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Quantitative Radiobiology for Proton Therapy
Figure 14.3. (a)–(c): Plots of RBE with dose per fraction showing sensitivity to changes of assumed aU, βUand
LET
, the maximum efficiency point LETU, for α/β = 2 Gy, where the LET is 2 keV mm−1.
U
14-9
Quantitative Radiobiology for Proton Therapy
It is clear from the above graphical displays that small improvements may be
possible and can only be achieved by appropriate experimentation. To find the true
LET–RBE turnover points it is also necessary to determine both the α and β changes
with LET, so that the entire model may be validated to greater accuracy and
compared with other models. This might involve either a very large international
collaboration, but preferably conducted in one laboratory under carefully controlled
conditions with the capacity to study a range of ion beams at different energies and
with delivery systems where the influence of inter-track distances on biological
effects can be studied, where the tracks are in the same primary direction and with
other geometrical combinations (e.g. orthogonal or opposed tracks) by varying the
irradiation conditions, and introducing variations in time between exposures. Such
mixed fields should also be tested at higher dose rates. Far more comprehensive data
of spread-out Bragg peak (SOBP) placement positions at gradually increasing
depths are urgently required for scattered beams as well as the introduction of
deliberate changes in dose rate (including both increase and reduction of the dose
rate) in scanned beams. It is paradoxical that so much work has been done to
commission beams with respect to physical dose before clinical use, but so little
preliminary investigation into the biological effectiveness.
Also required is a library of tabulated LET values for different field sizes and
SOBP dimensions at perhaps three standard points within the SOBP (e.g. max,
median and mean values) and/or their values at defined positions such as the entry,
middle and end of SOBPs. It is surprising that such work remains to be done.
14.5 What could be achieved in a single international laboratory
dedicated to high-LET radiobiology
The proposed Bio-LEIR project at CERN (Dosanjh et al 2013) was entirely capable
of addressing all the above issues. This was meticulously planned and remains
feasible, but unfortunately the CERN executives decided instead to fund detector
and radionuclide projects instead. Just as in the case of the CERN Large Hadron
Collider experiments, which confirmed the presence of all previously known subatomic particles during the first 6 weeks of energy ramp-up, before their later
confirmation of the Higgs boson hypothesis (and impressively to a much greater
level of parameter precision then achieved previously), so also could bioexperiments
benefit from a carefully planned experimental programme to confirm previous
phenomena, but provided with larger data sets to find robust and more accurate
parameters for predictive modelling purposes. Some examples of what might be
achieved are discussed below, although there could be many fringe benefits in other
fields such as radioprotection and space travel as well as in radionuclide effects in
medicine, etc.
14.5.1 Simulated experiments
Simulations have been performed of future experiments designed to determine the
LET–RBE turnover point positions at LET
(and for the underlying LET–α and
U
14-10
Quantitative Radiobiology for Proton Therapy
LET–β relationships) for protons and ions with different Z numbers. The methods
are as follows:
1. Use random-sampling computer techniques with typical coefficients of
variation for cell-survival studies to provide α and β values at the control
and reference LET values. The number of different cell-survival experiments
can be varied.
2. Then, vary the number of experiments for accurate estimation of the two
linear gradients of α and β (separately) with LET for lines before and beyond
LET
, in order to determine their intersection position at LETUwith a high
U
degree of accuracy for each Z number. The α and β parameters obtained
may be combined to give an RBE value for each given dose.
3. Confirm if LET
remains constant at three to four different dose levels, and
U
for different cell lines, for each different ion (i.e. Z value).
4. Confirm and strengthen the precision of mathematical relationship between
Z and LET
, with Monte Carlo simulations of these.
U
5. Estimate the increased precision of the gradient of α and β with LET and
determine their maximum values, α
and βU, at LETUfor each Z number
U
and for different cell types, and correlate these with their reference radiation
values (α
and βL).
L
6. Repeat the above in several typical beam-depth dose positions and for
different incident energies.
7. Apply statistical goodness-of-fit tests to find the best of the existing LETRBE models, or which models fit the data best in what situation, e.g. low/
intermediate/high dose.
8. Estimate to what extent the better prediction of RBE would improve results
of potential clinical applications.
Figure 14.4 shows an example simulation.
Four repeated simulations, using seeded random sampling, provide LET
values
U
of 29.6, 32.06, 33.73 and 27.64, yielding a mean of 30.75 ± 1.34 standard error of the
mean (SEM) when there are 20 LET-RBE data points. The output of one such
simulation is given in figure 14.5. The simulations were set up with an assumed real
LET
value of 30.5. This is a reasonably good result for medical purposes, but if the
U
numbers of LET-RBE data points are reduced to 16 the estimate falls to 29.96 ±
1.24, and if further reduced to 12 the estimate becomes 31.5 ± 1.92. The last two
examples were simulated with fewer repeat experiments leading up to the RBE
determination (three repeats rather than four for each irradiation, and six points
rather than eight on the reference radiation survival curve). Further reductions in the
number of repeat cellular experiments required to produce each RBE data point
show even more unreliable results. It follows that very large experiments are
necessary to produce the most reliable data, although it is important at this stage
to assess the clinical significance of an error in estimating LET
considerations, an experimental LET
result of, say, 28.8 or 31.8 keV μm−1(instead
U
. From geometrical
U
of the assumed correct 30.5) would lead to an approximately 5% error in RBE
estimation. However, by feeding this result into clinical isoeffect equations using the
14-11
Quantitative Radiobiology for Proton Therapy
Figure 14.4. Example of a single Mathematica (Wolfram, USA) simulation of a LETUdetermination
experiment for protons, using variations in cellular radiosensitivities for cell-survival assays. Here 20 RBE
data points are used. The LET
downward data linear regression fits. The expected LET
for this simulation is 27.64 (owing to a coefficient of variance of 20% for all radiosensitivity measurements).
value is obtained by obtaining the intersection point of the two upward and
U
is assumed to be 30.5 keV μm−1, but the fitted value
U
BED concept, in which RBE is represented by its maximum and minimum limits at
any specified LET,
2
min
ab
/
d
H
⎞
,
L
⎠
⎛
=+
BED RBE
nd
⎜⎟
H
RBE .
max
⎝
()
(as in chapter 2, equation (2.16)), where n is the number of doses given and the α/β
ratio is that of the reference (or control) radiation modality, the change in the
recommended dose for isoeffective neurological damage reaches a 5% difference
when the estimated LET
a 17% change in LET
value falls down to between 25 and 26 keV μm−1(around
U
), when the local LET is as high as only 9 keV μm−1, a value
U
which can appear on proton therapy three-dimensional LET maps. So these
estimates suggest that the magnitude of the error is not fully propagated in a
14-12
Quantitative Radiobiology for Proton Therapy
Figure 14.5. BED* and dose plots for electrons and hadrons and conventional (CONV = 0.03 Gy s−1) and
FLASH (60 Gy s
assumed hadron RBE parameters are RBE
transformed into BED here, is shown in this example only.)
−1
) dose rates, with BED transformed dose-reponse data published by Vozenin et al. (The
= 4.5 and RBE
max
2
= 1.5. The original experimental data,
min
practical clinical situation, where tissue is treated from multiple directions using
pencil beams and where the LET values are not close to their maximum possible
values. However, small deviations of dose beyond the already allowed International
Commission on Radiation Units and Measurements (ICRU) dose variation of −5%
to + 7% across a clinical target volume (consisting of the cancer plus surrounding
normal tissue at high risk of harbouring infiltrating tumour cells) might also
contribute to tissue complications. In general terms this would be at a rate of
around 1%–2% per additional Gy, and so an additional 5% difference could mean
up to 10% or more increased tissue complications and also possibly a reduction of
tumour control if the error propagates as a dose reduction to the tumour, at around
a 1% per Gy. These differences may seem small but could be of important clinical
significance.
However, the situation is further complicated by the present clinical practice of
allocating a constant RBE value of 1.1 for protons in all tissues regardless of dose
and LET. Then, for a LET of 9 keV μm
−1
, the discrepancies between the calculated
and normally given dose (normalised to 100%) are 80.21% for use of the correct
LET
and 76.92% for an incorrect LETUof 27 keV μm−1. So a correct allocation of
U
LET
would make a further dose change of around 4.2% over and above the large
U
difference due to a fixed versus flexible RBE allocation. This shows the considerable
potential importance of using a variable LET-based RBE system with an accurate
LET
value. To change the present assumption of a constant proton RBE regardless
U
of LET, dose, and cellular system would require a large series of careful experiments.
14-13
Quantitative Radiobiology for Proton Therapy
The same considerations would apply for heavier ions where the SOBP values of,
say, carbon ions are normally at a LET which is around 20%–30% of the LET
value, whereas the above proton example had a LET of up to 9 keV μm−1, i.e.
around 30% of the LET
value. Much more detailed work is required to pursue
U
these aspects further and for each ion species.
U
14.5.2 Uniqueness of LET
The uniqueness of LET
for each ion species
U
for each ion species is now considered further. This
U
hypothesis can be addressed only to a certain extent from existing data (see Jones
2015), owing to there being relatively few reliable data points available (for heavier
ions the turnover points are not so well defined due to data and range limitations, as
can be visualised in the data-mining report of Sørensen et al 2011). Only by combining
results from past experiments using different cell types and at different doses can the
LET
position be studied at the present time, but then such retrospective data cannot
U
possibly be used to test many other hypotheses mentioned earlier.
Two such examples, for carbon ions and helium ions, are shown in table 14.6,
where statistically significant differences in LET
experimental proof of unique LET
turnover points for each ion species would
U
oppose many existing statements, that a LET value of around 110 keV μm
positions are obtained. Rigorous
U
−1
represents the maximum obtainable RBE for all ion species, as stated in many
standard radiobiology textbooks, for example Hall & Giaccia (2011, 2019).
It was further argued in Jones and Hill (2019) that since the estimated LET
of
U
five different ion species (including protons) were all higher for increasing Z values
in the case of protons, helium, carbon, neon and argon ions that the probability of
this being due to chance was 1/5! (or 0.0083). Further LET
silicon and iron, again with LET
being proportional to Z, provides a probability of
U
estimations for ionic
U
1/7! (or 0.00019), so this is a viable hypothesis which overturns the widely held
previous assumptions of LET
(1971) that Z
2
and relativistic velocity did determine RBE in some way (although
without specific reference to the LET
being invariant, despite the earlier views of Katz et al
U
concept).
U
Further pragmatic experiments linked with theory could be performed, for
example the following:
Table. 14.6. Some details of the experimental data sets for helium and carbon ions used for comparison.
Estimated LET
Ion and data source Cell type
Carbon ions (Weyrather et al 1999; GSI,
Darmstadt, Germany)
Helium (Barendsen 1968; Netherlands) Human T cells 124.24 ± 0.56
The locations of the combined carbon ion and helium data are significantly different (Mann–Whitney
p = 0.028, t-test p < 0.0001).
CHO 145.81 ± 9.88
V-79 159.05 ± 3.95
Combined CHO +
V-79 data
(mean, standard error)
152.43 ± 4.29
(keV μm−1)
U
14-14
Quantitative Radiobiology for Proton Therapy
• Investigate the reduction in RBE with depth reported in France (F. MegninChanet’s experiments reported by Calugaru et al 2011) with a greater number
of data points and for different cell types and doses, and compare to Monte
Carlo simulations. This is likely to require additional information beyond
radiation fluence, kinetic energy released per unit mass (or KERMA),
absorbed dose and LET, which are defined in one plane only: the possibility
of quantifying the mean inter-track distance with depth needs to be considered, or by using a more volumetric interpretation of LET in the x-, y- and zplanes, due to increased Coulombic scattering with depth, especially in the
case of protons but less so with heavier ions. Indeed, this might be found to be
a proton-only effect, but it is vital to determine this as treatment-planning
systems could incorporate such effects.
• The biological effects of nuclear fragmentation products can be separately
studied.
• Establish comprehensive data sets for RBE
max
and RBE
values at different
min
LETs for different ion beams in panels of cells with known genetic
characterisation.
14.5.3 Priority in radiobiological experiments
The priority would be to establish the ‘ ground rules’ for RBE determination but with
greater precision and in a wider range of cellular systems. Later advanced experiments in collaboration with selected worldwide universities would inevitably follow,
examining cellular signalling and damage-response mechanisms at the molecular
level, and their modification. It is important to point out that during the more basic
RBE experiments, some cellular material can be stored for analysis at other centres
of excellence with great expertise in molecular mechanisms. Thus the experiments
could provide data for several purposes, as determined by an overall controlling
committee structure. Other universities are already aiming to sensitise/modify
radiation effects, or personalise radiation by attention to genetic and proteomic
screening, etc. Also, the capacity to do long, continuous low-dose-rate exposures for
nuclear medicine and eventually the use of mixed-field radiations (i.e. combinations
of ions), their modification by hypoxia and other molecular approaches would be of
great interest. Any such experiments should be based on the secure foundation of
more fundamental knowledge regarding LET and RBE, without which there is no
secure basis.
Before radiobiology studies can commence, it would be essential to begin with
beam characterisation work, sophisticated dosimetry and confirmation of dose in
humanoid-tissue-equivalent ‘phantom’ structures, to confirm the numbers of particles, their ranges with depth and to translate the energy released and absorbed to
the absorbed dose concept and determined to the quality standards demanded in
medical practice and as approved by registered medical physicists. The experience
gained would be invaluable and could be used to establish a dosimetry reference
laboratory for particle beams working closely with national standards laboratories
and international bodies such as the aforementioned ICRU and International
14-15
Quantitative Radiobiology for Proton Therapy
Commission on Radiological Protection. An entire range of diagnostic and
dosimetry equipment would be necessary for routine dose monitoring and would
present the opportunity for advanced detector research and development, using
direct beam monitoring, detectors inserted in tissue-equivalent phantoms and
remote detections of nuclear activation products.
14.5.3.1 Further studies using ultra-high or FLASH dose-rate effects
After comprehensive studies of the beam ballistics for the various ions, radiobiological studies would follow using the same experimental beam geometry, which
can be made to simulate the human body and the typical dimensions of treatments in
various anatomical sites. The relationship between inter-track distances (related to
fluence and dose rates) and RBE needs investigation in detail, as suggested in
chapter 1, with dose-rate equations given in chapter 2. Some preliminary modelling
initiatives are considered here. The equations given in Jones (2022, 2023) can be
modified to include RBE parameters. It was found that ultra-high (or FLASH) doserate in vivo data on a lung fibrosis experimental model used in Lausanne,
Switzerland by Vozenin et al (2019) could be fitted by plotting the BED* (the
excess BED beyond the threshold BED for the effect to occur). The fitted FLASH
data curve had a different threshold dose and intercept BED, and was shallower, its
gradients controlled by a much higher α/β ratio. The change in α/β ratio (from 3.4
for lung fibrosis at a dose rate of 0.03 Gy s
−1
), a factor of 9.63, due to the increased dose rate was closely approximated by
Gy s
−1
to become 32.74 Gy at a dose rate of 60
the function
0.3
R
==J
⎛⎝⎞
⎜⎟
R
ref
9.78,
⎠
14.1
()
where R is the FLASH dose rate and R
standard dose rates of around 1–2 Gy min
is the dose rate of the reference radiation at
ref
−1
, and which is close to the cube root
function implied by consideration of mean inter-track distances in a small volume
and must also be related to the oxygen depletion rate. It follows that J not only
modifies the α/β ratio but also is related to the change in dose rate, or time to deliver
a specified dose. It is important to understand that for dose rates 1 and 2 (which
appear in subscripts below), the S′ (mean track distance separation in a volume), F′
(the near instantaneous fluence rate), dose rates and exposure times (T )as
introduced in chapter 1, are related as
′
S
1
′
S
2
=
′
F
2
3
F
1
dose rate
33
==
′
dose rate
2
1
T
1
,
T
2
provided that the same total dose is given in these respective times (since any dose
d = dose rate × T).
These concepts can then be used within a BED framework. For further details,
see Jones (2022), where the argument is presented for dose-rate intensification
leading leading to enhanced micro-volumetric energy transfer (or MVET) and so
14-16
Quantitative Radiobiology for Proton Therapy
modify radiosensitivity by increasing the efficiency of energy transfer (similar to the
LET effect presented in chapter 8). At extremely high dose rates radiosensitivity may
be reduced because of the overkill effect and also, though even before overkill may
occur, concomitant oxygen depletion will cause reduction in radiosensitivities,
affecting the β parameter to a greater extent than the α parameter, since theamount
of oxygen depletion will cause radiosensitivity reductions, affecting the β parameter
to a greater extent than the α parameter because their oxygen enhancement ratios
(OER) differ, OER
being larger than OERα(Nahum et al 2003).
β
For a comparison of four different experimental conditions, the modified BED
equations (using the high-LET BED equations derived in chapter 2) are as follows,
where BED* is the BED above the threshold BED value for the experimental effect
of lung fibrosis and the α/β ratio (of 3.4 Gy) is that found for the reference low-LET
radiation (megavoltage electrons) from the data-fitting process:
1. The reference radiation (e.g. megavoltage electrons) at conventional dose
rate:
⎛
⎜⎟
=− −
* d
BED 1 44.0. 14.2
⎝
d
⎞
ab
/
()
⎠
()
2. The megavoltage electrons at FLASH dose rates:
⎛
⎜⎟
=− −
* d
BED 1 16.55. 14.3
⎝
d
ab
/
J
()
⎞
()
⎠
3. The proton or hadron with higher LET than the electrons used above at
conventional dose rate:
2
BED RBE
⎜⎟
⎛
=− −
* d
⎝
max
RBE .
RBE
d
min
()
ab
/
max max
44.0
⎞
RBE
⎠
. 14.4
()
4. The proton or hadron with higher LET than the electrons used above at the
FLASH dose rate:
2
BED RBE
⎜⎟
⎛
=− −
* d
⎝
max
RBE .
RBE .
max max
These changes include the fact that the ratio
chapter 2, where this ratio is given as R
. Thus dividing the
C
d
min
()
J
RBE
RBE
ab
/
max
2
min
⎞
⎠
()
=
16.55
RBE
ab
HighLET
()
ab//
RBE
. 14.5
, as explained in
ref
2
term by RBE
min
()
max
effectively modifies the reference α/β ratio to be that of the high-LET radiation. The
intercept terms (44 and 16.55 Gy) were the respective values of the data-fitted intercepts
for conventional and FLASH dose rates using electrons. These values are divided by
RBE
, since they occur at near-zero dose where only α cell kill occurs, to provide
max
modified intercept BED values for the higher-LET experiments.
14-17
Quantitative Radiobiology for Proton Therapy
Examples of some simulated experiments are shown in figure 14.5 for a source
using a higher-LET and higher-RBE hadron (e.g. neutrons or carbon ions) and
figures 14.6(a) and (b) for protons, which are compared with the original electron-
based experiments with superimposed lung fibrosis data in figure 14.5.Itcanbe
Figure 14.6. (a) and (b): Plots of the single fraction dose and the BED value for the observed effect above the
threshold BED for that effect for electrons and protons and conventional (CONV) and FLASH dose rates.
The assumed proton RBE parameters are RBE
2
RBE
= 1.12 in 5(b). The α/β ratio is modified by the J operator.
min
max
= 1.4 and
RBE
2
= 1.08 in 5(a), and RBE
min
max
= 1.8 and
14-18