The estimation of second cancer risk following radiotherapy: a discussion of two models
Regional Medical Physics Department, Newcastle General Hospital, Newcastle upon Tyne, United Kingdom
Purpose: Estimates of the probability of induction
of second cancers following radiotherapy requires several modifications and
extensions to the traditional linear dose-risk relationship. In this paper, two
models, based on cell kill and an hypothetical �flat� risk response
respectively, are modelled and compared using organ dose data from realistic
simulations of radiotherapy of the prostate and larynx.
Materials and methods: A general model for cancer
induction is used, which in principle takes into account the age profile of
radiotherapy patients, a dose dependent DDREF and a general modifying factor
which modifies induction probabilities at arbitrarily high doses. The model is
applied to measurements of organ doses derived from simulation of a radical
prostate treatment delivering 74 Gy to the target volume and a larynx
treatment delivering 50 Gy to the target.
Results: A suggested set of realistic conditions
gives a total second cancer induction risk of 2.2 - 8.2 cancers per 104
person years for the prostate and 4.4 - 4.7 cancers per 104
person years for the larynx, assuming a DDREF of 1.� Widely varying values may
be derived if certain key parameters in the models are varied.
Conclusion: Absolute determination of second cancer
risk is subject to large uncertainties, but could be used to assess the
relative dose and risk burden of alternative radiotherapy treatments,
particularly those involving the same clinical site. � 2007 Biomedical
Imaging and Intervention Journal. All rights reserved.
Keywords: Second cancers, radiotherapy dosimetry, radiotherapy treatment planning, radiation dose-risk relationships
The induction of second cancers following radiotherapy is
well documented , although the estimation of the probability of radiation carcinogenesis under these circumstances is far from straightforward. There are several reasons, however, why prospective estimates would be valuable.
For some cancers, there have been steady improvements in
therapy leading to survival times exceeding the latent period for radiation
carcinogenesis. For example, the 10-year survival rate for prostate cancer in
the UK has increased from 20% to 50% over the last 30 years and the
corresponding increase for breast cancer is from 40% to 70% in the same period .� In addition, the justification of medical exposures is a central tenet of radiation protection as formulated by ICRP . In order to justify an exposure, both the benefits and the risks must be evaluated and compared. One of the risks involved with radiotherapy is that of second cancer induction after a latent period.
New developments in radiotherapy, which may lead to
enhanced whole body exposure, are being implemented clinically. These include
intensity modulated radiotherapy (IMRT) , tomotherapy  and the increasing use of imaging techniques for both verification and fraction-by-fraction guidance of dose delivery (image guided radiotherapy � IGRT), involving multiple CT examinations throughout the course of treatment, using both kilovoltage or megavoltage x-rays. The impact of various IMRT regimens is of particular interest, since the whole body dose burden for a radiotherapy treatment will be considerably greater than for any realistic combination of concomitant images. The outstanding question is to what extent is the conformation to the target volume and the associated sparing of adjacent normal tissue offset by the increased doses (and overall risk) to more remote parts of the body due to an increased leakage component (due to higher number of
monitor units required) and a larger number of effective fields. Early work by
Followill et al.  showed that considerable variation in whole body doses might be expected and Hall and Wuu have suggested that the introduction of IMRT might double the incidence of second cancers .
The situation is complicated by the fact that the
administration of cytotoxic drugs has also been shown to result in induced
cancers  and the combined effect of concomitant radiotherapy and chemotherapy is therefore difficult to evaluate.
The validity of effective dose in a radiotherapy context
In considering a framework for risk estimation, it is
natural to consider dosimetric quantities which serve a similar purpose in
other cases of human irradiation. In this respect, effective dose has been
shown to be a useful quantity for combining organ doses from diverse exposure
patterns at low doses encountered during personal monitoring and its prime
function is to enable doses from external and internal sources to be combined
for legislative purposes. It has also been used extensively to compare the dose
burden for patients undergoing diagnostic radiological examinations. However,
several problems exist if this concept is applied to radiotherapy exposures.
Effective dose, E, is defined as:
where HT is the equivalent dose and wT
is the tissue weighting factor. Tissue weighting factors are derived from detriment,
a concept which may not be entirely relevant for cancer patients, for several
reasons. First, the age profile of cancer patients is different from the
population from which ICRP risk factors were derived. Second, the wide range of
organ doses resulting from radiotherapy means that the use of a single-valued
Dose and Dose Rate Effectiveness Factor (DDREF) may not be appropriate. Third,
the incorporation of genetic effects and relative length of life lost may not
be appropriate for patients who already suffer from cancer. For these reasons,
this paper does not seek to define a quantity analogous to effective dose for
radiotherapy purposes, but rather explores approaches to the estimation of the
risk of cancer incidence.
The dependence of risk on dose
Several organisations have developed estimates of stochastic
risk following irradiation, based largely on analysis of the survivors of
Hiroshima and Nagasaki (the Lifespan Study, LSS) . In this paper, we do not attempt to reconcile these risk estimates, but rather choose those proposed by UNSCEAR  to use as examples, since they facilitate the comparison between the two particular models for high dose response which are examined below. When considering their application to cancer patients who have received radiotherapy, three major issues need to be addressed:
Dose response relationships at high doses
At high doses, cell kill will become increasingly
important and a simple model would suggest that cancer induction probabilities
should decrease exponentially. In its simplest form, the risk of
radiocarcinogenesis RT to an organ T, following a dose D, may be
where fT,low is the absolute excess risk per
unit dose at low doses and is aT
a cell kill parameter. This model has been used by Schneider et al.  who derived values for aT from a study of second
cancer incidence in a population treated with radiotherapy for Hodgkin�s
disease. Modifications to this basic idea have been made by Wheldon et al.  who included mutation rate, intrinsic and mutational radiosensitivities and re-population effects in their two-stage model of radiocarcinogenesis. The introduction of more variables inevitably leads to a multiplicity of possible dose response relationships and furthermore, values for these parameters are not readily known in vivo. In fact, Equation 2 describes the special case of Wheldon�s model where no cell repopulation has taken place. However, these models, valuable as they are for exploring the relative effects of known parameters, do not explain several independent observations of induced cancers following radiotherapy where the risk appears to be approximately
independent of dose from a few gray to several tens of gray. This has been
discussed by Hall and Wuu  who selected studies on second cancers following radiotherapy for cancer of the cervix  and prostate . These studies showed that relative risks were approximately constant in the ranges 30 - 80 Gy and 48 - 67 Gy respectively. A further post-radiotherapy study of tumour incidence as a function of dose at the site of the second cancer  showed that approximately 35% of second cancers arose at sites which had received 10 - 30 Gy, with a small number at sites of higher doses up to 65 Gy. As Hall and Wu suggest, a constant risk with increasing dose represents an extreme possibility, and intuitively we may imagine that some risk reduction with dose is plausible, although the form of the functions for each organ or tissue is currently unknown.
A comprehensive study of risk factors derived from cohorts
of radiotherapy patients and comparison with similar cohorts derived from the
LSS  also showed excess risks at high doses. Excess relative risks from the radiotherapy groups were found to be either less than or comparable to those from the LSS. In some cases, the differences were not statistically significant because of the subdivision of data into individual cancer sites. Although this work showed that risk factors derived from the LSS may be used with caution in radiotherapy, effects of cell kill are difficult to predict with accuracy and uncertainties are large.
Dose and dose rate effectiveness factor (DDREF)
DDREF is given by:
is the slope of a linear relationship between high dose LSS data and dose,
where the line is constrained to pass through the origin, and alow is the gradient of the
dose response curve at very low doses. Thus the DDREF is essentially a factor
which is used to derive the hypothetical low dose slope of the dose-risk curve
from the high dose LSS data.
A range of values for DDREF, including many derived from
animal studies, has been discussed by several groups [15, 3]. Currently, it is usually assumed that the DDREF = 2  and UNSCEAR  have suggested that this value is adopted (i) for doses < 200 mGy, for all dose rates (i.e. acute doses) and (ii) for dose rates < 0.1 mGy min-1, for all doses, (i.e. chronic doses). For doses ≥ 200 mGy and dose rates ≥ 0.1 mGy min-1, it is implied that DDREF = 1.
The choice of two distinct doses and dose-rate related
values for the DDREF implies that the high dose (≥ 200 mGy) and
low dose (< 200 mGy) regions are assumed not to co-exist within the
same patient or subject. However, this is clearly not the case in radiotherapy
where organ doses ranging from a few milligray to tens of gray may result, thus
straddling the boundary between DDREF = 1 and DDREF = 2.
Even considering a single fraction delivering 2 Gy to the target, organs
and tissues close to the target volume will receive doses in excess of 200 mGy,
but distant organs will receive much lower doses. The integration time for the
dose rate criterion is approximately one hour, so the boundary between DDREF = 1
and DDREF = 2 is 6 mGyh-1, and based on this figure,
both values of DDREF may be invoked following a single fraction. Thus the use
of a discontinuous DDREF, as currently recommended, is counter-intuitive and
inapplicable to the radiotherapy case. A DDREF which varies continuously with
dose between defined limits might be more realistic, although both DDREF = 1
and DDREF = 2 have been used in the radiotherapy context, the latter
based on the argument that all fractionated radiotherapy is protracted compared
with the instantaneous irradiation of the LSS subjects.
Age profile of the exposed population
The age profile of cancer incidence in the UK is shown in Figure 1 (Rowan, private communication) and it may be assumed that the
distribution for patients receiving radiotherapy is similar. This distribution
may be different from those used to derive cancer incidence estimates from the
LSS data. Age related risk factors have been addressed by several authors (e.g.
) who show that the cancer induction risk decreases with increasing age at exposure. Whilst this implies that the use of LSS-derived risk factors may overestimate risks to most cancer patients, it is important to realise that the converse (i.e. higher risks for younger patients) may be equally important for the small fraction of patients receiving radiotherapy in childhood, particularly those with good prognoses, who may be expected to survive well into adulthood.
Models for risk estimation
It is clear from the preceding discussion that a linear
relationship between risk and dose, a bi-valued DDREF and an implicit
age-independence of low dose risk factors are inappropriate for radiotherapy
purposes. A modified framework for risk estimation is thus suggested, which
acknowledges a non-linear response at high doses, a variable DDREF and the age
profile of cancer patients.
Consider a critical organ, T, for which a low-dose
radiocarcinogenic risk per unit dose, fT,low, has been identified.
We assume that we may sub-divide this organ into a total of NT
independent volumes i, for each of which the dose DT,i, are known,
thus allowing for arbitrary dose heterogeneity.
The carcinogenic risk (excess absolute risk) to the whole organ,
RT, may be given by:
fT,low is the absolute excess risk per unit
dose at low doses, given, for example, by UNSCEAR .
apop is a dimensionless factor which allows for
the age dependence of fT,low
mi is the mass fraction corresponding to each
of the NT volumes which comprise the organ. Thus:
gT(D) is a dose-dependent multiplicative factor
which modifies fT,low at high doses (for example to account for cell
kill). DDREF is the dose and dose rate effectiveness factor.
Finally, the carcinogenic risk to the individual, Rtotal,
is given by summing the risks to all irradiated organs:
In this paper, we compare two models for gT(D),
based on cell kill  and �constant� risk , respectively, by using organ dose data from simulated prostate and larynx irradiations. Both models can draw support from epidemiological data in restricted circumstances, but only for the follow-up of certain radiotherapy treatments and for the induction of cancers in some organs.
Cell kill models
Here, the term gT(D) reflects an appropriate
cell kill model, the simplest being gT(D) = e-aTDT,i ,
Schneider et al.  have described this approach in which apop = 1, DDREF(D) = 1 and mi = 1/NT, for all i (i.e. a uniform spatial sampling of the organ). This gives:
Schneider et al. have defined the term in brackets as the
Organ Equivalent Dose (OED). This is the dose which, if given uniformly to an
organ, would result in the same carcinogenic risk as the non-uniform
irradiation. At low doses, the exponential term approximates to unity and the
term in brackets is simply the average organ dose. They have derived values for
aT for several critical
organs from observations of cancers following radiotherapy for Hodgkin�s
�Flat� dose response model
The extreme possibility described by Hall and Wuu  is modelled as follows.
We assume that risk is a linear function of dose up to
some dose Dc , is constant thereafter and is zero above a dose Dmax.
Thus gT(D) is given by:
Following , it might be reasonable to choose Dc = 4 Gy , following the shape of the solid cancer dose response function from the LSS (e.g ) and Dmax = 60 Gy, derived from the highest doses following which second cancers have been recorded [1, 12-14].
apop: Muirhead et al.  have proposed age dependent risk factors for radiation-induced fatal cancer and it is suggested here that these are represented by three age bands, 0 - 19, 20 - 49 and 50+ years, for which the average values of fatal cancer risk, normalised to 5.9% Gy-1, are 1.8, 0.8 and 0.4 respectively. It is assumed that these factors for cancer mortality will be equally applicable to cancer incidence.
DDREF(D): There are many possibilities for refining the
definition of the DDREF, and the choice depends, to a large extent, on the
definition of what is meant by �low� doses and dose rates. To be consistent
with UNSCEAR advice , DDREF(D) = DDREFmax for low doses << 200 mGy and should be unity for doses > 200 mGy. There are numerous empirical functions which would fulfil these criteria, for example the family of sigmoid functions given by
This is illustrated in Figure 2 (solid line) for k1 = 4.10-4
and k2 = 4.10-2 Gy-1.
The choice of k1 and k2 are entirely
arbitrary and given the large uncertainties in the estimates of DDREF, such
complexity is hardly justified. A simpler, albeit discontinuous, empirical
function describes a simple linear fall in DDREF from DDREFmax = 2
to DDREF = 1 as follows:
Figure 2 (dotted line) shows this function, in which D0 = 100 mGy,
and D1 = 300 mGy, so that DDREF = 1.5 at
the transition dose suggested by UNSCEAR .
Comparison of risk estimate models for simulated radiotherapy of the
prostate and larynx
A detailed description of the simulation of radiotherapy
treatments of the prostate and larynx has previously been given [17, 18]. An anthropomorphic phantom loaded with thermoluminescent dosimeters (TLD-100) was irradiated according to realistic treatment plans and doses to critical organs and tissues measured and scaled to give the doses which would have been received following delivered target doses of 74 Gy (prostate: 3-field, 15 MV, Siemens Primus H1 linear accelerator) and 50 Gy (larynx: 2-field 6 MV, Siemens Primus H1 linear accelerator). A neutron component was included for the prostate treatment. For organs close to the target volume, where part of the organ received doses > 4 Gy, sub-division of the organ according to Equation 4 was invoked. This was also invoked for distributed organs such as skin and bone surfaces. For organ doses < 4 Gy, mean organ doses have been used in Equation 4. In practice, the sub-volumes were taken as the volumes of the organ within each adjacent slice of the RANDO phantom, since the mass fractions for these volumes were known . Although this sampling is coarser than could be achieved by deriving the organ doses from the output of a treatment planning system, it will suffice to compare the models of radiocarcinogenesis described above. For simplicity, apop was assumed to be unity for the purposes of comparing the two models.
Values for the parameters in Equation 4 are given in Table
Excess absolute risks of carcinogenesis are given in
Tables 2 and 3 for prostate and larynx treatments respectively. They have been
calculated for a variable DDREF and also for the case of DDREF = 2.
Figure 3 shows RT as a function of Dc,
the dose at which it is assumed that a linear risk-dose response becomes
�Discussion and Conclusions
The estimation of the probabilities of induced cancers
following radiotherapy is in its infancy. Uncertainties exist in several
parameters and relationships, for example, risk as a function of age, risk
modification as a function of disease state, pre-disposition to cancer
induction and choice of risk model as a function of organ dose. The situation
is further complicated by the need to use, as a starting point, risk factors
derived for the LSS, i.e. for a wholly different population. However, in this
respect, the values of αT in the cell kill model of Schneider
et al.  is worthy of further development because they are derived from a radiotherapy population. In this paper, we have highlighted the inherent problems by outlining a general model for second cancer induction and calculating second cancer risks for two very different derived models, one based on cell kill and one based on epidemiological suggestions of a �flat� dose response.
In the latter, a critical parameter is Dc, the
dose at which it is postulated that the assumed linear relation between second
cancer risk and dose becomes a near flat response up to high doses. Figure 3
shows that RT increases from 3.68 Gy at Dc = 1 Gy
to 9.64 Gy at Dc = 5 Gy for prostate treatment,
where the overall risk is strongly dependent on the relatively high bladder
risk factor and high bladder dose, Dbladder. This means that RT
continues to increase with increasing values of Dc < Dbladder.
In the cell kill model, the risk of induced bladder cancer is negligible. This
is due partly to the high value of aT
 but also to the coarse dosimetric sampling resulting from the use of an anthropomorphic phantom. This has resulted in all the bladder locations receiving high doses (18 - 67 Gy), whereas it would be more realistic to assume that certain portions of the bladder wall would receive lower doses such that the effects of cell kill would not be so severe and increase the carcinogenic risk. In practice, the incidence of bladder cancer following prostate radiotherapy is significant . These authors  have also estimated a risk of 1 per 1220 PY for the absolute numbers of second solid tumours associated with prostate radiotherapy (all years after diagnosis). This corresponds to 8.2 (104PY)-1 in Figure 3, again demonstrating that the cell kill model cannot be tested adequately because of the coarse dosimetric sampling referred to above. The �flat� dose response model, on the other hand, gives second solid tumour incidence in broad agreement with , for Dc ~ 4 Gy.
In contrast, for the larynx case, the increase of RT
with increasing Dc is not so marked for Dc > 0.4
Gy. This is because the critical organs (thyroid, mouth, pharynx) have lower
risk factors than the bladder, and the comparatively smaller volumes which
exceed doses > Dc provide proportionately smaller
contributions to the overall risk. Compared with the variable DDREF model, the
assumption of DDREF = 2 will reduce the estimated risks by
approximately a factor of two, since most organs receive doses which are
sufficiently low, so that the variable DDREF approximates to DDREF = 1.
Thus the choice of model within the boundaries of those
described here is crucial, with ranges of RT by factors of 5 and 2
for prostate and larynx simulations respectively.
Treatment planning for modern radiotherapy can probably do
no more at the present than limit the doses to critical organs outside the
target volume to avoid deterministic effects. The current state of knowledge of
organ risk factors for a radiotherapy population, and for high doses greater
than a few gray, means that formal algorithms for quantitatively optimising
stochastic risks may not yet be feasible.
I would like to thank colleagues in the Regional Medical
Physics Department and Northern Centre for Cancer Treatment, Newcastle upon
Tyne for their contributions to the generation of the underlying simulation
Figure 1 Incidence of cancer v. age at diagnosis in England (1996-2000). Source: UK Office for National Statistics.
Figure 2 Hypothetical sigmoidal (solid line) and linear (dotted line) functions to describe a non bi-modal DDREF.
Figure 3 RT as a function of Dc, the dose at which it is assumed that a linear risk-dose response becomes dose-invariant. Closed squares are results for the prostate simulation and open circles for the larynx simulation. Values of RT for the cell kill model for larynx and prostate simulations are given by dotted and solid lines respectively.
Table 1 Values for fT,low ,a, Dc, Dmax, D0, and D1 used in the calculation of radiocarcinogenic risk
Table 2 Calculation of excess absolute risk to critical organs and tissues for a simulated prostate treatment
Table 3 Calculation of excess absolute risk to critical organs and tissues for a simulated larynx treatment
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|Received 25 May 2007; accepted 29 May 2007
Correspondence: Regional Medical Physics Department, Newcastle General Hospital, Newcastle upon Tyne, NE41 8EU, United Kingdom. . Tel.: +44 (0)191 233 6161; Fax: +44 (0)191 226 0970; E-mail: email@example.com (Roger Harrison).
Please cite as: Harrison RM,
The estimation of second cancer risk following radiotherapy: a discussion of two models, Biomed Imaging Interv J 2007; 3(2):e54
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