Purpose: Stereotactic body radiotherapy (SBRT) has been applied to lung tumors at different stages and sizes with good local tumor control (LC) rates. The linear quadratic model (LQM), in its basic formulation, does not seem to be appropriate to describe the response to radiotherapy for clinical trials, based on a few fractions. Thus, the main aim of this work was to develop a model, which takes into account the hypoxic cells and their reoxygenation.
Methods: A parameter named B has been introduced in a modified tumor control probability (TCP) from LQM and linear-quadratic-linear model (LQLM), and represents the fraction of hypoxic cells that survive and become oxygenated after each irradiation. Based on published trials evaluating LC at 3 yr (LC3), values of B were obtained by maximum likelihood minimization between predicted TCP and clinical LC3. Two oxygen enhancement ratio (OER) parameter sets (1 and 2) from literature have been adopted to calculate the B-factors. Initial hypoxic cell fractions (η(h)) from 0.05 to 0.50 were assumed. Log-likelihood (L) and Akaike information criterion (AIC) were determined in an independent clinical validation dataset.
Results: The B-values of modified TCPs spanned the whole interval from 0 to 1, depending on the fractionation scheme (number of fractions and dose/fraction), showing a maximum (close to 1) at doses/fraction of 8-12 Gy. The B-values calculated using the OER parameter set 1 exhibited a smoother falloff than set 2. An analytical expression was derived to describe the B-value's dependence on the fractionation scheme. The R(2)-adjusted values varied from 0.63 to 0.67 for LQ models and OER set 1 and from 0.75 to 0.78 for LQ model and OER set 2. Lower values of R(2)-adjusted were found for LQLM and both OER sets. L and AIC, calculated using a fraction of η(h) = 0.15 and the B-value from the authors analytical expression were higher than for other η(h)-values, irrespective of model or OER set.
Conclusions: The authors model allows to predict the clinical outcome associated with SBRT treatment, taking into account both direct killing and indirect vasculature or stromal damage.