reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55

Available online at www.sciencedirect.com

ScienceDirect

journal homepage: http://www.elsevier.com/locate/rpor

Original research article

Biological effects and equivalent doses in

radiotherapy: A software solution

Cyril Voyant a,b,∗ , Daniel Julian c , Rudy Roustit d , Katia Biffi b ,

Céline Lantieri b
a University of Corsica, CNRS UMR SPE 6134, Campus Grimaldi, 20250 Corte, France
b Hospital of Castelluccio, Radiotherapy Unit, BP 85, 20177 Ajaccio, France
c Joseph Fourier University, 38000 Grenoble, France
d Centre de la république, Radiotherapy Unit, 63000 Clermont-Ferrand, France

a r t i c l e i n f o a b s t r a c t

Article history: Background: The limits of TDF (time, dose, and fractionation) and linear quadratic models
Received 17 May 2013 have been known for a long time. Medical physicists and physicians are required to provide
Received in revised form fast and reliable interpretations regarding delivered doses or any future prescriptions relat-
11 July 2013 ing to treatment changes.
Accepted 22 August 2013 Aim: We, therefore, propose a calculation interface under the GNU license to be used for
equivalent doses, biological doses, and normal tumor complication probability (Lyman
Keywords: model).
Radiobiology Materials and methods: The methodology used draws from several sources: the linear-
Fractionation quadratic-linear model of Astrahan, the repopulation effects of Dale, and the prediction
Time effect of multi-fractionated treatments of Thames.
Linear quadratic Results and conclusions: The results are obtained from an algorithm that minimizes an ad-
Repopulation hoc cost function, and then compared to an equivalent dose computed using standard
calculators in seven French radiotherapy centers.
© 2013 Greater Poland Cancer Centre. Published by Elsevier Urban & Partner Sp. z o.o. All
rights reserved.

crucial to explain and understand these mechanisms.3–5 Pro-

1. Background: problems of the biologically
viding a conceptual basis for radiotherapy and identifying
equivalent dose
the mechanisms and processes that underlie the tumor and
normal tissue responses to irradiation can help to explain
It has long been known that radiation biology plays an impor- the observed phenomena.6 Examples include understanding
tant role and is necessary for radiotherapy treatments. The hypoxia, reoxygenation, tumor cell repopulation, or the mech-
time of radiation effects on normal and malignant tissues anisms of repair of DNA damage.3,7,8 The different biological
after exposure range from a femtosecond to months and effects of radiation should be divided into several phases:
years thereafter.1,2 Therefore, to optimize treatment, it is the physical phase (interaction between charged particles and

∗
Corresponding author at: University of Corsica, CNRS UMR SPE 6134, Campus Grimaldi, 20250 Corte, France. Tel.: +33 495293666;
fax: +33 495293797.
E-mail addresses: voyant@univ-corse.fr, cyrilvoyant@gmail.com, cyrilvoyant@hotmail.com (C. Voyant).
1507-1367/$ – see front matter © 2013 Greater Poland Cancer Centre. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved.
http://dx.doi.org/10.1016/j.rpor.2013.08.004
48 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55

number of fractions, and T the overall treatment time). How-

Nomenclature ever, this model has been often criticized.14 In short, some
researchers consider and have even shown that the NSD for-
˛ and ˇ fitting parameters of the linear quadratic model mula is not a valid description for all tumors and normal
of cell survival (Gy2 and Gy) tissues; instead, they maintain that the model incorrectly
˛UNSC adjustment parameter of the occurrence model describes the effects of fraction number and treatment dura-
of cancer radio-induced (Gy−1 ) tion.
(x) Heaviside function
/a parameter of the LQL model Dtol = NSD · Nn · T t (1)
 parameter adjustment necessary to take into
account the poly-fractionation in the model LQ The LQ model is most frequently used in radiotherapy
(h−1 ) units. It allows the equivalent dose to be easily evaluated for
BED biological equivalent dose (Gy) different fractionations. This concept involves the˛/ˇ ratio, as
D physical dose (Gy) shown in Eq. (2) (D is the total dose for a fraction size of d gray).
dt dose per fraction from which the curve of cell
survival becomes linear (Gy) d + (˛/ˇ)
Dprol proliferation dose (Gy/day) EQD2 = D (2)
2 + (˛/ˇ)
D1 et D2 equivalent doses for the treatments 1 and 2 (Gy)
EQD2 equivalent dose for a 2 Gy/fraction treatment EQD2 is the dose obtained using a 2 Gy fraction dose, which
(Gy) is biologically equivalent to the total dose D given with a frac-
EUD equivalent uniform dose (Gy) tion dose of d gray. The values of EQD2 may be added in
EUD2Gy EUD for an equivalent dose related to a refer- separate parts in the treatment plan. This formula may be
ence of 2 Gy per fraction adapted to fraction doses other than 2 Gy.
f cost function to minimize by the algorithm
ja number of day-offs 1.2. Limitations of the LQ model
Hm LQ model correction taking account the poly-
fractionation The LQ model is frequently used for modeling the effects of
Kincidence occurrences probability of radio induced can- radiotherapy at low and medium doses per fraction for which
cer (%) clinical data appear to fit reasonably well. The main disad-
m fraction number and slope factor of the NTCP vantage of the LQ approach is that the overall time factor is
model not taken into account, because in radiotherapy it is regarded
n number of fraction to be more complex than previously supposed.3 It is indeed
NTCP complications rate of post radiation (%) very difficult to include this parameter in the LQ equation.
PUNSC parameter related to the occurrence of However, a technique may be used to integrate a penalty term
radiation-induced cancers (Gy−1 ) in Eq. (2). Thus, for Tstop days off treatment, the dose recov-
T duration between two irradiations (heures) ered would be Tstop ·Dprol , where Dprol is the proliferation factor
T overall time (day) (in Gy/day; for example, 0.22 for laryngeal edema or 0.15 for
TD50 dose at which there is a 50% complication (Gy) rectosigmoid complications). This methodology is essentially
Tk time at which repopulation begins after start of validated for discontinuation during treatment. As a general
treatment (day) rule, the main limitations of using the LQ model are linked
Tpot potential doubling time (day) to repopulation (LQ does not take into account the dose pro-
Tstop days off during the treatment traction), bi-fractionated treatments and high-dose fractions
u boundary used in the NCTP calculus (Gy) (continuously bending survival curve versus linear behavior
observed at least in some cell lines). Other more sophisticated
models, however, do take into account these weaknesses. We
tissue atoms), chemical phase (the period during which the will later see that the LQ model requires further theoretical
damaged atoms and molecules react with other cellular com- investigation, especially in terms of a biologically effective
ponents in rapid chemical reactions), and biological phase dose (BED).
(impact of the generated lesions on the biological tissue4 ). Given the difficulty of computing the BED, we conducted a
The following section describes the models most often used study in seven radiotherapy centers in France: CHD Castel-
in radiotherapy. These are simplistic models that actual treat- luccio (Ajaccio; two classical calculators used), Center de
ments are based on and that are validated and approved.9–12 Cancérologie du Grand Montpellier (Montpellier), CRLCC Paul
Lamarque (Montpellier), Clinique Saint-Pierre (Perpignan),
1.1. Reference models Center de la République (Clermont Ferrand), CHU of Grenoble,
and CHU of Nîmes. A questionnaire was sent to medical physi-
Numerous models exist to evaluate the biological equiva- cists working at these centers with the aim of comparing the
lent dose, but the two most common ones are the nominal results of equivalence (for standard radiotherapy planning).
standard dose (NSD13 ) and linear quadratic (LQ9 ) models. The Table 1 presents the results of this survey which indicate that
NSD uses the power law described in Eq. (1) (Dtol is the toler- not all of the operators obtained the same results. The 95%
ance dose of the tissue, NSD is a constant, n and t ∈ R+ , N the confidence interval was often very large. Moreover, the relative
 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55 49

Table 1 – Methodologies for computing the equivalent dose used in eight clinical calculators from seven radiotherapy
centers. The median dose, average dose, and standard deviation are given in Gy. For the standard deviation, absolute
and relative modes (␴/average) were used. Bold font is used to represent values >5%.
Treatments Organs at risk Target volumes
Spinal cord Prostate (metastasis)

10 × 3 Gy Median 37.50 36.65

Average ± 95% CI 37.8 ± 1.2 36.6 ± 1.9
Stand dev 1.71/4.5% 2.87/7.8%

Spinal cord Breast (metastasis)

10 × 3 Gy Median 37.50 35.57

Average ± 95% CI 37.8 ± 1.2 35.97 ± 1.4
Stand dev 1.71/4.5% 2.06/5.7%

Spinal cord Prostate (metastasis)

1 × 8 Gy Median 20.00 14.90

Average ± 95% CI 19.1 ± 2.3 15.9 ± 3.2
Stand dev 3.38/17.7% 4.72/29.6%

Brain Breast (metastasis)

10 × 3 Gy Median 37.50 35.57

Average ± 95% CI 37.5 ± 0.9 35.9 ± 1.4
Stand dev 1.26/3.4% 2.03/5.6%

Spinal cord Prostate (metastasis)

1 × 8 Gy (1 month Median 33.30 21.50

gap time) 1 × 8 Gy Average ± 95% CI 33.6 ± 4.0 24.04 ± 6.8
Stand dev 5.78/17.2% 9.76/40.6%

Pericardium Lung (metastasis)

5 × 4 Gy Median 30.90 27.07

Average ± 95% CI 33.7 ± 5.9 28.9 ± 3.6
Stand dev 8.47/25.1% 5.14/17.8%

Oral mucosa Oropharynx

20 × 2 Gy (1 week gap Median 57.95 57.95

time) 10 × 2 Gy Average ± 95% CI 58.1 ± 0.5 57.6 ± 1.9
Stand dev 0.66/1.14% 2.76/4.8%

Oral mucosa Oropharynx

22 × 1.8 Gy Median 41.95 41.70

(bi-fractionated) Average ± 95% CI 41.0 ± 1.6 41.7 ± 2.2
Stand dev 2.32/5.6% 3.12/7.5%

Rectum Prostate

25 × 1.8 Gy then Median 72.58 72.75

15 × 2 Gy Average ± 95% CI 72.6 ± 0.4 72.6 ± 0.7
Stand dev 0.54/0.7% 1.00/1.37%

Lung Breast

20 × 2.5 Gy (4 Median 55.58 53.50

fraction/week) Average ± 95% CI 55.0 ± 1.1 53.5 ± 1.2
Stand dev 1.59/2.9% 1.71/3.2%

Optic chiasma Glioblastoma

4 × 4.5 Gy (2 week Median 50.25 42.15

gap time) 4 × 4 Gy Average ± 95% CI 49.9 ± 2.7 43.1 ± 2.8
Stand dev 3.96/7.9% 4.07/9.4%

Skin (early) Breast

28 × 1.8 Gy (1 week Median 46.65 46.36

gap time) Average ± 95% CI 46.7 ± 0.6 46.5 ± 0.8
Stand dev 0.90/1.9% 1.13/2.4%
50 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55

standard deviation (also known as the dispersion coefficient) (a) The d > dt case
was frequently greater than 5% (13 times out of 24). This dis- When the dose per fraction (d) is greater than the LQL
persion was larger in the case of target volumes; the maximal threshold (dt ∼ 2˛/ˇ), the BED is computed using Eq. (3) (one
volume (close to 40%) was related to high doses per fraction fraction permitted per day). This template regroups Astra-
with a gap between two radiotherapy cycles. In Table 1, it is han’s high-dose model17 and Dale’s repopulation model18
evident that all of the users did not estimate dose equivalence (n is the number of fraction, (x) the Heaviside function,
in the same manner. Only for a dose per fraction approaching /˛ the parameter of the LQL model and Tpot the potential
2 Gy and standard overall time were the results equivalent. doubling time in day).
Note that in the multi-fractionated treatments, only 50% of
  dt
 

the centers were able to give an equivalent dose, as this kind
BED = n dt 1 + + (d − dt )
of treatment was not computable. ˛/ˇ ˛
The numbers of centers included in this study was low, and ln(2)
− (T − Tk ) (T − Tk ) (3)
there was no consensus among the centers in terms of their ˛ · Tpot
methods for computing the doses. If we look more closely,
the biological equivalent dose was the only process that was The second term used in this equation is useful only when
calculated using non-official software. All of the other steps the overall time T is greater than the Tk value (kick-off
in treatment planning followed an official protocol. It is thus time). If this threshold is not achieved, the tumor is con-
legitimate to ask why centers use in vivo dosimeters or try sidered to be non-proliferative (early hypoxia).
to achieve a global error of 2% throughout treatment, if the (b) The d ≤ dt case
prospective calculation of the equivalent dose (and prescrip- When the fraction dose is low, it is possible to use the
tion) is greater than 20%. In order to address the question standard BED equations while considering one or more
of responsibility, the following section of this article is tar- fractions per day (Eq. (4)). This methodology follows the
geted at medical physicists, knowing that the prescriber is model of Thames,19 who introduced the repair factor Hm
the physician. In case of equivalent computations, the optimal related to the amount of unrepaired damage (Eq. (5)). If
operation would be for the technical work to be performed by the inter-fraction interval is reduced below the full repair
the physicist and validations by the physician (while taking interval (between 6 h and 1 day), the overall damage from
into account the clinical scenario). This methodology allows the whole treatment is increased because the repair of
for a double checking of the calculation results. damage due to one radiation dose may not be complete
before the next fraction is given (Hm is LQ model correction
taking into account the poly-fractionation, m the num-
2. Aim ber of fraction per day,  the incomplete repair and  the
parameter adjustment necessary to take into account the
We, propose a calculation interface under the GNU license poly-fractionation in the model LQ in h−1 ).
to be used for equivalent doses, biological doses, and nor-
mal tumor complication. The next section describes the  d
 ln(2)
theoretical methodology that we propose to compute the BED = n · d 1 + (1 + Hm ) − (T − Tk )
˛/ˇ ˛ · Tpot (T − Tk )
BED. (4)

3. Materials and methods: the developed  2    

models 1 − m
Hm = m− and  = e(−T)
m 1− 1−
The BED (introduced by Fowler9 ) is a mathematical concept (5)
used to illustrate the biological effects observed after irradi-
ation. In addition to being easily computable (BED = physical Note that in the case of mono-fractionation, the Hm factor
dose × relative efficiency), this notion is interesting because is null. These equations only relate to the target vol-
two irradiations with the same BED generate the same radio- ume calculation. For the organs at risk, the kick-off time
biological effects. For this reason, it is easy to compare is not relevant, meaning that it is necessary to use a
treatments with different doses, fractionations, and overall repopulation-specific approach.
times. The following section introduces the BED-based mod-
els that we advocate as well as the rules and guidelines for 3.2. Models for organs at risk
using the LQL Equiv software.
As in the precedent section on target volumes, this section
3.1. Target volume models similarly separates high and low doses per fraction. The BED
formulae are almost equivalent to the target volume model;
Let us examine two different treatment cases separately. The only the terms relating to the lack of dose by proliferation are
first one involves treatments with a high-dose fraction (one modified.
treatment per day, the fraction size d is greater than the dt
limit15 ), which requires a linear quadratic linear (LQL) model. (a) The d > dt case
The second case relates to other treatments (d < dt ), where the To understand this methodology, it is necessary to con-
LQ model is applicable to daily multi-fractionation.16 sult Van Dyk’s law.20 The kick-off time is no longer
 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55 51

considered, with the recovered dose (Drec = ln(2)/˛ · Tpot dispense with the days off treatment and multi-fractionation
in Gy/day) instead being added. The global model is per day in relation to the reference treatment. The following
described in Eq. (6). example concerns a tumor case with a dose per fraction less
than dt (second part of the target volume model), while the
  dt
 

BED = n dt 1 + + (d − dt ) − Drec T (6) cost function, f, is given in Eq. (11). Concerning the three other
˛/ˇ ˛ cases examined in the previous sections, a similar relationship
is found.
(b) The d ≤ dt case
In the case of low doses per fraction, the methodology is
 dref

f (nref , dref , n, d, ja) = |nref · dref 1 +
similar to the target volume model: the Hm parameter (Eq. ˛/ˇ
(5)) is nonetheless required, which allows us to take into ln(2)
 d

account more than one fraction per day. As seen in Eq. (7), − (Tref − Tk ) (T − Tk ) − n · d 1 + (1 + Hm )
˛ · Tpot ref ˛/ˇ
the recovered dose is used as in the previous case.
ln(2)
  − (T − Tk ) (T − Tk )| (11)
d ˛ · Tpot
BED = n · d 1 + (1 + Hm ) − Drec · T (7)
˛/ˇ
The global treatment duration can be seen to be directly
3.3. Computational methods for the equivalent dose
associated with the fraction number and days off during radio-
therapy. Following Eq. (11), the 2 Gy-per-fraction equivalent
The standard models used for the equivalent dose as based
dose (EQD2 ) for standard treatment with the characteristics
on the LQ approach are easily exploitable. The main formula-
is given by the algorithm shown in Eq. (12).
tion of the model (Eq. (2)) can be obtained by considering the
general formula described in Eq. (8) as follows. 
argminn f (nref , 2, n, d, ja) = n0
ref ∈ R+
(12)
(˛/ˇ + d2 ) EQD2 = 2n0
D1 = D2 (8)
(˛/ˇ + d1 )
All of the results obtained in this section were implemented
This equation may be validated using the BED methodol-
using a Matlab® standalone application known as LQL Equiv.
ogy. Considering the BED of two treatments to be equal, it
The characteristics of this software, its limitations, and guide-
appears that a simple relation links the two overall doses,
lines for its use are discussed in the following section.
D1 (=n1 d1 ) and D2 (=n2 d2 ). The detail of this procedure is shown
in Eq. (9).
4. Results: LQL Equiv software
 d1
  d2

BED1 = n1 · d1 1+ = BED2 = n2 · d2 1+ (9)
˛/ˇ ˛/ˇ The LQL Equiv software was developed in collaboration
by the CHD Castelluccio radiotherapy unit in Ajac-
In the case of more sophisticated BED formulations, it is
cio and the University of Corsica. It is a free software
not easy to determine a simple formula linking the D1 and
released under the GNU license. The source codes, exe-
D2 doses, as recovery and repopulation significantly compli-
cutable file, help files, and license terms are available at
cate the computational principle. Most of the existing software
http://cyril-voyant.univ-corse.fr/LQL-Equiv a34.html. Before
that uses the overall time correction does not calculate the
installing this software, it is advisable to refer to the installa-
equivalent dose; instead, it only provides the BED for the cho-
tion guide and to download and execute Matlab Component
sen treatments. In clinical use, it is more valuable for the
Runtime (MCR 32 bits, version 7.15 or later). This latter step
physician or physicist to work with the equivalent dose in
is necessary since the application was programmed using
standard fractionation. In this context, the methodology used
the GUI Matlab® software (32 bits, v. 7.12) and deployed with
in the LQL Equiv software is based on an innovative algorithm,
the Matlab Compiler® (v. 4.12) which use MCR (a standalone
which allows a cost function extremum to be determined
set of shared libraries enabling the execution of Matlab®
based on BED modeling. To explain this methodology, it is nec-
applications on a computer without an installed version
essary to consider two irradiations (Indices 1 and 2), which
of Matlab® ). Users of the LQL Equiv software are advised
are defined by a fraction number (n), dose per fraction (d), and
to provide us with comments on the software, its libraries
days of discontinuation (ja). The corresponding BED is noted as
(biological parameters for each organ or tumor type), or any
BED1 (n1 , d1 , ja1 ) and BED2 (n2 , d2 , ja2 ), while the cost function
bugs so as to allow us to develop the software. Note that the
f is defined in Eq. (10) as follows.
application requires Microsoft Windows® (the resolution and
colors are for Vista or later versions).
f (n1 , d1 , ja1 , n2 , d2 , ja2 ) = |BED1 (n1 , d1 , ja1 ) − BED2 (n2 , d2 , ja2 )|

(10) 4.1. Software

In clinical use, it is desirable to compare a radiotherapy trial The graphical interface of the LQL Equiv software is pre-
with one that is performed in a conventional manner (gener- sented in Fig. 1, divided into five sections: demographical
ally with 2 Gy per fraction without interruption). This concept zone, tissue choice (organs at risk and target volumes), refer-
of a reference dose simplifies the issue, as it is thus possible to ence zone (characteristics for computing the equivalent dose),
52 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55

Fig. 1 – Graphical interface for the LQL Equiv.

treatment planning zone (three juxtaposed and independent ˛/ˇ = 10 for oral mucosa and 2 for others) and the LQL Equiv
treatments), and, finally, the equivalent dose under the refer- software. The difference between the two approaches is sub-
ence conditions. Prior to using the software, it is important to stantial. The overall time effect and unusual doses per fraction
understand that repopulation or a high dose per fraction can result in completely different outputs. The maximum differ-
considerably alter the standard equivalent results. Therefore, ence is close to 25%; this value is linked to the cell repopulation
it is recommended for each user to verify the results obtained of prostate cancer. In this case, the non-specific methods are
and validate them during an initial test phase. The results certainly not usable.
must be consistent with routine procedures as well as the data In addition, for the BED and equivalent calculations,
in the literature. The details of the instructions allowing to use the LQL Equiv software allows two other parameters to be
the software are available in the Appendix A. obtained, which may be useful in clinical practice: the nor-
The ideal scenario would be to compare these results with mal tumor complication probability (NTCP22 ) and the ratio of
other softwares and obtain a mean score for the two outputs radiation-induced cancer after irradiation.
or for the outputs that minimize the physical dose. We rec-
ommend using this software as a secondary BED calculator. It 4.3. Others elements computed by the software
aims to provide assistance, but cannot be used as a substitute
for routine calculations made by a professional. The creators In the LQL Equiv software, the bottom of the interface is
of the LQL Equiv software cannot be held responsible for any dedicated to the calculation of the NTCP and ratio of radiation-
errors caused by the misuse of the results obtained. induced cancer. For the first parameter, the formula for its
computation (only for normal tissues) is based on the Lyman
4.2. Comparison with standard models model22 as presented in Eq. (12) (TD50 is the dose at which
there is a 50% complication in Gy, u the boundary used in the
This section compares the results of the LQL Equiv software NCTP calculus in Gy and m the slope factor). To use this for-
with the available clinical models. However, it is important to mula, it is necessary to first compute the EUD (Niemerko21 ).
note that all of the parameters used for calculating the equiva- However, in practice, this quantity is not feasible. It is instead
lence are available on the graphical interface. Using MatlabTM possible to use the equivalent dose related to a reference dose
and the downloadable source codes, it is easy to modify or of 2 Gy per fraction (EQD2 ≈ EUD2Gy ). However, the NTCP for-
complete these parameters. It is also possible to contact the malism is valid for 2 ± 0.2 Gy/fraction. Moreover, the DVH must
software authors for assistance in developing the software. be used, in which case the equivalent dose refers to the aver-
LQL Equiv is in direct competition with TDF Plan developed age dose for the parallel organs or the maximal dose (D5%) for
by Eye Physics LLC, which proposes a multitude of parame- the serial organs.
ters. However, the software is dedicated to the calculation of
⎧ u
BED and is not really consistent with the reference equivalent ⎪
⎨ NTCP(n, d, ja) = √
1
e−t
2 /2
dt
dose. Moreover, we aimed to develop ergonomic software with 2 −∞ (13)
minimum of adjustable parameters, which ultimately compli- ⎪
⎩ u = EUD2Gy (n, d, ja) − TD50
cate the interpretation of the output. These two approaches mTD50
are nevertheless complementary; for more information about
the different models used, refer to the TDF Plan website The second add-on in the software concerns the esti-
(http://www.eyephysics.com/tdf/Index.htm). Table 2 presents mation of radiation-induced cancer. The theory used
a comparison between outputs of the standard calculation was developed by the United Nations Scientific Com-
models described in section II (LQ without proliferation and mittee on the Effects of Atomic Radiation (UNSCEAR;
 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55 53

Table 2 – Comparison between the outputs of the LQL Equiv and standard calculation models (LQ without proliferation
and with ˛/ˇ = 10 for oral mucosa and 2 for others). Bold font is used to show differences >5%.
Treatments Organs at risk Target volumes
Spinal cord Prostate (metastasis)

10 × 3 Gy Classical output (Gy) 37.5 37.5

LQL Equiv output (Gy) 37.5 36
Difference (Gy/%) −0/−0% −1.5/−4%

Spinal cord Breast (metastasis)

10 × 3 Gy Classical output (Gy) 37.5 37.5

LQL Equiv output (Gy) 37.5 38.2
Difference (Gy/%) −0/−0% 0.7/1.9%

Spinal cord Prostate (metastasis)

1 × 8 Gy Classical output (Gy) 20 20

LQL Equiv output (Gy) 16 16.8
Difference (Gy/%) −4/−20% −3.2/−16%

Brain Breast (metastasis)

10 × 3 Gy Classical output (Gy) 37.5 37.5

LQL Equiv output (Gy) 43.5 38.2
Difference (Gy/%) 6/16% 0.7/1.9%

Spinal cord Prostate (metastasis)

1 × 8 Gy (1 month Classical output (Gy)) 40 40

gap time) 1 × 8 Gy LQL Equiv output (Gy) 32 33.3
Difference (Gy/%) −8/−4.63% −6.7/16.7%

Pericardium Lung (metastasis)

5 × 4 Gy Classical output (Gy) 30 30

LQL Equiv output (Gy) 37.5 23.3
Difference (Gy/%) 7.5/25% −6.7/−22.3%

Oral mucosa Oropharynx

20 × 2 Gy (1 week gap Classical output (Gy) 60 60

time) 10 × 2 Gy LQL Equiv output (Gy) 54.4 53
Difference (Gy/%) −5.6/−9.3% −7/−11.7%

Oral mucosa Oropharynx

22 × 1.8 Gy Classical output (Gy) 38.9 38.9

(bi-fractionated) LQL Equiv output (Gy) 45 36
Difference (Gy/%) 6.1/15.7% −2.9/−7.4%

Rectum Prostate

25 × 1.8 Gy then Classical output (Gy) 72.7 72.7

15 × 2 Gy LQL Equiv output (Gy) 71 73
Difference (Gy/%) −1.7/−2.3% 0.3/0.4%

Lung Breast

20 × 2.5 Gy (4 Classical output (Gy) 56.2 56.2

fraction/week) LQL Equiv output (Gy) 62.9 56.8
Difference (Gy/%) 6.7/11.9% 0.2/0.3%

Optic chiasma Glioblastoma

4 × 4.5 Gy (2 week Classical output (Gy) 53.2 53.2

gap time) 4 × 4 Gy LQL Equiv output (Gy) 42.8 47.4
Difference (Gy/%) −10.4/−19.5% −5.8/−10.9%

Skin (early) Breast

28 × 1.8 Gy (1 week Classical output (Gy) 47.9 47.9

gap time) LQL Equiv output (Gy) 47.6 42.3
Difference (Gy/%) −0.3/0.6% −5.6/−11.7%
54 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55

http://www.unscear.org/unscear/fr/publications.html). The
different meta-analyses of previous radiological incidents
Appendix A. Instructions for use
are used in this model. The ratio of radiation-induced cancer
(in %) relating to normal tissue is provided in Eq. (14) as The number of modifiable parameters in the LQL Equiv soft-
follows (˛UNSC is the adjustment parameter of the occurrence ware is minimal, while the items required to complete a dose
model of cancer radio-induced in Gy−1 , PUNSC the UNSCEAR equivalent calculation are limited. Only the white boxes can
probability and D2Gy the equivalent dose for a 2 Gy/fraction be modified.
treatment in Gy). The upper left part of the interface is dedicated to patient
demography (identity and pathology) and operator traceabil-
ity. These parameters are not essential for initiating the
2Gy
Kincidence = PUNSC · D2Gy · e−˛UNSC ·D (14) calculation. Below this, the reference dose per fraction should
be provided; by default, the dose is 2 Gy/fraction.
In the top-right of the interface, there are two dropdown
Note that methods used to compute NTCP and Kincidence are menus related to the organs at risk and target volumes cho-
simplified; it is evident that interested readers must identify sen by the operator to obtain the equivalent dose. Once these
more specialized documents. These parameters are given as steps are completed, it is necessary to define the desired treat-
additional information. ment plans. Only three plans are proposed, but the software is
able to test more by integrating the overall results in a single
treatment plan, such as the EQ1 (dose, days off, and number of
5. Conclusion fractions must be adjusted). The overall time must be verified
or else there may be some imprecision in the final calcula-
In this article, we have exposed the compiling results of var- tion. A null number of fractions or doses results in cancelling
ious published LQ model modifications, which have been the calculation of the equivalent dose (the duration of the
modified to be better suited for specialized radiotherapy tech- sequence does not contribute to the final output).
niques such as hypo- or hyperfractionation. The LQ model After selecting the treatment plan and clicking on the cal-
was modified to take into account multi-fractionation, repop- culation button, the BED and equivalent doses are given. The
ulation, high-dose fractions, and overall time. Moreover, we page may be printed, or otherwise, there is a digital archiving
propose a software program (LQL Equiv), integrating all of solution based on the WindowsTM print screen button.
these concepts regarding the main organs at risk or target When taking into account the days off, the weekend should
volumes. Moreover, this free and easy-to-use software allows not be considered; only discontinuations that occur dur-
the NTCP to be calculated. Finally, this software permits the ing weekdays should be included. Beyond 20 days off from
obtained results to be compared and validated against other treatment, the algorithms are no longer valid. In the first
“homemade” models, with the purpose of harmonizing prac- approximation, the side of caution indicates that healthy tis-
tices in interested centers. However, it is essential not to sues do not recover during the gap time. For the second cycle
consider models as “general biological rules”, parameters and of radiotherapy that occurs a long time after the first one,
output uncertainties can be very large; this phenomenon is we must be vigilant with regard to the treated organs. In the
related to the number of regression parameters (parsimony case of the skin, for example, we may consider a duration
principle) and to the data snooping (e.g. failure to adjust exist- of 2–5 years to be sufficient to negate any effects from the
ing statistical models when applying them to new datasets). previous treatment (this is, however, invalid if the effects are
already visible at the time of irradiation), while for the spinal
cord, it must be considered, where possible, that there exists a
dose memory, with the effects of gray radiation always being
Conflict of interest
present. In this regard, the software takes into account that
certain organs, such as spinal cord, have a low Drec in order
None declared.
to limit the consequences to the most critical organs. More-
over, it is necessary to consider all of the treatment phases if a
dose equivalent is required for the second stage of a prostate
Financial disclosure disease. In this case, the first phase of the treatment must be
considered, or otherwise, the kick-off time will not be correctly
None declared. taken into account.
To avoid the dose overestimation, we recommend first cal-
culating the dose equivalent for the organ, i.e., the limiting
Acknowledgments factor, and then estimating the fractionation effect on the tar-
get volume.
We would like to thank the following people for their contri- For organs at risk, it is possible to use the nominal dose.
bution: Stéphane Muraro (Center de Cancérologie du Grand Thus, in the case of the pelvis, for the first 45 Gy given in 25
Montpellier), Norbert Aillères and Sébastien Siméon (CRLCC fractions, the dose received by the rectum may be considered
Paul Lamarque; Montpellier), Vincent Plagnol (Clinique Saint- equal to 45 Gy. However, in order to optimize the methodology,
Pierre; Perpignan), Nicolas Docquière and Jean-Yves Giraud it seems more reasonable to utilize a more detailed analy-
(CHU de Grenoble), and Bérengère Piron (CHU de Nîmes). sis. If the validation criterion is D30, the software should be
 reports of practical oncology and radiotherapy 1 9 ( 2 0 1 4 ) 47–55 55

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