Impact of different biologically-adapted radiotherapy strategies on tumor control evaluated with a tumor response model

Abstract

Motivated by the capabilities of modern radiotherapy techniques and by the recent developments of functional imaging techniques, dose painting by numbers (DPBN) was proposed to treat tumors with heterogeneous biological characteristics. This work studies different DPBN optimization techniques for virtual head and neck tumors assessing tumor response in terms of cell survival and tumor control probability with a previously published tumor response model (TRM). Uniform doses of 2 Gy are redistributed according to the microscopic oxygen distribution and the density distribution of tumor cells in four virtual tumors with different biological characteristics. In addition, two different optimization objective functions are investigated, which: i) minimize tumor cell survival (OFsurv) or; ii) maximize the homogeneity of the density of surviving tumor cells (OFstd). Several adaptive schemes, ranging from single to daily dose optimization, are studied and the treatment response is compared to that of the uniform dose. The results show that the benefit of DPBN treatments depends on the tumor reoxygenation capability, which strongly differed among the set of virtual tumors investigated. The difference between daily (fraction by fraction) and three weekly optimizations (at the beginning of weeks 1, 3 and 4) was found to be small, and higher benefit was observed for the treatments optimized using OFsurv. This in silico study corroborates the hypothesis that DPBN may be beneficial for treatments of tumors which show reoxygenation during treatment, and that a few optimizations may be sufficient to achieve this therapeutic benefit.

Fig 1. Radial distribution of vascular fraction and tumor cell density in the investigated virtual tumors prior to irradiation.

Left axis: homogeneous (o) and inhomogeneous (.) tumor cell density distributions, ρ. Right axis: homogeneous (*) and inhomogeneous (□) vascular fraction distributions, vf. Each tumor consist of a combination of one vf and ρ profiles (see text for details).

Fig 2. Time points of dose optimization within the investigated treatment schedules.

Vertical arrows indicate the days (represented with dots) when dose optimization was performed. The optimized distributions are applied in all the treatment fractions from the day of optimization until a new optimization is performed. Note: No irradiations were performed at weekend (dots in red) and after 3 weeks (FBF3W) or 4 weeks (all other schedules), fractions were delivered with uniform dose (u.d. = 2Gy). The response of each virtual tumor was simulated for a uniform dose distribution as well as for the five adaptive schemes (1F, 2F, 3F, FBF3W and FBF4W) optimizing the dose distribution either with OF_surv and OF_std.

Fig 3. Tumor response to a uniform dose distribution.

(a) Number of surviving tumor cells with time for the 4 tumor types irradiated with a uniform dose distribution. The weekend treatment breaks lead to small plateaus in the cells survival curves, in which the number of tumor cells increases slightly due to proliferation. (b) TCP curves for the simulated tumors and experimental response of a 200 mm³ xenograft of the H&N FaDu line [67]. The D50_conv values (in Gy) of the simulated TCP curves are 68.6 ± 1.4, 65.6 ± 2.1, 71.3 ± 2.0 and 66.0 ± 2.0, for T1, T2, T3 and T4 respectively.

Fig 4. Radiation induced reoxygenation in the investigated virtual tumors.

Evolution of the vascular fraction (averaged in the 1 cm diameter tumor core) for the 4 tumors when irradiated with a uniform dose distribution.

Fig 5. Treatment gains.

Treatment gains obtained for the studied tumors (T1-T4) using dose distributions optimized with either OF_surv (∘) or OF_std (*) under different adaptive schemes.

Fig 6. Sthocastic and population radiosensitivity variability effects.

Response curves for tumor T1 when irradiated with the FBF4W scheme using OF_surv. Solid line, treatment response achieved when the treatment is optimized using the population-averaged radiosensitivity α; dashed line, TCP curve calculated using the same population-averaged radiosensitivity (the cell killing stochasticity produces the shallowing and displacement towards higher dose of the response curve); and dashed-dotted line, TCP curve calculated for a population with a normally distributed α radiosensitivity parameter (further shallowing and displacement).

Fig 7. Impact of the adaptive scheme on treatment gain.

Treatment gains associated to the DPBN treatments under the adaptive schemes 3F, FBF3W and FBF4W. Tumors ordered on the x-axis by ascending reoxygenation capability.