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Table 1 Dose-volume constraint or equivalent parameters for partly acceptable dose distribution in our example

From: Dose-volume constrained optimization in intensity-modulated radiation therapy treatment planning

Assigned region (color in Figure  1 )

Organ

Dose-volume constraint

Set of parameters for being partly acceptable

PTV (blue)

Prostate

\(V_{82.1} \ge87\%\)

\((D_{1}^{\mathrm{L}},\zeta_{1}^{\mathrm{L}}) = (82.1, 0.87)\)

\(V_{95.9} < 2\%\)

\((D_{1}^{\mathrm{U}},\zeta_{1}^{\mathrm{U}}) = (95.9, 0.98)\)

OAR1 (green)

Right femoral head

\(V_{30} < 10\%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm{U}}) = (30, 0.9)\)

OAR2 (red)

Bladder

\(V_{20} < 60\%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm {U}}) = (20, 0.4)\)

\(V_{45} < 30\%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm{U}}) = (45, 0.7)\)

\(V_{50} < 15\%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm{U}}) = (50, 0.85)\)

OAR3 (cyan)

Rectum

\(V_{20} < 40\%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm{U}}) = (20, 0.6)\)

\(V_{30} < 20 \%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm{U}}) = (30, 0.8)\)

\(V_{35} < 10\%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm{U}}) = (35, 0.9)\)

OAR4 (magenta)

Left femoral head

\(V_{30} < 10\%\)

\((D_{2}^{\mathrm{U}},\zeta_{2}^{\mathrm{U}}) = (30, 0.9)\)

  1. \(V_{d}\) denotes the percentage of volume receiving at least d Gy. Note that dose values 82.1 Gy and 95.9 Gy for PTV are 95% and 111% of prescribed dose of 86.4 Gy, respectively.