 Research
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Correlation between egfr expression and accelerated proliferation during radiotherapy of head and neck squamous cell carcinoma
Radiation Oncologyvolume 7, Article number: 143 (2012)
Abstract
Purpose
To investigate the correlation between the expression of Epidermal Growth Factor receptor (EGFr) and the reduction of the effective doubling time (T_{ D }) during radiotherapy treatment and also to determine the dose per fraction to be taken into account when the overall treatment time (OTT) is reduced in accelerated radiotherapy of head and neck squamous cell carcinoma (HNSCC).
Methods
A survey of the published papers comparing 3years of local regional control rate (LCR) for a total of 2162 patients treated with conventional and accelerated radiotherapy and with a pretreatment assessment of EGFr expression, was made. Different values of T_{ D } were obtained by a model incorporating the overall time corrected biologically effective dose (BED) and a 3year clinical LCR for high and low EGFr groups of patients (H_{EGFr} and L_{EGFr}), respectively. By obtaining the T_{ D } from the above analysis and the subsites’ potential doubling time (T_{ pot }) from flow cytometry and immunohistochemical methods, we were able to estimate the average T_{ D } for each subsite included in the analysis. Moreover, the dose that would be required to offset the modified proliferation occurring in one day (D_{ prolif }), was estimated.
Results
The averages of T_{ D } were 77 (2790)_{95%} days in L_{EGFr} and 8.8 (7.311.0)_{95%} days in H_{EGFr}, if an onset of accelerated proliferation T_{ K } at day 21 was assumed. The correspondent H_{EGFr} subsites’ T_{ D } were 5.9 (6.6), 5.9 (6.6), 4.6 (6.1), 14.3 (12.9) days, with respect to literature immunohistochemical (flow cytometry) data of T_{ pot } for OralCavity, Oropharynx, Hypopharynx, and Larynx respectively. The D_{ prolif } for the H_{EGFr} groups were 0.33 (0.29), 0.33 (0.29), 0.42 (0.31), 0.14 (0.15) Gy/day if α = 0.3 Gy^{1} and α/β = 10 Gy were assumed.
Conclusions
A higher expression of the EGFr leads to enhanced proliferation. This study allowed to quantify the extent of the effect which EGFr expression has in terms of reduced T_{ D } and D_{ prolif } for each head and neck subsite.
Background
HNSCC accelerates the production of clonogenic cells during radiotherapy, whereby an amount of a given dose of radiation may be used to sterilize cells produced during the treatment [1]. Therefore, by maintaining the same total dose, a reduction of OTT results in increased Tsite control.
The benefit of reduced OTT has been tested in several studies comparing conventional treatment with accelerated fractionation schedules. The data showed an improved 5year LCR [2, 3].
However, the response is heterogeneous with respect to the different expressions of EGFr in the patient population and also to the subsites, as accelerated repopulation of clonogenic tumour cells and locoregional control could arise.
EGFr is overexpressed in the majority of HNSCC [4] and activation of the receptor leads to phosphorylation of the tyrosine kinase domains on the intracellular part of the receptor, activating downstream cascades which result in altered gene activation and modulation of the cell products. This has been related to increased cell proliferation, decreased apoptotic activity, increased angiogenesis, increased invasive and metastatic potential, and hence increased resistance to anti tumour therapy.
Furthermore, it has been shown that tumours with high expression of EGFr have a better LCR when treated with accelerated radiotherapy, while there was no benefit of acceleration in tumours with low EGFr.
Consequently, high EGFr has been suggested as a negative prognostic factor when OTT is prolonged, and as a positive prognostic factor when treatment time is reduced [5].
The aim of the present study is to investigate the correlation between EGFr expression and the reduction of T_{ D } during radiotherapy treatment and also to determine the dose per fraction to be taken into account when the OTT is reduced in accelerated radiotherapy of HNSCC.
To achieve this goal, the data published in the literature were reviewed and analyzed by comparing different 3year LCR and OTT for various dose fractionation schemes, also taking into account different subsites of HNSCC.
Methods
Literature review
The primary end point considered for the present analysis was LCR, defined as the probability of avoiding local regional recurrence of cancer at the primary tumour site (T) or nodal (N) position, within 3years after the end of radiotherapy.
A survey of the published papers comparing LCR for patients with HNSCC treated with conventional and accelerated radiotherapy, respectively, and with a pretreatment assessment of EGFr expression, was made [6–11].
In the published papers, different criteria of EGFr expression assessment according to the intensity of staining were used. EGFr expression was classified by the investigators, with several quantitative or semiquantitative scoring systems, i.e., absent, minimal, moderate, or intense staining (Table 1). The main characteristics for selection were conventional and accelerated fractionations, different OTT, assessment of EGFr expression and LCR, as listed in Table 1.
Only those studies which reported a median followup of at least 3years were included in the analysis. Table 2 lists the main clinical characteristics of the patients, namely age, sex, primary site, T stage and N stage. Further clinical information are in the reviewed papers.
Radiobiological analysis
The tumour effects were evaluated by the overall time corrected BED as in eq. (1)
where n is the number of fractions of size d in Gy, α and β are the linear quadratic coefficients of dose, T is the overall time, T_{ k } is the onset time for accelerated proliferation and T_{ D } the effective doubling time. The first term in eq. (1) (the dosimetric component, see Appendix A), is affected by differences in EGFr expression because of modification to α and β parameters that describe the intrinsic and repair radiosensitivity of tumour types, respectively. We add the subscripts H and L to indicate high or low EGFr expression respectively (BED_{ H }(d) or BED_{ L }(d)). The second term (the temporal component, see Appendix A) is affected by differences in EGFr expression due to the presence of the α parameter (α_{ H } or α_{ L }) and T_{ D } (T_{ DH } or T_{ DL }). Superscripts S and F are specified to distinguish between conventional (S = Slow) and accelerated (F = Fast) fractionations, respectively.
From BED we have the standard model of tumour control probability (TCP) using the linearquadratic model incorporating the Poisson’s low [12],
where N = ρ·V (ρ = cell density and V = volume) represents the initial number of potential proliferating cells in the tumour. Therefore, the cell survival probability being S = exp(−α·BED), the TCP represents the probability of avoiding local recurrence [13] at total dose D = n·d whereby we write TCP = LCR.
Moreoever, in order to analyze the effects of EGFr expression due to the change in the OTT, the papers chosen in the survey had the same dose per fraction and total dose but a different OTT.
Thus, by taking the natural logarithms of eq. (2) written for fast and slow fractionations, dividing the resultant equations and by taking the natural logarithm again, we get
for high EGFr expression group, and
for low EGFr expression group (see Appendix A).
This expedient allows to eliminates the dependence of findings from the choice of dose fractionation and from the estimated values of α and β. The equations (3.a) and (3.b) are also independent notwithstanding the assumption about number of cells N. The uncertainties arising from these assumptions strongly influences the results of the other models that depend on such parameters. Therefore, this is the main advantage of equations (3.a) and (3.b).
In each of these equations appears only one unknown (the effective doubling time) for which, being in a linear form, they are suitable for an easy comparison between LCR due to different EGFr expression groups with different OTT. This assessment was done by evaluating the differences of angular coefficients (ln2/T_{ DH }vs ln2/T_{ DL }) from the correspondent regression lines obtained by LCR available in literature (Figure 1). For those papers, where in addition to differences of OTT there are also differences in terms of dose fractionation, the correction as described in Appendix B was done.
Furthermore, dividing equations (3.a) and (3.b), we also obtained the ratio of the actual doubling times between the H_{EGFr} and L_{EGFr} groups that allows a direct analysis of the EGFr effects (Figure 2) as follows
Clinical analysis
The actual doubling times obtained from the above analysis, represent a weighted average of the doubling times from different subsites as oral cavity (18.2% of patients), oropharynx (30.3% of patients), hypopharynx (14.8% of patients), and larynx (36.4% of patients).
These subsites contribute differently to the average T_{ D } because they have different T_{ pot }. However, the T_{ D } for each subsites can be estimated if T_{ pot } and the cell loss factor (ϕ) are known as described by Steel [14]. In particular T_{ pot } can be measured by a single biopsy with flow cytometry as well as immunohistochemistry techniques.
Therefore, the average cell loss factor was estimated using pretreatment data about T_{ pot } available in literature [15, 16], then the actual doubling time for each i subsite (^{i}T_{ D }) was obtained (see Appendix C).
Moreover, from ^{i}T_{ D } we also estimated the dose (in fractions of size d) that would be required to offset the effect of proliferation occurring in one day [17] by the follows equation
Statistical analysis
In all the original studies of the survey the primary endpoint was LCR, 3 or 5years after completion of radiotherapy, although only the 3year LCR were extrapolated in order to compare the homogeneous parameters. LCR were assessed by the KaplanMeier method with a log rank test (statistical significance: p ≤ 0.05, twosided). The LCR 95% confidence intervals are obtained by Greenwood’ formula [18]. Comparison between regression lines was done by Fisher’s exact test.
Results
Table 1 and 2 describe the main clinical characteristics and treatment parameters of the selected groups in the survey.
Linear regression lines from equations (3.a) and (3.b), for H_{EGFr} and L_{EGFr} groups, are shown in Figure 1 with respect to different choices of the onset for accelerated repopulation (T_{ k }). The significant distinction of the angular coefficients for different groups (pvalues ≤ 0.02) correspond to an average T_{ D } of 77 days (27–90)_{95%} for L_{EGFr} and to an average of 8.8 days (7.311.0)_{95%} for H_{EGFr}, if an onset of accelerated proliferation T_{ K } at day 21 was assumed.
In Figure 2 the significant H_{EGFr}T_{ D } reduction with respect to L_{EGFr}T_{ D } for each head and neck subsite, are shown by varying T_{ K }.
In Figure 3 the averages of D_{ prolif } are shown based on the flow cytometry and immunohistochemical methods to estimate the subsites ^{i}T_{ pot }. The maximum value of D_{ prolif }, up to about 0.5 Gy/day, is obtained corresponding to an onset of accelerated repopulation that starts from the fourth week (T_{ K } at about 28^{th} day). Sensitivity analysis is shown with respect to different values of α with α/β = 10 Gy.
The weighted average potential doubling times < ^{i}T_{ pot } > of 5.2 days and 3.4 days [15, 16] were obtained corresponding to averages for cell loss factors as < ϕ_{(FCM)} > = 0.41 (0.290.52)_{95%} and < ϕ_{(Hi)} > = 0.61 (0.530.69)_{95%} with respect to the flow cytometry and immunohistochemistry, respectively.
Table 3 reports numerical results for each subsite in H_{EGFr} group with ^{i}T_{ D } and ^{i}D_{ prolif } calculated for different values of α (α/β = 10 Gy). It may be noted that the ^{i}T_{ D } for each i subsite is almost twice of ^{i}T_{ pot } obtained by flow cytometry and more than double of ^{i}T_{ pot } obtained by immunohistochemistry. This means that a pretreatment assessment of D_{ prolif } by flow cytometry or immunohistochemistry may significantly overestimate the dose required to offset the accelerated proliferation occurring in one day.
In Figure 4, the histogram of the ratio between T_{ DL } and T_{ DH } (eq. 4) shows an average reduction of about 7 times in average (6.68.3)_{95%} for the H_{EGFr} group with respect to the L_{EGFr}. This ratio could have significant implications on the clinical management of these patient groups. In fact, while the H_{EGFr} group would benefit from an increase of the dose/fraction (Hypofractionation) and the consequent reduction of OTT to compensate for the increase in the proliferation rate  corresponding to a reduced T_{ D } , the L_{EGFr} group does not require a reduction of OTT for which it would be more indicated a reduction of the dose/fraction (Hyperfractionation) which would result in a reduced toxicity for all the organs at risk.
Discussion
In the recent years there has been a great interest to find factors that predict tumours suitable for accelerated radiotherapy and considerable interest has been given to cell kinetic parameters such as the T_{ pot }. Since regeneration and tumour cell proliferation are mechanisms at the cellular level, particular attention has been focused on identifying the specific cellular characteristics, such as variations in EGFr expression. The latter is an important mediator of cell growth and its overexpression has been associated with tumour progression and poor survival in many solid cancers. Several studies have demonstrate the potential of EGFr as a predictive and prognostic marker in radiotherapy for HNSCC [19].
In the present study a direct demonstration of the link between EGFr status and the time factor in fractionated radiotherapy, has been made. All the clinical studies surveyed, from the available literature, had a random allocation for “reduced” or “conventional” OTT and demonstrated an increase in LCR when the OTT was reduced.
Unfortunately, OTT reduction yields clinical benefits in terms of LCR but could worsen the radiationinduced acute side effects which need to be carefully evaluated using appropriate radiobiological models [20].
Moreover, some studies also demonstrated that tumours with high EGFr respond better to the reduction of the OTT compared to low EGFr tumours [6, 7, 9]. The response was heterogeneous if referring to the subsites included in the analysis.
Therefore, our intent was to evaluate the extent of accelerated proliferation due to an EGFr overexpression, in terms of reduced actual doubling time as well as required dose to offset the effect of proliferation occurring in one day.
To obtain these results no assumption was made with the exception of the validity of a linear quadratic and TCP model. Therefore, the fact that the EGFr expression changes the radiosensitivity and the proliferation rate of the cells, has to be necessarily included in these models as a variation of the parameters (α, β and T_{ D } ) describing them.
Although in all the studies selected for the survey, the accelerated repopulation of tumour cells during radiotherapy was suggested as an important cause of treatment failure, the main difficulty in our analysis was that head and neck cancer represents a heterogeneous group of cancers and the benefit is not act equal for the different tumours. We also attempted to estimate these differences.
We are aware that an important drawback in the analysis is to be found the differences among treatment modalities. Some studies have included radiotherapy alone, others postoperative radiotherapy, others the use of radiosensitizing hypoxic drugs. We therefore stress the versatility and enormous potential of the method we propose.
Indeed, the relationship between elements representative of the radiation effects calculated only on groups of patients who undergo the same treatment, is based accordingly. In other words, although radiotherapy alone is profoundly different from postoperative radiotherapy or from radiotherapy combined with radiosensitizing drugs, the relationship of the effects calculated within the same type of therapy, nullify these contributions, allowing to obtain only those due to the different expression of EGFr.
The validity of this statement is confirmed by the very low dispersion of data around the linear regression lines obtained from them. Our results clearly demonstrate proportionality between differences in treatment duration and correspondent ratios of LCR (the latter in logarithmic form). This strong linearity allowed us to quantify the reduction of actual doubling time of the H_{EGFr} group with respect to the L_{EGFr} group.
Unfortunately, in the papers, different definitions for the level of cutpoints of EGFr expression were used. In some studies a cutpoint of 50% was chosen as being objective and reproducible, others fixed a cutpoint of 33%, 40%, 80%, etc. However, it is obvious that no dichotomous division between high and low EGFr tumour expression exist and a continuous variable must apply. In addition, because samples for the various studies were collected from various pathology departments and staining intensity can be dependent on tissue fixation [21], the evaluation of staining intensity was not entirely homogeneous. This was certainly the greatest source of approximation in the quantitative results obtained.
Despite these limitations, our results indicate a clear reduction of effective doubling time T_{ D } in H_{EGFr} with respect to the L_{EGFr} groups. This reduction did not so excessive as the necessary to reach the minimum value which is represented by T_{ pot } (that is the limit where the cell loss fraction is reduced to zero and the proliferation is fastest).
We consider this result very important, especially because an accurate estimate of T_{ D } allows to obtain the equivalent dose for accelerated repopulation that is essential to making rational adjustments to the overall dose when the overall time is increased. This has become more than just an academic question in the area of IMRT when, instead of using shrinking field techniques, radiation oncologists commonly use a differential dose per fraction to deliver graded doses in the same overall treatment time.
Our results consisted of D_{ prolif } systematically lower than those accepted in the literature that are often obtained through an evaluation ofthe potential doubling time, which is a characteristic of each proliferative cell, and not through the effective doubling time, which isa characteristic of a group of cells [22].
In the case of oropharynx, for example, we obtained values up to 0.39 Gy/day (0.310.47)_{95%} while in the literature we have values between 0.480.68 Gy/day [23, 24]. For the larynx we obtained values up to 0.16 Gy/day (0.130.19)_{95%}, while other estimates for this tumour are between 0.3 and 0.5 Gy/day [17]. Only in the case of hypopharynx we had values greater than 0.5 Gy/day (0.400.59)_{95%}.
The difference can partly be explained by the heterogeneous behavior of the different subsites involved in our analysis (a specific subsite clinical study could discriminate more finely between different contributions). However, our opinion is mainly based on the interpretation of the correlation between T_{ D } and T_{ pot }.
As a first hypothesis, the reduction of T_{ D } can be easily explained with a correspondent reduction of T_{ pot }, but clinical data has shown that for patients with short T_{ pot } (fast tumours) there was no statistically significant trend to do worse [25]. Moreover, we found a reduction of T_{ D } with an average factor of about 7 in the H_{EGFr} with respect to the L_{EGFr} group, and the same extent was never found by measures that assess T_{ pot } from biopsy among patients.
Consequently, given that a shorter T_{ D } may also result from a reduced ϕ after the beginning of treatment (see Appendix C), our results suggest that the latter possibility is favored. In this case, the tendency of ϕ toward zero, indicates a reduction of the clonogen doubling time T_{ D } until it equals the pretreatment T_{ pot }. Hence, our results for T_{ D } can be easily explained from an incomplete reduction of ϕ toward zero.
Furthermore, a ϕ reduction being associated with a low differentiation, would correspond to an increase in a nondifferentiated component.
Thus, the question arises about how two different results may be reconciled.
On one hand, the simultaneous expression of a differentiated pattern and high levels of EGFr display a higher degree of accelerated repopulation compared to carcinomas with low levels of EGFr or poor differentiation [5]. On the other hand, as is clear from the Steel’s formula, the reduction of T_{ D } is due to a reduction of the differentiation levels.
A possible explanation could be that two different levels of differentiation may coexist locally.
This hypothesis is based on the clinical observation that high levels of EGFr expression were found to be more pronounced at the tumour borders compared to the central parts of the tumour tissue (p < 0.0001) [6]. Therefore, on the border of the tumour, the EGFr overexpression would be compatible with a low level of differentiation and rapid tumour growth (as from Steel’s formula). In more central tumour areas, the low EGFr expression may be compatible with a high level of differentiation and reduced tumour cell proliferation. This spatial nonuniformity, suggests that the precise location of biopsy sampling and a subsequent classification of tumours (high or low EGFr and level of differentiation) are crucial. A such hypothesis, of course, requires further investigation in clinical studies.
Conclusion
Increased expression of the EGFr can lead to enhanced proliferation which can be countervailed by reducing the time available for tumour cell proliferation, thereby reducing the overall treatment time. In this case, the impact of high EGFr expression changes from being a negative to a positive prognostic value in terms of local control rate.
In this study we introduced a model that allows to quantify the influence of EGFr expression in terms of reduced doubling time during the treatment and also the dose per fraction to be taken into account when the overall treatment time is reduced in accelerated radiotherapy. Furthermore, using this model, we can also estimate the parameters inherent in different subsites which may identify the optimal dose fractionation regime more likely to benefit these subsets of patients.
Appendix A
To simplify the radiobiological analysis, eq. (1) can be rewritten by considering the BED as the difference between a dosimetric and a temporal component:
The BED(d) for high EGFr expression group, for instance, is [26].
while the BED(T) for the same group is
Thus, to take into account the differences of radiosensitivity as well as OTT, two and four possible expressions of BED(d) and BED(T) are considered, respectively:
For different EGFr expressions and OTT we have also
where, for example
Therefore, by taking the natural logarithms of this expression and dividing it for the same expression with a different OTT, we can nullify the contributions of ρV and BED(d) – because of the same fractionation – obtaining only those due to the different expression of EGFr with respect to the OTT.For the high EGFr expression group, for instance, we have
from which, by taking the natural logarithms again, we have eq. (3.a). The same procedure leads to eq. (3.b).
Appendix B
The equations (3.a) and (3.b) are valid if the hypothesis of equal dosimetric component of BED in conventional and accelerated fractionation, is valid. However, this is not true for all the papers in the literature surveyed. The differences in terms of dose fractionation were corrected using the follows
where the indexes nc and c stand for “noncorrected” and “corrected”, respectively. BED^{S}(d) and BED^{F}(d) refer to different BED dosimetric components in conventional and accelerated fractionation, respectively. The exponential factor incorporates the difference of BED only due to the dosimetric BED component, and therefore enables the contribution to be corrected, thanks to this component.
Appendix C
In order to estimate the actual doubling time for each subsite in the analysis, different potential doubling times T_{ pot } were considered from literature [15]. The latter has been introduced by Steel as the clonogen doubling time that would be measured if cell loss was ignored, i.e. if both daughter cells remained clonogenic after mitosis [14].In practice clonogens are lost through many possible mechanisms, including differentiation, death, and metastasis, and the net result is that T_{ D } will be longer than T_{ pot }.Steel’s formula can be written as follows:
wherein ϕ is the cell loss factor. This equation shows that T_{ D } can be calculated if T_{ pot } and ϕ are known.In particular T_{ pot } can be measured by a single biopsy using flow cytometry or immunohistochemistry techniques, while the average cell loss factor < ϕ > was obtained in our analysis taking the average potential doubling time weighted on percentages for any subsite (<^{i}T_{ pot } > =∑_{ i }p_{ i }·^{i}T_{ pot } with i = 1,.,4 and p_{ 1 } = 21% for oral cavity, p_{ 2 } = 20% for oropharynx, p_{ 3 } = 17% for hypopharynx and p_{ 4 } = 42% for larynx), by the follows
The actual doubling time for each i subsite, was then obtained as follows
Results were reported in Table 3.
Abbreviations
 (BED):

Biologically Effective Dose
 (D_{prolif}):

Dose required to offset the proliferation occurring in one day
 (EGFr):

Epidermal Growth Factor Receptor
 (FCM):

Flow Cytometry
 (ϕ):

Cell Loss Factor
 (H_{EGFr}):

High EGFr expression group
 (Hi):

Immunohistochemistry
 (HNSCC):

Head and Neck Squamous Cell Carcinoma
 (LCR):

Local Control Rate
 (L_{EGFr}):

Low EGFr expression group
 (OTT):

Overall Treatment Time
 (TCP):

Tumour Control Probability
 (T_{D}):

Effective Doubling Time
 (T_{k}):

Time of onset of accelerated proliferation
 (T_{pot}):

Potential Doubling Time.
References
 1.
Overgaard J, Alsner J, Eriksen J, et al.: Importance of overall treatment time for the response to radiotherapy in patients with squamous cell carcinoma of the head and neck. Rays 2000, 25: 313319.
 2.
Overgaard J, Hansen HS, Specht L, et al.: Five compared with six fractions per week of conventional radiotherapy of squamous cell carcinoma of head and neck: DAHANCA 6 and 7 randomised controlled trial. Lancet 2003, 362: 933940. 10.1016/S01406736(03)143619
 3.
Hansen O, Overgaard J, Hansen HS, et al.: Importance of overall treatment time for the outcome of radiotherapy of advanced head and neck carcinoma: dependency on tumour differentiation. Radioth Oncol 1997, 43: 4751. 10.1016/S01678140(97)01904X
 4.
Dassonville O, Forment JL, Francoual M, et al.: Expression of epidermal growth factor receptor and survival in upper aerodigestive tract cancer. J Clin Oncol 1993, 11: 18731878.
 5.
Eriksen JG, Steiniche T, Askaa J, et al.: The prognostic value of epidermal growth factor receptor is related to tumour differentiation and the overall treatment time of radiotherapy in squamous cell carcinomas of the head and neck. Int J Rad Onc Bio Phys 2004, 58: 561566. 10.1016/j.ijrobp.2003.09.043
 6.
Eriksen JG, Steiniche T, Overgaard J, et al.: The role of epidermal growth factor receptor and Ecadherin for the outcome of reduction in the overall treatment time of radiotherapy of supraglottic larynx squamous cell carcinoma. Octa Oncol 2005, 44: 5058. 10.1080/02841860510007396
 7.
Eriksen JG, Alsner J, Steinich T, et al.: The possible role of TP53 mutation status in the treatment of squamous cell carcinomas of the head and neck (HNSCC) with radiotherapy with different overall treatment times. Radioth Oncol 2005, 76: 135142. 10.1016/j.radonc.2005.05.004
 8.
Bentzen SM, Atasoy BM, Daley FM, et al.: Epidermal Growth Factor Receptor Expression in Pretreatment Biopsies From Head and Neck Squamous Cell Carcinoma As a Predictive Factor for a Benefit From Accelerated Radiation Therapy in a Randomized Controlled Trial. J Clin Oncol 2005, 23: 55605567. 10.1200/JCO.2005.06.411
 9.
Suwinski R, Jaworska M, Nikiel B, et al.: Predicting the effect of accelerated fractionation in postoperative radiotherapy for head and neck cancer based on molecular marker profiles: data from a randomized clinical trial. Int J Rad Onc Bio Phys 2010, 77: 438446. 10.1016/j.ijrobp.2009.05.021
 10.
Smid EJ, Stoter TR, Bloemena E, et al.: The importance of immunohistochemical expression of egfr in squamous cell carcinoma of the oral cavity treated with surgery and postoperative radiotherapy. Int J Rad Onc Bio Phys 2006, 65: 13231329. 10.1016/j.ijrobp.2006.03.011
 11.
Chung CH, Zhang Q, Hammond EM, et al.: Integrating epidermal growth factor receptor assay with clinical parameters improves risk classification for relapse and survival in headandneck squamous cell carcinoma. Int J Rad Onc Bio Phys 2011, 81: 331338. 10.1016/j.ijrobp.2010.05.024
 12.
Tomé WA, Fowler JF, et al.: Selective boosting of tumour subvolumes. Int J Rad Onc Bio Phys 2000, 48: 593599. 10.1016/S03603016(00)006660
 13.
Tucker SL, Thames HD, Taylor JM: How well is the probability of tumour cure after fractionated irradiation described by poisson statistics? Radiat Res 1990, 124: 273282. 10.2307/3577839
 14.
Steel GG: Growth Kinetics of Tumours. Oxford: ClarendonPress; 1977.
 15.
Wilson GD, Discheb S, Saundersb MI: Studies with bromodeoxyuridine in head and neck cancer and accelerated radiotherapy. Radioth Oncol 1995, 36: 189197. 10.1016/01678140(95)01567Z
 16.
Bennett MH, Wilson GD, Dische S, et al.: Tumour proliferation assessed by combined histological and flow cytometric analysis: implications for therapy in squamous cell carcinoma in the head and neck. Br J Cancer 1992, 65: 870878. 10.1038/bjc.1992.183
 17.
Thames HD, Bentzen SM, Turesson I, et al.: Timedose factors in radiotherapy: a review of the human data. Radioth Oncol 1990, 19: 219235. 10.1016/01678140(90)90149Q
 18.
Collett D: Modelling survival datain medical research. London: Chapman and Hall; 1994:2226.
 19.
Smith BD, Haffty BG: Molecular markers as prognostic factors for local recurrence and radioresistance in head and neck squamous cell carcinoma. Radiat Oncol Investig 1999, 7: 125144. 10.1002/(SICI)15206823(1999)7:3<125::AIDROI1>3.0.CO;2W
 20.
Strigari L, Pedicini P, D'Andrea M, Benassi M: A model for predicting Acute Mucosal Toxicity (AMT) in head and neck cancer patients undergoing radiotherapy with altered schedule. Int J Rad Onc Bio Phys 2012, 83: e697e702. 10.1016/j.ijrobp.2012.02.004
 21.
Shi SR, Cote RJ, Chaiwun B, et al.: Standardization of immunohistochemistry based on antigen retrieval technique for routine formalinfixed tissue sections. Appl Immunohistochem 1998, 6: 8996. 10.1097/0002274419980600000006
 22.
Fowler JF: Is there an optimum overall time for head and neck radiotherapy? A review, with new modelling. J Clin Oncol 2007, 19: 822. 10.1016/j.clon.2006.09.008
 23.
Bentzen SM, Thames HD: Clinical evidence for tumour clonogen regeneration: interpretations of the data. Radioth Oncol 1991, 22: 161166. 10.1016/01678140(91)90019D
 24.
Bentzen SM, Johansen LV, Overgaard J, Thames HD: Clinical radiobiology of squamous cell carcinoma of the oropharynx. Int J Rad Onc Bio Phys 1991, 20: 11971206. 10.1016/03603016(91)90228V
 25.
Begg AC: The clinical status of T_{ pot } as a predictor? or why no tempest in the T_{ pot }. Int J Rad Onc Bio Phys 1995, 32: 15391541. 10.1016/03603016(95)00261V
 26.
Pedicini P, Caivano R, JereczekFossa BA, et al.: Modelling the correlation between EGFr expression and tumour cell radiosensitivity, and combined treatments of radiation and monoclonal antibody EGFr inhibitors. Theor Biol Med Model 2012,9(1):23. 19 10.1186/17424682923
Acknowledgements
We wish to thank Mrs Paula Franke for the English revision of the manuscript.
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The authors declare they have no competing interests.
Authors’ contributions
PP developed the model, designed the study and wrote the manuscript. AN, LS, BAJ, DA, MC, FB, RC, AF and GI checked the goodness of the study from oncology, radiotherapy and mathematical points a view. RC made the graphical illustrations. GS, MB, RO and MS supervised the manuscript from radiobiological and clinical points a view. All coauthors approved the manuscript.
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Keywords
 EGFr
 Doubling time
 Potential doubling time
 Cell loss factor
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