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Quantitative Radiobiology for Proton Therapy
Figure 5.2. (a) and (b): Plots of (a) RBE
from Jones et al. (
Press.
2011). Copyright (2014) The British Institute of Radiology. Published by Oxford University
Another consequence of the fact that the overall RBE is controlled by RBE
and RBE
, and that these parameters are, respectively, inversely and directly
min
and (b) RBE
max
against the reference low-LET α/β ratio. Adapted
min
max
related to the reference radiation α/β ratio or its square root (see Appendix A of this
chapter), then a practical RBE for a clinically used dose cannot be assumed to be
only related to RBE
. Mathematical models that predict RBE from the inverse or
max
reciprocal value of α/β must be incomplete. A better approach, shown in chapters 8
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Quantitative Radiobiology for Proton Therapy
Figure 5.3. (a) and (b): Relationship between (a) fast neutron dose per fraction and RBE for different α/β
ratios, and (b) the transformation of the above to provide a near-flat response for α/β of 10 Gy to simulate
proton data, as discussed in chapters
behave (α/β = 2 Gy), followed by a gradual change in α/β to faster-growing systems such as many rapidly
growing tumour types and acute-reacting normal tissues (α/β = 10 Gy).
7 and 9. The red curves suggest how brain and spinal cord tissues may
and 9, enable separate modification of α and β with increasing LET, and
consequently allow the RBE to be related to the reciprocal of α/β at low dose,
but to be dependent on √(α/β) at high dose, with a gradual transition between these
two limits with change of dose.
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Quantitative Radiobiology for Proton Therapy
Figure 5.4. Plotted data of the β-parameter for x-rays and neutrons. Cell lines labelled C and B were excluded
due to known radiation repair deficiencies and extreme values, β being difficult to measure when α is high.
Reproduced from Jones (
University Press.
2010). Copyright (2014) The British Institute of Radiology. Published by Oxford
Warenius and colleagues (Warenius & Britten 1994, Warenius et al 1994)
identified that the respective rank order of radiosensitivities for photons and
neutrons were not the same. This is a consequence of the above transition between
RBE
and RBE
max
and other effects such as the saturation or reduction of RBE
min
increments with increasing intrinsic (photon) radiosensitivity. This is discussed
further in chapter 9 with estimations of what might be expected for protons.
It has also been shown that the LET values produced by fast neutrons increases
the α radiosensitivity parameter by a factor of 3.17, but the β parameter increases as
1.59√β on average. Previously, it was thought that β did not increase with LET (as
evidenced in meticulous experiments involving only one cell line, the V-79 cell line
by Chapman 2003); but the Clatterbridge in vitro neutron data set contained over 20
cell lines, and the increase in β can be seen in figure 5.4 (Jones 2010).
There now remain very few advocates for neutron therapy in the world. In fact,
the only promising development for neutrons is arguably boron neutron capture
therapy—a complex binary therapy that involves a low-dose exposure to thermal or
epithermal neutrons which are selectively captured by boron-labelled molecules
taken up by rapidly growing tumour cells. The reaction creates more intense
localised ionisation by generating an alpha particle and a lithium ion, with tissue
ranges of only around 10 μm (around one cell diameter). Some pilot studies have
shown promise in highly malignant brain tumours or for recurrent tumours,
although in uncontrolled, highly selected patients (Kageji et al 2014, Lim et al
2015). Further discussion is beyond the scope of this book.
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Quantitative Radiobiology for Proton Therapy
Figure 5.5. Plot of tissue depth distance beyond a target volume and neutron dose, with estimated photon
equivalent dose and RBE. The assumptions made were an exponential attenuation coefficient of 0.1 cm
RBE
= 5, RBE
max
exit dose is considered.
= 1.3, intrinsic photon α/β = 3 Gy, in a multiple field arrangement where only a single
min
−1
Following the clinical fast neutron trials, the UK funding authorities decided not
to invest in further ambitious radiation projects, and as a result a general decline in
radiotherapy research followed, although the Clatterbridge cyclotron was successfully adapted for proton therapy in the eye. There emerged a clinical scepticism
regarding the use of cyclotrons in radiotherapy and high-LET radiations in general.
In other countries, more progress was achieved using charged-particle therapy
(protons or light ions) produced from cyclotrons or the larger synchrotrons. Some of
these countries had no prior experience of high-LET radiations in the form of
neutrons.
The extensive late tissue side effect of fibrosis (scarring) was prominent around
neutron-treated volumes. Although the falloff of dose was broadly the same in the
Clatterbridge trials, the reduction in neutron dose beyond a target volume will result
in an increased RBE because of the inverse relationship between RBE and dose per
fraction. Figure 5.5, which follows the dose falloff with distance beyond a target
volume, uses the RBE BED isoeffect equations to estimate the equivalent photon
dose and also provides the operative RBE value. It can be seen that the RBE
becomes progressively larger with increasing depth due to the lower dose per
fraction, which drives the equivalent photon dose to be higher than the actual
photon dose. The latter is higher than the neutron dose by a value determined by the
single (or constant) RBE used in the prescription process, in this case an RBE of
2.43. Thus the tissue effect will be the same as if the higher dose of photons had been
used.
,
5-12
Quantitative Radiobiology for Proton Therapy
Figure 5.6. Plots of equivalent dose in 2 Gy fractions for a fractional exposure, based on figure 5.5. The brown
curve is the simulated photon exit dose from a single beam and the grey curve the isoeffective photon dose
provided by the fast neutron beam.
These results can be converted into BED estimates and then to EQD-2 (the
equivalent dose in 2 Gy fractions) for each fraction, as displayed in figure 5.6, where
it can be seen more clearly than in figure 5.5 that there is a ‘triangle’ of unintended
excess dose over the first 3.65 cm beyond the target which is caused by the neutron
RBE. This excess dose might contribute to fibrosis development since there will be a
greater volume of tissue exposed to a higher than intended dose. The dose-volume
effect on normal tissue tolerances is substantial, as discussed in chapters 3 and 4.
Over this initial distance of 3.65 cm from the target volume, the mean EQD-2 for the
photon beam is 1.03 Gy per fraction, but the equivalent mean EQD-2 of the neutron
beam is estimated to be 1.59 Gy per fraction. This excess dose will probably make a
significant contribution to fibrosis development since there will be a greater volume
of tissue exposed to a higher than intended dose. The dose-volume effect on normal
tissue tolerances is substantial, as discussed in chapters 3 and 4, although there is no
adequate predictive model, which is probably a consequence of the local vascularity
pattern having different spatial distributions according to the precise anatomical
location.
A major radiotherapy research question over the next few decades will be whether
carbon ions are superior to protons in specific cancers, because of better beam
ballistics and dose localisation and/or the apparent greater reduction in the oxygen
effect. Suit et al (2010) have pointed out that since even the neutron studies did not
show a convincing overall local tumour control improvement, it should not be
expected that carbon ions will provide improved efficacy since the oxygen effect
dependency is greater for spread-out carbon-ion peaks than for fast neutrons (OER
ratios of around 1.8–2 compared with 1.6–1.8, respectively).
5-13
Quantitative Radiobiology for Proton Therapy
The process of reoxygenation in tumours during radiotherapy, lasting a week or
more, may be the reason why hypoxic radioresistance is not especially important;
dose escalation for hypofractionation may also overcome initial hypoxia. But it is
intriguing that identification of tumours with slow reoxygenation kinetics may yet be
important since high-LET therapy and dose escalation may be important. Again,
the reality of treating tumours in situ appears more difficult than the in vitro
treatment of cells, for many reasons.
5.5 Estimation of neutron RBE from neutron energy
Further analysis of the important Clatterbridge neutron-photon data sets and
other detailed RBE studies by Hall et al (1975) was written during the COVID-19
pandemic by the present author (see Jones 2021), where many further references
can be found. To predict the neutron RBE, it was assumed that recoil proton
energies of around 50% of the neutron energy would be mainly responsible for
RBE e ffect s, and on this basis a predictive model was constructed, which is
described below.
It is known that roughly half the dose due to megavoltage neutrons is due to recoil
(elastically scattered) protons, mainly from hydrogen atoms in the biological systems
or in water. The remaining half consists of 10%–35% from nuclear recoils (elastic
neutron scattering) and 35%–40% from neutron-generated light ions (including
protons, deuterons, tritons,
have their own LET–RBE relationship. Furthermore, the neutron energies in most
beams form part of a spectrum, and consequently the neutron products will also
have their related energy distributions.
The present report describes a tentative and approximate method for estimating
fast neutron RBE values by considering elastically scattered recoil proton energies
and their LET values and assumes a proportional averaged higher LET contribution
from all other ionic products including non-elastic (nuclear) scattering.
A diagram of the nuclear events which lead to the radiobiological change in the α
parameter is shown in figure 5.7.
The link between neutron energy, proton recoil energy and LET is obtained by
listing outputs of LET for proton kinetic energies (assumed to be half those of the
relevant neutrons) in liquid water by using the SRIM software package (see Jones
2021). The outputs form a non-linear relationship, the obtained function F[Pr]LET,
to express proton recoil LET with changes in neutron kinetic energy (NKE) by the
sum of three-exponential functions as
F Pr LET 73.55e 21.05e 5.04e .
[]
=++
3
He and alpha particles). Each of these ionic species will
−−−
1.64 NKE 1.65 NKE 0.016 NKE
5.1
()
This function was fitted to SRIM-estimated proton energies, as shown in figure 5.8.
Hall et al (1975) showed that for quasi-monoenergetic neutrons, the maximum
neutron RBE was around 0.4 MeV. A neutron kinetic energy of 0.4 MeV, when
inserted in equation (5.1), provides a recoil proton LET
value of 62.88 keV μm−1.
U
It was then shown that only the ratio of the proton recoil LET values at any
energy divided by the proton recoil energies at LET
5-14
is necessary in order to map
U
Quantitative Radiobiology for Proton Therapy
Figure 5.7. A summary of the typical energy relationships that contribute to the biological effectiveness via the α
radiosensitivity parameter. Reproduced from Jones (
2021). © The Author(s). Published by IOP Publishing Ltd. CC BY 4.0.
Figure 5.8. The curve given by equation (5.1), which expresses recoil proton LET as a function of neutron
kinetic energy, is plotted with data points obtained using the SRIM software for protons in water. Reproduced
from Jones (2021). © The Author(s). Published by IOP Publishing Ltd. CC BY 4.0.
5-15
Quantitative Radiobiology for Proton Therapy
any neutron energy onto the proton LET curve shown in figure 5.1. The relative
proportion of proton recoils to the LET of the other ions generated is not necessary
for these scaling procedures.
Thus the fractional LET will be
F Pr LET
[]
=Fractional LET
LET Pr
[]
U
,
5.2
()
where LETUwill be the specific value for protons, estimated above to be around
62.88 keV μm
−1
.
This fractional LET method has been used in previous publications for protonand ion-beam modelling (see chapters 8 and 9), which assumes that the increment of
radiosensitivity with LET is linear. Also, the same method can be used for neutron α
and β parameters, as in the following.
The α term at any neutron energy (α
[]
N
F Pr LET
LET Pr
aaa=−
) becomes
N
[]
U
UC
,
()
5.3
where αCis the reference radiation α value.
The same form of equation can be used for β, with similar symbolism, namely
N
F Pr LET
[]
LET Pr
U
UC
.
()
5.4
bbb=−
[]
The model described above can be applied easily in a short basic programme (see
Appendix B) and was then applied to simulate the Hall RBE data sets for
monoenergetic neutrons, as shown in figures 5.9(a)–(d).
The relationship between the maximum neutron energy NE
spectrum) and the effective neutron energy (NE
fitted by a linear function (R
2
= 0.97; p < 0.01) as
=NE NE0.087 .
eff max
) which determines the RBE can be
eff
(within an energy
max
5.5
()
The data and fitted line are shown in figure 5.10, which shows one anomalous point
where there is insufficient data about the actual beam energy spectrum.
The resulting relationship between RBE and NE
The present study suggests that the LET
keV μm
−1
, which is considerably larger than the value of 30.4 keV μm−1derived
U
is shown in figure 5.11.
eff
value of protons is around 62–63
from the data of Belli et al (2000), and upon which some proton models are based, as
discussed in chapter 9. Various authors have suggested higher values around 60–80
keV μm
−1
or higher, as reviewed by Friedrich et al (2013) and also found in the later
discussion in Jones & Hill (2020), but many experimental groups included an
increasing proportion of deuterons in order to maintain particle range; deuterons
probably have a higher LET
value. The Belli et al (2000) data set contained protons
U
only, and it is possible that their range was limited in comparison with the average
cellular thicknesses of 6–7 μm found using confocal microscopy, whereas when the
experiments took place a thickness of 4 μm was measured using older optical
5-16
Quantitative Radiobiology for Proton Therapy
Figure 5.9. (a)–(d): The Hall data set RBE values at cell survival fractions of 0.8, 0.37, 0.1 and 0.01 are shown
as black dots, the plotted modelled providing the blue curve and dots (with 95% confidence limits given by the
shaded area surrounding the curve). Reproduced from Jones (
Publishing Ltd. CC BY 4.0.
2021). © The Author(s). Published by IOP
5-17
Quantitative Radiobiology for Proton Therapy
Figure 5.10. The relationship between neutron maximum kinetic energy in a beam and the effective neutron
energy for bioeffectiveness. The individual beam codes are for the following cyclotrons: T = TAMVEC,
C = Clatterbridge], D = Detroit, N = NRL (Washington), H = Hammersmith, followed by the fission sources
at P = Petten, B(A) = Brookhaven (full spectrum), and B(B) = Brookhaven (using a late converter assumed to
have max energy of 6 MeV). An assumed (0, 0) coordinate point was also used to obtain the slope. For further
details see Jones (2021).
Figure 5.11. Plot of RBE as a function of effective neutron energy for different radiosensitivity ratios (α/β) and
reference photon dose, d
The access link for changing the other input parameters is
InteractivePlots_Jones_IOP/. Credit: Joshua Moore.
methods (Dr P O’Neill, personal communication). Thus if proton energies increase
beyond 30.4 keV μm
reduce with further increases in LET. This may now explain the Belli et al (2000)
results where a linear increase is not maintained beyond 30.4 keV μm
. Note that a reference low LET β = 0.03 Gy−2is used for the reference radiation.
low
−1
they may fail to reach cellular nuclei, so the RBE is likely to
https://josh-will-moore.shinyapps.io/
−1
. In contrast,
5-18