the high and lowLET cases. In practice, when the
fraction numbers differ, RBEtumcan be determined by
application of Equation A2, which calculates the RBE
required for use in Equation 1.
In most forms of radiotherapy, but especially in CPT, a
degree of physical normal tissue sparing is expected,
such that the physical dose (dH) to a critical region of
normal tissue (e.g. the maximum or modal dose given to
a clinically relevant normal tissue point or volume
according to local anatomical constraints) is given by:
dH~zHPH
ð2Þ
where PH is the physical sparing factor of highLET
radiation and is the fraction of the tumour dose (zH) that
is delivered to the normal tissue. Ideally, PHshould be as
small as possible. For lowLET radiation, the associated
sparing will probably be less, i.e. the physical sparing
factor (PL) will be greater than PH. For example, if a
vertebral tumour is given a dose zLby low LET or zHby
high LET, the dose at the surface of the spinal cord a few
millimetres away might be PH6zH5dHin the highLET
case and PL6zL5dLin the lowLET case.
Using Equations 1 and 2, the normal tissue highLET
dose per fraction, dH, can be converted back to an
equivalent lowLET dose per fraction, (dLeq) by use of the
normal tissue RBE (RBEnorm),to give:
dleq~zHPHRBEnorm
ð3Þ
where zH6PHreplaces dH, which is itself obtained from
the prescription dose zHby multiplying it by the high
LET sparing factor PH(Equation 2).
Then by substituting zHfrom Equation 1:
dLeq~zLPHRBEnorm
REBEtum
ð4Þ
For the lowLET radiation, the normal tissue dose is:
dL~zLPL
ð5Þ
where PL is the physical sparing factor for low
LET radiation and PH,PL in most circumstances.
Combining Equations 4 and 5 and rearranging the terms
leads to:
dleq
dL~PH
PLRBEnorm
RBEtum
ð6Þ
which can be written as:
S0~PH
PLRBEnorm
RBEtum
ð7Þ
where S05dLeq/dLand represents the combined physical
and radiobiological sparing. S0, which could also be
called the biological sparing advantage factor, needs to
be as small as possible for particle therapy to have
advantage over conventional Xray therapy. It is clear
that the precise value of S0not only will depend on the
physical dose sparing ratio but will also be highly
sensitive to errors made in estimating RBE for both
tumours and normal tissue, especially as the RBEs are
themselves dependent on fraction size and tissue cell
kinetics. To give an S factor that includes error terms (SI),
the errors in the estimation of RBE values can be
incorporated as multiplicative terms on the normal
tissue and tumour RBEs values (defined as Errordand
ErrorZ, respectively):
SI~PH
PLRBEnorm
RBEtum1+Errord
ð
ð
Þ
Þ
1+Errorz
ð8Þ
The error term can be treated simply as a factor from 0 to
1 or as a percentage change. For example, if the RBE is
assumed to be 3, while it is actually 1.5 in a particular
tissue of interest, this represents a 50% error, whereas if
the actual RBE is 6, there is a 100% error. In Equation 8,
such an error of 50% would be included as a factor of 0.5,
an error of 30% as 0.3 etc. For the highLET case to be
advantageous relative to lowLET, SImust be less than
unity, and for optimal healthy tissue sparing, SIshould
be kept as low as possible.
Modelling parameter assumptions
The examples in this paper are not intended for
practical use, but rather to illustrate the general prin
ciples involved.
B Jones, T S A Underwood and R G Dale
S62The British Journal of Radiology, Special Issue 2011
Page 3
For such purposes, it is assumed that:
carbon: RBEmax59.8, RBEmin51.3
protons: RBEmax53.3, RBEmin51.0.
These values are based on V79 cell line data [5, 6],
where a and b were investigated as functions of LET for
carbon ions and protons, respectively (in both cases
compared with Xray radiation). RBEmax and RBEmin
were calculated for all LET values investigated in the
papers, and the values considered here correspond to the
LETs associated with the greatest differential between
RBEmaxand RBEmin. These were 153.5keVmm–1for car
bon and 20keVmm–1for protons. V79 cells probably pro
vide a poor representation of human cells in vivo, but it
must be stressed that there is a lack of available data on
this topic, and the values employed here are for illu
strative purposes. For protons, an RBEmaxof 3.6 may be
applicableto the last fewmillimetres of a Bragg peak only.
For this reason, the following (realistic spread out Bragg
peak) RBEmaxparameters are also considered, where an
error increment of 10% is applied to the standard clinical
RBE values of 1.1 for protons and 3 for carbon ions, so that
for most practical situations we assume:
carbon: RBEmax53.3, RBEmin51.3
protons: RBEmax51.2, RBEmin51.0.
In both cases, RBEminis maintained at the estimates
indicated above (from [5, 6]). In the absence of further
data, the RBE values were assumed to be the same in the
normal tissue and the tumour but with use of generic,
lowLET, a/b values of 3 Gy for normal tissues and
10 Gy for tumours, unless otherwise stated.
The equations given in Appendix A (A3–A6) provide
a working RBE function that expresses an effective
dose multiplying factor as the ratio of the dose per
fraction for low LET divided by the highLET dose
per fraction. These calculations utilise the fractional doses
for both low and highLET radiations. In the case of
unequal fractions, the total dose provides the working
RBE: the dose per fraction is multiplied by the number of
fractions in each case. For inclusion within the S factor,
however, the ratios of RBEs are required for the normal
and tumour tissues, as shown in Equation 8 above. These
ratios can be expressed as:
RBEnorm
RBEtum
~
NLdLeq
NHdH
NLzL
NHzH
?
?
?
? ~
dLeq
dH
zL
zH
?
?
?
?
ð9Þ
So, it is only necessary to include the ratios of the dose
per fraction within the S factor, although the solution for
dose per fraction in the normal tissue and tumour cases
will include the relevant fraction numbers as given in
Equations A2 and A5.
The sequence of the computer programming to obtain
S is given at the end of Appendix A.
Results and worked examples
Considering the effects of errors
To assume a worstcase scenario, from Equation 8 let
the errors be of equal magnitude and include a positive
error on the numerator (increasing the assumed normal
tissue RBE) and a negative error on the denominator
(decreasing the assumed tumour RBE). This gives:
Sw~PH
PLRBEnorm
RBEtum
1zError
1{Error
ð10Þ
where Sw now represents the worstcase scenario for
equal errors on both healthy tissue and tumour RBE
values. Uncertainties in RBE values might also prove
favourable and a bestcase scenario, Sb(where the signs
of the errors in the numerator and denominator are
reversed) can also be considered. The two extremes are
shown in Figure 1, where equal physical sparing for both
the high and lowLET radiations has been assumed
(PH5PL).
Figure 1 shows that relatively modest errors in
assumed RBE values can potentially change the S factors
by significant amounts. For example, in the case of Sw, a
20% error in both normal tissue and tumour RBE values
would increase S by 50%. For highLET therapy to
remain the better treatment option in the presence
of such errors, a new requirement would be placed
on the highLET physical dose sparing factor (PH): it
would have to be reduced by a factor of onethird (as
shown in Table 1). This example highlights the interplay
between physical dose sparing and RBE uncertainty. If
incorrect RBE values (as in the worstcase scenario)
are used in dose prescriptions, then increased reliance is
placed on the dose sparing capability of highLET
radiation to provide the desired improvement over
the lowLET case. In such instances, alternative low
LET therapies, such as Xraybased intensity modulated
radiotherapy, may be a less speculative treatment option
because there is no reliance on RBE estimation.
Figure 1. The percentage change in S as a function of the
percentage errors in relative biological effectiveness (RBE)
for the best (Sb) and worstcase (Sw) scenarios, where the
RBE errors are assumed to be equal for both normal tissue
and tumour and with PHset equal to PL. PH, physical sparing
factor of high linear energy transformation; PL, physical
sparing factor of low linear energy transformation.
Impact of RBE uncertainty on charged particle treatments
The British Journal of Radiology, Special Issue 2011 S63
Page 4
Magnitude of RBE errors
Paganetti et al [7] concluded (from experimental in
vitro and in vivo data) that a generic RBE value of 1.1 for
proton therapy could reasonably be employed. This
conclusion was based on the desirability of using a ‘‘one
number’’ RBE correction factor in clinical protocols.
However, the RBE value was obtained using fast
growing cells and tissue assays with high a/b ratios.
Such experiments may not adequately provide the true
RBEs for late reacting issues, which have low a/b ratios.
The need for further work to reduce the uncertainty in
RBE values for specific tissue, dose per fraction, proton
energy etc. was also highlighted by the group. They
found the average RBE value at mid spreadout Bragg
peak in vivo to be 1.1, but their data had a range of 0.7–1.6
(i.e. 236% to +45% relative to 1.1). Taking these
percentages and applying them as errors to both normal
tissue and tumour RBEs as in Equation 9, in the best case
the S factor would be reduced by 64%, and in the worst
case it would be increased by <127%.
The effects of fractionation
Using the LQ (linear quadratic model of radiation
effect)based equations given in Appendix A and the
RBEmaxand RBEminvalues quoted in the methods sec
tion, the combined radiobiological and physical normal
tissue sparing factor, S (as defined in Equation 8 and
referred to as S in all further plots), was determined for
different numbers of highLET fractions (Figures 2–5). In
each case, the number of lowLET fractions was main
tained at 30 using a dose of 2 Gy per fraction and the
highLET dose per fraction gave the same tumour BED.
The effect of increasing the number of fractions for
carbon ions is shown in Figure 2 for a range of assumed
errors in RBE where 0.2, for example, indicates a 20%
error set in the worstcase direction. For assumed RBE
errors of 20%, and where PLis 0.8, then to maintain an S
ratio below unity, PHvalues below approximately 0.5 are
required for the single fraction case (Figure 2a), PHvalues
of below approximately 0.6 for the 4fractions case
(Figure 2b) and PHvalues of approximately 0.7 for the
15fractions case (Figure 2c). In general, the S values for all
levels of error improve with fractionation. Similarly, for
the proton examples, we obtain S ratios below unity for PH
values of ,0.45, 0.5 and 0.6 for fraction numbers of 1, 15
and 30, respectively (Figure 3).
The influence of a change in the Xray normal tissue
sparing ratio (PL) is shown for carbon and protons in
Figure 4. The achievement of good sparing with Xrays
requires even greater sparing with CPT if these therapies
are to provide a therapeutic improvement; for example, if
Xraysachieveasparingfactorof0.7,sparingfactorsofless
than 0.5 and 0.45 are needed for CPT involving carbon and
protons, respectively (assuming that the RBE estimates are
unfavourable and in the worse direction by 20%).
The separate influence of tumour a/b ratio on the S
ratio is shown for carbon and protons in Figure 5. The
variation of S with changing a/b ratio is greater for
carbon ions than for protons because of the larger range
of RBE values for carbon. The proton relationship
shifts towards the carbon relationship if extreme hypo
fractionation is used, in which case the lowest a/b
tumour ratio becomes the lowest curve (such graphics
are not reproduced here because of space restrictions).
For isoeffective tumour control (without accounting for
repopulation), the increment in S is greatest for low
fraction numbers. This shows that fractionation pro
cesses continue to exert a change in S.
It is clear that hypofractionation is capable of provid
ing good therapeutic ratios provided that the normal
tissue sparing is good. When good physical dose sparing
cannot be achieved with highLET radiation, increased
fraction numbers are likely to be a better option. In
most cases, the modelled worstcase scenario (derived
using Equation 8) implies that hypofractionation will
be justified only if a very good PH of (0.3 can be
achieved (i.e. if the physical dose to the clinically relevant
Table 1. Worked example
Applying 20% errors to Equation 10:
Sw, 20%~PH
PL
RBEnorm
RBEtum
1z0:2
1{0:2
??
ð10Þ
gives:
Sw, 20%~PH
PL
RBEnorm
RBEtum
3
2
??
ð11Þ
substituting S0, the S value assumed prior to the consideration of RBE errors (Equation 7) into Equation 11:
Sw, 20%~S03
2
ð12Þ
Thus, for S0to be maintained in the case of Sw,20%, the highLET physical dose sparing factor, PH, would have
to be reduced by onethird:
Sw, 20%~ PH2
3
??
1
PL
RBEnorm
RBEtum
3
2
??
[Sw, 20%~S0
ð13Þ
H, highLET transformation; L, lowLET transformation; LET, linear energy transfer; norm, normal tissue RBE; P, physical sparing
factor; RBE, relative biological effectiveness; S, sparing factor; tum, tumour volume RBE; w, worstcase scenario.
B Jones, T S A Underwood and R G Dale
S64The British Journal of Radiology, Special Issue 2011
Page 5
volume of healthy tissue is (30% of the tumour
prescription dose). Even better degrees of sparing are
required if the RBE uncertainty is greater. If the error in
RBEmay operateinthe oppositedirection,however,these
constraints will not be so marked but other dangers may
ensue. For example, if RBE is generally underestimated in
both tumour and normal tissue, then the tumour dose will
be greater than expected. Should the Bragg peaks be
inadvertently located within normal tissue (or include
normal tissue as an intended margin) in such cases,
however, normal tissue would be overdosed. The level of
uncertainty in RBE that should be accepted has yet to be
decided on an international basis.
Discussion
This provisional study has shown only a small number
of the many complex interactions that affect treatment
planning. Further modelling along these lines should aid
the process of treatment plan acceptance when there is a
choice between CPT and Xray therapy. The overall
process of prescribing highLET CPT is more complex
than that for megavoltage Xraybased radiotherapy and
must include consideration of RBE, which is itself related
to dose and modified by local LET values. Because of
this, greater care and a good appreciation of radio
biological effects are required to ensure that CPT is
administered optimally. The literature currently contains
active discussion regarding both the potential merits of
using variable rather than fixed RBE values and the role
of fractionated vs singledose RBEs [1, 2, 7–12]. We have
adopted a definition of RBE that is based on the ratio of
high and lowLET radiations in the dose per fraction
rather than in the total dose because dose per fraction is a
single entity rather than a combination of two para
meters. Total doses can be misleading if not qualified by
dose per fraction.
Although the S factor contains the essential parameters
for tentative modelling purposes, it is not intended
for direct clinical application; rather it represents the
possible form of an (as yet) incomplete methodology that
contains both fractionation and RBE effects. The S factor
can, in principle, be extended to more complex volume
based situations. Importantly, it also allows for the
calculation of an isoeffective highLET fraction dose
when the number of highLET fractions differs from the
(a)
(c)
(b)
Figure 2. Relationship between S ratio and degree of normal sparing (PH) achieved by carbon ions for variation in error of relative
biological effectiveness (RBE) used. PLis assumed to be 0.8. The ‘‘ERROR FACTOR’’ key describes the assumed error in RBE where 0.2,
for example, indicates a 20% error set in the worstcase direction. (a) Only 1 high linear energy transfer (LET) fraction, (b) 4 highLET
fractionsor(c)15highLETfractionswereusedtogiveanisoeffectivetumourdoseequivalenttothatgivenby30fractionsof2 Gyof
lowLET Xrays.
Impact of RBE uncertainty on charged particle treatments
The British Journal of Radiology, Special Issue 2011 S65
Page 6
(a)
(c)
(b)
Figure 3. Relationship between S ratio and degree of normal sparing (PH) achieved by protons for variations in error of relative
biological effectiveness (RBE) used. PLis assumed to be 0.8. The ‘‘ERROR FACTOR’’ key describes the assumed error in RBE where
0.2, for example, indicates a 20% error set in the worstcase direction. (a) Only one high linear energy transfer (LET) fraction, (b)
15 highLET fractions or (c) 30 highLET fractions were used to give an isoeffective tumour dose equivalent to that given by 30
fractions of 2 Gy of lowLET Xrays.
(a) (b)
Figure 4. (a) Relationship between S ratio and the degree of normaltissue sparing for carbon ions (PH) at varying amounts of X
ray sparing of normal tissues (PL). 15 high linear energy transfer (LET) carbon fractions were given compared with 30 treatments
of lowLET Xray radiation (at 2 Gy dose per fraction). (b) Relationship between S ratio and the degree of normal tissue sparing
for protons (PH) at varying amounts of Xray sparing of normal tissues (PL). 30 ‘‘high LET’’ proton treatments were given, the same
as for lowLET Xrays.
B Jones, T S A Underwood and R G Dale
S66 The British Journal of Radiology, Special Issue 2011
Page 7
number of lowLET fractions, while taking into account
the classical definition of RBE. The normal tissue RBE
term within S, if found using the equations given in
Appendix A, will contain the normal tissuesparing
factor as dose per fraction determines RBE. This does not
undermine the validity of this approach as long as these
parameters are included and RBE values are not just
assumed.
Despite the dose improvements afforded by the Bragg
peak effect, there are severe limitations in the knowledge
of accurate RBE values in most situations. Dale et al [13]
have warned that the lack of radiobiological precision in
RBE is in marked contrast to the expectation that
physical dosimetry will be of a high standard, dosimetric
errors of .10% being legally reportable in the UK and an
expected attainment of 3% accuracy being the norm. Our
study shows, however, that when the degree of normal
tissue sparing with CPT is excellent, the radiobiological
factors become less important. Another issue is the
possibility that latereacting normal tissues and slow
growing tumours could have a different (and higher)
RBE value from that of acutereacting normal tissues and
rapidly growing tumours [3]. If this is so, then additional
fractionation sensitivity constraints will be required and
we are currently working on this.
RBE exerts a very significant influence on the degree
of radiobiological normaltissue sparing that can be
achieved in highLET therapy, and it has been shown
here that errors in RBE determination can mean that the
true degree of sparing may be very different from that
which might otherwise be assumed. Consequently, it is
necessary to take the uncertainty in RBE into account,
because the error may reduce the apparent benefit of
reduced physical dose to normal tissues afforded by
highLET radiations. In many CPT applications, the
physical dose sparing may be so good that uncertainties
in RBE will have only trivial impact on the treatment
outcome. When significant volumes of normal tissue are
included in a highLET highdose target region, how
ever, these tissues could be unintentionally overdosed if
the RBE of the slowly dividing normal tissues is signi
ficantly higher than that of the tumour. Even in
apparently satisfactory situations where a small degree
of physical dose sparing is achievable by using CPT, the
apparent benefit could be overridden by wide uncer
tainties in RBE estimation.
Although the methodology used here is essentially
simplistic, it is useful for the purposes of illustrative
modelling. In reality, more than one organ at risk of
complication will be present and the principles con
tained in this study will need to be extended to include
effects in a threedimensional situation within the human
body.
For a complete and reliable decisionmaking process, it
will be necessary to know how RBE varies with fractiona
tion and LET in different tissue types. This require
ment would need considerable investment of resources to
uncover the most appropriate values in typical situations
and, more so, in individuals, with use of predictive
modelling. It may be that such knowledge will always be
incomplete. In this case, the acceptable dose in normal
tissues must include realistic RBE values within expected
limits of accuracy, so that the clinician is alerted to the
range of equivalent doses with reasonable statistical
accuracy.
The accurate prediction of RBE values remains an
essential longterm objective in this field. Various
microdosimetric systems currently claim to achieve this
[14, 15], but they involve multiple assumptions and are
essentially incomplete, with limitations at high dose.
Some have been found wanting when tested empirically
[16] and there is a tendency for these methods to
underestimate RBE. Ideally, they should be capable of
predicting uncertainties in RBE and not only point
estimates of RBE. Further research is required to achieve
this goal.
Any estimation of RBE will include multiple uncer
tainties ranging from those associated with the estima
tion of physical dose using different dosemeters to
biological variation. Typical values for the means and
standard errors (SEs) of RBEs for protons are small [7]:
mean of 1.22 and SE of 0.02 for in vitro systems and mean
of 1.10 and SE of 0.01 for in vivo systems. For fast neutrons,
the RBEs in vivo are typically approximately 3 with an
SE of approximately 0.1–0.2 [17]. An interesting study of
carbon ion RBEcarried outinGermanyandJapan showed
mean RBEvaluesof1.879andSEof0.074inGermany,and
mean RBE values of 1.906 and SE of 0.13 in Japan [18]. In
(a)(b)
Figure 5. Relationship between S ratio and degree of normal tissue sparing achieved by (a) carbon ions and (b) protons for
variations in tumour a/b ratio. PLis assumed to be 0.8. RBE, relative biological effectiveness.
Impact of RBE uncertainty on charged particle treatments
The British Journal of Radiology, Special Issue 2011 S67
Page 8
all cases, exceptions involving much larger variations are
found and thus SEs are not as informative as 95%
confidencelimitsinthesecircumstances.Furthermore,these
data are all from carefully controlled laboratory studies,
oftenusinginbredanimalsorselectedcelllines,thatwillnot
adequately reflect the variation between different human
patients and across different organ systems.
One potential method of overcoming the RBE uncer
tainty would be to reanalyse a large number of CPT
treated patients in terms of physical dose and LET and
ion species (with reference to both particle charge and
mass) in order to build up a new experience of tissue
tolerances and tumour control probabilities without the
need for prospective assumptions about RBE. With
sufficient retrospective information, it might be possible
to proceed with safe CPT without excessive reliance on
experimental or theoretical RBE values.
Our findings demonstrate the continuing influence of
fractionation inthesparingof normal tissuesathighLET.It
has been shown that the use of high fraction numbers
becomes increasingly important when excellent physical
dose sparing cannot be achieved with highLET radiation.
Thus, the trend to lower fraction numbers, for example to
extreme limits of one, two and four fractions using carbon
ions in Japan, could prove problematic if good overall
(physical plus radiobiological) sparing cannot be achieved.
This issue also imposes a demand for better predictive
modelling in order to provide a secure basis for decision
making and appropriate patient selection [19]. Until RBE
can be predicted with good accuracy, probable errors in
RBE estimation should be included as additional con
straints in the treatmentplanning process. Physicists and
clinicians embarking on CPT need to familiarise them
selves with these concepts, and further research must be
encouraged if CPT is to be used in the most optimal way.
References
1. Wambersie A, Hendry JH, Andreo P, DeLuca PM,
Gahbauer R, Menzel H, et al. The RBE issues in ionbeam
therapy: conclusions of a joint IAEA/ICRU working group
regarding quantities and units. Radiat Prot Dosimetry
2006;122:463–70.
2. Jones B. Joint Symposium 2009 on carbon ion radiotherapy.
Br J Radiol 2009;82:884–9.
3. Ca ´rabeFerna ´ndez A, Dale RG, Jones B. The incorporation of
the concept of minimum RBE (RBEmin) into the linear
quadratic model and the potential for improved radiobiologi
cal analysis of highLET treatments. Int J Radiat Biol
2007;83:27–39.
4. Jones B, Ca ´rabeFerna ´ndez A, Dale RG. Calculation of high
LET radiotherapy dose required for compensation of overall
treatment time extensions. Br J Radiol 2006;79:254–7.
5. Weyrather WK, Kraft G. RBE of carbon ions: experimental
data and the strategy of RBE calculation for treatment
planning. Radiother Oncol 2004;73 Suppl 2:S161–9.
6. Belli M, Cera F, Cherubini R, Dalla Vecchia M, Haque AM,
Ianzini F, et al. RBELET relationships for cell inactivation
and mutation induced by low energy protons in V79 cells:
further results at the LNL facility. Int J Radiat Biol
1998;74:501–9.
7. Paganetti H, Niemierko A, Ancukiewicz M, Gerweck LE,
Goitein M, Loeffler JS, et al. Relative biological effectiveness
(RBE) values for proton beam therapy. Int J Radiat Oncol
Biol Phys 2002;53:407–21.
8. Tilly N, Johansson J, Isacson U, Medin J, Blomquist E,
Grusell E, et al. The influence of RBE variations in a clinical
proton treatment plan for a hypopharynx cancer. Phys Med
Biol 2005;50:2765–77.
9. Dasu A, TomaDasu I. What is the clinically relevant
relative biological effectiveness? A warning for fractionated
treatments with high linear energy transfer. Int J Radiat
Oncol Biol Phys 2008;70:867–74.
10. Wilkens JJ, Oelfke U. Direct comparison of biologically
optimized spreadout Bragg peaks for protons and carbon
ions. Int J Radiat Oncol Biol Phys 2008;70:262–6.
11. Jones B, Dale RG. Estimation of optimum dose per frac
tion for high LET radiations: implications for proton
radiotherapy. Int J Radiat Oncol Biol Phys 2000;48:
1549–57.
12. Karger CP, Jakel O, Scholz M, Peshke P, Debus J. What is
the clinically effective relevant relative biological effective
ness? A warning for fractionated treatments with high LET
radiation: in regards to Dasu and TomaDasu. Int J Radiat
Oncol Biol Phys 2008;70:1614–16.
13. Dale RG, Jones B, Ca ´rabeFerna ´ndez A. Why more needs to
be known about RBE effects in modern radiotherapy. Appl
Radiat Isot 2009;67:387–92.
14. Scholz M, Kraft G. Track structure and the calculation of
biological effects of heavy charged particles. Adv Space Res
1996;18:5–14.
15. Hawkins RB. A microdosimetrickinetic model for the effect
of nonPoisson distribution of lethal lesions on the variation
of RBE with LET. Radiat Res 2003;160:61–6.
16. Beuve M, Alphonse G, Maalouf M, Colliaux A, Battiston
Montagne P, Jalade P, et al. Radiobiologic parameters and
local effect model predictions for headandneck squamous
cell carcinomas exposed to high linear energy transfer ions.
Int J Radiat Oncol Biol Phys 2008;71:635–42.
17. McNally NJ, De Ronde J, Hinchcliffe M. Survival of V79
cellsfollowingsimultaneous
and neutrons in air or hypoxia. Int J Radiat Biol 1985;48:
847–55.
18. Uzawa A, Ando K, Koike S, Furusawa Y, Matsumoto Y,
Takai N, et al. Comparison of biological effectiveness of
carbonion beams in Japan and Germany. Int J Radiat Oncol
Biol Phys 2009;73:1545–51.
19. Jones B, Dale RG. Radiobiological modelling and clinical
trials. Int J Radiat Oncol Biol Phys 2000;48:259–65.
irradiationwithXrays
Appendix A
Tumour RBE values are found by solving the iso
effective BED relationship for zL(the lowLET tumour
dose per fraction). Variables within this relationship are
the assumed RBE limits of RBEmax(the RBE at very low
dose per fraction) and RBEmin(the RBE at very large dose
per fraction), both designated by the prefix ‘‘tum’’.
For isoeffective conditions, lowLET BED5highLET
BED, so,
NLzL 1z
zL
ð
tum a=b
Þ
??
~NHzH
tumRBEmaxztumRBE2
minzH
Þ
tuma=b
ð
??
ðA1Þ
where NLis the number of lowLET fractions, NHis the
number of highLET fractions, zLis the lowLET tumour
dose per fraction, zHis the highLET tumour dose per
fraction andtum(a/b) is for the lowLET tumour case.
The value of zH is the solution of Equation A1,
that is:
B Jones, T S A Underwood and R G Dale
S68The British Journal of Radiology, Special Issue 2011
Page 9
zH~
{tum
a
b
? ?
NHtumRBEmaxz
ffiffiffiffiffiffiffi
NH
p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
bb
2NHtumRBEmin2
tum
a
? ?2
NHz4zLtum
a
? ?
NLtumRBEmin2z4NLzL2tumRBEmin2
s
ðA2Þ
It should be noted that if NL5NHthe last equation will
not contain these fractionation numbers, since they will
cancel in Equation 1.
It then follows that the ‘‘working’’ tumour RBE is zL
divided by zH, so
tumRBE~
zL2NHtumRBEmin2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
bb
e{tum
a
b
? ?
NHtumRBEmaxz
ffiffiffiffiffiffiffi
NH
p

tum
a
? ?2
NHz4zLtum
a
? ?
NLtumRBEmin2z4NLzL2tumRBEmin2
s
ðA3Þ
Similarly, for normal tissues, using the prefixes ‘‘norm’’,
the isoeffect is defined by
NLdLeq 1z
dLeq
ð
norma=b
Þ
??
~NHdH normRBEmaxznormRBEmin2dH
norma=b
ðÞ
??
ðA4Þ
where dHis the highLET normal tissue dose per fraction
andnorm(a/b) is for the lowLET normal tissue.
Then the ‘‘working’’ RBE (defined here as dLeq/dH) is
given by the solution of Equation A3 for dLeq, which is:
dLeq~
{norm
a
b
? ?
NLz
ffiffiffiffiffiffiffi
NL
p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
bb
2NL
norm
a
? ?2
NLz4dHnorm
a
? ?
NHnormRBEmaxz4dH2NHnormRBEmin2
s
ðA5Þ
It then follows that the ‘‘working’’ RBE of the normal
tissues is given by dLeqdivided by dH, which is
normRBE~
{norm
a
b
? ?
NLz
ffiffiffiffiffiffiffi
NL
p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
bb
2dHNL
norm
a
? ?2
NLz4dHnorm
a
? ?
NHnormEmaxz4dH2NHnormRBEmin2
s
ðA6Þ
In both tumour and normal tissue cases, the RBE
concept can be extended to schedules that have different
fractionation plans (i.e. where NLis different from NH).
Then, the ‘‘fractionated RBE’’ will be:
(lowLET dose per fraction 6 number of low
LET fractions) divided by (highLET dose per frac
tion 6 number of highLET fractions). However,
the working RBE in terms of dose per fraction (i.e.
Equations A3 and A6) can be used in Equation 8
because the fraction numbers cancel, as explained
above.
Programming sequence for calculating S:
1. Set zL as the prescribed tumour dose and find zH
using equation A2.
2. Find the working tumour RBE from Equation A3.
3. Find dHby multiplying zHby PH.
4. Find dLeqfrom equation A5 and then the working
normal tissue RBE from Equation A6.
5. S is found from Equation 8 by allocation of the
physical sparing factors and the two working RBEs
together with an RBE error.
Impact of RBE uncertainty on charged particle treatments
The British Journal of Radiology, Special Issue 2011S69
An error occurred while rendering template.
gl_544d6d8ad3df3e6c378b465b
rgreq438be3b059c34dba8682a927931be153
false