Population TCP estimators in case of heterogeneous irradiation: a new discussion of an old problem

Analysis of a cohort of prostate patients treated with HDR mono-brachytherapy

The aim of this study is to perform volumetric and basic radiobiological analyses using the database on prostate patients treated by HDR brachytherapy in our institution during the period 2011-2016. Real-time ultrasound based technique was used, with Oncentra Prostate planning software. The whole period was divided into two sub-periods, according to the 100% dose per fraction, which was 10.5 Gy during the first period (2011-2012), and 11 Gy during the second period (2013-2016), for each of the three fractions. The follow up time varied from 19 to 81 months, with a median of 45 months and a mean of 47 months. The uniformity of the treatment technique for both periods is investigated. Tumour Control Probability (TCP) values for the expected local control are calculated according to a population phenomenological TCP model for different values of the α/β ratio. The calculations are based on the obtained averaged Dose Volume Histograms for the two investigated sub-periods. 74 patients were treated in total. Local control failure is observed in 5 cases, which corresponds to an observed TCP = 93.2%. The comparison of the calculated population average DVH with the DVHs of the cases with local control failure shows that in 4 of them, doses higher than average were delivered to the prostate. It is shown that the uniformity of the treatment was improved during the second sub-period. A possible explanation of the observed failures may be that these cases exhibit inherent tumour cell radio-resistance higher than average. Our radiobiological analysis indicates a α/β ratio value somewhat higher than the one currently accepted. The value of the prostate α/β ratio is estimated to be in the range of [3.5-6] Gy.

Direct evaluation of radiobiological parameters from clinical data in the case of ion beam therapy: an alternative approach to the relative biological effectiveness

The relative biological effectiveness (RBE) concept is commonly used in treatment planning for ion beam therapy. Whether models based on in vitro/in vivo RBE data can be used to predict human response to treatments is an open issue. In this work an alternative method, based on an effective radiobiological parameterization directly derived from clinical data, is presented. The method has been applied to the analysis of prostate cancer trials with protons and carbon ions.Prostate cancer trials with proton and carbon ion beams reporting 5 year-local control (LC5) and grade 2 (G2) or higher genitourinary toxicity rates (TOX) were selected from literature to test the method. Treatment simulations were performed on a representative subset of patients to produce dose and linear energy transfer distribution, which were used as explicative physical variables for the radiobiological modelling. Two models were taken into consideration: the microdosimetric kinetic model (MKM) and a linear model (LM). The radiobiological parameters of the LM and MKM were obtained by coupling them with the tumor control probability and normal tissue complication probability models to fit the LC5 and TOX data through likelihood maximization. The model ranking was based on the Akaike information criterion.Results showed large confidence intervals due to the limited variety of available treatment schedules. RBE values, such as RBE = 1.1 for protons in the treated volume, were derived as a by-product of the method, showing a consistency with current approaches. Carbon ion RBE values were also derived, showing lower values than those assumed for the original treatment planning in the target region, whereas higher values were found in the bladder. Most importantly, this work shows the possibility to infer the radiobiological parametrization for proton and carbon ion treatment directly from clinical data.

Analytical investigation of the possibility of parameter invariant TCP-based radiation therapy plan ranking

PURPOSE

To analytically investigate the possibility of a parameter invariant ranking of radiotherapy (RT) plans based on comparing the tumor control probabilities (TCPs) produced by the competing plans for different values of the radiobiological model parameters determining the radiation response.

METHOD

Individual TCP models based on the Single hit model of cell kill and on the linear-quadratic (LQ) model of cell damage, with and without repopulation, are considered. The tumor dose distributions in case of heterogeneous dose irradiation are described by a Gaussian distribution function on the basis of which a TCP expression is derived depending only on the mean dose to the tumor and its standard deviation and the TCP model parameters.

RESULTS

It is shown that in case of homogeneous dose to the tumor the plan ranking in terms of TCP is parameter invariant. In case of heterogeneous dose to the tumor there are cases when the plan ranking is parameter invariant and cases when the parameter invariance is violated. An interesting dependence of the extent of the parameter invariance violation on the model of cell kill as well as on the size and repopulation rate of the tumor is noted.

CONCLUSION

We conclude that in many cases RT plan ranking in terms of TCP is parameter invariant. However, since there exist cases where the parameter invariance is lost an investigation of the specific plans to be ranked should be performed applying the proposed approach.