A new definition of biological effective dose: The dose distribution effects

Technical Note: Break-even dose level for hypofractionated treatment schedules

PURPOSE

To derive the isodose line R relative to the prescription dose below which irradiated normal tissue (NT) regions benefit from a hypofractionated schedule with an isoeffective dose to the tumor. To apply the formalism to clinical case examples.

METHODS

From the standard biologically effective dose (BED) equation based on the linear-quadratic (LQ) model, the BED of an NT that receives a relative proportion r of the prescribed dose per fraction for a given α/β-ratio of the tumor, (α/β)_T , and NT, (α/β)_NT , is derived for different treatment schedules while keeping the BED to the tumor constant. Based on this, the "break-even" isodose line R is then derived. The BED of NT regions that receive doses below R decreases for more hypofractionated treatment schedules, and hence a lower risk for NT injury is predicted in these regions. To assess the impact of a linear behavior of BED for high doses per fraction (>6 Gy), we evaluated BED also using the LQ-linear (LQ-L) model.

RESULTS

The formalism provides the equations to derive the BED of an NT as function of dose per fraction for an isoeffective dose to the tumor and the corresponding break-even isodose line R. For generic α/β-ratios of (α/β)_T  = 10 Gy and (α/β)_NT  = 3 Gy and homogeneous dose in the target, R is 30%. R is doubling for stereotactic treatments for which tumor control correlates with the maximum dose of 100% instead of the encompassing isodose line of 50%. When using the LQ-L model, the notion of a break-even dose level R remains valid up to about 20 Gy per fraction for generic α/β-ratios and D T = 2 ( α / β ) .

CONCLUSIONS

The formalism may be used to estimate below which relative isodose line R there will be a differential sparing of NT when increasing hypofractionation. More generally, it allows to assess changes of the therapeutic index for sets of isoeffective treatment schedules at different relative dose levels compared to a reference schedule in a compact manner.

Impact of target dose inhomogeneity on BED and EUD in lung SBRT

PURPOSE

To evaluate the effect of dose heterogeneity in the treatment target on biologically effective dose (BED) for frequently used hypofractionation regimens in stereotactic body radiation therapy (SBRT).

METHODS

In the case of non-uniform target dose, BED in the planning target volume (PTV) is determined by using the linear-quadratic model. An expression for BED is obtained for an arbitrary dose distribution in the PTV in the case of small variance of the target dose. Another analytical expression for BED is obtained by assuming a Gaussian dose distribution in the target.

RESULTS

Analytical expressions for BED as a function of the variance of the target dose have been derived. It is shown that a relatively small dose inhomogeneity (<5%-6%) can cause a significant reduction (i.e. >10%) in the corresponding BED and equivalent uniform dose (EUD) compared to the case of uniform target dose.

CONCLUSIONS

Small variations in the absorbed dose can significantly reduce BED and EUD in the PTV. The effect of dose non-uniformity on BED increases with increasing dose per fraction. The observed reduction in BED compared to that for uniform target dose can be several times greater for SBRT than for standard fractionation with dose per fraction varying between 1.8 and 2 Gy.

Evaluation of lung toxicity risk with computed tomography ventilation image for thoracic cancer patients

Background

Four-dimensional computed tomography (4D-CT) ventilation is an emerging imaging modality. Functional avoidance of regions according to 4D-CT ventilation may reduce lung toxicity after radiation therapy. This study evaluated associations between 4D-CT ventilation-based dosimetric parameters and clinical outcomes.

Methods

Pre-treatment 4D-CT data were used to retrospectively construct ventilation images for 40 thoracic cancer patients retrospectively. Fifteen patients were treated with conventional radiation therapy, 6 patients with hyperfractionated radiation therapy and 19 patients with stereotactic body radiation therapy (SBRT). Ventilation images were calculated from 4D-CT data using a deformable image registration and Jacobian-based algorithm. Each ventilation map was normalized by converting it to percentile images. Ventilation-based dosimetric parameters (Mean Dose, V5 [percent lung volume receiving ≥5 Gy], and V20 [percent lung volume receiving ≥20 Gy]) were calculated for highly and poorly ventilated regions. To test whether the ventilation-based dosimetric parameters could be used predict radiation pneumonitis of ≥Grade 2, the area under the curve (AUC) was determined from the receiver operating characteristic analysis.

Results

For Mean Dose, poorly ventilated lung regions in the 0–30% range showed the highest AUC value (0.809; 95% confidence interval [CI], 0.663–0.955). For V20, poorly ventilated lung regions in the 0–20% range had the highest AUC value (0.774; 95% [CI], 0.598–0.915), and for V5, poorly ventilated lung regions in the 0–30% range had the highest AUC value (0.843; 95% [CI], 0.732–0.954). The highest AUC values for Mean Dose, V20, and V5 were obtained in poorly ventilated regions. There were significant differences in all dosimetric parameters between radiation pneumonitis of Grade 1 and Grade ≥2.

Conclusions

Poorly ventilated lung regions identified on 4D-CT had higher AUC values than highly ventilated regions, suggesting that functional planning based on poorly ventilated regions may reduce the risk of lung toxicity in radiation therapy.

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

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 (OF_surv) or; ii) maximize the homogeneity of the density of surviving tumor cells (OF_std). 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 OF_surv. 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.