Abstract
This study aimed to evaluate how planning target volume (PTV) size influences treatment-planning parameters and their relationship to tracking and irradiation accuracy. A high-resolution two-dimensional diode array mounted on a motion phantom was irradiated under four respiratory waveforms using Fiducial Tracking with Respiratory Correlation mode. Spherical PTVs with diameters of 1–4 cm were defined. Treatment-planning parameters, including beam-on time, couch speed, gantry period, kilovoltage imaging interval and modulation factor, were analyzed to assess their relationship with tracking and irradiation accuracy. The root-mean-square error (
) between tracked and reference target positions, γ pass rate and potential difference as the control parameter of the correlation model were compared across PTV sizes. Correlation and partial correlation analyses were performed to evaluate the relationships between the 
and treatment-planning parameters. The 
was influenced by the inherent interdependence of beam-on time, gantry period and the kV imaging interval. The kV imaging interval for the PTV of φ1 cm was 4.2 s, longer than those for the other PTV sizes, which made the potential difference unstable during the initial tracking period and kept γ pass rates below 92% across all respiratory waveforms. For the PTVs of φ2–3 cm, potential difference stabilized within ~20 s after beam-on and was associated with an improvement in the γ pass rate. In contrast, for the PTV of φ4 cm, degradation of tracking accuracy was reflected in a reduction in the γ pass rate. Optimizing treatment-planning parameters for each PTV size was essential for precise motion-synchronized irradiation.
Keywords: SBRT, Radixact Synchrony, tomotherapy, respiratory tracking
INTRODUCTION
Stereotactic radiotherapy is an irradiation technique that delivers a high radiation dose to a localized tumor in a small number of fractions to achieve high local tumor control [1–3]. Accurate management of respiratory-induced tumor motion is essential to maintain treatment accuracy during irradiation [4]. In clinical practice, several respiratory-motion management techniques, such as the internal target volume (ITV) method, breath-hold and respiratory gating, have been widely implemented [5, 6]. Nevertheless, each technique has inherent limitations. The ITV method tends to increase the irradiated volume and expose normal tissues to higher radiation doses [7]. Breath-hold and respiratory gating often prolong treatment time and impose additional burden on patients with impaired respiratory function [5, 8, 9].
To address these limitations, real-time tumor-tracking radiotherapy has been increasingly adopted for managing respiratory motion [10, 11]. This approach synchronizes the treatment beam with real-time tumor motion, allowing a reduction in the planning target volume (PTV) margin and minimizing radiation exposure to surrounding normal tissues. In this technique, PTV size is one of the important factors. Houda et al. reported that larger tumor diameters were associated with higher tracking accuracy using CyberKnife XSight Lung Tracking system [12]. Ding et al. demonstrated that, in pancreatic cancer, larger tumors tend to be located closer to organs at risk, which reduces the tolerance window for respiratory motion [13].
Radixact Synchrony (Accuray, Sunnyvale, CA, USA) is one of the real-time tumor-tracking systems integrated into the helical tomotherapy platform [14, 15]. The system constructs a correlation model by linking respiratory signals from LED markers placed on the abdomen with kilovoltage (kV) X-ray images acquired at multiple gantry angles to estimate tumor positions. The kV X-ray tube and detector are mounted on the Tomotherapy gantry and provide an orthogonal view of the patient relative to the MV beam. Because the linear accelerator and kV tube rotate together as a single unit, tracking accuracy depends on parameters such as gantry rotation speed and plan characteristics. Radixact Synchrony has been applied to various treatment sites, including the lung, liver and prostate [16, 17]. However, both PTV size and respiratory-induced motion vary across individual cases. In particular, variations in PTV size directly affect treatment-planning parameters such as couch speed and gantry rotation speed, which may influence tracking and irradiation accuracy.
Few reports have focused on the impact of PTV size, although the effectiveness of Radixact Synchrony has been demonstrated in several studies. Sano et al. investigated optimal control parameter settings for a tumor position correlation model using a phantom and performed measurements with Fiducial Tracking with Respiratory Correlation (FWR) tracking mode, which tracks fiducial markers. However, only a single target size was evaluated [18]. Ferris et al. created quality assurance (QA) plans based on 13 clinical cases of lung, liver and pancreatic tumors using FWR mode. They verified tracking accuracy under patient-specific respiratory motion [19], but did not assess dependence on PTV size. Göksel et al. evaluated Lung with Respiratory mode, which enables direct tumor tracking for lung cancer without fiducial markers [20]. However, their evaluation was limited to a single sinusoidal respiratory waveform, and the effects of irregular breathing patterns were not assessed. A recent case report demonstrated favorable treatment accuracy and clinical outcomes using FWR mode of Radixact Synchrony for a small lung lesion with large respiratory motion [21]. Despite these findings, clinical guidelines for the safe and effective use of Radixact Synchrony according to tumor size have yet to be established. In this study, we investigated the effect of tumor size on the tracking and irradiation accuracy of Radixact Synchrony under multiple respiratory waveforms.
MATERIALS AND METHODS
Measurements were performed using Radixact Synchrony under various respiratory motion conditions with a high-resolution two-dimensional (2D) detector. Treatment-planning parameters, tracking accuracy and irradiation accuracy were compared among different PTV sizes.
Experimental procedure
The experiments were conducted using a Tomotherapy system, Radixact X9, version 3.0.3 (Accuray, Sunnyvale, CA, USA). Measurements were performed using a 2D diode array SRS-MapCHECK (Sun Nuclear Corp., Melbourne, FL, USA) and a radiotherapy QA phantom StereoPHAN (Sun Nuclear Corp., Melbourne, FL, USA). Computed tomography (CT) imaging of the phantom was performed using a 64-slice CT scanner (SOMATOM go. Open Pro; Siemens Healthineers, Forchheim, Germany) with a tube voltage of 120 kV, a field of view of 600 mm and a slice thickness of 1 mm. The acquired CT images were imported into Accuray Precision treatment planning system (version 3.3.1; Accuray, Sunnyvale, CA, USA). Treatment plans were optimized using VoloUltra algorithm. The treatment beam was 6 MV flattening-filter-free with a dose rate of 1000 MU/min. The jaw width was set to 2.5 cm in the Dynamic mode, which is commonly used in clinical practice [22]. The pitch was determined based on the optimal pitch condition reported by Chen et al. [23]. Under the conditions of this study, the optimal pitch was calculated to be ≤0.233; therefore, the pitch was fixed at 0.20. Four treatment plans were calculated for different PTV sizes. In each plan, a spherical PTV with a diameter of 1, 2, 3 and 4 cm was defined at the center of the phantom. A dose of 6 Gy per fraction was prescribed to cover 95% of each PTV. The mass density of the entire phantom contour was overridden to 1.2 g/cm3 to account for dose attenuation. The modulation factors (MF), representing the complexity of the dose distribution, were used in each plan. The MFs were automatically calculated by Precision system under identical optimization conditions.
SRS-MapCHECK and StereoPHAN were mounted on a one-dimensional (1D) motion platform 1D-MP Model 008PL (CIRS, Norfolk, VA, USA), as shown in Fig. 1. In Radixact Synchrony system, tumor-motion tracking is achieved by synchronizing jaw swing for the longitudinal direction and multileaf collimator (MLC) shifts for the lateral and vertical directions. To verify that the jaw and MLC operated synchronously, the 1D-MP was rotated by 30° around the vertical axis, as recommended by the vendor [24, 25]. The experiment was designed to simulate tumor-tracking radiotherapy in the thoracoabdominal region. Kawabata et al. reported that patient-specific QA results for motion tracking using the SRS-MapCHECK and StereoPHAN were comparable to those obtained with a microchamber and radiochromic film [26]. Measurements were performed using FWR mode, which provides high positional detection accuracy, to clarify the influence of PTV size and treatment-planning parameters. Two metal markers placed on the gantry side of SRS-MapCHECK detector array were tracked (Dots in Fig. 1). In clinical practice, 4–6 markers are recommended, while 1–8 markers are acceptable. In this study, two metal markers were used because the target and the markers moved identically, and rotational and torsional corrections were not required. The kV X-ray imaging parameters were as follows: a tube voltage of 120 kV and a tube current-time product of 1.0 mAs. Six projections were acquired per gantry rotation at 60° intervals (45°, 105°, 165°, 225°, 285°, 345°). Radixact Synchrony system allows acquisition of 2–6 kV X-ray images per gantry rotation from arbitrary angular directions, and previous reports have commonly employed 4–6 images [19, 25, 27]. The present imaging configuration was consistent with that reported by Sano et al. [18]. The motion platform was controlled according to a respiratory waveform, and the dose delivery was initiated after a pre-correlation model was established with a gantry period of 10 s/rotation.
Fig. 1.
Schematic illustration of the phantom setup. (a) Side view. (b) Top view. SRS-MapCHECK and StereoPHAN were mounted on the 1D-MP. StereoPHAN was fixed on a polystyrene foam base, and the center of SRS-MapCHECK was aligned with the isocenter defined by room lasers. The 1D-MP was tilted by 30° around the vertical axis. LED markers were placed on the surrogate stage of the motion platform. Dots indicate the positions of the metal markers.
Respiratory motion
Four types of respiratory waveforms were used in this study: one basic waveform and three irregular amplitude (IA) waveforms.
The basic waveform simulated regular respiratory motion and was defined by Eq. (1):
 |
(1) |
where 
is the motion amplitude and 
is the respiratory cycle. The reference respiratory condition was defined by the motion amplitude 
of ±10 mm, the respiratory cycle 
of 5 s, and the sampling interval of 10 ms. In clinical cases of locally advanced disease, the amplitude of respiratory motion is typically limited to ±5 mm, although it may increase to ~±15 mm in some cases [28]. Therefore, an intermediate amplitude of ±10 mm was adopted in this study. The respiratory cycle of 5 s corresponds to a respiratory rate of 12 breaths per minute, which is within the normal range of 12–18 breaths for adult respiration.
The IA waveform was generated by introducing random variations in the amplitude of a sinusoidal waveform, as expressed by Eq. (2):
 |
(2) |
where the amplitude 
was updated every respiratory cycle according to Eq. (3):
 |
(3) |
where the amplitude 
was based on the reference amplitude of ±10 mm. 
represents the maximum amplitude variation, and 
is a random coefficient ranging from −1 to 1, generated using Mersenne Twister algorithm. Mersenne Twister algorithm was adopted as a standard random number generation method for stochastic simulations because of its exceptionally long period and high-dimensional equidistribution properties [29]. As Mersenne Twister provides statistically unbiased pseudorandom numbers, it minimizes algorithm-dependent bias and is suitable for fairly reproducing respiratory irregularity. The coefficient 
was constant within each respiratory cycle and was updated at the beginning of every new cycle. The 
values were set to 2, 4 and 6 mm, corresponding to the IA2, IA4 and IA6 waveforms, respectively. All measurements were performed using pre-generated respiratory waveforms to ensure consistent motion reproduction throughout all measurements.
Data analysis
Treatment-planning parameters were compared among the four PTV sizes to identify the impact of the parameters on tracking and irradiation accuracy. The evaluated parameters included beam-on time, couch speed, gantry period defined as the time per full gantry rotation, kV imaging interval and MF. All parameter values were obtained from Accuray Precision system.
The root-mean-square (RMS) error (
), γ pass rate and potential difference (PD) were evaluated among the PTV sizes. The 
was evaluated as an index of tracking accuracy. Calculations were performed using Synchrony analysis software MotionQA (Accuray, Sunnyvale, CA, USA). The 
was computed according to Eq. (4):
 |
(4) |
where 
denotes the target position tracked by Synchrony, and 
denotes the reference phantom position input to the 1D-MP, and 
is the number of samples. The 
data were extracted from post-irradiation delivery logs. The temporal resolutions of 
and 
were matched by resampling with a sampling interval of ~10 ms. The time offset between 
and 
was determined from the lag of their cross-correlation, and this lag correction was applied prior to the RMS calculation. Irradiation accuracy was evaluated by 2D gamma analysis of the dose distribution measured with SRS-MapCHECK. The gamma analyses were performed using SNC Patient Software version 8.4 (Sun Nuclear Corporation, Melbourne, FL, USA). The gamma analysis criteria were 1 mm for the distance-to-agreement, 3% for the dose difference and 10% for the dose threshold. To eliminate the contribution from kV imaging, a dose distribution acquired under kV imaging only was estimated by simulation and subtracted from the measured dose distribution prior to evaluation.
The PD was used as an index of the predictive uncertainty of the correlation model. The PD represents the overall uncertainty in predicting the internal target position. It is evaluated through statistical estimation of three-dimensional positional variability between the target positions predicted by the correlation model and those measured on kV imaging. Values are expressed in millimeters (mm). The PD is recalculated with each kV imaging acquisition. Continuous monitoring of PD is clinically important because small fields are highly sensitive to fine positional variations. A previous study reported an association between PD and irradiation accuracy [18]. A beam-hold is automatically triggered when the PD exceeds the site-specific threshold. In this study, the PD threshold was intentionally set to 10 mm to avoid unintended beam holds during measurements. The PD values were obtained from a delivery log file recorded during irradiation. For analysis, the PD95 was calculated for each measurement. The PD95 was defined as the maximum PD value obtained during beam-on time after excluding the highest 5% of PD values. In addition, time zero was defined at beam-on, and the temporal change of PD was evaluated for each measurement.
Differences in the 
, γ pass rate and PD95 among PTV sizes were evaluated separately for each respiratory waveform. Measurements for each respiratory waveform were repeated four times. Multiple comparisons were performed using Dunnett’s test. To evaluate the relationship between tracking accuracy and treatment-planning parameters, Pearson’s and Spearman’s correlation coefficients were calculated between the mean 
and each treatment-planning parameter. Furthermore, partial correlation analyses were conducted to assess the independent association between 
and beam-on time while controlling for other interdependent treatment-planning parameters, including gantry period, couch speed and kV imaging interval. Partial correlation coefficients were calculated using Pearson’s method. All statistical analyses were conducted in R version 4.5.0.
RESULTS
Table 1 summarizes the treatment-planning parameters for each PTV size. As the PTV size decreased, the beam-on time became shorter and the couch speed became slower. The beam-on times for the PTVs of φ1, φ2, φ3 and φ4 cm were 127.5, 136.3, 152.0 and 173.0 s, respectively. The corresponding couch speeds were 0.2, 0.3, 0.4 and 0.4 mm/s. A decrease in PTV size was associated with longer gantry periods and longer kV imaging intervals. The gantry periods for the PTVs of φ1, φ2, φ3 and φ4 cm, were 25.4, 15.8, 14.3 and 13.7 s/rotation, respectively. The corresponding kV imaging intervals were 4.2, 2.6, 2.4 and 2.3 s. The gantry period was ~15 s/rotation for the PTVs of φ2–4 cm; however, it was 25.4 s/rotation for the PTV of φ1 cm. The MFs were 2.0 for all PTV sizes.
Table 1.
Treatment-planning parameters for each PTV size
| PTV size [cm] | ||||
|---|---|---|---|---|
| 1.0 | 2.0 | 3.0 | 4.0 | |
| Beam-on time [s] | 127.5 | 136.3 | 152.0 | 173.0 |
| Couch speed [mm/s] | 0.2 | 0.3 | 0.4 | 0.4 |
| Gantry period [s/rotation] | 25.4 | 15.8 | 14.3 | 13.7 |
| kV imaging interval [s] | 4.2 | 2.6 | 2.4 | 2.3 |
| MF | 2.0 | 2.0 | 2.0 | 2.0 |
Figure 2 shows the 
for each respiratory waveform. The 
for IA waveforms showed a statistically significant dependence on PTV size. As the PTV size increased, the 
values became larger. For IA2, there were no significant differences in the 
between the PTVs of φ1 and φ2 cm (P = 0.343) or between φ1 and φ3 cm (P = 0.110). No significant difference in the 
was observed between the PTVs of φ2 and φ3 cm for IA6 (P = 0.057). The 
for the PTVs of φ1, φ2, φ3 and φ4 cm were 1.35 ± 0.05, 1.52 ± 0.07, 1.69 ± 0.09, and 1.93 ± 0.05, respectively. For the Basic waveform, the 
for the PTV of φ1 cm exhibited considerable inter-measurement variability compared with those for the PTVs of φ2 and φ3 cm. In contrast, the PTV of φ4 cm showed smaller variability but higher 
values. A statistically significant difference was observed between the PTVs of φ2 and φ4 cm (P < 0.05), whereas no significant differences were found among the other PTV size combinations. For the Basic waveform, 
for the PTVs of φ1, φ2, φ3 and φ4 cm were 1.65 ± 0.25, 1.54 ± 0.13, 1.63 ± 0.11, and 1.77 ± 0.02, respectively.
Fig. 2.
among PTV sizes for each respiratory waveform.
Figure 3 presents the γ pass rates measured with SRS-MapCHECK. The γ pass rate for the PTV of φ1 cm for all respiratory waveforms was the lowest among all PTV sizes and remained below 92%. The γ pass rates for the PTV of φ1 cm were 88.6 ± 3.8%, 91.0 ± 2.7%, 90.6 ± 2.5% and 90.9 ± 5.2% for the Basic, IA2, IA4 and IA6 waveforms, respectively. For the Basic waveform, the γ pass rate for the PTV of φ1 cm was significantly lower than those for the PTVs of φ3 and φ4 cm (P < 0.05). The γ pass rates for the PTVs of φ1, φ2, φ3 and φ4 cm were 88.6 ± 3.8%, 94.3 ± 4.8%, 97.3 ± 1.2%, and 96.3 ± 1.1%, respectively. For IA2, the γ pass rate for the PTV of φ1 cm was also significantly lower than those for the PTVs of φ3 and φ4 cm (P < 0.05). The γ pass rates for the PTVs of φ1, φ2, φ3 and φ4 cm were 91.0 ± 2.7%, 94.8 ± 3.1%, 95.4 ± 1.7%, and 95.6 ± 1.1%, respectively. A significant difference in the γ pass rate was observed between the PTVs of φ1 and φ4 cm for IA4 (P < 0.05). The γ pass rates for the PTVs of φ1, φ2, φ3 and φ4 cm were 90.6 ± 2.5%, 94.8 ± 1.9%, 95.3 ± 1.6%, and 95.3 ± 0.7%, respectively. For IA6, the γ pass rate for the PTV of φ1 cm was significantly lower than that for φ3 cm (P < 0.05). The γ pass rate for the PTV of φ4 cm was below 95% and significantly lower than that for φ3 cm (P < 0.05). For IA6, the γ pass rates for the PTVs of φ1, φ2, φ3 and φ4 cm were 90.9 ± 5.2%, 95.8 ± 4.4%, 97.5 ± 0.3%, and 91.7 ± 2.3%, respectively.
Fig. 3.
γ pass rates for PTV sizes and respiratory waveforms.
Figure 4 shows the PD95 among PTV sizes for each respiratory waveform. Across all respiratory waveforms, the PD95 for the PTV of φ1 cm was the highest among all PTV sizes. The PD95 values for the φ1 cm PTV were 0.61 ± 0.19 mm, 0.82 ± 0.26 mm, 0.99 ± 0.48 mm and 0.96 ± 0.49 mm for the Basic, IA2, IA4 and IA6 waveforms, respectively. In contrast, for the PTVs of φ2–4 cm, the PD95 values were consistently lower across all respiratory waveforms and exhibited smaller variability. Figure 5 shows the temporal variation of the PD for each PTV size. The PD values for all PTV sizes were the largest immediately after beam-on. The values then gradually decreased to a plateau at ~0.5 mm. Across all respiratory waveforms, the PD for the PTVs of φ2–4 cm reached a plateau within 20 s after beam-on and remained stable. In contrast, ~60 s were required for the PTV of φ1 cm to reach a plateau.
Fig. 4.
PD 95 among PTV sizes for each respiratory waveform.
Fig. 5.
Temporal variation of PD for each PTV size under different respiratory waveforms. (a) Basic (b) IA2 (c) IA4 (d) IA6. Each PTV size was measured four times, with time normalized to 0 s at beam-on.
Figure 6 shows the residual positional errors between the tracked positions and the reference positions input to the 1D-MP after lag correction, as obtained from MotionQA. For IA6, the residual positional errors for both the PTVs of φ1 and φ4 cm were smallest during the mid-phase of irradiation and tended to increase toward the beginning and the end of delivery (Fig. 6a and b). A similar trend was observed for the basic waveform; however, for the PTV of φ1 cm, large fluctuations were observed in the lateral direction during the early phase of irradiation (Fig. 6c).
Fig. 6.
The residual positional errors after lag correction for the 1 and 4 cm PTVs. Time courses of the difference between the tracked positions and the reference positions input to the 1D-MP are shown for each direction. (a) IA6—Lateral (b) IA6—Longitudinal (c) Basic—Lateral (d) Basic—Longitudinal.
Table 2 presents Pearson’s and Spearman’s correlation coefficients between the mean 
values and each treatment-planning parameter. Across all respiratory waveforms, a strong positive correlation was observed between the 
and beam-on time, with both Pearson’s and Spearman’s correlation coefficients exceeding 0.900 and reaching statistical significance. In contrast, gantry period and kV imaging interval did not show statistically significant correlations with the 
in the Pearson analysis; however, significant monotonic relationships were consistently observed across all waveforms in the Spearman analysis (P < 0.01). Couch speed did not exhibit a statistically significant correlation with the 
for any respiratory waveform using either correlation metric. Table 3 summarizes the partial Pearson correlation coefficients between the 
and beam-on time after controlling for individual treatment-planning parameters. For all irregular-amplitude waveforms, beam-on time remained significantly correlated with the 
after controlling for couch speed, gantry period or kV imaging interval, with partial correlation coefficients consistently exceeding 0.80. In contrast, for the Basic waveform, the partial correlation weakened and did not reach statistical significance after controlling for couch speed.
Table 2.
Pearson’s and Spearman’s correlation coefficients between mean 
and treatment-planning parameters.
| Parameter | Waveform | Pearson r | P-value | Spearman ρ | P-value |
|---|---|---|---|---|---|
| Beam-on time | Basic | 0.994 | <0.05 | 1.000 | <0.01 |
| IA2 | 0.989 | <0.05 | 1.000 | <0.01 | |
| IA4 | 0.999 | <0.01 | 1.000 | <0.01 | |
| IA6 | 0.994 | <0.01 | 1.000 | <0.01 | |
| Couch speed | Basic | 0.911 | 0.089 | 0.949 | 0.051 |
| IA2 | 0.950 | 0.050 | 0.949 | 0.051 | |
| IA4 | 0.867 | 0.133 | 0.949 | 0.051 | |
| IA6 | 0.911 | 0.089 | 0.949 | 0.051 | |
| Gantry period | Basic | −0.828 | 0.172 | −1.000 | <0.01 |
| IA2 | −0.874 | 0.126 | −1.000 | <0.01 | |
| IA4 | −0.765 | 0.235 | −1.000 | <0.01 | |
| IA6 | −0.828 | 0.172 | −1.000 | <0.01 | |
| kV imaging interval | Basic | −0.818 | 0.182 | −1.000 | <0.01 |
| IA2 | −0.864 | 0.136 | −1.000 | <0.01 | |
| IA4 | −0.754 | 0.246 | −1.000 | <0.01 | |
| IA6 | −0.818 | 0.182 | −1.000 | <0.01 |
Statistically significant results are shown in bold.
Table 3.
Partial Pearson correlation between mean 
and beam-on time after controlling for individual treatment-planning parameters.
| Control parameter | Waveform | Partial r (Pearson) | P-value |
|---|---|---|---|
| Couch speed | Basic | 0.467 | 0.068 |
| IA2 | 0.894 | <0.01 | |
| IA4 | 0.944 | <0.01 | |
| IA6 | 0.828 | <0.01 | |
| Gantry period | Basic | 0.526 | <0.05 |
| IA2 | 0.916 | <0.01 | |
| IA4 | 0.967 | <0.01 | |
| IA6 | 0.904 | <0.01 | |
| kV imaging interval | Basic | 0.527 | <0.05 |
| IA2 | 0.918 | <0.01 | |
| IA4 | 0.968 | <0.01 | |
| IA6 | 0.908 | <0.01 |
Statistically significant results are shown in bold.
DISCUSSION
The 
values became larger in association with treatment-planning parameters that changed with increasing PTV size. Among these parameters, beam-on time had the strongest influence on 
and remained significantly correlated even in the partial correlation analysis. The temporal variation of the residual positional errors observed for the IA6 waveform indicates that tracking accuracy is not uniform throughout the irradiation (Fig. 6). The 
values were larger for the PTV of φ4 cm than for φ1 cm. The longer beam-on time led to a prolonged duration of large positional deviations. In addition, gantry period and kV imaging interval also affected 
. These treatment-planning parameters were not independent of each other and were shown to have interdependent effects on 
. Taken together, these results indicate a trend toward improved tracking accuracy under conditions of shorter beam-on time, shorter gantry period and shorter kV imaging interval.
The PTV of φ1 cm exhibited the lowest γ pass rate and required the longest time for PD to reach a plateau among all PTV sizes. This behavior was primarily attributed to the longer gantry period and longer kV imaging interval. Because the pre-correlation model was constructed with a shorter gantry period than that used during treatment delivery, this difference led to larger initial PD values. In contrast, for the PTVs of φ2 and φ3 cm, the PD stabilized earlier, and higher γ pass rates were maintained throughout irradiation. Although the γ pass rate decreased for the PTV of φ1 cm, no clear deterioration in 
was observed. This discrepancy can be explained by the different error characteristics reflected by these metrics. The 
represents a time-averaged tracking error over the entire irradiation period and is therefore relatively insensitive to transient positional errors occurring immediately after beam-on. In contrast, the γ pass rate is a dose-based metric, and for small PTVs, even brief positional deviations in high-dose-gradient regions can readily manifest as dose discrepancies. Consequently, the initial instability in PD likely contributed to the reduced γ pass rate observed for the φ1 cm PTV. It should be emphasized that PD represents the predictive uncertainty of the correlation model rather than the actual tracking error. Ferris et al. reported that PD is relatively insensitive to tracking errors and should therefore not be used as a direct surrogate for tracking accuracy [30]. Nevertheless, PD provides clinically valuable information regarding the stability and reliability of the correlation model during irradiation. Even when 
remains relatively small, an increase in PD may indicate an elevated risk of dosimetric degradation, particularly in situations where small positional uncertainties can have a substantial impact on dose distribution.
For the Basic waveform, the 
for the PTV of φ1 cm exhibited considerable inter-measurement variability compared with those for the PTVs of φ2 and φ3 cm. Immediately after beam-on, the residual positional error between the tracked position and the reference position input to the 1D-MP in the lateral direction transiently increased (Fig. 6c, black circle). The 
value obtained in a single measurement became larger, although the transient increase in the residual positional error decreased within 20 s. This behavior was attributable to the delay in PD reaching a plateau, which was caused by the longer gantry period for the PTV of φ1 cm. In contrast, an increase in residual positional error immediately after beam-on was not observed for the irregular-amplitude waveforms. The Basic waveform is based on the fourth power of a sine wave with a relatively long expiration period. An accurate association between the motion of LED markers and internal fiducial markers is essential for constructing the correlation model. However, the fiducial markers are captured repeatedly at nearly the same position when kV imaging is performed during phases with small positional change. The lack of variability in the amplitude distribution of the motion makes it difficult to construct an accurate correlation model. Therefore, acquiring kV imaging at time points that sufficiently capture the full fiducial marker motion may improve tracking accuracy.
Compared with the PTV of φ1 cm, the γ pass rate improved for the PTVs of φ2 and φ3 cm, whereas a decreasing trend was observed for the PTV of φ4 cm. For the PTVs of φ2–3 cm, the early stabilization of PD immediately after beam-on likely contributed to the improvement in the γ pass rate. In contrast, treatment-planning parameters affected by increasing PTV size, such as beam-on time, resulted in a gradual increase in 
, indicating deterioration in tracking accuracy. For the PTV of φ4 cm, although PD stabilized early, further degradation of tracking accuracy was reflected in the dose distribution as a reduction in the γ pass rate.
This study has several limitations. Although four different PTV sizes were evaluated, the current dataset remains relatively small for a fully quantitative assessment of the complex interactions among all treatment-planning parameters. Furthermore, because PTV size was treated as a predefined experimental condition, the statistical interpretations in this study are limited to trend-level observations within the scope of the experimental setup. Future studies involving systematic variations of multiple treatment-planning parameters for the same PTV size, as well as more finely discretized PTV size configurations, would enable more rigorous multivariate modeling and further enhance the robustness of these conclusions.
This study suggested how PTV size influences treatment-planning parameters and their relationship to tracking and irradiation accuracy. The 
was shown to be interdependently influenced by multiple planning parameters, including beam-on time, gantry period and kV imaging interval. For the PTV of φ1 cm, the longer gantry period delayed PD stabilization and the γ pass rate decreased. In addition, the small irradiation volume increased the susceptibility of the γ pass rate to slight positional deviations. For the PTVs of φ2 and φ3 cm, earlier stabilization of PD contributed to an improvement in the γ pass rate. In contrast, for the PTV of φ4 cm, degradation of tracking accuracy associated with prolonged beam-on time and shorter gantry period was reflected in a decrease in the γ pass rate. Optimization of the gantry period and kV imaging conditions according to PTV size is essential for accurate motion-synchronized treatment.
Contributor Information
Ryoto Kaido, Division of Health Sciences, Graduate School of Medical Sciences, Kanazawa University, 5-11-80 Kodatsuno, Kanazawa, Ishikawa Prefecture 920-0942, Japan; Radiological Center, University of Fukui Hospital, 23-3 Matsuoka Shimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui Prefecture 910-1193, Japan.
Akihiro Takemura, Faculty of Health Sciences, Institute of Medical, Pharmaceutical and Health Sciences, Kanazawa University, 5-11-80 Kodatsuno, Kanazawa, Ishikawa Prefecture 920-0942, Japan.
Kakeru Sato, Division of Health Sciences, Graduate School of Medical Sciences, Kanazawa University, 5-11-80 Kodatsuno, Kanazawa, Ishikawa Prefecture 920-0942, Japan; Radiological Center, University of Fukui Hospital, 23-3 Matsuoka Shimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui Prefecture 910-1193, Japan.
Naoki Kinoshita, Department of Radiological Sciences, Faculty of Medical Science Technology, Morinomiya University of Medical Sciences, 1-26-16 Nankokita, Suminoe-ku, Osaka Prefecture 559-8611, Japan.
Kouhei Sasamoto, Radiological Center, University of Fukui Hospital, 23-3 Matsuoka Shimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui Prefecture 910-1193, Japan.
Tomohiro Kotsuji, Department of Radiology, Faculty of Medical Sciences, University of Fukui, 23-3 Matsuoka Shimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui Prefecture 910-1193, Japan.
Hiroki Shioura, Department of Radiology, Faculty of Medical Sciences, University of Fukui, 23-3 Matsuoka Shimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui Prefecture 910-1193, Japan.
Toshiki Tateishi, Radiological Center, University of Fukui Hospital, 23-3 Matsuoka Shimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui Prefecture 910-1193, Japan.
Tetsuya Tsujikawa, Department of Radiology, Faculty of Medical Sciences, University of Fukui, 23-3 Matsuoka Shimoaizuki, Eiheiji-cho, Yoshida-gun, Fukui Prefecture 910-1193, Japan.
CONFLICT OF INTEREST
SRS-MapCHECK used in this study was loaned by Sun Nuclear Corporation. The authors declare no other conflicts of interest related to this work.
FUNDING
This work was not supported by no external funding.
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