Beyond the margin recipe: the probability of correct target dosage and tumor control in the presence of a dose limiting structure

Abstract

In the past, hypothetical spherical target volumes and ideally conformal dose distributions were analyzed to establish the safety of planning target volume (PTV) margins. In this work we extended these models to estimate how alternative methods of shaping dose distributions could lead to clinical improvements. Based on a spherical clinical target volume (CTV) and Gaussian distributions of systematic and random geometrical uncertainties, idealized 3D dose distributions were optimized to exhibit specific stochastic properties. A nearby spherical organ at risk (OAR) was introduced to explore the benefit of non-spherical dose distributions. Optimizing for the same minimum dose safety criterion as implied by the generally accepted use of a PTV, the extent of the high dose region in one direction could be reduced by half provided that dose in other directions is sufficiently compensated. Further reduction of this unilateral dosimetric margin decreased the target dose confidence, however the actual minimum CTV dose at 90% confidence typically exceeded the minimum PTV dose by 20% of prescription. Incorporation of smooth dose-effect relations within the optimization led to more concentrated dose distributions compared to the use of a PTV, with an improved balance between the probability of tumor cell kill and the risk of geometrical miss, and lower dose to surrounding tissues. Tumor control rate improvements in excess of 20% were found to be common for equal integral dose, while at the same time evading a nearby OAR. These results were robust against uncertainties in dose-effect relations and target heterogeneity, and did not depend on 'shoulders' or 'horns' in the dose distributions.

Figure 1

Generic sigmoid curves representing non-linear tumor dose-effect relations. Combinations of steepness parameters k and dose levels D₅₀ were chosen such that at 60 Gy the TCP is close to either 70% (blue lines), or 30% (red lines).

Figure 2

Central slices through 60 Gy prescription dose distributions (a) based on the PTV; (b) optimized to reach a 90% confdence of 95% dose prescription in the CTV under geometric errors with Σ=σ =3 mm while minimizing integral dose, using 60 Gy; (c) 64.2 Gy; (d) without maximum dose constraint. Dose to the stationary OAR was limited to 30 Gy, and the OAR was brought in as close as possible while still reaching a 90% CTV dose confidence. (e) Dose profiles in the OAR direction. (f) DVHs of the PTV.

Figure 3

Dose distributions optimized for minimum CTV dose confidence with an OAR (D_max = 0.5D_presc) placed at various distances. Overdosage was allowed up to 7% over prescription level. (a) The resulting confidence of reaching at least 95% of prescription dose in the CTV. (b) The minimum CTV dose at 90% confidence (solid), and minimum PTV dose (dashed).

Figure 4

Dose distributions optimizing expected TCP for a homogeneous CTV with k = 16, D₅₀ = 57 Gy. Integral dose was forced to equal that of the PTV-based distribution at 60 Gy prescription (figure 2(a)). For geometric errors Σ=σ=3 mm the dose shows (a) concentric shells in the absence of an OAR, but instead (b) a single hot region if an OAR is placed at small distance. These features disappear (c) and (d) for single fraction treatment. Two possible locations of a 1 cc tumor focus are identified as foc_A and foc_B. (e) Dose profiles in the OAR direction. (f) DVHs of the PTV.