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A characterization of robust radiation therapy treatment planning methods—from expected value to worst case optimization
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10.1118/1.4737113
/content/aapm/journal/medphys/39/8/10.1118/1.4737113
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/39/8/10.1118/1.4737113

Figures

Image of FIG. 1.
FIG. 1.

The C-shaped geometry. The solid line indicates where the line doses are taken and the dashed lines indicate the beam directions. The radius of the inner arc of the target is 1.5 cm and that of the outer arc is 5 cm. The OAR has radius 1cm and the external ROI has radius 8 cm.

Image of FIG. 2.
FIG. 2.

Color table indicating the dose levels for the dose distributions. The tick labels denote percentage of the reference dose level, which is 1 for total doses and 0.5 for beam doses.

Image of FIG. 3.
FIG. 3.

Total doses for the robust methods for systematic errors. (a)–(c) Nominal scenario; and (d)–(f) isocenters shifted 0.5 cm to the right and density two standard deviations lower than measured.

Image of FIG. 4.
FIG. 4.

Beam doses for the robust methods for systematic errors. (a)–(f) Nominal scenario; and (g)–(l) isocenters shifted 0.5 cm to the right and density two standard deviations lower than measured.

Image of FIG. 5.
FIG. 5.

DVH families for the robust methods for systematic errors over the 89 systematic error scenarios. The dashed lines correspond to the nominal scenario DVHs.

Image of FIG. 6.
FIG. 6.

(a) Worst (lowest target , highest OAR ), mean, and best (highest target , lowest OAR ) case trade-off curves for the target importance weight in [100, 1000]; and (b) DPHs. Both figures are resulting from the robust methods for systematic errors evaluated over the 89 systematic error scenarios.

Image of FIG. 7.
FIG. 7.

Total nominal scenario doses for the expected value optimization for random errors with fixed standard deviation for the number of fractions (a) n = 30 and (b) n = ∞; and (c) line doses for n in {1, 5, 30, ∞} taken along the line shown in Fig. 1.

Image of FIG. 8.
FIG. 8.

Nominal scenario total and beam doses for the CVaR optimization for random errors with uncertain standard deviation. The other robust methods resulted in similar dose distributions (root mean square differences from CVaR below 0.02).

Image of FIG. 9.
FIG. 9.

DVH families for the robust methods for random errors with uncertain standard deviation over 100 realizations of random standard deviations and random errors in 30 fractions. The optimizations were performed with n = ∞. The dashed lines correspond to the nominal scenario DVHs.

Image of FIG. 10.
FIG. 10.

DPHs for the robust methods for random errors with uncertain standard deviation based on 1000 simulations of random standard deviations and random errors in 30 fractions. The optimizations were performed with n = ∞.

Image of FIG. 11.
FIG. 11.

Nominal scenario line doses taken along the line shown in Fig. 1 for the robust methods for random errors with uncertain standard deviation for the number of fractions n in {1, 5, 30, ∞}.

Image of FIG. 12.
FIG. 12.

(a) Total nominal scenario dose for the CVaR optimization for systematic errors and random errors with fixed standard deviation. The number of fractions n = ∞. The other robust methods resulted in similar heterogeneous dose distributions, which is reflected in inset (b), the line doses taken along the line shown in Fig. 1.

Image of FIG. 13.
FIG. 13.

Total nominal scenario doses for the robust methods for systematic errors and random errors with uncertain standard deviation. The number of fractions n = ∞.

Image of FIG. 14.
FIG. 14.

Nominal scenario beam doses when random errors with uncertain standard deviation are handled by the robust methods. The number of fractions n = ∞.

Image of FIG. 15.
FIG. 15.

DVH families for the robust methods for systematic errors and random errors with uncertain standard deviation over 100 realizations of systematic errors, random standard deviations, and random errors in 30 fractions. The optimizations were performed with n = ∞. The dashed lines correspond to the nominal scenario DVHs.

Image of FIG. 16.
FIG. 16.

(a) Worst (lowest target , highest OAR ), mean, and best (highest target , lowest OAR ) case trade-off curves of the methods accounting for systematic errors and random errors with uncertain standard deviation and n = ∞, for the target importance weight in [100, 1000]; (b) DPHs of the methods accounting for systematic errors and random errors with uncertain standard deviation and n = ∞; and (c) DPHs of the methods accounting for systematic errors only. The three figures are resulting from the robust methods evaluated over 1000 simulated treatments of systematic errors, random standard deviations, and random errors in 30 fractions.

Image of FIG. 17.
FIG. 17.

Nominal scenario line doses taken along the line shown in Fig. 1 for the robust methods for systematic errors and random errors with uncertain standard deviation. The number of fractions n = ∞.

Image of FIG. 18.
FIG. 18.

Doses and DVH families for the conventional method with a 5 mm margin. (a) Total dose; (b) and (c) beam doses. (d) DVH family over the 89 systematic error scenarios; (e) over 100 realizations of random standard deviations and random errors in 30 fractions; and (f) over 100 realizations of systematic error as well as random standard deviations and random errors in 30 fractions. The dashed lines correspond to the nominal scenario DVHs.

Tables

Generic image for table
TABLE I.

Notation for the different types of uncertainties.

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/content/aapm/journal/medphys/39/8/10.1118/1.4737113
2012-07-31
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A characterization of robust radiation therapy treatment planning methods—from expected value to worst case optimization
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/39/8/10.1118/1.4737113
10.1118/1.4737113
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