Combination effects of tissue heterogeneity and geometric targeting error in stereotactic body radiotherapy for lung cancer using CyberKnife

Abstract

We have investigated the combined effect of tissue heterogeneity and its variation associated with geometric error in stereotactic body radiotherapy (SBRT) for lung cancer. The treatment plans for eight lung cancer patients were calculated using effective path length (EPL) correction and Monte Carlo (MC) algorithms, with both having the same beam configuration for each patient. These two kinds of plans for individual patients were then subsequently recalculated with adding systematic and random geometric errors. In the ordinary treatment plans calculated with no geometric offset, the EPL calculations, compared with the MC calculations, largely overestimated the doses to PTV by ~ 21%, whereas the overestimation were markedly lower in GTV by ~ 12% due to relatively higher density of GTV than of PTV. When recalculating the plans for individual patients with assigning the systematic and random geometric errors, no significant changes in the relative dose distribution, except for overall shift, were observed in the EPL calculations, whereas largely altered in the MC calculations with a consistent increase in dose to GTV. Considering the better accuracy of MC than EPL algorithms, the present results demonstrated the strong coupling of tissue heterogeneity and geometric error, thereby emphasizing the essential need for simultaneous correction for tissue heterogeneity and geometric targeting error in SBRT of lung cancer.

Figure 1

Box‐and‐whisker plots for differences in ${\mathrm{D}}_{99\%}$ for tumor volumes (GTV and PTV) and ${\mathrm{D}}_{1\%}$ for critical structures (lungs, spinal cord, esophagus, and heart) in between the EPL plans and MC plans recalculated with the same MUs. The differences are calculated as $2({\mathrm{D}}_{\text{EPL}}-{\mathrm{D}}_{\text{MC}})/({\mathrm{D}}_{\text{EPL}}+{\mathrm{D}}_{\text{MC}})$, where ${\mathrm{D}}_{\text{EPL}}$ and ${\mathrm{D}}_{\text{MC}}$ are the doses in the EPL and MC plans, respectively.

Figure 2

Dose‐volume histograms (DVHs) for Patient A calculated with the EPL (solid lines) and MC (dashed lines) algorithms, respectively: (a) DVHs for GTV, PTV, and lungs, and (b) DVHs for spinal cord, heart, and esophagus. The inset in (a) is the enlarged view of DVH for lungs.

Figure 3

Variations of ${\mathrm{D}}_{99\%} (\text{GTV})$ in the EPL (filled squares) and MC (filled circles) plans for individual patients (A to H) as a function of systematic beam offset (Σ) along the cranial‐to‐caudal direction. The plus (minus) sign for Σ indicates the shift toward the cranial (caudal) direction. The 95% prescription dose level (solid line), as well as the dose to 99% of PTV levels in the ordinary EPL (dashed line) and the renormalized MC (dotted line) plans, are given in each plot, for reference. The offset range less than the PTV margin (i.e., $-3 \text{mm} \Sigma \le 3 \text{mm}$) is gray shaded in each figure.

Figure 4

(a) Doses to 99% of GTV (i.e., ${\mathrm{D}}_{99\%} (\text{GTV})$) calculated at $\pm 3 \text{mm}$ offsets to craniocaudal direction using the EPL (red squares and error bars) and MC (blue squares and error bars) plans for individual patients (A to H), where the mean values between ${\mathrm{D}}_{99\%} (\text{GTV})$ at $+3 \text{mm}$ (toward the cranial) and $-3 \text{mm}$ (toward the caudal direction) are marked by squares and the ranges of the values are indicated by error bars. (b) Acceptable ranges for systematic shift that resulted in ${\mathrm{D}}_{99\%}(\text{GTV}) \ge 95\%$ in EPL (red boxes) and MC (blue boxes) plans for individual patients, which were obtained with the interpolations of raw data given in Fig. 3.

Figure 5

Differences between ${\mathrm{D}}_{99\%} (\text{GTV})$ at $\pm 3 \text{mm}$ offsets and the ordinary planned ${\mathrm{D}}_{99\%} (\text{PTV})$ calculated using the EPL (red squares and error bars) and MC (blue squares and error bars) plans for individual patients (A to H). The mean of the differences between at $+3 \text{mm}$ (toward the cranial) and −3 mm (toward the caudal direction) are marked by squares, and the minimal and maximal values of the differences are indicated by error bars.

Figure 6

Variations of ${\mathrm{D}}_{99\%}(\text{GTV})$ in the EPL (filled squares) and MC (filled circles) plans for Patient H as a function of random targeting error (${\sigma }_{\text{tot}}$), where the 95% prescription dose level (solid line) as well as ${\mathrm{D}}_{99\%} (\text{PTV})$ levels in the ordinary EPL (dashed line) and the renormalized MC (dotted lines) plans are given, for reference. The gay shaded region shows the error range less than the PTV margin (i.e., $-3 \text{mm} \le {\sigma }_{\text{tot}}\le 3 \text{mm}$).