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Quantitative Radiobiology for Proton Therapy
10.5 Conclusions
The above methods should be helpful to guide clinical decision-making in difficult
treatment situations, in order for the full potential of proton therapy to be achieved
by minimising adverse late-reacting tissue effects, leading to improved quality of life
while maintaining reasonably long survival for patients who have tumours where the
full advantages of proton- or ion-beam therapy may not be obtained because their
anatomical location does not allow adequate neurological tissue dose sparing. The
various disciplines within radiation oncology need to collaborate closely and
understand the broad issues, which range from the clinical facts through medical
physics and radiobiology, in order to achieve the best achievable outcomes.
Certain sections of text in this chapter have been reproduced from Jones (2022).
CC BY 4.0.
References
Bijl H P, van Luijk P, Coppes R P et al 2006 Influence of adjacent low-dose fields on tolerance to
high doses of protons in rat cervical spinal cord Int. J. Radiat. Oncol. Biol. Phys.
Chowdhry V K, Liu L, Goldberg S et al 2016 Thoracolumbar spinal cord tolerance to high dose
conformal proton-photon radiation therapy Radiother Oncol.
Eulitz J, Troost E, Klünder L et al 2023 Increased relative biological effectiveness and
periventricular radiosensitivity in proton therapy of glioma patients Radiother. Oncol.
109422
Grassberger C, Trofimov A, Lomax A and Paganetti H 2011 Variations in linear energy transfer
within clinical proton therapy fields and the potential for biological treatment planning Int. J.
Radiat. Oncol. Biol. Phys.
Howard M E, Denbeigh J M, Debrot E K et al 2021 Dosimetric assessment of a high precision
system for mouse proton irradiation to assess spinal cord toxicity Radiat. Res.
Jones B, Dale R G, Deehan C, Hopkins K I and Morgan D A L 2001 The role of biologically
effective dose (BED) in clinical oncology Clin. Oncol. (R Coll. Radiol.) 13 71–81
Jones B, Cominos M and Dale R G 2003 Application of biological effective dose (BED) to
estimate the duration of symptomatic relief and repopulation dose equivalent in palliative
radiotherapy and chemotherapy Int. J. Rad. Oncol. Biol. Phys.
Jones B, Cominos M and Dale R G 2003 Application of biological effective dose (BED) to
estimate the duration of symptomatic relief and repopulation dose equivalent in palliative
radiotherapy and chemotherapy Int. J. Rad. Oncol. Biol. Phys. 55 736–42
Jones B 2006 Implications of quality adjusted survival for clinical trials in radiation oncology Br.
J. Radiol
Jones B and Dale R G 2007 Further radiobiological modelling of palliative radiotherapy: use of
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441–8
Jones B 2015 Towards achieving the full clinical potential of proton therapy by inclusion of LET
and RBE models Cancers (Basel)
Jones B 2016 Why RBE must be a variable and not a constant in proton therapy Br. J. Radiol. 89
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10-12
Quantitative Radiobiology for Proton Therapy
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and opportunities around relative biological effectiveness Clin. Oncol. (R. Coll. Radiol.)
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on relative biological effectiveness in scanned proton beams: an in vitro study based on
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McNamara A L, Willers H and Paganetti H 2020 Modelling variable proton relative biological
effectiveness for treatment planning Br. J. Radiol.
93 20190334
Moore J W, Woolley T E, Hopewell J H and Jones B 2021 Further development of spinal cord
retreatment dose estimation: including radiotherapy with protons and light ions Int. J.
Radiat. Biol.
97 1657–66
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for cognitive structures in proton therapy of pediatric brain tumors Acta Oncol.
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Sørensen B S, Pawelke J, Bauer J et al 2021 Does the uncertainty in relative biological
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d
10-13
IOP Publishing
Quantitative Radiobiology for Proton Therapy
Bleddyn Jones
Chapter 11
Radiobiological interpretation of the finding of
RBE changes within similar SOBPs placed at
superficial and deep locations in passively
scattered beams but not in scanned pencil beams
Marked differences in relative biological effect (RBE) were found in studies where
spread-out Bragg peak (SOBP) placements were at (a) superficial depth and (b) at
close to the maximum depth by varying the incident energy in each case. For pencil
beam scanning, RBE did not change with SOBP placement depth (Britten et al
2013), but for passively scattered beams (PSBs), high RBE values (typically 1.2–1.3)
in superficially placed SOBPs reduced to very low values (1–1.07) within SOBPs
placed at an extreme depth (Calugaru et al 2011).
The physical parameters of dose, linear energy transfer (LET) distributions and
kinetic energies along each SOBP were closely comparable regardless of SOBP depth
placement. However, instantaneous changes in particle fluence, dose rate and intertrack distances must change substantially in the PSB beam with increasing SOBP
depth placement, although the dose-rate changes that occurred in these experiments
is insufficient to substantially increase sub-lethal damage DNA repair in the above
experiments.
Equations are provided which allow α and β changes, resulting in reduced α/β
ratios with falling dose rate (the converse to FLASH studies), and compatible with a
reduction in micro-volumetric energy transfer (or MVET), with commensurate
reductions in RBE. The published depth distances, the observed dose rates and the
radiosensitivity ratios found in the experiments can be used to estimate the changes
in RBE, which are compatible with the experimental PSB results of Calugaru et al
(2011) to within a 5% tolerance limit, but with no significant RBE change for pencil
beams, where high fluence rates and the same inter-track distances are maintained
along the beam, compatible with the experimental results of Britten et al (2013).
doi:10.1088/978-0-7503-6209-2ch11 11-1 ª IOP Publishing Ltd 2024
Quantitative Radiobiology for Proton Therapy
There are considerable clinical implications since excess proton therapy toxicity
might occur with intense pencil spot beams when compared with PSBs when the
SOBP is placed in a deep position. This poses a dilemma for scanned pencil beam
users, who need to be vigilant about RBE allocations in proton therapy.
11.1 Introduction
It is crucial to appreciate that, although relative biological effect (RBE) always
increases along a spread-out Bragg peak (SOBP), placement of the SOBP at a much
greater depth (by means of an increase in incident beam energy) results in a marked
reduction in RBE within the SOBP in the case of passively scattered beams (PSBs),
although not in pencil scanned beams. This was found in comparative experimental
studies. The last few pages of chapter 1 contain figures 1.4 and 1.5, which
demonstrate the relevant experimental arrangements. It is essential to understand
these, as confusion often occurs in readers who assume a more direct and simplistic
interpretation of the meaning of depth in this context. The depth mainly being
considered here is the placement depth of the SOBP and not the quite separate depth
along the SOBP, a measurement which is carefully preserved in the experimental
studies independently of the depth of the SOBP placement. The studies then go on to
measure RBE at similar relative depths within the SOBPs themselves (these are
referred to as point depths, called points 1, 2 and 3 at similar distances within the
SOBP). Substantial comparative reductions in RBE were found between SOBPs
placed at relatively superficial depths (with the highest RBE values) when compared
with SOBPs placed at the deepest depths (the lowest RBE values) for scattered
proton beams in the experiments of Calugaru et al (2011). These are in marked
contrast with the remarkably constant ranges of RBE found in similarly designed
experiments using scanned pencil beams by Britten et al (2013). For further details,
see chapter 1, including the aforementioned figures 1.4 and 1.5, which illustrate the
RBE findings for different SOBP placement depths; reading of the two experimental
studies is also recommended in order to understand the experimental setups
thoroughly.
These contrasting findings were noted from 2017 onwards and interpreted as
being due to reduction in near-instantaneous beam fluence rate, dose rate and
increased inter-track distances caused by scattered beam diversion that exceeds the
more minimal diversion along pencil beams, which also maintain their higher doserate intensity in each pencil beam per unit time, as discussed in Jones (2017), Jones
et al (2018) and Jones (2022). Such an effect on instantaneous dose rate is not found
with scanned pencil beams, which maintain a fairly constant fluence rate and intertrack distances for SOBPs placed superficially or at the extreme depth.
This chapter considers how the PSB results in a reduced beam intensity per unit
time if the SOBP is placed at a near end-of-range depth, which can then influence the
radiosensitivity parameters that control RBE, probably caused by considerable
reductions in the near-instantaneous dose rates and increased inter-track separations, but which do not have a substantial impact on enzymatic repair processes in
the relevant short times.
11-2
Quantitative Radiobiology for Proton Therapy
11.2 Methods
The linear quadratic (LQ) model of radiation effect α and β radiosensitivity
parameters are modified by linear energy transfer (LET) and dose rate. The
SOBP depth positions and the three points of interest related to them, with the
relevant dose rates as used by Calugaru et al (2011), are used to determine the most
likely falloff in dose rate as an exponential function of depth. It is noted that the
relationship with distance could be anywhere between an inverse square (1/d
where d is the depth, to a 1/d function, and this will vary with the type and
functionality of scattering system used, which is often double rather than single. An
exponential function linking dose rate and depth of SOBP is used in this chapter for
minor changes in depth, but only to further refine the much larger reductions of dose
rate found at the deepest SOBP placement.
The experimental designs included three designated points: P1 in the entrance
region before the true SOBP, P2 in the mid-SOBP, and P3 towards the end of the
SOBP for the 76 and 201 MeV beams in the Calugaru et al (2011) experiments. In this
way, the three depths within each SOBP were kept constant and the only variable was
the depth of SOBP placement. The Britten et al (2013) experiments followed a similar
design, but used slightly different proton energies. These SOBP positions ensure
comparable LET ranges for each energy used, since the dimensions of each SOBP
were identical for each energy, ensuring that their LET distributions were comparable,
the chief variable then being dose and fluence rates. The change in treatment times
with beam energy change was insufficient to influence enzymatic DNA repair of
sub-lethal damage, due to the much longer half-times of repair of 15–30 min occurring
in cellular experiments: to give 2.86 Gy (the quoted D
2.86/3 = 0.95 min at 3 Gy hr
7.5 Gy hr
−1
for the 76 MeV beam.
−1
for the 201 MeV beam, but 2.86/7.5 = 0.38 min at
dose) would require
37
2
),
11.2.1 Linear quadratic model base equations
The radiosensitivity parameters α and β and the α/β ratio will vary with dose or
fluence rate due to changes in micro-volumetric energy transfer (or MVET, since the
product of fluence rate and LET provides energy transfer per unit volume and time),
and so influence radiosensitivity and RBE, using the equations derived by Jones
(2022), where α/β changes with dose rate, in the context of FLASH radiotherapy,
according to
0.3
()
==J
R
⎛⎝⎞
⎜⎟
R
⎠
//ab
R
()
ab
Rref
ref
()
,
11.1
where R is a dose rate, which can be greater or lesser than the reference dose rate
R
, and where the same subscript symbols are used for their associated α/β ratio
ref
values.
These dose-rate changes are applied to the depth positions used for the two
extreme SOBP positions used by Calugaru et al (2011), and for the reference
11-3
Quantitative Radiobiology for Proton Therapy
radiation at the specified superficial and deep SOBP depth positions. No allowance
for sub-lethal damage DNA repair is necessary.
11.2.2 The modelling method
1. The experimental reference photon dose rates reduce with depth (from 7.5 to
3 Gy min
applied for 76 MeV protons (7.5 Gy min
min
−1
) at each SOBP depth placement. The same dose rates were
−1
), although with further changes for different locational points.
−1
) and 201 MeV protons (3 Gy
2. The field cross-sectional areas were 3 and 12 cm diameters at depths of 3 and
18 cm for 76 and 201 MeV beam energies, respectively. For exploratory
modelling purposes, these areas are assumed to be changing exponentially as
−Δ
pp=
ad22
e1.5 6 . ,
()
11.2
where the depth is Δd, since there is an inevitable component of scattering and
attenuation as well as pure geometrical contributions, from which a = 0.06 cm
−1
3. α/β ratios can be influenced not only by high-LET effects but also by doserate effects when these fall into the domain where repair enzyme activity is
low or insignificant (Jones 2022a). This is achieved by the operator J, where
/
ab
()
//
ab ab
() ()
==JJ.so that.,
RR
ref
R
/
ab
()
R
ref
11.3
()
and where the subscripts R and R′ are, respectively, the reference dose rate
and the altered dose rate for the same type of radiation. J is also a function of
dose rate and consequently of beam divergence.
4. The LQ reference radiation BED is
d
BED 1 , 11.4
ref
⎛
⎜⎟
=+d
⎝
and for the 76 MeV proton beam must include RBE
ref
⎞
/ab
()
ref
⎠
max
and
RBE
()
2
(the
min
ratio of α and β parameters obtained, respectively, divided by those of the
reference radiation), with the subscripts ‘pr’ for proton dose:
2
RBE
⎛
=+ddBED RBE
⎜⎟
pr max pr
⎝
Equations (11.4) and (11.5) are then equated and solved for d
by d
given for the caesium-137 (
to provide an estimated RBE using the RBE
pr
137
Cs) reference radiation and with 76 MeV
min
⎞
/ab
()
ref
⎠
, 11.5
, then divided
ref
and
max
RBE
()
2
values
min
protons in Calugaru et al (2011), given by the solution
.
0.5
d
pr
// /ab ab ab=− + +
() () ()
()
ref ref
2
ddRBE
4. RBE 4 RBE .
pr
ref
max
+
2
2
pr
min
()
11.6
11-4
Quantitative Radiobiology for Proton Therapy
For the higher energy, the J operator can be used with each of the RBE limit
terms as a product with RBE
max
, but
RBE
2
is divided by J. J must also
min
operate on the reference α/β ratio, since the reference dose rate also has
changed in a time frame where DNA repair can be neglected. The partitioning of J between RBE
and β, respectively), using an index parameter m, ensures that the product of
m
J
and J
(1−m)
provides J. The partitioning should respect the unit of dose
max
and
(which contributes to RBE although RBE is itself dimensionless) and also the
units of α and β, namely Gy
2
RBE
−1
and Gy−2, respectively, so that α and √β
(which determines the changes in α
min
should be used. Then the indices should follow the relationship
+=mm0.5 1, 11.7()
where m = 0.667 and 1 − m = 0.333 approximately.
The BED for the 201 MeV protons is then given by
⎛
m
dJ d
RBE
pr max
⎜
+
pr
⎝
()
JJ
RBE
1
−
2
min
m
/ab
.
()
⎞
. 11.8
⎟
ref
⎠
()
For isoeffective conditions, equation (11.8) can then be equated with the
reference radiation BED given by
d
⎛
⎜⎟
+d
1 . 11.9
ref
⎝
ref
/ab
J
()
⎞
ref
⎠
()
5. J is found from its original definition with respect to dose rates as in equation
(11.1). The dose rates are incorporated in the J function by correction for
depth based on the given dose rates at mid-SOBP positions: 7.5 and 3 Gy
−1
min
for points 2 in the SOBPs of the 76 and 2001 MeV beams, respectively.
These dose rates are further corrected for positional changes relative to the
mid-SOBP P2 positions in the case of points 1 and 3 by using equation (11.2),
which results in P1: J = 0.95, P2: J = 0.76 and P3: J = 0.74 when the
appropriate dose rates are divided and a 0.3 exponent applied to these ratios
[5].
6. The isoeffect is then found by solving equation (11.8), equated with equation
(11.9) for d
⎛
0.5
=− +
RBE
⎜
d
⎜
pr
⎝
, and divided by the operative dprvalue to provide the RBE as
ref
+
/
ab
J
()
3
22
//
ab ab
JdJ dJ
.4. RBE4.RBE
() ()
ref
+
ref
m
pr
ref
max
J
m
2
pr
+
2
min
⎞
. 11.10
⎟
⎟
⎠
7. When J = 1, as in the pencil scanned beams, equation (11.10) becomes equal
to equation (11.6).
11-5
()
Quantitative Radiobiology for Proton Therapy
Table 11.1. Estimated RBEs for points of interest within the SOBPs. For the most
superficial SOBP, α and β values were used to estimated RBE using equation (11.6); for
the deep SOBP equation (11.10) was used. The RBE ranges in parentheses refer to 137Cs
and 60Co as the reference radiation sources respectively
Designated point in SOBP 76 MeV RBE 201 MeV RBE
P1 (J = 0.95) 1.00 (0.99, 1.07) 0.98 (1–1.07)
P2 (J = 0.76) 1.08 (1.07, 1.14) 0.97 (1–1.07)
P3 (J = 0.74) 1.21 (1.25, 1.33) 1.05 (1–1.07)
1
From data of Calugaru et al (2011).
1
.
11.3 Results
Table 11.1 shows the close agreement between the predicted and experimental
results obtained for the HeLa cells in the study by Calugaru et al (2011).
The HeLa cell analysis is consistent with LQ theory, with α increasing to a greater
extent than β with increased LET, although the β values do reduce slightly which is
probably due to β being more difficult to estimate.
The SQ20B cell line showed considerably more statistical variation and there is
inconsistency in that the α and β values do not conform with their expected increases
with distance along a SOBP (with β increasing by more than α with increasing LET,
probably due to the imposed curve fitting due to the excessive surviving fraction
variations) and so should not be taken further in terms of predicting RBE changes
with depth of SOBP placement, since the input radiosensitivity α and β values would
not be appropriate.
The 76 MeV energy resulting in a superficially placed SOBP shows consistent and
supra-linear changes in RBE with depth along the SOBP as seen in figure 11.1.
Similarly, the Britten et al (2013) RBE values increase with depth along each of
the two SOBPs, but in a linear placed at superficial and deep positions, as displayed
in figure 11.2.
11.4 Discussion
From the above data, it can be appreciated that, although RBE increases along each
SOBP, regardless of their depth placement, RBE can be reduced markedly in a
scattered beam when the SOBP placement is near the extreme depth range compared
with SOBP placement at a superficial depth. Such a change is not found with
scanned pencil beams.
The modelled results in HeLa cells presented are compatible with the hypothesis that
beam divergence of the entire beam in a scattered beam causes a marked reduction in
RBE when a proton SOBP is repositioned from a superficial to a much deeper distance
by increasing beam energy. Such changes were not found in closely comparable
experiments using non-divergent (scanned) beams where particle tracks are near-parallel
and no such change in dose and fluence rate occurs with increasing depth.
11-6
Quantitative Radiobiology for Proton Therapy
Figure 11.1. Results of Calugaru et al showing the experimental RBE results (exp) for each cell line compared
with the estimated RBE results (est) obtained from the published α and β radiosensitivity values. The Hela cell
line RBE at a depth of 0.5 cm were very close to 1, so are not shown.
Figure 11.2. Plots of RBE with depth along SOBP obtained from the experiments of Britten et al using two
different cell lines. The results obtained at energies at 200 MeV are marked; other points are results obtained
using the 87 MeV beam energy.
These are important experiments, since the analysis of past proton therapy
clinical results could be infl uenced similarly by the reduction in RBE: serious late
normal tissue side effects might then be reduced in treatments where SOBP positions
were at significant depths, e.g. in some CNS treatments with targets near midline
where depths of around 7–10 cm may be used, but mostly in pelvic or thoracic
treatments where greater skin-to-target distances occur. There could also be changes
in tumour control if RBE falls to below the actual RBE used in the treatment
prescription process.
At present, there has been a considerable shift in commercial accelerator beam
delivery systems to produce only scanned beams for two reasons, namely some
11-7
Quantitative Radiobiology for Proton Therapy
concern about low-dose fast neutron beam contamination from the scattering foils,
and range shifters as published, respectively, by Polf & Newhauser (2005), Brenner &
Hall (2008), Gerweck et al (2014) and Leite et al (2021). Pencil beam scanning
techniques avoid much neutron generation before beam entry into the patient and can
also achieve better dose–target ‘conformity’, as in the study by Brigitta et al (2004).
These two physical advantages could, in some critical clinical circumstances, be
overridden by the higher RBE values maintained for SOBPs placed at increasing
depths. A reliance on a fixed RBE of 1.1 would then incur greater susceptibility to
produce unintended normal tissue damage if the RBE exceeds 1.1 and also if it is
maintained with increasing depth. This is most likely to occur in anatomical sites
such as the brain, where RBE values probably exceed 1.1, due to neural tissue
having a low α/β ratio and the inevitable inclusion of brain tissue in the margin
around a malignant tumour, as discussed in Jones (2016, 2022b) and covered in
chapters 7 and 10 of this book.
A suggested method for immediate reduction of this risk has already been
published (Jones 2022b), and the description forms chapter 10 in this book, whereas
more complex methods involving LET and RBE considerations may take many
years to be accepted depending on what level of rigorous proof is deemed necessary.
It also remains to be seen whether some more scientifically informed clinicians will,
in carefully selected patients, elect to use scattered beams for deeper tumour sites in
order to deliberately reduce the risk of tissue damage caused by elevated RBE
values. This may especially be required in re-treatment situations where enhanced
RBE considerations can be especially important (Moore et al 2021).
There are reports containing higher than expected findings of neural radionecrosis, or radiation-induced brain injuries, amounting to 64 events in 21 of
42 studied low-grade glioma patients (Eulitz et al 2023), and the above 10% risk of
radio-necrotic changes in the treatment of skull-base tumours reported by Weber
et al (2016) may be at least partly caused by non-divergent scanned beams and the
inappropriate use of a 1.1 RBE.
Clinical commissioning of proton beams is at present limited mainly to physical depth–
dose and reproducibility considerations. There needs to be greater attention to radiobiology along the beam for multiple SOBP depth placement positions. Users should ideally
have a choice between the use of scattered and scanned beams in clinical circumstances
where the correct choice may be advantageous. Analysis of clinical data sets should also
take account of which beam scanning techniques and depth positions were used.
11.5 Conclusions
• The substantial fall of RBE in passively scattered beams in SOBPs placed at
extreme depth ranges compared with superficially placed SOBP is compatible
with a reduction with dispersion-related dose rates during such continuous
exposures.
• Pencil beam scanning will not allow such an effect since the beam sweep,
although covering the same area of dispersion, is delivered to separate small
volumes at a much higher dose rate.
11-8