1. QUANTITATIVE TUMOUR CONTROL PREDICTIONS FOR THE RADIOTHERAPY OF
NON-SMALL-CELL LUNG TUMOURS
Nahum1, J. Uzan1, P. Jain1, Z. Malik1, J. Fenwick2, C. Baker1 1Clatterbridge Centre for Oncology, Bebington UK, 2Gray Institute for Radiation Oncology & Biology, University of Oxford, UK.
INTRODUCTION
Radiotherapy of non-small-cell lung tumours (NSCLC) is in a period of significant development due to a combination of conformal planning, strategies for compensating motion due to respiration, hypofractionation (e.g. SBRT), and “isotoxic” prescription-dose individualisation (e.g. Fenwick et al 2009; Panettieri et al 2010; Uzan and Nahum 2011). In order to maximise the efficacy of these various approaches a model for predicting local-control probability as a function of the (absolute, total) dose distribution, number of fractions, tumour volume and radiosensitivity, and overall treatment time is essential; the ‘Marsden’ TCP model fulfills these conditions (Webb and Nahum 1993; Nahum and Sanchez-Nieto 2001). We have analysed three contrasting dose and fraction regimens (CHART – Bentzen et al 2002; Martel et al 1999; and our own Clatterbridge clinical experience: 55 Gy in 20 fractions - unpublished) using the ‘Marsden’ quasi-mechanistic, LQ-based, population TCP model (Nahum, Webb, Sanchez-Nieto 1993, 2000). The aim of the exercise is to derive a set of parameters for the Marsden TCP model based on clinical data which can then be employed in modelling studies to search for radiobiologically optimal regimens.
METHODS AND MATERIALS
Reference TCP data
A cohort of 24 patients treated at Clatterbridge Centre for Oncology (CCO), for which PTV DVHs were available, was used to derive ‘best fit’ values of population mean radiosensitivity a, (assumed to vary according to a log-normal distribution), population standard deviation, , the delay (days) before accelerated tumour repopulation begins, Tk, and the tumour doubling time, Td (days). a/b and the tumour clonogen density were fixed at values of 10 Gy and 107 cm-3 respectively. Four alternative dose/fractionation schedules were considered for this cohort, each having an expected population TCP (based on clinical outcome at our centre or reported in the literature) as follows:
1TCP defined as progression-free survival at 3 years.
2local control at 3 years [Bentzen et al 2002].
3local progression-free survival at 30 months. Overall time via number of fractions, n, plus weekends (w/e) [Martel et al 1999].
Parameter fitting
Population TCP was computed for each patient PTV DVH, consisting of M dose bins, for each dose and fractionation schedule via:
where j is the index over patients in the cohort, P(a) is the log-normal probability of a patient (with this DVH) having radiosensitivity a, and Nc is the number of clonogens of radiosensitvity, a, remaining after having received a dose described by the differential dose-volume histogram, dDVH (normalized to unit total volume):
It is important to note that we have used the GTV to estimate the original number of tumour clonogens but the PTV DVH was used as the best estimate of the accumulated dose to the tumour (i.e. as a very approximate way of accounting for tumour displacement).
The predicted population TCP for the entire patient cohort receiving a given dose/fractionation schedule is then simply given by:
Starting from an initial point in parameter-space, (a , sa , Tk , Td), the Simplex method, as implemented in Matlab version R2010a was used to determine best-fit parameter values via least-squares fitting to reported TCP, through a simple objective function of the form:
where s denotes the index over dose/fractionation schedules, TCPs is the reported tumour control and the predicted tumour control. Fitted parameter values were subject to upper and lower bounds of (0.5, 0.5, 50, 50) and (0.1, 0.001, 1.0, 1.0) respectively. A number of initial starting points within these bounds were used to ensure that a robust, global solution was found.
For CCO and CHART (trial and control arms), PTV DVHs in terms of relative dose were simply scaled by the intended prescribed dose. For the UMCC data, CCO patients were mapped to prescribed dose according to individual GTVs. It was found that mapping in this way produced a representative sub-set of the full UMCC cohort for GTVs smaller than 200cm3.
RESULTS
Results of fitting are shown graphically in figure 1, where each dose/fractionation schedule is represented in terms of 2Gy-per-fraction equivalence.
Figure 1. Comparison of reported tumour control for each dose/fractionation schedule with predicted control for fitted parameters; = Gy-1,= Gy-1,Tk = 20.9 days, Td = 3.7 days.
The fit is virtually “exact” as the figure demonstrates; the “best-fit‟ parameters are:
 Gy-1,
3 Gy-1,
TK = 20.9 days,
Td = 3.7 days
with Gy-1 and clon 7 cm-3 as the fixed parameters.
Robustness against reported control rates
In order to estimate the effect of uncertainties in reported control data on derived parameters, fitting was repeated for target TCP values sampled from normal distributions. A target control rate for each dose/fractionation schedule was sampled from a normal distribution with mean equal to the reported TCP and 5% standard deviation. Parameter fitting was then performed on each sampled set of outcome TCPs and the process repeated for 50 such outcome samples to provide a mean and standard deviation in
resulting fitted parameters. Results were found to be surprisingly stable against this variation in ‘observed’ tumour control rates. Mean parameter values and standard deviations (in brackets) were as follows: = (0.002) Gy-1,= (0.002) Gy-1,Tk = 20.9 (1.1) days, Td = 3.7 (0.2) days. Note that in all cases clonogen density and a/b remained fixed.
SOME APPLICATIONS
Finally we give two illustrations of the use of this new “best fit” set of parameters in the TCP model.
Figure 2 shows ‘dose-response’ curves for two clinical dose-escalation strategies, constant fraction number (20 in this case) and constant fraction size (2.75 Gy per fraction). The effect of weekend breaks (pink curve) due to clonogen proliferation can be observed (computed using BioSuite [Uzan and Nahum 2011]).
Figure 3 [Uzan and Nahum 2011] shows how twice-a-day fractionation can be advantageous in certain cases; here the NTCP has been held constant i.e. ‘isotoxic’ schedules.
CONCLUSIONS
The ‘Marsden’ TCP model can now be used together with the above parameters in developing new clinical radiobiological optimisation protocols such as twice-a-day fractionation (see above) for more advanced tumours and intermediate-fraction-number (8 to 15) schedules for tumours which are too large or too centrally positioned to qualify for the 3-5 fraction “SBRT” techniques.
REFERENCES
Bentzen SM, Saunders MI, Dische S, From CHART to CHARTWELL in non-small cell lung cancer: clinical radiobiological modelling of the expected change in outcome Clin. Oncol. (R Coll Radiol)
Fenwick JD, Nahum AE, Malik ZI, Eswar CV et al Escalation and intensification of radiotherapy for stage III non-small cell lung cancer: Opportunities for treatment improvement. Clinical Oncology
Martel MK, Ten Haken RK, Hazuka MB, Kessler ML et al, Estimation of tumor control probability model parameters from 3-D dose distributions of non-small cell lung cancer patients. Lung Cancer,
Nahum AE and Sanchez-Nieto B, Tumour Control Probability Modelling: Basic Principles and Applications in Treatment Planning Physica Medica 17, Suppl. 2,
Panettieri V, Malik Z I, Eswar CV, Landau DB et al, Influence of dose calculation algorithms on isotoxic dose-escalation of non-small cell lung cancer radiotherapy, Radiotherapy and Oncology
Uzan J and Nahum AE, Radiobiologically guided optimisation of the prescription dose and fractionation scheme in radiotherapy using BioSuite, submitted to Br. J. Radiol. July 2011.
Webb S. and Nahum A.E. A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density, Phys. Med. Biol. 38, , 1993.
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2011 Joint AAPM/COMP meeting, July 31 – August 4, Vancouver.