Coverage optimized planning: probabilistic treatment planning based on dose coverage histogram criteria

Abstract

This work (i) proposes a probabilistic treatment planning framework, termed coverage optimized planning (COP), based on dose coverage histogram (DCH) criteria; (ii) describes a concrete proof-of-concept implementation of COP within the PINNACLE treatment planning system; and (iii) for a set of 28 prostate anatomies, compares COP plans generated with this implementation to traditional PTV-based plans generated with planning criteria approximating those in the high dose arm of the Radiation Therapy Oncology Group 0126 protocol. Let Dv denote the dose delivered to fractional volume v of a structure. In conventional intensity modulated radiation therapy planning, Dv has a unique value derived from the static (planned) dose distribution. In the presence of geometric uncertainties (e.g., setup errors) Dv assumes a range of values. The DCH is the complementary cumulative distribution function of D(v+). DCHs are similar to dose volume histograms (DVHs). Whereas a DVH plots volume v versus dose D, a DCH plots coverage probability Q versus D. For a given patient, Q is the probability (i.e., percentage of geometric uncertainties) for which the realized value of Dv exceeds D. PTV-based treatment plans can be converted to COP plans by replacing DVH optimization criteria with corresponding DCH criteria. In this approach, PTVs and planning organ at risk volumes are discarded, and DCH criteria are instead applied directly to clinical target volumes (CTVs) or organs at risk (OARs). Plans are optimized using a similar strategy as for DVH criteria. The specific implementation is described. COP was found to produce better plans than standard PTV-based plans, in the following sense. While target OAR dose tradeoff curves were equivalent to those for PTV-based plans, COP plans were able to exploit slack in OAR doses, i.e., cases where OAR doses were below their optimization limits, to increase target coverage. Specifically, because COP plans were not constrained by a predefined PTV, they were able to provide wider dosimetric margins around the CTV, by pushing OAR doses up to, but not beyond, their optimization limits. COP plans demonstrated improved target coverage when averaged over all 28 prostate anatomies, indicating that the COP approach can provide benefits for many patients. However, the degree to which slack OAR doses can be exploited to increase target coverage will vary according to the individual patient anatomy. The proof-of-concept COP implementation investigated here utilized a probabilistic DCH criteria only for the CTV minimum dose criterion. All other optimization criteria were conventional DVH criteria. In a mature COP implementation, all optimization criteria will be DCH criteria, enabling direct planning control over probabilistic dose distributions. Further research is necessary to determine the benefits of COP planning, in terms of tumor control probability and/or normal tissue complication probabilities.

Figure 1

Steps to generate a DVCM, DCH, and PDVH for a target structure or OAR. (a) Generate DVHs for different setup errors. (b) For each DVH, increment all grid squares lying below or to the left of the DVH. (c) Divide by total number of DVHs to obtain the DVCM. Each grid square contains the probability that, in an individual treatment course, the realized DVH will lie above or to the right of that grid square. A DCH is obtained by plotting probability versus dose across a grid row. A PDVH for a target structure is obtained by connecting grid squares containing a probability of, e.g., 0.95. (d) A PDVH for an OAR is obtained by connecting grid squares containing a probability of, e.g., 0.05.

Figure 2

Example DCHs for CTV D₉₈ and OAR D₅₀ in the current optimization iteration. The DCH gives the probability that, in an individual treatment course, the realized value of the dose metric (CTV D₉₈ or OAR D₅₀) will exceed the dose on the x-axis. In this example the OAR DCH passes through the point (OD,0.05), where OD is the OAR dose, ensuring Pr[D₅₀≤OD]=95%. The CTV DCH passes to the left of the point (TD, 0.95), where TD is the target dose. The desired coverage criterion is: Pr[D₉₈≥TD]≥95%. The figure shows a strategy for meeting this criterion. At each iteration, one uses the current DCH to find the DAPC. In this example, the prescription coverage is 0.95. The objective function sums contributions from all voxels with doses d such that DAPC≤d≤TD. This causes the optimizer to increase dose to these voxels, pushing the current DCH toward the desired DCH.

Figure 3

Average rectum and bladder doses D_max,5 (●), D_15,5 (◼), D_25,5 (◆), D_35,5 (▲), and D_50,5 (●) plotted against CTV D_min,95. Results are averaged over 28 prostate anatomies. Results for PTV plans (criterion sets PTV_0–PTV_4, Table 1) are represented by dotted lines and hollow symbols. Results for COP plans (criterion sets COP_0–COP_4, Table 1) are represented by solid lines and solid symbols. Dotted horizontal lines mark the RTOG 0126 dose limits for rectum D_max (84.7 Gy), D₁₅ (75 Gy), D₂₅ (70 Gy), D₃₅ (65 Gy), and D₅₀ (60 Gy); and bladder D_max (84.7 Gy), D₁₅ (80 Gy), D₂₅ (75 Gy), D₃₅ (70 Gy), and D₅₀ (65 Gy).

Figure 4

Patient 10 rectum and bladder doses D_max,5 (●), D_15,5 (◼), D_25,5 (◆), D_35,5 (▲), and D_50,5 (●) plotted against CTV D_min,95. Line and symbol conventions are as in Fig. 3. For this patient, bladder doses are actively limiting the CTV D_min,95, rectum doses are not.

Figure 5

Average rectum and bladder doses D_max,5 (●), D_15,5 (◼), D_25,5 (◆), D_35,5 (▲), and D_50,5 (●) plotted against CTV D_min,95. Results are averaged over 28 prostate anatomies. Rectum and bladder doses D_v,5 falling below the dose limits in Table 1 were set equal to those limits to avoid penalizing increased doses below the optimization objectives. Line and symbol conventions are as in Fig. 3.

Figure 6

(a) Percentile DVHs for the same patient (patient 10) as in Fig. 4 for COP_4 (solid) and PTV_4 (dashed) plans. The CTV DVH is the 95% DVH (DVH₉₅), while the rectum and bladder DVHs are 5% DVHs (DVH₅). (b) Static DVHs for patient 10. In both plots, static OAR optimization criteria are indicated by circles (see Table 1).

Figure 7

(a) Percentile DVHs averaged over all 28 prostate anatomies for COP_4 (solid) and PTV_4 (dashed) plans. The CTV DVH is the 95% DVH (DVH₉₅), while the rectum and bladder DVHs are 5% DVHs (DVH₅). (b) Static DVHs averaged over all 28 prostate anatomies. In both plots, static OAR optimization criteria are indicated by circles (see Table 1).

Figure 8

(a) CTV D_min DCH (DCH₁₀₀) for patient 10. (b) CTV D_min DCH (DCH₁₀₀) averaged over all 28 prostate anatomies. In both plots, the prescription dose of 79.2 Gy is indicated by the dotted line.