Dose distribution estimation toward CT-less adaptive carbon ion radiotherapy for liver tumors using the divided-volume matching technique

Figure 1 illustrates the concept of this study to verify whether DVM CTs are sufficiently representative of in-room CTs for dose distribution evaluations. The planning CT (PlanCT) was divided into two volumes: VOI (the yellow region of PlanCT in figure 1) and BV (the grey region of PlanCT in figure 1). The orthogonal 2D setup images were the DR images captured from the daily patient positioning before treatment. For DVM optimization, DRRs of the PlanCT were iteratively generated by adjusting the 3D positions and rotation angles of the VOI and BV of the PlanCT until the DRRs best match the 2D setup images. Upon matching, a virtual CT (DVM CT) reflecting the final DRRs is obtained, and this DVM CT is expected to reflect patients' anatomical structures at the positioning. The treatment room at Gunma University Heavy Ion Medical Center (GHMC) was equipped with an in-room CT (Aquilion™ LB, Canon Medical Systems, Japan) to evaluate the daily dose distribution; the in-room CT was the comparison target of the proposed DVM CT. To decrease inaccuracies resulting from anatomical changes during the acquisition time gap between the in-room CT and the DRs, the 2D setup images for DVM optimization were replaced by DRRs of the in-room CT.

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The VOI and BV displacements along three directions and three rotational axes were obtained from the DVM optimization, as well as the final coordinates of the VOI and BV, respectively. By applying those to the isocenter of the PlanCT, the VOI and BV shifts could be calculated as follows (Tashiro et al 2019):

$$\begin{eqnarray}&&{\mathop{r^{\prime} }\limits^{ \rightharpoonup }}_{IC}^{\mathrm{BV}}={H}_{\mathrm{BV}}{\mathop{r}\limits^{ \rightharpoonup }}_{IC},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\mathop{r^{\prime} }\limits^{ \rightharpoonup }}_{IC}^{\mathrm{VOI}}={H}_{\mathrm{BV}}{H}_{\mathrm{VOI}}{\mathop{r}\limits^{ \rightharpoonup }}_{IC},\end{eqnarray} \tag{ 2 }$$

where ${\mathop{r^{\prime} }\limits^{ \rightharpoonup }}_{IC}^{\mathrm{BV}}$ and ${\mathop{r^{\prime} }\limits^{ \rightharpoonup }}_{IC}^{\mathrm{VOI}}$ are the isocenter positions obtained after applying the BV and VOI shifts, respectively, in the DVM CT; ${H}_{\mathrm{BV}}$ and ${H}_{\mathrm{VOI}}$ are the $4\times 4$ matrix transformations representing the 3D displacements in both the translations and rotations of the BV and VOI, respectively; and ${\mathop{r}\limits^{ \rightharpoonup }}_{IC}$ is the original isocenter position.

Phantom simulations were implemented to test the workflow under a basic condition: steady BV with only shifted VOI and no unknown or complex motions. Two scenarios were simulated, both using chest phantoms: (1) phantom N-1 (Kyoto Kagaku Co., Ltd, Kyoto, Japan) inserted with a customized cuboid phantom as the clinical target volume (CTV) (figure 2(a)), and (2) a cylindrical four-dimensional CT (4DCT) imaging insert of the QUASAR^TM (Modus Medical Devices Inc. London, Canada) with the relatively high-density region as the CTV (figure 2(b)). Two CT scans of the chest phantom were performed in each scenario; the first scan was considered the PlanCT, and the second was considered the in-room CT containing manually shifted insertions with approximately 20 mm in the superior direction. The cuboid or cylindrical insertions were set as the VOI, and the remaining CT volume was considered the BV (figure 2).

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Bone matching (BM; figure 3(a)) and tumor matching (TM; figure 3(b)) are the two common methods of patient positioning correction adopted in clinical practice to determine the isocenter for irradiation of the day (Abe et al 2017). The dose distribution of the original treatment plan generated from the XiO-N^® treatment planning system (Elekta Sweden; Mitsubishi Electric, Japan) was recalculated on the in-room and DVM CTs with different isocenters based on BM or TM to obtain the dose distributions for comparison. In addition, the dose distribution of the original plan was recalculated on the DVM CT with the isocenters calculated by the VOI and BV shifts to obtain the dose distribution of the DVM CT with the isocenter based on TM, which was DVM-TM, and that based on BM was DVM-BM. The dose distribution of the in-room CT with the isocenter based on TM was named InRoom-TM, and that on BM was InRoom-BM.

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DVM was initially applied to liver tumors for dose distribution evaluations because liver tumors can be relatively easily located in DR images by the contrast agent Lipiodol and/or fiducial markers. The diaphragm is another landmark for image registration besides bones (Yue et al 2012, Chan et al 2016). Data on ten hepatocellular carcinoma (HCC) patients treated with carbon ion radiotherapy at GHMC were collected in this retrospective study, which was approved by the institutional review board (approval number HS2022-044) of Gunma University Hospital; all patients were treated with two orthogonal beam directions. Of the patient treatment positions, four were prone, and six were supine; the tumor locations were S4 for two, S5 for one, S6 for two, S6 and S7 for one, S7 for three, and S8 for one.

Both the PlanCTs and daily in-room CTs were acquired at the gated end-exhalation phase; they were matched based on bony structures and markers to obtain the BM and TM shifts, respectively, from the isocenter on the in-room CT for dose recalculation. TM was typically achieved either by fiducial markers, such as metal markers implanted at the peripheral liver tissue near the target, or by residual Lipiodol deposition after transcatheter arterial chemoembolization (Abe et al 2017). The liver or the liver and surrounding tissues were delineated as the VOIs. The dose distributions of the original plans were recalculated on the in-room CTs and DVM CTs based on BM and TM for dose distribution comparison. As in the phantom study, we compared DVM-BM with InRoom-BM and DVM-TM with InRoom-TM.

The planning target volume (PTV) coverage (V95%, the percentage of the PTV receiving ≥95% of the prescribed dose) was used for dose comparison because the CTV coverage (V95%) differences between the PlanCT, InRoom-BM, DVM-BM, InRoom-TM, and DVM-TM were not significant. Sufficient geometrical PTV margins were provided to compensate for the uncertainties from the setup, beam range, and organ motion, ensuring CTV dose coverage (Langen and Zhu 2018). The geometric margin of the PTV in this study was generated from the calculation of the internal (IM) and setup margins (SM) based on Tashiro et al 2013. IM was derived from the tumor motions in six directions within the gating window on the 4DCT images. SM considered the system accuracy and potential patient positioning errors, including various machine characteristics, range uncertainties, and image-intrinsic errors. PTV was commonly defined geometrically for all directions, independent of the beam directions. Gamma index analysis was another supportive tool using a gamma criterion of 3%/3 mm, (Low et al 1998) provided a quantitative comparison to evaluate the point-by-point difference between the evaluated (DVM CT) and referenced (in-room CT) dose distributions in terms of dose difference and distance-to-agreement.

To test the performance of the DVM technique with large inter-fractional motions in patient data, patients' 4DCT images were used following the same workflow as the above section. Five patients among the 10 HCC patients with relatively more significant liver shifts (6.8–23.5 mm) on their 4DCTs between the end-of-exhalation and end-of-inhalation were selected. The end-exhalation phase of each 4DCT was considered the PlanCT, and the end-inhalation phase of the same 4DCT was considered the in-room CT to simulate large liver shifts. DVM CTs were generated from the DVM optimization based on the PlanCT and the 2D setup images, which were the two orthogonal DRRs of the in-room CT. The dose distribution comparison and the analysis between the DVM CTs and the in-room CTs were the same as reported in the above section.

The CTV coverage (V95%) and dose distributions in both scenarios are illustrated in figures 4 and 5. The CTV coverage (V95%) differences between InRoom-BM and DVM-BM and between the InRoom-TM and the DVM-TM, were minor in both scenarios (0.46% and −0.28% for scenario 1, −1.95% and −0.38% for scenario 2, respectively; figure 4). The dose distributions of the DVM-BMs (figures 5(c) and (h)) were similar to those of the InRoom-BMs (figures 5(b) and (g)), as were the DVM-TMs (figures 5(e) and (j)) and the InRoom-TMs (figures 5(d) and (i)). With different isocenters, the dose coverage of the DVM CT changed consistently with those of the in-room CT, indicating that estimating daily dose distribution from two radiographs was feasible.

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A summary of the dose distribution comparison between the DVM CT and in-room CT for each HCC patient is shown in figure 6, tables 1 and 2. Moreover, the dose distribution of a representative patient is illustrated in figure 7. Between the in-room CT and DVM CT, the PTV coverage (V95%) differences were less than 3%, except for Patient 1 in the BM scenario and Patient 2 in the TM scenario, and the normal liver (total liver minus GTV) dose differences (V_20Gy(RBE) and V_10Gy(RBE)) were less than 2% (V_20Gy(RBE) and V_10Gy(RBE) were 0.28 ± 0.62% and 0.14% ± 0.68% for BM and 0.20 ± 0.26% and 0.08 ± 0.30% for TM, respectively). The gamma passing rates with a 3%/3 mm criterion were above 90% in all cases and above 96%, excluding Patient 1.

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For Patient 2 in the TM scenario, the PTV coverage of the InRoom-TM was significantly lower than that of the InRoom-BM, unlike the other nine cases, which were approximately equal. This may be because the marker shifts inside the liver did not always represent the motions of the entire liver and/or tumor; the distance between the isocenters of BM and TM in the in-room CT and the DVM CT was different by 4.2 mm ($\left|{\boldsymbol{d}}-{\boldsymbol{d}}{\boldsymbol{\text{'}}}\right|$ in figure 6(d)) for Patient 2, i.e. the isocenter position of TM in the in-room CT was considerably different from that determined by DVM CT. Applying the difference to determine the new isocenter for InRoom-TM, the new dose distribution for InRoom-TM (InRoom-TMnew, called Patient 2^a) could be obtained by recalculating the dose based on the new isocenter. By comparing InRoom-TMnew to DVM-TM, the PTV coverage difference decreased to 0.25%, which was considerably lower than the PTV coverage difference between InRoom-TM and DVM-TM (−8.45%). Conversely, obtaining the new dose distribution the same way as the above for DVM-TM (DVM-TMnew, called Patient 2^b), the PTV coverage difference between InRoom-TM and DVM-TMnew decreased to 4.46%. The PTV coverage comparisons between PlanCT, InRoom-TM, DVM-TMnew, InRoom-TMnew, and DVM-TM for Patient 2 are presented in figure 6(e).

The dose coverage differences between InRoom-BM and DVM-BM were 0.42 ± 1.35%, excluding Patient 1; they were −0.46 ± 0.91% between InRoom-TM and DVM-TM, excluding Patient 1 and replacing Patient 2 with Patient 2^a. The same trend can be seen in the clinical data as in the phantom data that the dose coverage of the DVM CT changed consistently with those of the in-room CT with different isocenters. The results showed that the DVM CT was similar to the in-room CT for liver cases; therefore, DVM CT is sufficiently representative of in-room CT for evaluating dose distributions for liver cases.

The CTV and PTV coverage comparisons of five patients simulating large inter-fractional motions are shown in figure 8 and table 1. CTV coverage differences between InRoom-BM and DVM-BM and between InRoom-TM and DVM-TM were 2.18 ± 2.82% and −0.24 ± 0.42%, respectively. PTV coverage differences between InRoom-BM and DVM-BM and between InRoom-TM and DVM-TM were 1.59 ± 3.36% and −0.7 ± 1.6%, respectively. The dose coverage differences between in-room CTs and DVM CTs were small in both BM and TM scenarios. The magnitude of the change in dose coverage of the DVM CT followed that of the in-room CT at different isocenters in all selected patients. This indicated that in-room CTs and DVM CTs had high similarities in dose distribution, and the DVM technique could be applied to patient data with relatively large inter-fractional motions. The dose coverage differences between InRoom-TM and DVM-TM were slightly smaller than those between the InRoom-BM and DVM-BM. A possible reason for this is that the proportion of the CTV/PTV located on the steep dose gradient region was higher for BM than TM, making the dose coverage sensitive to small displacement differences.

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