Tumor control probability modeling for stereotactic body radiation therapy of early-stage lung cancer using multiple bio-physical models

Abstract

This work is to analyze pooled clinical data using different radiobiological models and to understand the relationship between biologically effective dose (BED) and tumor control probability (TCP) for stereotactic body radiotherapy (SBRT) of early-stage non-small cell lung cancer (NSCLC). The clinical data of 1-, 2-, 3-, and 5-year actuarial or Kaplan-Meier TCP from 46 selected studies were collected for SBRT of NSCLC in the literature. The TCP data were separated for Stage T1 and T2 tumors if possible, otherwise collected for combined stages. BED was calculated at isocenters using six radiobiological models. For each model, the independent model parameters were determined from a fit to the TCP data using the least chi-square (χ²) method with either one set of parameters regardless of tumor stages or two sets for T1 and T2 tumors separately. The fits to the clinic data yield consistent results of large α/β ratios of about 20Gy for all models investigated. The regrowth model that accounts for the tumor repopulation and heterogeneity leads to a better fit to the data, compared to other 5 models where the fits were indistinguishable between the models. The models based on the fitting parameters predict that the T2 tumors require about additional 1Gy physical dose at isocenters per fraction (⩽5 fractions) to achieve the optimal TCP when compared to the T1 tumors. In conclusion, this systematic analysis of a large set of published clinical data using different radiobiological models shows that local TCP for SBRT of early-stage NSCLC has strong dependence on BED with large α/β ratios of about 20Gy. The six models predict that a BED (calculated with α/β of 20) of 90Gy is sufficient to achieve TCP⩾95%. Among the models considered, the regrowth model leads to a better fit to the clinical data.

Keywords: Early stage non-small cell lung cancer; Stereotactic body radiation therapy; Tumor control probability modeling.

Fig. 1

Simultaneous fits to the 1, 2, 3, and 5 year TCP data with a) one set of parameters regardless of the tumor stages, and b) two sets for the stage T1 and T2 tumors, respectively. The data points are shown with error bars of one standard deviation. The BED was calculated using the α/β obtained during the fitting. In Fig. 1b, the BED is calculated using the parameters for the T1 tumors. The fit curves from Fig. 1b are overlaid with the c) T1 and d) T2 sub-datasets.

Fig. 2

Fits to the 1 year TCP data with different models. The fit with the regrowth model is also shown for comparison.

Fig. 3

Fits to the 2 (left) and 3 (right) year TCP data with the regrowth and LQ models. The fits to other four models (not shown) are similar to the fits with the LQ model. The fits with the regrowth model are also shown for comparison. The BED was calculated using the α/β obtained during the fitting.

Fig. 4

Weighted averages of 1, 2, and 3 year TCP data in BED bins overlaid with the fit curves in Figs. 2 and 3 for the regrowth (left) and LQ (right) models. The remaining four models show similar patterns (not shown) as the LQ model.