 Research
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 Published:
Optimization of training periods for the estimation model of threedimensional target positions using an external respiratory surrogate
Radiation Oncologyvolume 13, Article number: 73 (2018)
Abstract
Background
During therapeutic beam irradiation, an unvisualized threedimensional (3D) target position should be estimated using an external surrogate with an estimation model. Training periods for the developed model with no additional imaging during beam irradiation were optimized using clinical data.
Methods
Dualsource 4DCBCT projection data for 20 lung cancer patients were used for validation. Each patient underwent one to three scans. The actual target positions of each scan were equally divided into two equal parts: one for the modeling and the other for the validating session. A quadratic target position estimation equation was constructed during the modeling session. Various training periods for the session—i.e., modeling periods (T_{M})—were employed: T_{M} ∈ {5,10,15,25,35} [s]. First, the equation was used to estimate target positions in the validating session of the same scan (intrascan estimations). Second, the equation was then used to estimate target positions in the validating session of another temporally different scan (interscan estimations). The baseline drift of the surrogate and target between scans was corrected. Various training periods for the baseline drift correction—i.e., correction periods (T_{C}s)—were employed: T_{C} ∈ {5,10,15; T_{C} ≤ T_{M}} [s]. Evaluations were conducted with and without the correction. The difference between the actual and estimated target positions was evaluated by the rootmeansquare error (RMSE).
Results
The range of mean respiratory period and 3D motion amplitude of the target was 2.4–13.0 s and 2.8–34.2 mm, respectively. On intrascan estimation, the median 3D RMSE was within 1.5–2.1 mm, supported by previous studies. On interscan estimation, median elapsed time between scans was 10.1 min. All T_{M}s exhibited 75th percentile 3D RMSEs of 5.0–6.4 mm due to baseline drift of the surrogate and the target. After the correction, those for each T_{M}s fell by 1.4–2.3 mm. The median 3D RMSE for both the 10s T_{M} and the T_{C} period was 2.4 mm, which plateaued when the two training periods exceeded 10 s.
Conclusions
A widelyapplicable estimation model for the 3D target positions during beam irradiation was developed. The optimal T_{M} and T_{C} for the model were both 10 s, to allow for more than one respiratory cycle.
Trial registration
UMIN000014825. Registered: 11 August 2014.
Background
Realtime detection of a target’s position in threedimensional (3D) space is essential to ensure that highdose radiation is delivered only to the target, where thus is possible with the aid of fourdimensional conebeam computed tomography (4DCBCT). However, the temporal resolution of 4DCBCT is too low to precisely monitor target motion [1]. Highprecision radiotherapy requires detection of the 3D position at high temporal resolution (sampling rate > 1 Hz). Localization of 3D target position during beam irradiation is used for the doseoftheday calculations [2], planning target volume verification [3], and realtime tumor tracking [4,5,6].
Optimal detection of timeresolved 3D position involves the triangulation of two simultaneous twodimensional (2D) projections using predefined camera parameters [7]. Modern radiotherapy treatment machines are configured with a singlesource kilovoltage (kV) imaging subsystem perpendicular to the megavoltage (MV) beam and an electronic portal imaging device. Some machines are equipped with orthogonal dualsource kV imaging subsystems; such machines allow kV/MV or kV/kV triangulation. However, depending on the extent of multileaf collimator motion during beam irradiation, the target on MV images may not be detectable. Detection of 3D target positions using a monoscopic view is now possible with techniques such as kV intrafraction monitoring [8, 9] and markerless tumor detection [10,11,12]. However, these methods are inapplicable if the target or tumor cannot be detected via kV projections at certain gantry angles.
To estimate target positions in these situations, there is no alternative but to employ external respiratory surrogates. Cho et al. developed a linear internalexternal correlation model with frequent model updating during beam irradiation [13,14,15]. In their studies, the linear model was selected and updated by minimization of the difference between the measured kV projections and estimated trajectory projected onto a 2D projection geometry. As mentioned above, however, updating cannot be applied if the target or tumor cannot be detected on kV projections, as this would lead to model degradation. This problem has more of an impact on markerless tumor tracking.
Akimoto et al. pointed out that the visibility of gold markers implanted in the lung on kV projections could be poor in the following situations: (1) overlap of the gold markers and (2) when there is a lowintensity ratio between the gold marker and its surroundings [16]. Bahig et al. investigated the applicability of a markerless tumor tracking system using CyberKnife (XSight Lung Tracking System) via a fixed dualsource kV imaging subsystem [17]. They revealed that 50% of tumors smaller than 2 cm cannot be visualized on the kV projection. Thus, a means to evaluate the estimation model without updating during beam irradiation is required, regardless of whether gold markers are implanted.
Fassi et al. developed a target estimation method using a patientspecific breathing model derived a priori from 4DCT images [18]. Model parameters were retrieved and updated for each treatment fraction according to inroom radiography acquisition and optical surface imaging. However, the low temporal resolution and imaging artifacts associated with 4DCT may affect the model accuracy and cannot be improved by updating the model at each treatment fraction.
In this study, we developed a method to estimate target positions employing an external surrogate which was an infrared reflective (IR) marker; our approach is widely applicable and does not require additional imaging during beam irradiation. We applied the quadratic polynomial equation used by the Vero system [19]. The equation incorporated data from the internal target, and position and velocity data from the external IR marker placed on the patient’s abdomen; data were acquired at a frequency of 5 Hz. To validate the method, we used the dualsource 4DCBCT projection data of lung cancer patients who underwent stereotactic body radiotherapy (SBRT); data included the actual 3D target positions during the 4DCBCT scan, calculated from 2D orthogonal projections featuring kV/kV triangulation. First, the estimation equation was modeled using the detected 3D target positions and IR marker positions prior to target position estimation in the same scan (intrascan estimation). Second, the equation was used to estimate target and surrogate positions in the validation session of another scan (interscan estimation). The baseline drifts of the target and IR marker between scans were corrected. Thus, the training periods for these sessions were optimized using the data from clinical practice.
Methods
Patient characteristics
Twentytwo consecutive lung cancer patients (17 males, 5 females; median age, 81 years; range: 65–90 years) who underwent SBRT by Vero4DRT (Mitsubishi Heavy Industries, Ltd., Hiroshima, Japan, and BrainLAB AG, Feldkirchen, Germany) after implantation of twotofour 1.5mmdiameter gold markers (Olympus, Tokyo, Japan) were enrolled in an institutional review boardapproved trial. Each patient underwent three 70s 4DCBCT scans, except for Patient 17, and Patients 10 and 18, who underwent only one, and two scans, respectively. Three scans were performed for Patients 1 and 2 were employed in this study; the second scan of three scans for the other patients was taken for a different purpose, and with different scan parameters, and was not applied 4DCBCT image reconstruction. Thus, the first and third scans of the other patients were used for the validation process. Both scans for Patients 10 and 18 were used for the validation.
A set of three IR markers was placed on each patient to record abdominal motion in the anteriorposterior (AP) direction. IR marker movement was captured using a portable Polaris Spectra camera (Northern Digital Inc., Ontario, Canada) placed close to the patient; the camera operated independently of the Vero4DRT system. Due to unexpected system problems, the IR marker signals from Patients 8 and 12 were not available. Thus, 20 patients were studied.
Data acquisition
We recorded 351 projection images (70s scans per source; i.e., the sampling time, Δt = 0.2 s). All gold markers were simultaneously detected on all projections. The gold marker located nearest the tumor was considered the best surrogate of the target. The 2D positional data of each projection, or each discrete time t_{ k } (k = 0, 1, ⋯, 350 [=70/Δt]), were converted into 3D data using the predefined camera parameters, to yield actual 3D target positions P_{actual}(t_{ k }). Data acquisition details have been described previously [1].
The respiratory period during a scan was defined as the average interval between two consecutive end inhalations. The respiratory amplitude was defined as the average difference between the endexhalation and endinhalation positions of a single respiratory cycle.
Target position estimation using the external surrogate
Our proposed estimation method is shown in Fig. 1. We assumed that the target position would be estimated during beam irradiation using an estimation equation modeled before the irradiation. Thus, we considered two sessions: the modeling and validating sessions. To estimate the target positions during the validating session, construction of the estimation equation was necessary during the modeling session. The quadratic polynomial equation used in the proposed method can be written as follows:
C_{i, γ} = (a_{i, γ} b_{i, γ} c_{i, γ} d_{i, γ} e_{i, γ}) is the coefficient of the equation for IR marker number i ∈ {1, 2, 3} in direction γ ∈ {left − right (LR), superior − inferior (SI), anterior − posterior}, and \( \mathbf{W}\left({t}_k\right)={\left({w}^2\left({t}_k\right)\kern0.5em w\left({t}_k\right)\kern0.5em 1\kern0.5em {\left(\frac{\Delta w}{\Delta t}\right)}^2\kern0.5em \left(\frac{\Delta w}{\Delta t}\right)\right)}^{\mathrm{T}} \) is the IR marker data set at the discrete time t_{ k }, containing the IR marker position w(t_{ k }) and its derivative—i.e., velocity, Δw/Δt—where Δw = w(t_{ k }) − w(t_{k − 1}) andΔt = t_{ k } − t_{k − 1} = 0.2 [s]. Because the following methodology is the same for any IR marker number and direction, we eliminated i and γ for simplicity. We divided each of the 351 projections into a first (175 projections, approximately 35 s) and second (176 projections, approximately 35 s) half for modeling and validating sessions, respectively.
First, we determined the coefficients of the estimation equation during the modeling session and then estimated the target positions during the validating session of the same scan; i.e., an intrascan estimation. To construct the estimation equation, coefficient C was determined by the leastsquares method using the data of the modeling session. We employed various training periods for modeling—i.e., the modeling period T_{M} ∈ {5,10,15,25,35} [s]—as shown in Fig. 2a. Thus, a coefficient was determined for each T_{M} and written as:
Note that the data at \( {t}_{\left(35{T}_{\mathrm{M}}\right)/\Delta t} \) were also used because the velocity of the IR marker was necessary. Hereinafter, we use the hat symbol for coefficients determined by the leastsquares method, and the estimation equation that included the coefficients, or \( {\widehat{P}}_{T_{\mathrm{M}}}\left({t}_k\right) \). The target positions within the validating session of the same scan were estimated using the estimation equation in each direction.
Second, we estimated the target positions in the validating session using the estimation equation constructed during the modeling session of another scan in a one patient; i.e., an interscan estimation (Fig. 2b). In clinical cases, the baseline drift correction will be applied between fields or arcs if multiple beams are used in the plan. Let \( {\widehat{P}}_{T_{\mathrm{M}}}^{\mathrm{A}\to \mathrm{B}}\left({t}_k\right) \) be the estimation equation for the target positions of scan B by using the coefficients determined by the data of scan A. Due to the elapsed time between the two scans, the baseline drift of the IR marker and target should be corrected. The baseline of scan A is defined as the median position in the training period for the baseline drift correction—i.e., the correction period T_{C} ∈ {5,10,15; T_{C} ≤ T_{M}} [s]—at the end of the modeling session or prior to the validating session (Fig. 2b). The baseline of scan B is defined as the median position in the correction period T_{C} immediately prior to the validating session of scan B. The amount of the baseline drift between scans A and B was calculated by subtracting the baseline of scan A from that of scan B. First, we corrected the baseline drift of the IR marker. The amount of baseline drift of the IR marker, defined as follows:
Then, we incorporated the baseline drift of IR marker by transforming w^{B}(t_{ k }) into \( {w}^{\mathrm{B}}\left({t}_k\right){\mathrm{B}\mathrm{D}}_{\mathrm{IR},{T}_{\mathrm{C}}}^{\mathrm{B}\mathrm{A}} \) and let \( {\left[{\widehat{P}}_{\left({T}_{\mathrm{M}},{T}_{\mathrm{C}}\right)}^{\mathrm{A}\to \mathrm{B}}\left({t}_k\right)\right]}^{\prime } \) be the estimation equation \( {\widehat{P}}_{T_{\mathrm{M}}}^{\mathrm{A}\to \mathrm{B}}\left({t}_k\right) \) scaled by \( {\mathrm{B}\mathrm{D}}_{\mathrm{IR},{T}_{\mathrm{C}}}^{\mathrm{B}\mathrm{A}} \). To incorporate the baseline drift of the target, we compensated for internal residual errors resulting from the baseline drift of \( {\left[{\widehat{P}}_{T_{\mathrm{M}}}^{\mathrm{A}\to \mathrm{B}}\left({t}_k\right)\right]}^{\prime } \)—i.e., \( {\mathrm{B}\mathrm{D}}_{\mathrm{Target},{T}_{\mathrm{C}}}^{\mathrm{B}\mathrm{A}} \)—which can be written as
Then, we subtracted \( {\mathrm{B}\mathrm{D}}_{\mathrm{Target},{T}_{\mathrm{C}}}^{\mathrm{B}\mathrm{A}} \) from \( {\left[{\widehat{P}}_{\left({T}_{\mathrm{M}},{T}_{\mathrm{C}}\right)}^{\mathrm{A}\to \mathrm{B}}\left({t}_k\right)\right]}^{\prime } \), and let \( {\left[{\widehat{P}}_{\left({T}_{\mathrm{M}},{T}_{\mathrm{C}}\right)}^{\mathrm{A}\to \mathrm{B}}\left({t}_k\right)\right]}^{\mathrm{C}\mathrm{or}} \) be the baseline driftcorrected estimation equation. To increase the number of data sets, we estimated the target positions in the validating session of scan A using the estimation equation constructed in the modeling session of scan B. The relationship between the intra and interscan estimations is shown in Fig. 2c. The 4DCBCT projection data for Patient 17 were only used to validate the intrascan estimation, because the patient underwent 4DCBCT only once.
For comparison, we also used a T_{M} of 70 s. Note that the validating session was included to model the estimation equation \( {\widehat{P}}_{T_{\mathrm{M}}=70}\left({t}_k\right) \) for the intrascan estimation. For the interscan estimation, the baseline drifts of the IR marker and target were calculated, and correction was carried out using the process described above.
The linear estimation equation constructed from eight 4DCBCT positions was also utilized. Eight averaged target positions for each phase, P_{4D − CBCT}(l) (l ∈ {0, 1, ⋯, 7}), were obtained from one 4DCBCT scan. In addition, eight averaged IR marker positions, w_{ave}(l) (l ∈ {0, 1, ⋯, 7}), were obtained for each phase. We defined phases 0 and 4 as endexhalation and endinhalation, respectively. The linear estimation equation was constructed between each phase; between phase α and β, it was written as follows:
In the validating session, the IR marker position w(t_{ k }) was distinguished as midexhalation and midinhalation when Δw/Δt > 0 and Δw/Δt < 0, respectively. In the interscan estimation, the centroid position of the eight averaged target positions was recognized as the baseline for a 4DCBCT scan. The baseline drift correction for Eq. (5) was employed similarly as mentioned above. The number of internal residual errors resulting from the baseline drift of \( {\left[{\widehat{P}}_{\mathrm{Linear}}^{\left(\alpha, \beta \right)}\left({t}_k\right)\right]}^{\prime } \) is given by
Because the estimation equation is constructed for each IR marker i, the estimated target position is defined as the average of the target position estimated from each IR marker, written as follows: \( {\widehat{P}}_{\mathrm{estimated}}\left({t}_k\right)=\frac{1}{3}\sum \limits_{i=1}^3{\widehat{P}}_i\left({t}_k\right) \). The difference between the estimated target position \( {\widehat{P}}_{\mathrm{estimated}}\left({t}_k\right) \) and actual target position P_{actual}(t_{ k }) in each direction was evaluated in terms of the rootmeansquare error (RMSE).
Statistical analysis
We tested for equality of variance prior to performing multiple pairwise comparisons. Depending on the equality of variance status, we used either oneway analysis of variance or the nonparametric Kruskal–Wallis test to compare the differences. If a difference was significant, the nonparametric Steel–Dwass test was performed subsequently to simultaneously evaluate all differences between training periods. A pvalue < 0.05 was considered statistically significant.
Results
Respiratory patterns
The range of mean period was 2.4–13.0 s; the range of mean IR marker amplitude in the AP direction was 1.7–14.6 mm; and the range of mean target amplitude in the LR, SI, AP directions, and 3D motion were 0.3–11.7, 1.4–28.7, 0.7–18.1, and 2.8–34.2 mm, respectively. The respiratory amplitudes during the various scan periods of all patients, and the correlation coefficients between IR marker motion along the AP direction and target motions along the LR, SI, and AP directions, are shown in Fig. 3; large error bars indicate irregular breathing, such as apnea, tachypnea, hypopnea, hyperpnea, or combinations of these. The target motion in the SI direction was strongly positively correlated with IR marker motion.
Intrascan estimations
The RMSEs in the LR, SI, AP, and 3D directions of the intrascan estimations are shown in Fig. 4. The RMSEs in the SI direction were associated with larger errors than those of the other directions. The median RMSEs in the LR and AP directions were < 1.0 mm. The median 3D RMSEs for all T_{M}s were 1.5–2.1 mm and gradually declined as T_{M} became longer. Although the Kruskal–Wallis test revealed significant differences among T_{M}s values in the LR direction (p < 0.05), the 3D RMSEs did not differ significantly. However, the T_{M}s of 5 s—i.e., T_{M} = 5 s—showed large outliers in all directions, and the 3D RMSE of Patient 10 resulted in large outliers in T_{M} = 5, 10, 15, 25, and 35 s. Note that although the estimation equation modeled by T_{M} = 4DCBCT and T_{M} = 70 s showed small errors, these T_{M}s had included P_{actual} to construct the linear and quadratic estimation equations, respectively.
Interscan estimations
The median elapsed time between scans was 10.1 min (range: 1.7–15.0 min). The absolute baseline drift of an IR marker, which was calculated during each baseline drift T_{C} is shown in Fig. 5. The median absolute baseline drift for T_{C} = 5, 10, and 15 s was 1.5 mm (range: 0.1–9.6 mm), 0.8 mm (range: 0.0–5.0 mm), and 1.2 mm (range: 0.0–5.5 mm), respectively. No significant difference among each T_{C} values was found. The time series of the 3D RMSEs in T_{C} for each T_{M} is shown in Fig. 6. Although 3D RMSEs for all T_{M}s exhibited large values without the baseline drift correction, they were decreased drastically by the correction, except for the 4DCBCT data.
Figure 7 shows P_{actual} and \( {\widehat{P}}_{\mathrm{estimated}} \) without and with baseline drift correction of the first scan of Patient 2, determined using the estimation equations \( {\widehat{P}}_{T_{\mathrm{M}}=10}^{3\mathrm{rd}\to 1\mathrm{st}}\left({t}_k\right) \) and \( {\left[{\widehat{P}}_{\left({T}_{\mathrm{M}}=10,{T}_{\mathrm{C}}=10\right)}^{3\mathrm{rd}\to 1\mathrm{st}}\left({t}_k\right)\right]}^{\mathrm{C}\mathrm{or}} \), respectively; both the T_{M} and the T_{C} was 10 s. In this case, 3D RMSE was reduced from 5.4 mm to 1.1 mm with the baseline drift correction. In contrast, in several cases the 3D RMSE was over 6 mm even with the baseline drift corrections, due to a sudden change in the correlation between the IR marker and the target in the validating session in Fig. 6. Once again, the T_{M} = 5 s data exhibited large outliers in all directions. Moreover, the 3D RMSE of Patient 10 resulted in severe outliers in all T_{M}s, except for the T_{M} = 4DCBCT data.
Boxplots of the 3D RMSEs are shown in Fig. 8. The 75th percentile 3D RMSEs without baseline drift correction were 5.0–6.4 mm. After baseline drift correction, the 75th percentile 3D RMSEs for each T_{M}s fell by 1.4–2.3 mm, except for the T_{M} = 4DCBCT, which increased by 0.6–1.2 mm. Prolongation of both T_{M} and T_{C} reduced the median 3D RSMEs; however, this effect plateaued at T_{M}s and T_{C}s > 10 s. The Steel–Dwass test revealed significant differences between T_{M} = 4DCBCT with baseline drift correction and several T_{M}s (all p < 0.05).
Discussion
Similar to other studies [20, 21], the patients enrolled in this study exhibited various combinations of respiratory period and amplitude; the mean respiratory period was approximately 4 s. Target motion along SI direction had strong correlation with IR marker motion along the AP direction, as also found by Ionascu et al. [22]. Several target motions correlated only weakly with IR marker motion because breathing was sometimes irregular, as shown by the large error bars on the amplitude axis in Fig. 3a–3d. As target positions were estimated using only the IR marker, the weak correlations between target and IR marker positions created large RMSEs [23].
Following intrascan estimations, the median RMSEs for the estimated target positions—i.e., —in the LR, AP, and SI directions were 12 mm, as also found by Ruan et al. [24]. Although the 75th percentile 3D RMSE for the T_{M} of 5 s was < 4 mm in most patients, several large RMSEs were observed. The proportion of patients with a respiratory period within 5 and 10 s was 78 and 98%, respectively. Thus, T_{M} must cover at least one respiratory cycle, which was set to 10 s in this study. The median 3D RMSEs fell as the T_{M} was prolonged. The median 3D RMSE for T_{M} = 10 s and T_{M} = 35 s was 2.1 and 2.0 mm, respectively. No significant difference was apparent among the RMSEs for each T_{M}. Therefore, a training period of 10 s would be appropriate to model the estimation equation. In comparison, T_{M} = 70 showed a median 3D RMSE of 1.7 mm.
Cho et al. developed a method in which the 3D target position could be estimated using a linear equation that included the position of the external surrogate, and thus requires frequent model updating was required during beam irradiation [13]. Fortysix thoracic and abdominal cancer patients were investigated in their study and they calculated that updates at 1 Hz yielded 3D RMSEs of nearly 1 mm, similar to the RMSEs of stereoscopic estimations. However, the range in the mean 3D motion of the targets located at the left or right lower lobe of the lungs was 0.2–14.4 mm in the study [13,14,15, 25], whereas in our study we observed a range of 3.7–28.4 mm. For instance, excluding the data that showed a 3D target amplitude larger than 14.4 mm, the 3D RMSE for T_{M} = 10 s was 1.1 mm (data shown in Additional file 1). As mentioned above, updating is impossible if the kV image is temporarily unavailable, which would lead to degradation of the model and greater impact on markerless tumor tracking. Again, the implanted gold markers were not always visible in situations with marker overlap and low marker contrast relative to the surroundings. Moreover, the model developed by Fassi et al. required no additional imaging during beam irradiation [18]. Although the cited authors evaluated the estimation errors from 2D positions on CBCT, which were projected from estimated 3D positions, the errors were about 2 mm. One advantage of our method is that MV and kV images are not required during beam irradiation; additionally, the RMSE associated with our method is comparable to those of previous study [13].
Regarding interscan estimations, the estimation equations were applied to other scans, and optimal T_{M} and T_{C} values were determined. The 3D RMSEs for the T_{C} of each T_{M} fell when the baseline drift corrections were applied, except in the case of T_{M} = 4DCBCT. Twentynine of fortysix interscan estimations for T_{M} = 4DCBCT estimations exhibited no improvement upon baseline drift correction. The 3D RMSEs for corrected T_{M} = 4DCBCT values showed a larger interquartile range and longer error bars than did those without the correction, as well as the 3D RMSEs of all other T_{M}s (Fig. 8). This is because the power of the linear estimation equation is firstorder in nature, and thus is insensitive to baseline drift correction. On the other hand, the 3D RMSEs of other T_{M}s after correction exhibited small interquartile ranges and lower error bars. The median 3D RMSE fell as T_{M} and T_{C} were prolonged, plateauing at T_{M} = 10 s for each T_{C}. The minimum median 3D RMSE was 2.0 mm when T_{M} = 70 s and T_{C} = 15 s were combined; the difference between this value and the median 3D RMSE of the T_{M} = 10 s plus T_{C} = 10 s combination was < 0.4 mm. No significant differences were apparent among the RMSEs for T_{M} = 70 or the other T_{M}s, except in the case of T_{M} = 4DCBCT. Based on the population of patients and results of the interscan estimation, a combination of T_{M} = 10 s and T_{C} = 10 s would be appropriate.
Our method is independent of the beam delivery technique and is widely applicable. Although no additional imaging is needed during beam irradiation, baseline drift correction, applied between fields or arcs, may be required in some cases. Thomas et al. investigated treatment times, including the time from the start of the first field or arc to the cessation of the last [26]. The treatment time of patients undergoing lung SBRT via flattening filterassociated intensitymodulated radiotherapy was ~ 15 min. In such cases, baseline drift correction may be essential; the median elapsed time in this study was 10.1 min. However, during flattening filterfree volumetricmodulated arc therapy, the treatment time can be reduced to < 3.3 min. Thus, baseline drift correction may not be necessary with a short treatment time.
One limitation of this study was the additional imaging dose. The imaging dose delivered to a 2cm^{3} volume of skin during a 70s dualsource 4DCBCT scan was 7.4–10.5 cGy [27]. The imaging dose delivered by our method during the 10s training period was approximately oneseventh of that value. However, if abdominal motion is captured during 3DCBCT performed to ensure appropriate patient positioning, projection data can also be used to model the estimation equation; thus, in the absence of baseline drift correction, no additional imaging doses would be required.
Conclusions
We developed a widely applicable method to estimate 3D target positions using an external respiratory surrogate without additional imaging during beam irradiation, and optimized training periods for modeling and baseline drift correction by reference to clinical data. The developed method is independent of beam delivery technique. We revealed that a long training period was not necessary; the optimal training period to model the estimation equation and baseline drift correction was determined to be 10 s, to include more than one respiratory cycle for most patients in this study.
Abbreviations
 2D:

Twodimensional
 3D:

Threedimensional
 4D:

Fourdimensional
 AP:

Anteriorposterior
 CBCT:

Conebeam computed tomography
 CT:

Computed tomography
 IR:

Infrared reflective
 kV:

Kilovoltage
 LR:

Leftright
 MV:

Megavoltage
 RMSE:

Rootmeansquare error
 SBRT:

Stereotactic body radiotherapy
 SI:

Superiorinferior
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Funding
This research was supported, in part, by the Practical Research for Innovative Cancer Control (No. 17ck0106303h0001) of Japan Agency for Medical Research and Development (AMED), and the Japan Society for the Promotion of Science (JSPS) GrantinAid for JSPS Fellows (No. 16J08928).
Availability of data and materials
The dataset supporting the conclusions of this article is included within (Additional file 1).
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Affiliations
Contributions
HI developed and validated the method, performed the statistical analysis, and drafted the manuscript. MN, YI, TM, YM and TM conceived the study, and participated in its design and coordination, and helped draft the manuscript. IK helped to draft the manuscript. All authors have read and approved the final manuscript.
Corresponding author
Correspondence to Mitsuhiro Nakamura.
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Authors’ information
Hiraku Iramina: Research Fellow of the Japan Society for the Promotion of Science.
Ethics approval and consent to participate
This study followed all dictates of the Declaration of Helsinki. The Ethical Review Board of Kyoto University Hospital and Faculty of Medicine approved the research (approval number C862). Written consent to participate was obtained from each patient.
Consent for publication
Written consent was obtained from all patients for publication of this report and any accompanying images.
Competing interests
The authors declare that they have no competing interests.
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Additional file
Additional file 1:
Dataset supporting our findings. (XLSX 1259 kb)
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Keywords
 3D target motion estimation
 Baseline drift correction period
 CBCT projection
 External surrogate
 Training period
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