Biologically effective dose-response relationship for breast cancer treated by conservative surgery and postoperative radiotherapy.
ABSTRACT To find a biologically effective dose (BED) response for adjuvant breast radiotherapy (RT) for initial-stage breast cancer.
Results of randomized trials of RT vs. non-RT were reviewed and the tumor control probability (TCP) after RT was calculated for each of them. Using the linear-quadratic formula and Poisson statistics of cell-kill, the average initial number of clonogens per tumor before RT and the average tumor cell radiosensitivity (alpha-value) were calculated. An alpha/beta ratio of 4 Gy was assumed for these calculations.
A linear regression equation linking BED to TCP was derived: -ln[-ln(TCP)] = -ln(No) + alpha(*) BED = -4.08 + 0.07 (*) BED, suggesting a rather low radiosensitivity of breast cancer cells (alpha = 0.07 Gy(-1)), which probably reflects population heterogeneity. From the linear relationship a sigmoid BED-response curve was constructed.
For BED values higher than about 90 Gy(4) the radiation-induced TCP is essentially maximizing at 90-100%. The relationship presented here could be an approximate guide in the design and reporting of clinical trials of adjuvant breast RT.
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ABSTRACT: Radiotherapy (RT) after tumorectomy in early breast cancer patients is an established treatment modality which conventionally takes 6-7 wk to complete. Shorter RT schedules have been tested in large multicentre randomized trials and have shown equivalent results to that of standard RT (50 Gy in 25 fractions) in terms of local tumor control, patient survival and late post-radiation effects. Some of those trials have now completed 10 years of follow-up with encouraging results for treatments of 3-4 wk and a total RT dose to the breast of 40-42.5 Gy with or without boost. A reduction of 50% in treatment time makes those RT schedules attractive for both patients and health care providers and would have a significant impact on daily RT practice around the world, as it would accelerate patient turnover and save health care resources. However, in hypofractionated RT, a higher (than the conventional 1.8-2 Gy) dose per fraction is given and should be managed with caution as it could result in a higher rate of late post-radiation effects in breast, heart, lungs and the brachial plexus. It is therefore advisable that both possible dose inhomogeneity and normal tissue protection should be taken into account and the appropriate technology such as three-dimensional/intensity modulated radiation therapy employed in clinical practice, when hypofractionation is used.World journal of radiology. 06/2010; 2(6):197-202.
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ABSTRACT: The continuous increase of breast cancer (BC) incidence, the logistic constraints of the protracted standard 5-week radiations regimen have led to test short hypofractionated whole breast radiation therapy schemes. Three prospective randomized trials and a pilot trial have been published. Large numbers of patients were included, with follow-up duration ranging from 5 to 12 years. The conclusions of these trials were similar, showing local control and toxicity equivalent to those of the standard regimen, and supporting the use of three schemes: 42.5 Gy/16 fractions/3 weeks, 40 Gy/15 fractions/3 weeks or 41.6 Gy/13 fractions/5 weeks. However, the patients in these trials had favourable prognostic factors, were treated to the breast only and the boost dose, when indicated, was delivered with a standard fractionation. Hypofractionated treatment can only be recommended in patients treated to the breast only, without nodal involvement, with grade<3 tumours and who are not candidate to chemotherapy. If a boost is to be given, a standard fractionation should be used. Particular care should be taken to avoid heterogeneities leading to high fractional doses to organs at risk (lung and heart).Cancer/Radiothérapie 09/2011; 15(6-7):445-9. · 1.11 Impact Factor
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ABSTRACT: Aim-Background Patients with invasive ductal breast cancer undergoing breast-conserving surgery with lymphectomy, with negative or 3(+) LN (lymph nodes), T<5cm, and excellent expectant survival are submitted to either conformal fractionated irradiation (50Gy in 25 fractions, at 2Gy/fraction) or hypofractionated conformal 3D irradiation (fewer fractions at higher doses per fraction). Patients may or may not undergo chemotherapy, and irradiation commences ≤ 16 weeks after surgery. Methods From 2009 to 2010, 11 patients aged between 30 and 50 years, who matched the above criteria and had undergone invasive breast cancer and breast-conserving surgery, received hypofractionated radiotherapy. All patients received 42.5Gy in 16 fractions of 2.66Gy/fraction five times per week. Computed tomography simulation was used to design 3D conformal treatment planning with two tangentional fields and a multileaf collimator linear accelerator. Results After completion of radiotherapy, all patients showed Grade 0-1 skin reaction and no cosmetic impairment (oedema, fibrosis, telangiectasia). No side effects were observed in normal tissue structures and at-risk organs, such as the heart and lung. At 3, 6, 12, 18, 24, 30, and 36-month follow-up, none of the patients displayed post-radiation pneumonitis, pericarditis or dermatitis, nor did any patient develop a recurrence or regional distant metastases. Cosmetic assessment of the irradiated breast showed excellent results in terms of skin reaction compared with the healthy breast. Furthermore, the size and shape of the irradiated breast remained unchanged during and after irradiation. Conclusions Hypofractionated conformal irradiation in invasive breast cancer achieves optimal disease control and an excellent cosmetic result. Patients can be treated in fewer days with a safe and biological effective dose (BED), as that given by conformal fractionated irradiation. This development results in improved safety and enhanced quality of life for breast cancer patients.Hellēnikē cheirourgikē. Acta chirurgica Hellenica 03/2013; 85(2).
BIOLOGICALLY EFFECTIVE DOSE–RESPONSE RELATIONSHIP FOR BREAST
CANCER TREATED BY CONSERVATIVE SURGERYAND POSTOPERATIVE
GEORGE A. PLATANIOTIS, M.D., PH.D.,* AND ROGER G. DALE, PH.D., FIPEM., FRCR (HON).y
*Department of Oncology, Aberdeen Royal Infirmary, Aberdeen, United Kingdom; andyImperial College Healthcare NHS Trust,
London, United Kingdom
Purpose: To find a biologically effective dose (BED) response for adjuvant breast radiotherapy (RT) for initial-
stage breast cancer.
Methods and Materials: Results of randomized trials of RT vs. non-RTwere reviewed and the tumorcontrol prob-
ability(TCP) afterRTwas calculated foreach ofthem.Using the linear-quadratic formula andPoissonstatistics of
cell-kill, the average initial number of clonogens per tumor before RTand the average tumor cell radiosensitivity
(alpha-value) were calculated. An a/b ratio of 4 Gy was assumed for these calculations.
Results:Alinearregression equationlinkingBED toTCPwasderived:-ln[-ln(TCP)]=-ln(No)+ a*BED=-4.08+
0.07 * BED, suggesting a rather low radiosensitivity of breast cancer cells (alpha = 0.07 Gy-1), which probably
reflects population heterogeneity. From the linear relationship a sigmoid BED–response curve was constructed.
Conclusion: For BED values higher than about 90 Gy4the radiation-induced TCP is essentially maximizing at
90–100%. The relationship presented here could be an approximate guide in the design and reporting of clinical
trials of adjuvant breast RT. ? 2009 Elsevier Inc.
Adjuvant breast radiotherapy, Fractionation, Dose response.
Although postoperative radiotherapy (RT) for early breast
cancer treated by lumpectomy is an established treatment,
the issue of optimal RT dose and fractionation schedule re-
mains unresolved. The most widely used schedule for
whole-breast irradiation is 50 Gy in 25 fractions in 5 weeks,
whereas a variety of shorter (hypofractionated) RT schedules
has also been used in clinical practice.
lan et al. (1) have reported equivalent results (regarding local
control, survival, and postradiation effects) between the stan-
dard fractionation schedule of 50 Gy in 25 fractions in
32 days anda hypofractionated scheme of42.5 Gy in16 frac-
tions over 22 days, for women with node-negative early
breast cancer. Another short RT schedule (40 Gy in 15 frac-
tions) has been employed traditionally at Christie Hospital in
Manchester; reported results over 2,159 treated patients are
comparable to those reported from other centers (2–4).
The most influential trials are expected to be the recently
published START (Standardizing Radiotherapy) trials from
the UK. START A trial (5) has shown that 41.6 Gy/13 frac-
tions or 39 Gy/13 fractions are similar to the control regimen
of 50 Gy/25 fractions in terms of locoregional tumor control
and late normal tissue effects, a result consistent with the re-
sult of START Trial B (6), which has shown that a radiation
schedule of 40 Gy/15 fractions also offers equivalent results
with the standard schedule of 50 Gy/25 fractions.
Therefore, the need for establishing a dose-response rela-
tionship for postoperative breast radiotherapy is increasingly
needed as: (1) modified fractionation may offer useful prac-
tical advantages (1–9), (2) there is an international interest
in accelerated partial breast radiotherapy, especially with ad-
vanced treatment techniques such as IMRT and partial breast
RT (10, 11), and (3) highly hypofractionated RT schedules
are being explored currently, such as the FAST trial (FASTer
Radiotherapy for breast cancer), which investigates the limits
of hypofractionation for breast cancer RT (i.e., five fractions
of 5.7 Gy or 6.0 Gy delivered in 2–5 weeks) (12, 13).
Moreover, the size of dose per fraction in postoperative
breast RT is expected to strongly influence the therapeutic re-
sults as it has been anticipated that fractionation sensitivity of
breast cancer clonogens is rather high and broadly similar to
that of late-reacting normal tissues: the value of a/b ratio in
the linear quadratic model has been proposed to be approxi-
mately 4 Gy (14), a value confirmed by the results of START
trials (5, 6). As a result, the biologically effective dose (BED)
Aberdeen Royal Infirmary, Foresterhill AB25 2ZN, Aberdeen, UK.
Tel: (+44) 1224-553483; Fax: (+44) 1224-554183; E-mail: george.
Conflict of interest: none.
Received Feb 6, 2009, and in revised form May 11, 2009.
Accepted for publication May 11, 2009.
Int. J. Radiation Oncology Biol. Phys., Vol. 75, No. 2, pp. 512–517, 2009
Copyright ? 2009 Elsevier Inc.
Printed in the USA. All rights reserved
0360-3016/09/$–see front matter
will more properly reflect the relatively high fractionation
sensitivity of breast tumors, a fact that would make the use
of a BED-response relationship more clinically relevant
than a simple dose–response one.
In the present study, we have attempted to find the under-
lying BED-response relationship with the use of the existing
data from RCTs of postoperative vs. no postoperative RT.
METHODS AND MATERIALS
A MedLine search of the literature for randomized controlled tri-
als comparing lumpectomy alone vs. lumpectomy plus RT has
shown nine published randomized trials demonstrating that breast
irradiation substantially reduces the risk of local recurrence and pre-
vents the need for subsequent mastectomy (Table 1) (15–23).
Those studies have used dose/fractionation schedules ranging
from 40 Gy/15 fractions to 50 Gy/25 fractions for the whole breast
RT. The BED for each RT schedule consisting of N fractions, each
of d Gy, was calculated as:
BED ¼ n ? d½1 þ d=ða=bÞ?
was not taken into account. An important issue is the way in which
tumor control probability (TCP) is calculated from clinical data.
As proposed by Withers et al. (24), TCP should be calculated as:
TCP ¼failure rate without RT ? failure rate with XRT
failure rate without XRT
For example, if the recurrence rate was 5% in irradiated patients
compared with 25% in surgery-only patients, the TCP (expressed
as a percentage) is (25-5)/25; that is, 80%, not 95%. The second
from the right column in Table 1 lists the calculated TCPs for
each RCT. The surviving fraction (S) of cells after a RT regimen
may be calculated from BED via the relationship:
BED ¼ ?lnðSÞ
0S ¼ e?a$BED
If N0is the initial number of cells before RT (i.e., that remaining
after the preceding surgery or surgery and chemotherapy) then the
number (N) of cells surviving after RT is:
N ¼ N0? S
Given that a tumor is assumed to be controlled when every single
clonogenic cell has been eliminated then the TCP, assuming a Pois-
son distribution of surviving cells, is:
TCP ¼ e?N¼ e?N0S¼ e?N0e?a,BED
lnðTCPÞ ¼ ?N0e?a$BED0ln½?lnðTCPÞ?
¼ lnðN0Þ ? a$BED0 ? ln½?lnðTCPÞ?
¼ ?lnðN0Þ þ a$BED
Thus, plotting ?ln[–ln(TCP)] (y-axis) against BED (x-axis) will
give a straight line of slope a and intercept ?ln(N0), these parame-
ters representing the averages over the considered population.
Because the choice of the value of alpha to beta ratio would in-
fluence the results of the present analysis, we have performed a sen-
sitivity analysis similar to that performed recently by Fowler (25) to
examine how the BED is varying with the variation of a/b ratio
within a range of values of ?25% (range D50%) (i.e., in the range
of 3–5 Gy). We have used two breast RT schedules for this
Table 1. Studies of postoperative RT vs. no RT for breast cancer patients treated by conservative surgery
No RTRTRT scheduleTCP*BED (Gy4)
Fisher et al. (15) 570
Liljegren G et al. (16)54 Gy/27y
Malstrom et al. (21)48–54 Gy/20–25y
Holli et al. (20)8050 Gy/25y
BED breast RT + boost
Clark et al. (17)421
40 Gy/16y+ 12.5 Gy/5y
78.665 + 20=85
Veronesi et al. (18)50 Gy/25y+ 10 Gy/5y
96.675 + 15=90
Forrest et al. (19)50 Gy/20–25y+ 10–15 Gy Gy
45 Gy/25y+ 14 Gy/7y
76.375–81 + 15 = 90–96
317 Hughes et al. (22)
7565 + 21=86
Fyles et al. (23) 383
40 Gy/16y+ 12.5 Gy/5y
9265 + 20 = 85
Abbreviations: RT = radiotherapy; BED = biologically effective dose; TCP = tumor control probability.
The last four studies are boost vs. no boost after whole-breast RT. In the first two columns, the first row in each column corresponds to the
number of patients; the second to the % of local recurrence.
* TCP was calculated as: TCP= (failure rate without RT ? failure rate with RT)/failure rate without RT.
yNumber of fractions.
Dose-response for adjuvant breast radiotherapy d G. A. PLATANIOTIS AND R. G. DALE
analysis: 50 Gy in 25 fractions and 40 Gy in 15 fractions. For each
RT schedule the full range deviation D50% was divided by the cen-
tral value (the BED corresponding to a/b= 4 Gy) and finally
divided by 50.
Simple linear regression performed with Equation (2) has
?ln½?lnðTCPÞ? ¼ ?lnðN0Þ þ a?BED
¼ ?4:08 þ 0:07?BED
This equation corresponds to the graph in Fig. 1. The con-
stant term ?4.08 in the above equation corresponds to
?ln(N0) (95% confidence interval [CI] of ?12.4 to 4.2)
and gives a N0= 59.2 (0.01–243,000). The slope of the
line corresponds to a = 0.07 Gy-1(95% CI ?0.3 to 0.17).
The R2in the above model was calculated as 0.28 (SE 0.8,
p = 0.14). The low a-coefficient estimate indicates a rather
radioresistant cell population. This, however, is a common
finding when cohorts are analyzed and is usually ascribed
to inter-tumor heterogeneity; in particular, patients with the
most radioresistant tumors (low a) have a marked influence
tainly represents an average value (aeffective) useful for some
insight into the process. In addition we have calculated that
the average initial (before RT) number of clonogens per
tumor (to be killed by adjuvant RT) is 59.2. Then, best-fit
sigmoid relationship between TCP and BED can be recon-
structed (Fig. 2).
The resultsof the sensitivity analysisare shown in Table 2.
For the 50 Gy/25, a 1% change in a/b ratio results to 0.355%
change in BED, whereas for the 40 Gy/15, a 1% change in a/
bratioresults to0.425% changeinBED.Theabovevariation
is graphically shown in Fig. 3.
It has been shown by Withers et al. (24) that the biological
effectiveness of adjuvant irradiation should be measured by
the percentage decrease in recurrence rate, not by improve-
ments in the rate of control. Demonstration of success in
100 9080706050 403020100
Fig. 1. Fitted linear regression line corresponding to the equation:
–ln[–ln(TCP)] = ?ln(No) + a * BED = ?4.08 + 0.07* BED
(BED = biologically effective dose).
Fig. 2. The calculated biologically effective dose-tumor control
probability sigmoid curve from the data extracted from randomized
trials of radiotherapy (RT) vs. no RT after tumorectomy for initial-
stage breast cancer. Each data point corresponds to a randomized
Table 2. The change of BED in two breast RT schedules as
a result of variation in a/b ratio in the range of ?25%, around
the central value of 4 Gy (i.e., a/b= 3–5 Gy)
a/b ratio (Gy)
BED of 50 Gy/25
BED of 40 Gy/15
Abbreviations: RT = radiotherapy; BED = biologically effective
Bold indicates a/b ratio values of integral numbers.
514I. J. Radiation Oncology d Biology d PhysicsVolume 75, Number 2, 2009
clinical trials of adjuvant therapy is thus more likely the
adjuvant treatments, as has been done in this current study.
However, the difficulty in establishing such a dose–
response relationship in postoperative breast RT may be rel-
atively greater than for some other solid tumors, because:
(1) an unknown proportion of patients actually have no re-
sidual cancer cells left after operation, whereas others
have a subclinical (microscopic) amount of residual tu-
mor cells that must be eradicated by radiation (24, 26).
This is an inherent problem when analyzing the results
of any adjuvant therapy.
(2) dose-escalation studies are usually lacking, therefore any
informationshould beobtained onlyfrom RCTof RT vs.
no RT and which have used a (narrow) range of RT
(3) there are a number of factors that may seriously affect the
homogeneity of clinical data in the examined random-
ized trials: biologic aggressiveness of the treated tumors
(ranging from elderly patients with T1N0, Grade 1 hor-
mone receptor–positive tumors to women with multiple
positive nodes, hormone receptor negative, HER2-posi-
tive tumors), variable surgical techniques and skills
among centers, variable chemotherapy/endocrine re-
ally, local recurrence could be the result of regrowth of
tumor at the initial tumor bed, or of tumor in the same
breast but outside initial tumor bed from cells existing
there at the time of initial treatment, or finally a
de novo development of a new tumor in the same breast.
This source of heterogeneity also contributes to an over-
all decrease in the slope of the response curve.
In addition, when fitted to clinical data, linear quadratic
model gives parameter estimates approximately 10 times
(an order of magnitude) lower than estimates based on tumor
cells in vitro, because of inter-tumor heterogeneity (27).
However, additional (to the previously mentioned) heteroge-
neity may be a result of the combination of differences in in-
herent radiosensitivity, hypoxia, number of clonogens, and
repopulation. In addition, in vitro studies do not usually
take into account potentially lethal damage repair or cell
contact effects which could be a cause of radioresistance
Therefore, given the heterogeneity of the clinical material,
the calculated a value in this and similar studies is rather
a measure of an a-effective value. Although an effective
a of 0.07 Gy-1is seemingly characteristic of a cell population
of a low radiosensitivity an assumed homogenous radiosen-
sitivity coefficient (not applicable to individuals) is workable
for the interpretation of clinical data, as has been reported
We have also found that the pre-RT average clonogen
number per tumor is 59.2. This seemingly low value is
also, in part, a consequence of the ‘‘flattened out’’ population
response curve. A further possible reason for a low N0value
is that the residual hierarchical status of differentiating tu-
mors will cause them to have quite small numbers of rela-
tively undifferentiated regenerative cells (29). However, in
the present report, wehave studied RTasan adjuvantpostop-
erative treatment, i.e., after removal of the gross tumor and as
a result ‘‘initial’’ clonogen numbers are generally expected to
It should also be noted that, in analyses such as that per-
formed here, there is an intrinsic pairing between the derived
a and No values. Undoubtedly, further refinement of these
paired parameter values could be made if there were more
clinical results involving lower overall BEDs. At present,
the data points are all clustered around relatively high BED
values, meaning that the curve fit is considerably less rigor-
ous as a result, as indicated by the very wide range in the
95% CIs. However, in all cases it will be the paired parame-
ters that, together, define the ‘‘best fit’’ to the observed re-
sponses; in isolation the individual parameters may not
possess any meaningful biological interpretation and should
therefore not be used out of context. Carlone et al. (30), in
considering theoretical models of TCP, have demonstrated
that a range of paired values of a-radiosensitivity and clono-
gen number may fit the data acceptably well when inter-pa-
measurements are required to fix absolute values of individ-
Repopulation of tumor cells during RT has not been taken
into account in the present analysis. Given the relatively high
RT schedules used in the reported studies, repopulation
factor would not make any significant difference in our
The optimal fractionation schedule for the postoperative
RT of early breast cancer remains undefined and is a subject
of wide variety in clinical practice. Yamada et al. (14) have
reported that the BED values for two RT schedules (again
tio. The upper (continuous) line represents the BED for the schedule
of 50 Gy in 25 fractions and the lower (dashed) line the BED for the
schedule of 40 Gy in 15 fractions.
Dose-response for adjuvant breast radiotherapy d G. A. PLATANIOTIS AND R. G. DALE
calculated using a/b = 4 Gy for breast cancer cells) are: 40
Gy/16 fractions, BED = 65 Gy4, and 50 Gy/25 fractions,
BED = 75 Gy4. The 5-year local recurrence rates were
12.7% vs. 6.8%, respectively. They noted that, although
the latter fractionation schedule offers a smaller local recur-
rence rate with a relative difference of (12.7–6.8)/12.7 =
46.5%, this difference was not statistically significant
(p = 0.09).
However, the present analysis is suggestive of a TCP
>90% for BEDs >90 Gy4. It is noteworthy that, in a recent
RCT by the European Organization of Research and Treat-
ment of Cancer, 251 initial-stage breast cancer patients with
positive surgical margins after tumorectomy received
whole breast RT of 50 Gy/25 fractions (BED = 75 Gy4)
and were randomized to either a boost of 10 Gy (total
BED = 90 Gy4) or a boost of 26 Gy (total BED = 114
Gy4). Although this study was of a rather low power (37
‘‘events’’/local recurrences), its results are also suggestive
of a peaking in TCP after RT with a BED of higher than
Estimates of population radiosensitivity coefficients, such
as is attempted in the present study, would probably contrib-
ute to a more efficient reporting and comparisons of isoeffec-
tive doses of various fractionation schedules employed in
accelerated partial breast RT (10). For example, a commonly
used fractionation schedule for partial breast RT is 34 Gy in
10 fractions in 5 days (RT given twice daily) (10). This
schedule gives a BED = 63 Gy4(with incomplete repair be-
tween fractions not taken into account- otherwise the BED
would be somewhat higher). This, according to Figure 2, cor-
responds to a TCP of around 50%, meaning that a failure rate
without RT of, say 20%, would become approximately 10%
after this RT schedule.
quiring further judgment based on a number of factors that
mal tissue post-radiationeffects,socialandeconomicfactors,
and health care resources. Simple modeling such as is pro-
posed in this study could offer some guidance for planning
and assessment of clinical trials on adjuvant breast RT.
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Dose-response for adjuvant breast radiotherapy d G. A. PLATANIOTIS AND R. G. DALE