Validation of robust radiobiological optimization algorithms based on the mixed beam model for intensity-modulated carbon-ion therapy

Abstract

Currently, treatment planning systems (TPSs) that can compute the intensities of intensity-modulated carbon-ion therapy (IMCT) using scanned carbon-ion beams are limited. In the present study, the computational efficacy of the newly designed IMCT algorithms was analyzed for the first time based on the mixed beam model with respect to the physical and biological doses; moreover, the validity and effectiveness of the robust radiobiological optimization were verified. A dose calculation engine was independently generated to validate a clinical dose determined in the TPS. A biological assay was performed using the HSGc-C5 cell line to validate the calculated surviving fraction (SF). Both spot control (SC) and voxel-wise worst-case scenario (WC) algorithms were employed for robust radiobiological optimization followed by their application in a Radiation Therapy Oncology Group benchmark phantom under homogeneous and heterogeneous conditions and a clinical case for range and position errors. Importantly, for the first time, both SC and WC algorithms were implemented in the integrated TPS platform that can compute the intensities of IMCT using scanned carbon-ion beams for robust radiobiological optimization. For assessing the robustness, the difference between the maximum and minimum values of a dose-volume histogram index in the examined error scenarios was considered as a robustness index. The relative biological effectiveness (RBE) determined by the independent dose calculation engine exhibited a -0.6% difference compared with the RBE defined by the TPS at the isocenter, whereas the measured and the calculated SF were similar. Regardless of the objects, compared with the conventional IMCT, the robust radiobiological optimization enhanced the sensitivity of the examined error scenarios by up to 19% for the robustness index. The computational efficacy of the novel IMCT algorithms was verified according to the mixed beam model with respect to the physical and biological doses. The robust radiobiological optimizations lowered the impact of range and position uncertainties considerably in the examined scenarios. The robustness of the WC algorithm was more enhanced compared with that of the SC algorithm. Nevertheless, the SC algorithm can be used as an alternative to the WC IMCT algorithm with respect to the computational cost.

Fig 1. Treatment plan for the biological study.

(a) Beam arrangement to a donut-shaped target. Dose distribution (b) and dose–volume histogram (c) of the treatment plan.

Fig 2. The heterogeneous phantom.

Three-dimension (a), axial (b), sagittal (b), and coronal (d) are depicted.

Fig 3. Dose distribution comparisons.

Physical dose distribution of the independent calculation (a) and TPS (b), and gamma analysis result (c). Clinical dose distribution of the independent calculation (d) and TPS (e), and gamma analysis result (f).

Fig 4. The SF of HSGc-C5 cells comparison among the experiment irradiated by IMCT (blue bar), the independent calculation (orange bar), and the experiment irradiated by SFUD (gray bar).

The black horizontal solid line represents 10% of SF.

Fig 5

Individual dose distributions in the homogeneous phantom of the beams with the port angles of 0° (the first column from the left), 90° (the second column from the left), and 270° (middle column) and the total physical dose distribution (the second column from the right) and clinical dose distribution (the first column from the right) for plan-1 (upper row), plan-2 (middle row) and plan-3 (lower low) optimized with the SC algorithm. The CTV and OAR are represented by the red and yellow lines, respectively.

Fig 6

Total clinical dose distributions optimized with the SC algorithm in the homogeneous phantom for plan-1 (upper row), plan-2 (middle row), and plan-3 (lower row) recalculated with the efficient density perturbations of −3.5% (left column) and +3.5% (right column) at the intentional translation of +2 mm in each direction for all fields. The red and yellow lines depict the CTV and OAR, respectively.

Fig 7

The variation of the DVHs of dose distributions optimized using the SC algorithm in homogeneous (upper row) and heterogeneous (lower row) phantoms reassessed for 28 different perturbations of beam ranges and positions in the CTV and OAR for plan-1, plan-2, and plan-3. The DVHs in the nominal case are represented by the thick solid line.

Fig 8

The individual dose distributions in the heterogeneous phantom of the beams with the port angles of 0° (the first column from the left), 90° (the second column from the left), and 270° (middle column) and the total physical dose distribution (the second column from the right) and clinical dose distribution (the first column from the right) for plan-1 (upper row), plan-2 (middle row) and plan-3 (lower low) optimized using the SC algorithm, respectively. The red and yellow lines demonstrate the CTV and OAR, respectively.

Fig 9

The total clinical dose distributions optimized using the SC algorithm in the heterogeneous phantom for plan-1 (upper row), plan-2 (middle row), and plan-3 (lower row) reassessed with the perturbations of the efficient density of −3.5% (left column) and +3.5% (right column) at the intentional translation of +2 mm in each direction for all fields. The red and yellow lines denote the CTV and OAR, respectively.

Fig 10

The individual dose distributions in the homogeneous phantom of the beams with the port angles of 0° (the first column from the left), 90° (the second column from the left), and 270° (middle column) as well as the total physical dose distribution (the second column from the right) and clinical dose distribution (the first column from the right) for conventional IMCT (upper row) and WC IMCT (lower low) optimized using the WC algorithm. The red and yellow lines denote the CTV and OAR, respectively.

Fig 11

The total clinical dose distributions optimized using the WC algorithm in the homogeneous phantom for conventional IMCT (upper row) and WC IMCT (lower row) reassessed with the perturbations of effective density of −3.5% (left column) and +3.5% (right column) at the intentional translation of +2 mm in each direction for all fields. The red and yellow lines represent the CTV and OAR, respectively.

Fig 12

The variation of the DVHs of dose distributions optimized using the WC algorithm in homogeneous (upper row) and heterogeneous (lower row) phantom recalculated for 28 different perturbations of beam ranges and positions in the CTV and OAR for conventional IMCT and WC IMCT. The DVHs in the nominal case are represented by the thick solid line.

Fig 13

The individual dose distributions in the heterogeneous phantom of the beams with the port angles of 0° (the first column from the left), 90° (the second column from the left), and 270° (middle column) as well as a complete physical dose distribution (the second column from the right) and clinical dose distribution (the first column from the right) for conventional IMCT (upper row) and WC IMCT (lower low) optimized using the WC algorithm. The red and yellow lines denote the CTV and OAR, respectively.

Fig 14

The total clinical dose distributions optimized with the WC algorithm in the heterogeneous phantom for conventional IMCT (upper row) and WC IMCT (lower row) reassessed with the perturbations of effective densities of −3.5% (left column) and +3.5% (right column) at the intentional translation of +2 mm in each direction for all fields. The red and yellow lines represent the CTV and OAR, respectively.

Fig 15

The individual dose distributions in the patient case of the beams with the port angles of 0° (the first column from the left), 90° (the second column from the left), and 270° (middle column) and the total physical dose distribution (the second column from the right) and clinical dose distribution (the first column from the right) for conventional IMCT (upper row), a range (setup) and gradient robust IMCT (middle row), and WC IMCT (lower low). The orange line depicts the CTV.

Fig 16. The variation of the DVHs of dose distributions in the patient case reassessed for 28 different perturbations of beam ranges and positions in the CTV (orange) and OAR (light blue) for conventional IMCT, the range (setup) and gradient robust IMCT, and WC IMCT.

The thick solid line depicts the DVHs in the nominal case.