Significance of intra-fractional motion for pancreatic patients treated with charged particles

The breathing signals and beam delivery sequence of fourteen pancreatic patients was monitored during irradiation. The free-breathing planning CTs (CT_plan) and 4DCTs were acquired in the Somaton Sensation Open scanner (Siemens, Erlangen, Germany), which performs a relative phase-based reconstruction on the basis of the surrogate signal of the motion-monitoring system AZ-733 V Respiratory Gating System (Anzai Medical Co.,Ltd., Japan), herewith referred to as “Anzai”. The 4DCT images were sorted in eight standard motion states, using the breathing phases (0%Ex, 40%Ex, 70%Ex, 100%Ex, 75%In, 50%In, 25%In and 20%In), where In corresponds to the inspiration and Ex to the expiration process. The state 0%Ex is the end-exhale and 100%Ex is the end-inhale state. A sample of the breathing signal, with the length of a typical treatment, was acquired for the majority of the patients during the CT session. A description of the set of patients is available in Table 1.

Patients were immobilized, lying in a prone position, using a vacuum mattress. This positioning resulted from the need to use irradiation with posterior beams, in order to reduce the inter-fractional anatomy variations in the delivered dose [5], and a limitation of our beam delivery system at the time (no accurate delivery of beams coming through the treatment table and indexing support). As a consequence of this prone immobilization, no abdominal compression was applied and the patients were imaged and irradiated under free-breathing.

The patient position was verified in-room by a 2D-3D bony anatomy image registration between the orthogonal X-ray taken at the isocenter and the DRRs calculated from the planning CT. This enabled the translational and rotational shifts to be determined meaning that the patient could be accurately positioned on the treatment couch.

Treatment planning was performed using the TPS Syngo® RT Planning, which uses the LEM model for effective dose calculation of the carbon ions and a fixed RBE factor of 1.1 for protons. In general, the plans were optimized using IMPT for an initial dose of 45 Gy (RBE) - 54 Gy (RBE) with an additional boost of 9 Gy (RBE) for some cases, as specified in Table 1.

A scanning raster spacing of 3 × 3 mm in the lateral direction, and an iso-energy slice spacing of 3 mm water-equivalent was used for both the proton and carbon plans. The initial optimization parameter for the pencil beam focus was 8 mm FWHM for the proton beams (range between 8 and 30 mm depending on energy). For the carbon ion beams, however, a maximum width of 10 mm FWHM was selected (range between 6 and 10 mm). These parameters were chosen in view of the results from a previous study [10], in which the interplay effects were minimized for an enlarged FWHM of the pencil beam.

The selected beam configuration for each patient was consequence of: (i) the superior inter-fractional robustness of ion-beams posterior to the patient (according to [5]); and (ii) the need to sparing the OARs (spinal cord and kidneys) from unwanted doses. It was therefore treated twelve of the fourteen patients with two posterior oblique fields. The remaining two patients were treated with a different geometry due to OARs constraints. Treatment was nonetheless considered robust from the inter-fractional point of view. The beam arrangements used are illustrated in Fig. 1.

In all cases, plans were optimized to the PTV in order to deliver the prescribed dose (D_presc) to the CTV while keeping the OARs doses below the dosimetric constraints of the spinal cord, kidneys and intestines. Due to the short distance between the tumor bed and the intestine, the prescribed dose was not achieved for all the patients over the entire CTV.

The PTV was assigned as an ITV expansion, by 7 mm in beam direction and 5 mm laterally, while the ITV corresponds to the union of the CTV in each of the 4DCT phases.

The 4DCTs were rigidly registered using the bony anatomy of the CT_plan. Deformable image registration (DIR) was performed between the CT_plan and the reference 4DCT state, CT_0Ex, with the aim of contour propagation using the vector field obtained. Moreover, each of the 4DCT states was registered against the CT_0Ex with the objective of deriving motion information during the calculation of the time resolved dose distribution. The DIR was performed with Plastimatch, using two successive registrations with a B-Spline algorithm [11]. The quality of the 4DCT DIR was assessed using the platform 3D Slicer [12], in particular using the Registration Quality Module [13], which was developed by external contributors as a set of tools that can be incorporated into 3D Slicer. The evaluation was performed through visual inspection and numerical quantification, such as the determinant of the Jacobian matrix (JD) of the vector field, inverse consistency error (ICE) and mean absolute difference.

A pre-treatment acquisition of the breathing signal was performed for twelve of the patients during the CT_plan acquisition session, as indicated in Table 1. For the other two patients, the signal wasn’t acquired during the CT session. As such, a standard Lujan motion with a patient representative period of 3 s was considered [14].

The beam delivery structure was simulated using a tool developed in-house, makeLmdout-MH [7, 15], based on the synchrotron base data. The base data was obtained from irradiated plans and considers the acceleration times, energy dependence and random intensity fluctuations. The output of this tool is the random simulation of the accelerator timing and intensity patterns for the given plan.

The inputs for the tool are the optimized treatment plan, the breathing signal and the accelerator spill information. The spill was characterized by the maximal extraction time of 5.0 s, pause length and pause length at the end-of-plan of 4.2 s (i.e. the time set to start a new spill within the same IES, and the beam pause when a IES is finished and the beam goes to the next IES, respectively).

As output, a simulated BDS is obtained, which will be given as input for the 4D dose calculation. In order to describe the spectrum of possible irradiation scenarios [16, 17], which results in different interplay patterns, a temporal shift to the starting phase of the surrogate signal was applied, i.e. a temporal delay between the starting of the breathing signal. This will correspond to the irradiation of a different raster point in a defined breathing phase. These shifts were spaced 500 ms in a total of five different starting points of the irradiation for the pre-treatment breathing signal and are given as input for the 4DDSim.

During the patient irradiation, the Anzai system was used to monitor motion. This system was connected to a data acquisition system, known as the EtherCat system, which correlated the breathing signal and the beam delivery temporal sequence of the accelerator in time. In order to improve the acquisition statistics, the different intensity rate from the proton and carbon beams was considered and the sampling time was defined as 0.15 msec and 0.25 msec for protons and carbon ions respectively. The calculation of 4DDRec was therefore performed on the basis of the measured data (breathing and irradiation sequence) during the irradiation of the individual treatment fractions. The number of available fractions with monitoring data is listed in Table 1.

The calculation of 4DDSim and 4DDReco was performed using TRiP4D [17, 18]. The forward calculation was based on the treatment plan information (raster points, energies and beam focus), breathing signal and the accelerator temporal pattern, either simulated or measured, respectively. In addition, the vector fields obtained for the DIR between each of the 4DCT states and the reference state (CT_0Ex) were given as input.

For both particles types, the forward dose calculation followed the same parameters as in the Syngo® RT TPS, differing for the proton plans only, where the physical or absorbed dose was computed in TRiP4D. However, in order to render negligible the effect of differences between the beam models, the dose distribution was also calculated in the static case, i.e. for the CT_plan, and this dose distribution was taken as reference for the comparison.

The internal tumor motion of each patient was quantified using the vector field obtained from the DIR between the CT_0Ex and each of 4DCT states, and in particular by measuring the median vector field length (VFL) inside the ITV_0Ex. The maximum of these values was used as a quantification of the intra-fractional tumor motion, generally corresponding to the CT_100Ex.

The dose distributions, namely the static, the 4DDSim, and 4DDReco, were evaluated by taking as metric the volume receiving at least 95% of the prescribed dose (V_95CTV) and the target dose homogeneity (H_CTV = D₅-D₉₅).

Note that the 4DDSim corresponds to a set of dose distributions, as representative of different interplay patterns, resulting in the need to display the results as mean and standard deviations and the DVHs as band-DVHs.

In order to simplify the analysis, only the initial plan was considered in the evaluation and the dose distribution for the boost plan was ignored.

In order to evaluate the impact of the dose modulation on the plan robustness to intra-fractional changes and interplay events, the normalized variation of the number of particles per irradiation field was evaluated (\( {\overline{\sigma np}}_{field} \)). This parameter is given by eq. (1). In (1) mean_np,field is the mean number of particles (np) for the respective field and σ_np is the respective root-mean-square of the mean of the squared differences between the number of particles at each IES (i_ies) and raster point (i_rp) in the total number iso-energy slices (nIES) and all the raster points in each IES (nrp). The parameter nRP is the total number of raster points for the evaluated field.

In addition, to account for variations between adjacent raster points, the concept of Modulation Index (MI) was applied (eq. 2a). The MIs were calculated from the treatment plan information of each field (MI_field), given by the raster points (rp) intensity and location.

This index accounts with the changes in adjacent raster points through the calculation of a function F (eq. 2b). Here, for each raster point, the magnitude of the difference between its intensity and the intensity of neighboring raster points is calculated through ∆ = |I _rp  − I_rp − 1|.where

Secondly, the number of raster points (nrp) in each IES, whose ∆ is above a factor, δ, of the variation of its IES is counted. This parameter is called N.

In brief, the function F quantifies the modulation of a plan by the measure of changes in adjacent raster points that exceed a certain fraction of the variation in each IES. Hence, the area of this spectrum of deviations, namely the area below the F function, gives the degree of modulation i.e. MI.

The value of δ was selected as 1.2, in an iterative process in a way to be sensitive to variations of the number of particles between adjacent raster points. For this purpose, the value of δ was varied, and the resulting function F was compared with the dose distribution per beam. For clinically homogeneous plans, therefore the function F has a small value, while it becomes gradually larger for regions with larger dose gradients.

As both parameters are applied per field, a weighted mean per plan for the different fields was used, giving the parameters \( {\overline{\sigma np}}_{plan} \) and MI_plan. The weighting was approximated in view of the number of particles per beam.

To assess the correlation between the plan parameters (V_95CTV, H_CTV, MI_plan, \( {\overline{\sigma np}}_{plan} \)) and the motion vector magnitude, a multi-pairwise analysis was performed. For this purpose, the Pearson linear correlation coefficient (r) for each pair of variable and respective significance (p-value) were calculated. Correlations with a p-value < 0.05 were considered significant. The entire statistical evaluation was performed using R libraries [19].

The median vector field length inside the ITV is shown in Table 1. The median of the vector field for this set of patients was (5.2 ± 2.7) mm, ranging from 2.2 to 12.7 mm. The main component of the motion was detected in the cranio-caudal direction, followed by the anterior-posterior direction. Figure 2 shows the vector field for the patient H1.

In order to eliminate differences in dose calculation between TRiP4D and Syngo® RT the shown evaluation of the 4D dose distributions is the comparison to the static dose distribution also calculated with TRiP4D. Note that the results for the 4DDSim and 4DDReco correspond to the propagated CTV (CTV_0Ex) contour from the CT_plan to the reference state CT_0Ex.

Figure 3 illustrates the overall results. At first glance, these results seem to show that a large number of plans were strongly affected by beam interplay and displacements. In the simulated cases, the variation of theV_95CTV reached values of up to − 28.0% with a mean of (− 7.6 ± 7.6)%. The H_CTV was also impaired, increasing from (15.9 ± 7.5)% in the static case to (27.8 ± 8.5)% under motion.

Guiding the interpretation of these results, Fig. 4 shows the DVH for the CTV of the reference dose distribution (i.e. static) and of the set of 4D simulations, for the two patients with the largest and smallest internal motion. Patient H12, due to a large internal motion (> 10 mm), shows a broad DVH and a mean reduction of the V_95CTV of (− 15.8 ± 8.1)%. In contrast, patient H15, with a mean tumor motion below 3 mm, shows a reduction in the V_95CTV of (− 6.7 ± 1.6)%, not being expected high dose variations between different treatment sessions.

Our analysis shows that the dose degradation is affected by the internal motion amplitude, with a strong correlation between the motion amplitude within the tumor and the standard deviation of the V_95CTV variations relative to the static case (r = 0.86, p-value < 0.05). However, we also see a non-significant correlation with the mean V_95CTV variations relative to the static case (p-value > 0.05). The homogeneity dose, H_CTV, was seen to be more sensitive to motion, with the mean and standard deviation differences strongly correlated (r = 0.61 and 0.77, respectively, p-value < 0.05).

The variation of the V_95CTV is represented against the internal motion amplitude in Fig. 5. The patients were categorized in three groups: red (> 5 mm motion and > 5% of CTV dose degradation), yellow (large motion, i.e. > 5 mm), and green (reduced impact on the dose distribution and motion below 5 mm). The definition of these limits represents the clinical practice at our facility.

This comparison suggests that as expected, patients belonging to the red group show a reduction in the target coverage (reduced mean variation of the V_95CTV relative to the planned dose distribution) throughout the entire course of treatment. Other patients however, such as H7, do not support this hypothesis. In fact, we observed that five patients for whom the motion amplitude was below 5 mm the target suffered strong dose degradation (yellow region). Another conclusion was that no patient with a large internal motion (> 5mm) showed small dose distribution degradation, i.e., no patients were observed in the grey region in Fig. 5). This justifies the need to monitor the motion amplitude for pancreatic patients throughout treatment, applying an appropriate strategy to reduce its impact (e.g. gating, robust optimization, rescanning, etc.).

The evaluation of the 4DDReco is also shown in Fig. 3, where each green cross represents one treatment fraction, overlaid with the static and 4DDSim results. This figure indicates that the 4DDSim resulted in a good approximation of the robustness of the plan for some treatment fractions, while for others it can be used as an indicator of the probability of seeing a reduction of the CTV dose, either by the mean or width of the boxplot of a set of simulations. The mean V_95CTV obtained from the 4DDSim strongly correlates with the mean V_95CTV from the set of 4DDReco (r = 0.87, p-value < 0.05).

Figure 6 shows an example (patient H3) of the dose distribution at one axial slice in the static, 4DDSim and 4DDReco situation, in which similar results to the 4DDSim and 4DDReco are seen, i.e. increase of the dose inhomogeneities and reduction of the target coverage dose. Nevertheless, other patients (such as H7 and H12) exhibit a 4DDReco for a specific fraction outside the predicted set of 4DDSim.

In general, patients with minor internal motion tend to have more similar 4DDSim solutions, i.e. a small interplay effect and therefore a small box width in Fig. 3. However, the number of calculated simulations has limited value for the description of all possible interplay patterns over and above those detected during the 4DDReco. It would be necessary to carry out further simulations in order to cover a larger range of solutions. Nonetheless, the 4DDSim results presented here, do indicate whether a plan is or is not robust (high correlation found between 4DDSim and 4DDReco).

From the visual inspection of the example dose distributions, patient H3 shown in Fig. 6, one can observe that the static plans were highly modulated for this patient. This effect was also observed for other patients. This was associated with the dose optimization constraints of the OARs (mainly bowel) and target coverage, which result in sharp dose gradients between the tumor and the bowel contour. Hence, another studied conjecture was the influence of the plan modulation on the plan robustness to the breathing motion.

The normalized standard deviation of the number of particles (\( {\overline{\sigma np}}_{plan} \)), the modulation index and the variation of the V_95CTV and H_CTV for all the patients and plans are presented in Table 2. The significant linear correlations between parameters are also seen here. The values per patient are available in the Additional file 1: Table S1.

An example of these MI_field variation patients, namely H9 and H11, are presented in Fig. 7. These patients’ plans were selected because although both of them exhibit the same amount of tumor motion (median VFL inside the ITV), their 4D dose distribution varies significantly. In Fig. 7, the function of the modulation, F, in which the MI_field corresponds to the area below the curve, is represented as a function of the IES for these cases. In both cases, it was observed that the Syngo® RT optimizer tended to have a strong modulation at tumor borders, as a result of an optimization resembling distal edge tracking. This effect is stronger; that is, more IESs show a higher F value, when the tumor is in the proximity of OARs, as in H11. Where this is not the case, the shape of the function is similar to the one seen for patient H9, where the first and last IES show a higher F value and the values in-between F are close to zero. Syngo® RT prioritizes the OARs constraints against the tumor irradiation, resulting in an increase of the MI_field when more constraints for the OARs are defined. Moreover, Syngo® RT uses a Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to solve the optimization problem. The solutions found by the BFGS algorithm, however, do not include regularization of the number of particles between neighboring raster points (regularization means a smoothing of the distribution of particle numbers in the target volume). This allows a greater difference between the particle numbers in neighboring raster points. For the set of patients the MI_plan using the TPS Syngo® RT was 11.2 ± 6.2. In comparison, the common values obtained for the other set of patients with the TPS TRiP4D and different constraints were of 1.8 ± 2.6. This indicates that different optimizers and different optimization constraints might result in contrasting modulation levels. Having said this, this comparison is beyond the scope of this study, as only a certified TPS is used for clinical treatment optimization.

The statistical evaluation of the data showed that \( {\overline{\sigma np}}_{plan} \) and MI_plan do not exhibit a significant linear correlation with the variation of the H_CTV or V_95CTV (p-value > 0.05).

The difference between these two concepts (\( \overline{\sigma np} \) and MI) is that \( \overline{\sigma np} \) ignores the location of the raster points and may not be representative of intensity differences between neighboring points and the plan modulation. MI does not, however, include the energy information and the use of multiple beams may diminish its significance. Nevertheless, when this parameter is weighted by the internal motion magnitude, it becomes highly correlated with variations in the target coverage and inhomogeneity, r = 0.76 (p-value 0.002) and r = 0.75 (p-value 0.001), respectively for the standard deviation of the V_95CTV and H_CTV differences.

A rough and intuitive method used to observe the relationship between dose degradation under motion and plan modulation is the comparison of the depth profile of the dose distribution per radiation field. It was observed that patients with a higher MI showed strong dose gradients in the beam path for each individual field. As a consequence, when a large internal motion is detected for these patients; it results in 4DDSim and 4DDReco with target under-dosage or OAR over-dosage in at least some fractions.