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Quantitative Radiobiology for Proton Therapy
• Greater care is required for pencil beam scanning proton prescriptions since
the average RBE for different SOBP placement depths will be higher than for
passively scanned beams.
References
Brenner D J and Hall E J 2008 Secondary neutrons in clinical proton radiotherapy: a charged
issue Radiother. Oncol.
Brigitta G, Baumert B G, Norton I A, Lomax A J and Davis J B 2004 Dose conformation of
intensity-modulated stereotactic photon beams, proton beams, and intensity-modulated
proton beams for intracranial lesions Int. J. Radiat. Oncol. Biol. Phys.
Britten R A, Nazaryan V, Davis L K et al 2013 Variations in the RBE for cell killing along the
depth-dose profile of a modulated proton therapy beam Radiat. Res.
Calugaru V, Nauraye C, Noel G et al 2011 Radiobiological characterization of two therapeutic
proton beams with different initial energy spectra used at the Institut Curie Proton Therapy
Center in Orsay Int. J. Radiat. Oncol. Biol. Phys.
Eulitz J, Troost E G C, Klünder L et al 2023 Increased relative biological effectiveness and
periventricular radiosensitivity in proton therapy of glioma patients Radiother. Oncol.
109422
Gerweck L E, Huang P, Lu H-M, Paganetti H and Zhou Y 2014 Lifetime increased cancer risk in
mice following exposure to clinical proton beam-generated neutrons Int. J. Radiat. Oncol.
Biol. Phys.
Jones B 2016 Why RBE must be a variable and not a constant in proton therapy Br. J. Radiol. 89
20160116
Jones B 2017 Particle physics for biological interactions Practical Radiobiology for Proton Therapy
Treatment Planning
Jones B, McMahon S J and Prise K M 2018 The radiobiology of proton therapy: challenges
and opportunities around relative biological effectiveness Clin. Oncol. (R. Coll. Radiol.)
285–92
Jones B 2022 The infl uence of hypoxia on LET and RBE relationships with implications for ultra-
high dose rates and FLASH modelling Phys. Med. Biol.
Jones B 2022a The influence of hypoxia on LET and RBE relationships with implications for
ultrahigh dose rates and FLASH modelling Phys. Med. Biol.
Jones B 2022b Risk assessment for proton therapy in the central nervous system by assuming
small increments in RBE Radiat. Phys. Chem.
LeiteAMM,RongaMG,GiorgiMet al 2021 Secondary neutron dose contribution from pencil
beam scanning, scattered and spatially fractionated proton therapy Phys.Med.Biol.
Polf J C and Newhauser W D 2005 Calculations of neutron dose equivalent exposures from range-
modulated proton therapy beams Phys. Med. Biol.
Moore J W, Woolley T E, Hopewell J W and Jones B 2021 Further development of spinal cord
retreatment dose estimation: including radiotherapy with protons and light ions Int. J.
Radiat. Biol.
Weber D C, Malyapa R, Albertini F et al 2016 Long term outcomes of patients with skull-base
low-grade chondrosarcoma and chordoma patients treated with pencil beam scanning proton
therapy Radiother. Oncol.: J. Eur. Soci. Ther. Radiol. Oncol.
89 161–6
97 1657–66
86 165–70
60 1314–24
179 21–8
81 1136–43
178
(Bristol: Institute of Physics Publishing) ch 1 (1.5–1.15)
30
67 125011
67 125011
200 110213
66 225010
50 3859–73
120 169–74
11-9
IOP Publishing
Quantitative Radiobiology for Proton Therapy
Bleddyn Jones
Chapter 12
Particle therapy dose–time compensations in
unintended interruptions and re-treatments
This chapter is concerned with the following:
(1) Numerical methods of how to compensate for unintended treatment
interruptions by using biological effective dose (BED) and tumour cell
repopulation considerations in the context of high-linear-energy-transfer
(LET) therapy, which are more complex than in the case of conventional
treatments since there must be associated RBE-related effects. Worked
examples are presented.
(2) The difficult clinical problem of estimating changes in the recovery of
normal tissue tolerance, which increases with time after an interval of
around 90 days after previous radiation exposures in the central nervous
system. The estimation process can be assisted by using carefully designed
mathematical methods which have now been automated. These produce
estimated re-treatment tissue tolerances in the central nervous system as a
function of elapsed time following the initial treatment (expressed as the
percentage BED of the accepted tissue tolerance BED). In the special
context of particle therapy RBE factors must also be included in these
formulations, since they will be sensitive to dose-per fraction changes, and
which provide a final treatment BED obtained from the percentage
tolerance BED given by the time-dependent equations.
12.1 Introduction
Two separate time-related issues are considered with respect to the estimation of the
dose required to compensate for:
1. Continuing tumour cell repopulation during unintended treatment interruptions resulting in extension of the overall treatment time, usually by a few
days or weeks, but may be longer.
doi:10.1088/978-0-7503-6209-2ch12 12-1 ª IOP Publishing Ltd 2024
Quantitative Radiobiology for Proton Therapy
2. Recovery of normal tissue radiation tolerances at extended times between 3
and 6 months to many years after a treatment course, and which may allow
further radiation therapy to be given.
To distinguish between these two different types of problems, it is important to
recognise that interruptions of under 90 days should be considered as treatment
interruptions (since normal tissue tolerance for late central nervous system (CNS)
effects does not appear to change) but intervals of over 90 days should be classified
as re-treatments (since normal tissue tolerance will then change after that time). This
distinction was especially important during the COVID-19 pandemic when many
treatment interruptions occurred, sometimes amounting to many months.
12.2 Unintended treatment interruptions
12.2.1 Background
A reduction in tumour control with extended overall treatment times was shown in
classical experimental studies, such as Fowler et al (1974). The clinical problem of
compensating for treatment interruptions was initially modelled using power-law
equations, but which proved unreliable, since the parameters used were derived from
acute-reacting tissue studies and inappropriately applied to late-reacting tissues; as a
result, enhanced late toxicities occurred.
More realistic identification of the clinical problem was made by Withers et al
(1988). Subsequent publications showed a reduction in tumour control by about
1%–2% per extended treatment day in the case of squamous cell cancers and
transitional cell cancers. Rapid repopulation is now a better-understood cause of
treatment failure (Kim & Tannock 2005). Ample references for the above facts can
be obtained in the report of the UK Royal College of Radiologists (2008 and 2019).
A longer time was required to identify a reduction in tumour control rates with
treatment protraction in other forms of cancer, especially those associated with
slower tumour cell kinetics such as prostate cancer (Thames et al 2010), which
appear to manifest as around 0.25 Gy day
behaves similarly). Further clinical data-set analysis is likely to produce new
information about other classes of tumour in the future.
Modelling is used in these circumstances as the best guide to compensatory dose
estimation, since clinical trials that allow deliberate treatment interruptions would
not be ethical. The methods use equations given in chapter 2 (equations (2.6)–
(2.10)). Especially important is the basic biological effective dose (BED) equation,
which includes repopulation, but modified for high-linear-energy-transfer (LET)
radiations as
–1
after 6–7 weeks (breast cancer probably
⎛
=+ −−
nd
⎜
2
min
⎜
⎝
12-2
⎞
d
⎟
a
⎟
()
b
L
⎠
KT TBED RBE RBE . , 12.1
LKmax
()
Quantitative Radiobiology for Proton Therapy
where T is the overall time, KLthe low-LET daily BED repopulation equivalent and
a lag time until repopulation is active. This BED equation has been obtained
T
K
from the basic equation given as equation (2.7) in chapter 2 by dividing throughout
by α
, so the BED units of KLare the same as for any photon treatment, just as the
L
α/β ratio used, with the RBE limits, is that of the low-LET condition. This last
equation, with these specific parameters, will be the method used below. However, if
(α/β)
essential to use K
obtained by dividing by α
is used to compute BED without the necessity for using RBE values, then it is
H
and not KLvalues. The alternative repopulation factor will be
H
rather than αL, so that
H
0.693
H
a=KT
.
H eff
,
()
12.2
and the relationship between KLand KHis given by
K
RBE
L
.
max
12.3
()
=K
H
Then the BED will be
⎛
=+ − −
nd
⎜
⎜
⎝
⎞
d
⎟
a
⎟
()
b
H
⎠
KT TBED 1 . 12.4
() ()
HK
12.2.2 Treatment delays
The causes of treatment delays are numerous and include accelerator breakdown,
patient illness, severe tissue reactions, chemotherapy complications, transport
delays, etc. Particle therapy is especially vulnerable, since treatments normally
depend on only one accelerator (rather than one per room for x-ray-based treatments). For long accelerator or gantry breakdowns, close liaison between the
physicist and oncologist is required to discuss alternative treatment approaches
such as x-ray intensity-modulated radiation therapy (or IMRT) or other focal x-raybased techniques.
12.2.3 Calculations for compensation of treatment interruptions
The calculations are relatively simple but involve many steps and potential pitfalls
(Dale et al 2002, Bese et al 2007). It must be appreciated that exact compensations
for either a normal or a tumour tissue isoeffect will lead to a detriment in the other,
so it is necessary to provide a range of solutions which can be chosen by the clinician
in charge, and—where possible—the views of the patient.
Interruptions occurring early in the treatment course are easier to compensate, for
example by working on weekends or by using two well-spaced treatments on some
days close to the end of the week. The difficult cases are those interruptions which
occur later during the treatment course. A model calculation for a delay in treatment
12-3
Quantitative Radiobiology for Proton Therapy
when only part of the treatment was carbon ions has already been published (Jones
et al 2006), and is more briefly given again below. In the case of hadrontherapy,
great care is required, especially regarding the units of dose: if calculations involve
the true physical dose (for example by conversion from the cobalt equivalent, or
equivalent dose, or RBE-Gy) then the answer is in physical dose and any correction
would need to be further adjusted to the original units such as RBE-Gy.
The following two worked examples are based on (1) pure proton and (2) pure
carbon treatments. Protons are used to show how subtle differences in results are
found from the two different calculation methods. The values used are not intended
to be specific for any particular tumour, and the modelling examples are intended to
demonstrate general principles. LET values have not been used in order to reduce
the complexity, but the models described in other chapters 8 and 9 can be used to
translate the working LET values to RBE
max
and RBE
values, which then allows
min
the RBE to vary according to the specific dose per fraction under consideration. The
results are compared with the use of a fixed (constant) RBE.
Worked example 1
A proton treatment of 46 Gy-eq in 23 fractions is prescribed for a paediatric sarcoma
affecting the posterior orbit, treating daily five times per week over 31 days; the child
does not require anaesthesia but mild sedation. The treatment is interrupted in the fourth
week, on the day after 15 fractions had been given and for a duration of 7 days.
Assume that a simple 1.1 RBE factor has been applied to provide the Gy-eq dose,
and that the tumour shows a constant low rate of repopulation equivalent to 0.3 Gy-
–1
eq day
. Then we use standard BED equations since it is assumed that there all
doses are convertible by the 1.1 RBE factor. This assumption is used initially and
will be compared with a more flexible RBE value using RBE
max
and RBE
min
later.
For the sake of simplicity, equal doses to critical normal tissue and tumour are
assumed; readers can calculate different BEDs for different isodose values using the
following formula:
⎛
=+
BED 1 , 12.5
xnd
⎜
⎜
⎝
⎞
xd
⎟
a
⎟
()
b
⎠
()
where x refers to the change in dose, n is the number of fractions and would be 0.6
for a 60% isodose line and 0.35 for a 35% isodose line, etc.
Calculations using a fixed RBE value for two different tissue types within the
planning target volume (PTV).
Tissue A: Intended BED to PTV containing normal tissue late-reacting soft tissue
using α/β = 3 Gy; the BED is 46 (1 + 2/3) = 76.67 Gy
12-4
.
[3]
Quantitative Radiobiology for Proton Therapy
Tissue B: Intended BED to PTV containing normal tissue late-reacting brain/
neural tissue using α/β = 2 Gy; the BED is 46 (1 + 2/2) = 92 Gy
.
[2]
Tumour: Intended tumour BED, using α/β = 10 Gy, is 46(1 + 2/10) − 0.3 T
= 45.90 Gy
[10]
.
BEDs before interruptions:
Tissue A: 30 (1 + 2/3) = 50 Gy
Tissue B: 30 (1 + 2/2) = 60 Gy
Tumour: 30 (1+2/10) = 30.3 Gy
.
[3]
.
[2]
.
[10]
The BED deficit is then
Tissue A: 26.67 Gy
Tissue B: 32 Gy
Tumour: 15.6 Gy
.
[3]
.
[2]
.
[10]
If uncorrected, the tumour BED (over 31 + 7 days) would be
= 46(1 + 2/10) − 0.3 × 38 = 43.8 Gy
[10]
.
By treating with the same dose per fraction through one weekend, 2 days can be
saved, so the tumour BED is then
= 46(1 + 2/10) − 0.3 × 36 = 44.4 Gy
[10]
.
By treating twice a day for all remaining weekday treatments (i.e. eight fractions
in 4 days) the overall time is 32 days and the BED is then
= 46(1 + 2/10) − 0.3 × 32 = 45.6 Gy
[10].
This seems a good alternative and almost completely restores the BED, but may
not be feasible if twice daily sedation is unacceptable.
Another way forward would be to give additional daily fractions, extending
overall time further. If, for example, we try to give the remaining compensatory dose
in one additional fraction of 2 Gy in one extra day after completing the prescribed
dose, with all delays we obtain an overall treatment time of around 39 days.
For d = 2 Gy, the BED is
= 46(1 + 2/10) + d(1 + d/10) − 0.3 × 39 = 45.9 Gy,
which is almost the same tumour BED as the original prescription, but the normal
tissue BEDs will then be tissue A BED = 80 Gy
and tissue B BED = 96 Gy
[3]
[2]
These have increased. This additional normal tissue BED can be reduced by
fractionating the final day of additional treatment into two treatments of 1.1 Gy,
so that the BED is
= 46(1 + 2/10) + 2 × 1.1(1 + 1.1/10) − 0.3 × 39.
The tumour BED is then 45.94 Gy
. The normal tissue BEDs have reduced a little.
Gy
[2]
, tissue A = 79.67 Gy
[10]
and tissue B = 95.41
[3]
Consider what might happen if treatment is hypofractionated and given in only
three remaining fractions in order to complete in the same overall treatment time but
matched to give the same CNS effect in tissue B (a deficit BED of 32 Gy
).
[2]
First, solve 32 = 3×d(1 + d/2); d = 3.73 Gy.
Then the tumour BED would then be lower:
BED = 30 (1 + 2/10) + 3 × 3.73(1 + 3.73/10) − 31 × 0.3 = 42.06 Gy
[10]
.
This BED is probably unacceptable, so the alternative method given above would
be preferred to maintain reasonable tumour control.
12-5
.
Quantitative Radiobiology for Proton Therapy
Another approach would be to give twice daily treatment for the entire remainder
of treatment. In this way, 16 fractions could be given in 8 further days after the
unintended gap, completing treatment in 36 days. For a dose per fraction of 1.15 Gy,
we obtain the following.
The tumour BED would be
5 2 1 2 10 1.15 16 1 1.15 10 36 0.3() ( )
//×+ + × + −×
= 45.72 Gy
[10]
.
The tissue A BED is then
5 2 1 2 3 1.15 16 1 1.15 3 75.45 Gy .
//×+ + × + =
() ( )
[]
3
And the tissue B BED is
5 2 1 2 2 1.15 16 1 1.15 2 88.98 Gy .
//×+ + × + =
() ( )
[]
3
These BEDs all are slightly below the intended BEDs. It should be noted that these
twice daily fractions have not taken into account the possibility of incomplete repair
between fractions.
Since the above calculations have been done using a fixed RBE, it should be noted
that dose units for the particle therapy are in equivalent Gy rather than Gy.
12.2.4 Calculations using a variable RBE value
In this case the actual physical dose of protons must be used along with the RBE
and RBE
–1
day
. For the sake of simplicity, the repopulation equivalent remains 0.3 Gy
min
as a physical dose.
max
The 2 Gy fraction was actually calculated from a 1.1 RBE so the actual dose
given is 2/1.1 = 1.82 Gy. If we assume RBE
and a higher value of RBE
tissue, but all have the same RBE
= 1.2 for normal tissue and RBE
max
(remember that RBE
min
= 1.15, RBE
max
= 1.05 for tumour,
min
= 1.3 for brain
max
is mainly operative at
min
high dose per fraction and will have little influence on the calculations below), we
obtain the following.
Tissue A: Intended PTV containing normal soft tissue (late reacting) with
α/β = 3 Gy, the BED is then 23 × 1.82 (1.2 + 1.05
Tissue B: Intended PTV containing late-reacting brain/neural tissue with
α/β = 2 Gy, the BED is then 23 × 1.82 (1.3 + 1.05
Tumour: intended tumour BED, using α/β = 10 Gy, is 23 × 1.82(1.15 + 1.05
1.82/2) − 0.3 × 31 = 47.24 Gy
The BEDs given before interruptions are as follows:
Tissue A: 15 × 1.82 (1.2 + 1.05
Tissue B: 15 × 1.82 (1.3 + 1.05
Tumour: 15 × 1.82 (1.15 + 1.05
.
[10]
2
× 1.82/3) = 51.02 Gy
2
× 1.82/2) = 62.88 Gy
2
× 1.82/10) − 0.3 × 19 = 31.17 Gy
2
× 1.82/3) = 78.23 Gy
2
× 1.82/2) = 96.42 Gy
.
[3]
.
[2]
[10]
.
[3]
.
[2]
2
.
The BED deficit is then as follows:
Tissue A: 27.21 Gy
Tissue B: 33.54 Gy
Tumour: 16.07 Gy
[2]
[10]
.
[3]
.
.
If uncorrected, the tumour BED (over 31 + 7 days) would
be
()
2
/=× + × − ×=23 1.82 1.15 1.05 1.82 10 0.3 38 45.14 Gy .
[]
10
×
12-6
Quantitative Radiobiology for Proton Therapy
By treating through one weekend 2 days can be saved, so the tumour BED is then
()
2
/=× + × − ×=23 1.82 1.15 1.05 1.82 10 0.3 36 45.74 Gy .
[]
10
By treating twice a day for all remaining weekday treatments (i.e. eight fractions
in 4 days), the overall time is 32 days and the BED is then
()
2
/=× + × − ×=23 1.82 1.15 1.05 1.82 10 0.3 32 46.94 Gy
10 .
[]
This seems a good alternative but may not be feasible if twice daily sedation is
unacceptable.
Another possibility would be to give additional daily fractions, extending overall
time further. If, for example, we try to give the remaining compensatory dose in one
fraction in 1 extra day after completing the prescribed course (and the delay), we
obtain an overall treatment time of around 39 days, then
()
2
/=× + × ×=BED 24 1.82 1.15 1.05 1.82 10 0.3 39 47.30 Gy ,
10
[]
which is almost the same tumour BED as the original prescription, but the normal
tissue BEDs will then be tissue A BED = 81.63 Gy
Gy
. These have increased. This additional normal tissue BED can be reduced by
[2]
and tissue B BED = 100.61
[3]
fractionating the final days treatment into, say, two treatments of 1 Gy (physical
dose).
The tumour BED is then 47.04 Gy
tissue B BED = 99.42 Gy
. This appears to be a reasonable compromise.
[2]
, the tissue A BED = 80.89Gy
[10]
and the
[3]
Consider what might happen if the remaining treatment is hypofractionated and
given in only three fractions in order to complete in the same overall treatment time
but matched to give the same CNS effect in tissue B (a deficit BED of 33.53 Gy
First, solve 33.53 = 3×d(1.3 + 1.05
2
d/2); d = 3.47 Gy.
[2]
Then the tumour BED would be low at
ED 15 1.82 1.15 1.05 1.82 10 3 3.47 1 3.47 10 31 0.3 43.58 Gy .
()
2
//=× + × +× + −× =
()
[]
10
).
This is probably not acceptable since the BED is less than the originally intended
47.24 Gy
. So, the alternative methods given above would be preferred to maintain
[10]
reasonable tumour control.
Another possibility would be to use a dose such as 0.98 Gy (physical) twice daily
for 8 days, completing treatment in 36 days.
The tumour BED would be
22
()()
//× +×+×+×−×=15 1.82 1.15 1.05 1.82 10 0.98 16 1.15 1.05 0.98 10 0.3 36 45.80Gy .
The tissue A BED is then
5 1.82 1.2 1.05 1.82 3 0.98 16 1.2 1.05 0.98 3 75.48Gy .
()()
22
//× +×+×+×=
And the tissue B BED is then
5 1.82 1.3 1.05 1.82 2 0.98 16 1.3 1.05 0.98 2 91.73Gy .
22
//× +×+×+×=
12-7
3
[]
[]
10
2[]
Quantitative Radiobiology for Proton Therapy
Again, incomplete repair between fractions has not been used in the example, but
could be used to further refine the BED.
12.2.5 Comparison of the two methods
The fixed and flexible RBE calculations give different answers when dose per
fraction is changed. A comparison for one of the above alternatives is given in
table 12.1. Also, in the case of giving three hypofractionated doses as compensation,
we have BED values of 42.06 Gy
and 43.58 Gy
[10]
for the fixed and flexible RBE
[10]
methods, respectively. These differences—due to the assumed changes in RBE with
dose per fraction—provide a good reason why it might be best to deliver the
remaining dose mostly using the same fraction size where possible and using altered
fractionation on only a few days, especially those days preceding weekends if there is
to be a further break in treatments, since over weekends accumulated incomplete
repair will not occur. There is a difficulty in using 2 Gy twice daily for many
treatments in acute-reacting tissues, since reactions can be made worse. General
guidelines for limits of acute-reacting normal tissues have been given by Fowler et al
(2003).
Worked example 2
An ion-beam schedule of 64 Gy-eq in 20 fractions over 26 days is interrupted after 15
fractions, for the entire fourth week and for a further 3 days into the following week
(i.e. for 10 days). The tumour being treated is a squamous cell carcinoma of the
peripheral bronchial tree. Here we assume a significant change in RBE with dose per
fraction and only use the RBE
max
and RBE
concepts. There is no spinal cord dose.
min
To simplify the calculations, we assume that the dose to lung tissue within the PTV will
obliterate all lung function within the PTV; also that a surrounding volume (VLNT)
for lung function receives approximately 50% of the prescribed dose and is relevant to
the patients future wellbeing.
In this example the following assumptions are made:
RBE for dose conversion = 2.6, tumour RBE
tumour and normal tissue RBE
Table 12.1. BED calculations using two different modelling methods for twice daily
fractions of 1.15 Gy-equivalent and 0.98 Gy (physical) on 8 treatment days, with
treatment completion in 36 days.
BED tumour (Gy
BED tissue A (Gy
BED tissue B (Gy
) 45.72 45.80
[10]
) 75.45 75.48
[3]
) 88.98 91.73
[2]
= 1.2, tumour α/β = 10 Gy and late-reacting normal
min
Fixed RBE Flexible RBE
= 3.2, normal tissue RBE
max
max
= 4,
12-8
)
)
)
)
Quantitative Radiobiology for Proton Therapy
tissue α/β = 3 Gy. Tumour repopulation is modelled by no repopulation for 21 days
followed by a repopulation rate equivalent to 0.9 Gy day
The 64 Gy-eq dose is a physical dose of 64/2.6 = 24.62 Gy and the physical dose
per fraction consequently is 24.62/20 = 1.23 Gy.
Using the flexible RBE model we obtain the following.
The intended tumour BED is given by
×+
0 1.23 3.2
since the intended T is less than T
The intended normal tissue BED is
×× +
01.230.54
The delivered tumour BED is
×+
5 1.23 3.2
The delivered normal tissue BED is
×× +
51.230.54
The deficit BEDs are then as follows:
Tumour deficit: 83.08 – 62.31 = 20.77 Gy
Normal tissue deficit: 52.83 – 39.62 = 13.21 Gy
If it is intended to proceed by either
(1) giving the same fraction number (five) over 7 days (that is, 10 days longer
(2) giving six fractions of a lower dose in 3 days (that is, 6 days longer) by
(
(
than intended), but increasing the total dose; or
treating twice daily including on a Saturday.
2
1.2 1.23
(
2
1.2 1.23
(
×
10
×
10
− 0.9(T – TK). The final repopulation term is zero
2
××
1.2 1.23 0.5
3
= 62.31 Gy
2
××
1.2 1.23 0.5
3
, so the BED is 83.08 Gy
K
= 52.83 Gy
.
[10]
= 39.62 Gy
.
[10]
–1
.
[10].
.
[3]
.
[3]
.
[3]
Then for (1):
(a) If tumour control is to be maintained, we solve
20.77 = 5d (3.2+1.2
d = 1.63 Gy
The normal tissue BED will then have increased to be
39.62 + 0.5 × 5 × 1.63 (4 + 1.2
from 52.83 Gy
volume of concern if complications increase at 1%–2% per Gy. If such a policy were
to be followed, it might be appropriate to reduce the dose per fraction to, say,
1.5 Gy. This would then give a compromised tumour BED of
62.31 + 5 × 1.5 (4 + 1.2
intended 83.1 Gy
Ultimately, it is the oncologist who has to decide which policy to pursue and alter
the radiation prescription, but since the risks and benefits may have changed the
patient should be informed as to the decision made and, ideally, they should be
consulted when it comes to the choice of risks.
For method (2), where six fractions are given in 3 consecutive days (a total of
32 days), we can maintain the same tumour BED by solving for d in
[3]
2
d/10) − (36 − 28) 0.9,
2
× 1.63 × 0.5/3) = 57.52 Gy
. This could amount to 5%–10% additional complications in the
2
× 1.5/3) − (36 − 28) 0.9 = 80.73 Gy
.
[10]
12-9
, which has increased
[3]
, instead of the
[10]