Francesca Di Franco

Thomas Baudier

Frédéric Gassa

Alexandre Munoz

Murielle Martinon

Sarah Charcosset

Emilie Vigier-Lafosse

Pascal Pommier

David Sarrut

Marie-Claude Biston
email: marie-claude.biston@lyon.unicancer.fr

Francesca Di Franco

Minimum non-isotropic and asymmetric margins for taking into account intrafraction prostate motion during moderately hypofractionated radiotherapy

Keywords: Prostate cancer, Hypofractionation, Intrafraction motion, Margins

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Hypofractionated (HF) radiation therapy protocols have shown their effectiveness in treating prostate cancer patients [START_REF] Hegemann | Hypofractionated radiotherapy for prostate cancer[END_REF][START_REF] Benjamin | The Role of Hypofractionated Radiotherapy in Prostate Cancer[END_REF]. However, these protocols require a high level of accuracy in dose delivery to allow reducing treatment margins because of an increased risk of toxicity to the surrounding organs at risk (OARs) [START_REF] Clemente | Role of the technical aspects of hypofractionated radiation therapy treatment of prostate cancer: A review[END_REF]. The use of reduced clinical target volume to planning target volume (CTV-to-PTV) margins for HF versus conventional fractionated treatments has shown to lead to similar late effects between the 2 cohorts (4) whereas early side effects were more pronounced for HF treatments [START_REF] Widmark | Ultra-hypofractionated versus conventionally fractionated radiotherapy for prostate cancer: 5-year outcomes of the HYPO-RT-PC randomised, non-inferiority, phase 3 trial[END_REF].

Using a monitoring device to control intrafraction prostate motion would enable to further reduce HF treatment margins, thus decreasing the risk of early side toxicity [START_REF] Litzenberg | Influence of intrafraction motion on margins for prostate radiotherapy[END_REF].

The effect of geometric uncertainties is known to be one of the major concerns in prostate cancer. These are generally due to rectum and bladder motion, which has been shown to be correlated to their fullness [START_REF] Chen | Dosimetric impact of different bladder and rectum filling during prostate cancer radiotherapy[END_REF]. Prostate motion can be important (displacements > 1 cm) but also irregular and sometimes unpredictable [START_REF] Li | Reduction of prostate intrafractional motion from shortening the treatment time[END_REF]. Many authors have already studied the magnitude of prostate shifts occurred during treatment fractions, using different prostate monitoring devices [START_REF] Lovelock | Continuous monitoring and intrafraction target position correction during treatment improves target coverage for patients undergoing sbrt prostate therapy[END_REF][START_REF] Langen | Observations on Real-Time Prostate Gland Motion Using Electromagnetic Tracking[END_REF][START_REF] Baker | Determining intrafractional prostate motion using four dimensional ultrasound system[END_REF][START_REF] Sihono | Determination of Intrafraction Prostate Motion During External Beam Radiation Therapy With a Transperineal 4-Dimensional Ultrasound Real-Time Tracking System[END_REF][START_REF] Richardson | Intrafraction monitoring of prostate motion during radiotherapy using the Clarity® Autoscan Transperineal Ultrasound (TPUS) system[END_REF]. Thus, using the Calypso system (Varian Medical Systems, Palo Alto, CA) to monitor prostate motion, Langen et al. [START_REF] Langen | Observations on Real-Time Prostate Gland Motion Using Electromagnetic Tracking[END_REF] reported that displacements > 3 mm could be observed 5 min after alignment. Using a transperineal ultrasound (TP-US) probe (Clarity®, Elekta AB, Stockholm, Sweden) for monitoring prostate displacement, Baker et al. [START_REF] Baker | Determining intrafractional prostate motion using four dimensional ultrasound system[END_REF] observed deviations up to 2.8 mm after only 2.5 min of treatment, and Sihono et al.

observed displacements of more than 6 mm after 4 minutes of treatment [START_REF] Sihono | Determination of Intrafraction Prostate Motion During External Beam Radiation Therapy With a Transperineal 4-Dimensional Ultrasound Real-Time Tracking System[END_REF]. Magnetic resonance-linac technology is also very accurate in retrieving prostate intrafraction motion, but little available due to its high cost compared to other technologies. Using this technology de Muinck Keizer et al. [START_REF] De Muinck Keizer | Prostate intrafraction motion during the preparation and delivery of MR-guided radiotherapy sessions on a 1.5 T MR-Linac[END_REF] also reported important displacements (>4 mm in posterior and superior directions) after 6 minutes of treatment time.

While the shifts observed are likely to have little impact on dose distribution if the treatment is delivered with a high number of fractions, this is not true for HF treatments [START_REF] Herschtal | Calculating geometrical margins for hypofractionated radiotherapy[END_REF][START_REF] Vanhanen | Dosimetric effect of intrafraction motion and different localization strategies in prostate SBRT[END_REF]. Besides, during HF treatments, because of an increased risk of toxicity to the surrounding organs, CTV-to-PTV margins should be reduced compared to conventional treatments, which seems difficult in the absence of monitoring systems. Therefore, a finer determination of the planning target volume (PTV) margin is crucial for safe dose escalation. Consequently an adapted margins strategy is needed. The most used method to estimate the required CTV-to-PTV margins is the van Herk's formula [START_REF] Van Herk | The probability of correct target dosage: Dose-population histograms for deriving treatment margins in radiotherapy[END_REF]. Several assumptions and simplifications have been used for this approach to be valid [START_REF] Van Herk | The probability of correct target dosage: Dose-population histograms for deriving treatment margins in radiotherapy[END_REF]: patient population was assumed to be homogeneous (same standard deviations' values were assumed for each patient) and many fractions were considered in order to put treatment average execution error as zero. Those simplifications cannot be ignored in presence of a heterogeneous population, where large random variations occur, or in presence of a reduced number of fractions [START_REF] Herschtal | Calculating geometrical margins for hypofractionated radiotherapy[END_REF]. In addition, margins recipes only take into account interfraction motion with few guidelines for intrafraction movements [START_REF] Pang | Analysis of intra-fraction prostate motion and derivation of duration-dependent margins for radiotherapy using real-time 4D ultrasound[END_REF]. Thus, other alternatives must be explored in order to accurately estimate treatment margins for taking into account intrafraction movements.

Another method which could be more relevant is the voxel shifting method. It consists in shifting the dose map according to translations or rotations observed during the treatment process. This way, the effect of movements on the dose distribution is directly visible, which makes it possible to extract a margin taking into account the movements on a patient population. This method is particularly relevant for photon treatment, since the photon range is little disturbed by a change in patient anatomy, which enabled the dose distribution to be calculated using the static dose cloud approximation [START_REF] Unkelbach | Robust radiotherapy planning[END_REF]. This method appears all the more appropriate when used in a homogeneous environment as it is the case for prostate cancer [START_REF] Unkelbach | Robust radiotherapy planning[END_REF].

Hence, the goal of this work was to propose a population-based study to retrieve non-isotropic and asymmetric (NI-AS) CTV-to-PTV minimum margins only taking into account intrafractional prostate motion. Forty-six patients (876 fraction) having received moderate HF prostate treatment (60 Gy in 20 fractions) and daily monitored using Clarity TP-US probe were considered in this study. The retrieved displacements were used to study the CTV-target coverage during treatment, in presence of motion. The CTV structure was perturbed with the recorded prostate displacements using the voxel shifting method and the static dose cloud approximation [START_REF] Unkelbach | Robust radiotherapy planning[END_REF]. Then, to evaluate the effectiveness of NI-AS margins, treatment plans were re-computed using an autoplanning algorithm [START_REF] Biston | Evaluation of fully automated a priori MCO treatment planning in VMAT for head-and-neck cancer[END_REF]. Several studies dealing with intrafraction prostate monitoring during treatment can be found in the literature [START_REF] Langen | Observations on Real-Time Prostate Gland Motion Using Electromagnetic Tracking[END_REF][START_REF] Baker | Determining intrafractional prostate motion using four dimensional ultrasound system[END_REF][START_REF] Sihono | Determination of Intrafraction Prostate Motion During External Beam Radiation Therapy With a Transperineal 4-Dimensional Ultrasound Real-Time Tracking System[END_REF][START_REF] Richter | Evaluation of intrafraction prostate motion tracking using the Clarity Autoscan system for safety margin validation[END_REF] as well as many margins recipes that consider interfractional motion [START_REF] Van Herk | The probability of correct target dosage: Dose-population histograms for deriving treatment margins in radiotherapy[END_REF][START_REF] Pang | Analysis of intra-fraction prostate motion and derivation of duration-dependent margins for radiotherapy using real-time 4D ultrasound[END_REF][START_REF] Pang | Duration-dependent margins for prostate radiotherapy-a practical motion mitigation strategy[END_REF]. However, to our knowledge, this is one of the first that uses monitoring device to investigate non homogeneous and time-dependent margins for intrafractional prostate motion during moderate HF radiation therapy. An ulterior novel feature proposed by this work is the use of an automatic treatment plan algorithm that enabled assessing the impact of intrafraction motion on CTV coverage without having operator variability in the planning process which could bias the conclusions.

Materials and methods

TP-US monitoring device

The Clarity 3D TP-US system is based on a 2D TP-US probe tracked by an infrared camera [START_REF] Lachaine | Intrafractional prostate motion management with the Clarity Autoscan system[END_REF]. For each acquisition, hundreds of 2D US slices are acquired during an automated probe sweeping movement performed by a step-by-step motor and merged into a 3D image. The probe can complete a 75° sweep in 0.5 seconds and the patient does not perceive any motion other than a slight vibration, as all motion is internal to the probe housing. For patients' positioning, a specific immobilization device made of a base plate and 2 cushions for the knees enables the probe to be fixed between patient's legs.

Patients' cohort and clinical protocol

Forty-six patients receiving a moderate HF volumetric modulated arc therapy (VMAT) treatment of the prostate in our institution were included in this study, which was approved by the hospital ethics committee. The prescribed dose was 60 Gy in 20 fractions delivered to the PTV. A dose objective was fixed for CTV: 99% of the CTV covered by 100% of the prescribed dose. VMAT treatments were delivered using a VersaHD® (Elekta AB) Linac. Before the treatment, a USdaily image followed by a Cone Beam CT (CBCT) acquisition was performed for pretreatment positioning. The CBCT was the reference modality for patient positioning whereas the TP-US probe was only used for controlling intrafraction motion of the prostate (876 fractions). Treatment durations ranged between 200-600 s. Among the cohort, 18 patients (346 fractions) were randomly selected for treatment plan re-computation using increased CTV-to-PTV margins (i.e., 0, 1, 2, 3, 4, 5 and 6 mm margins around the CTV). Patients followed an individual bladder preparation of 1-2 cups of water (330-500 ml) 1 hour before the treatment. Specific dietary advices were given for a period of 7 days before the CT scanner. Patients were also encouraged to empty their bowels and bladder prior to each fraction.

Treatment planning

One hundred and forty four VMAT treatment plans were re-computed using increased CTV-to-PTV margins with mCycle auto-planning solution, which is implemented in a research version of Monaco TPS (V.5.59.11, Elekta AB, Stockholm). This concept, using lexicographic Multi Criteria Optimization (MCO) has been extensively described before [START_REF] Biston | Evaluation of fully automated a priori MCO treatment planning in VMAT for head-and-neck cancer[END_REF]. To summarize, the first step is defining a "tumor and protocol" specific wish-list containing the constraints and prioritized objectives. Then through the optimization process, firstly the algorithm is optimizing the individual objectives to meet the different requested goal values and all defined constraints while respecting the priority order. Then it tries to further reduce the objectives that were below the goal value in the first pass, as low as possible in a second pass. All plans were performed using the same beam geometry (two 360° arcs), the same wish-list, and the same sequencing parameters to avoid any bias in dosimetric comparisons related to the planning process.

Quantification of the impact of intrafraction motion on target coverage

The robustness of a treatment plan was evaluated by performing transformations of the nominal dose distribution and estimating differences. The voxel shifting method [START_REF] Unkelbach | Robust radiotherapy planning[END_REF] and the static dose cloud approximation were used to move the CTV RT structure with the prostatic displacements observed during the treatment process. An in-house automated Python routine was developed to take as input the planning CT, RT structures and 3D displacements of the prostate (left-right (LR), superior-inferior (SI) and anterior-posterior (AP)) and generate as output the moved structures. Hence, the RT structures were moved each 5 seconds according to the given displacements. The 60 Gy isodoses RT structures were retrieved from the calculated plans using different CTV-to-PTV margins, and then superimposed onto the moved CTV to verify the dosimetric coverage. This way, the theoretical coverage of the CTV was evaluated each 5 seconds, in presence of motion.

Margin's analysis (statistical analysis)

As reported elsewhere [START_REF] Pang | Analysis of intra-fraction prostate motion and derivation of duration-dependent margins for radiotherapy using real-time 4D ultrasound[END_REF][START_REF] Pang | Duration-dependent margins for prostate radiotherapy-a practical motion mitigation strategy[END_REF], the van Herk's non-linear margin recipe ( 16) was used to estimate the duration-dependent margins for every minute up to 10 min as followed:

(

As defined by van Herk (23) Σ is the standard deviation of the mean displacements (systematic errors) and σ is the standard deviation of the random variations (prostate motion). The parameter σ p (3.2 mm) describes the width of the penumbra modeled by a cumulative Gaussian.

C 1 is the confidence level corresponding to a percentage of the population and C 2 is the dose level's coefficient. C 1 and C 2 were chosen to achieve the two following dosimetric criteria: 90% of population which CTV was covered by 95% of total dose (90PP-95D) and 95% of population having the CTV covered by 99% of the total dose (95PP-99D). For the 90PP-95D dosimetric criteria, C 1 and C 2 values were chosen as 2.50 and 1.64, respectively. Instead, for 95PP-99D dosimetric criteria, C 1 and C 2 values were set as 2.79 and 2.34, respectively [START_REF] Van Herk | The probability of correct target dosage: Dose-population histograms for deriving treatment margins in radiotherapy[END_REF]. Whereas the first criterion was the one used by van Herk [START_REF] Van Herk | The probability of correct target dosage: Dose-population histograms for deriving treatment margins in radiotherapy[END_REF] and largely reported in literature, the second one was chosen to better consider the specific conditions relating to HF treatments (reduced number of fractions and higher treatment accuracy needed).

Results

Motion analysis

The evaluation of 876 fractions after 5 min of treatment resulted in a mean displacement of -0.02 ± 0.52 mm, 0.27 ± 0.78 mm and -0.43 ± 1.06 mm in the LR, SI and AP directions respectively. After 10 min of treatment mean displacements were -0.03 ± 0.76 mm, 0.45 ± 1.08 mm and -0.72 ± 1.50 mm. To visualize the data over all the fractions, 425 104 displacement values were plotted in a histogram (Fig. 1). Mean absolute displacements > 3, 5 and 7 mm were observed for 16%, 5%, and 2% of the total number of fractions. Rare large deviations > 8 mm were detected but the frequency was less than 1%. On average, the evaluation of the trajectories revealed a directional dependence of the intrafractional prostate movements. The prostate position was rather stable in LR direction, with median and maximum values of -0.02 and 7.60 mm after 10 min of treatment. In contrast, the evaluation in SI and AP directions showed a wider variation of displacements values (standard deviation of 1.08 and 1.50 mm after 10 min treatment respectively). Prostate movements were more important in inferior and posterior directions, with median values of 0.28 and -0.50 mm and maximum values of 9.54 and 9.50 mm after 10 min of treatment, respectively.

CTV coverage study using homogeneous margins

Isotropic margins of 0, 1, 2, 3, 4, 5 and 6 mm were added to each pre-treatment CTV structure and, after applying the registered 3D shifts, the corresponding shifted CTV covered by 60 Gy isodose RT structure was recorded each 5 seconds from 0 to 600 s for each CTV-to-PTV margin value. The median CTV dosimetric coverage obtained depending on time, using the above mentioned CTV-to-PTV margins is shown in Fig. 2. The CTV coverage increased with increased CTV-to-PTV margins but it decreased with time. Median shifted dose distribution results showed that, fixing 300 s as observation time and considering 330 fractions, the prescription constraint (99% of the CTV covered by 100% of the prescribed dose) on the CTV was achieved in 77%, 77%, 78%, 84%, 92%, 98% and 100% of fractions using 0, 1, 2, 3, 4, 5 and 6 mm margins, respectively. Considering that the average duration of a HF treatment is about 5 min, a homogeneous margin of 5 mm was considered as sufficient to take into account intrafraction motion. Then, considering that the prostate can move during the imaging and pretreatment verification phase, the observation time was increased to 7 and 10 min, corresponding to a 2 and 5 min imaging phase, respectively. In the first case, fixing 420 s as observation time (277 fractions) the prescription constraint on CTV prostate was achieved in 71%, 71%, 72%, 85%, 89%, 95% and 98% of fractions using 0, 1, 2, 3, 4, 5 and 6 mm margins, respectively. Alternatively, fixing 600 s as observation time (97 fractions) the prescription constraint on CTV prostate was achieved in 67%, 68%, 69%, 69%, 70%, 85% and 95% of fractions using 0, 1, 2, 3, 4, 5 and 6 mm margins, respectively. Hence, after 7 min total treatment time, a homogeneous margin of 5 mm should guarantee a correct prostate target coverage, whereas 10 min total treatment time, would require a 6 mm CTV-to-PTV margin.

Treatment margins

Based on the data acquired in this study (46 patients, 876 fractions), time-dependent margins were calculated to account for intrafraction motion. Non-isotropic margins were first calculated using van Herk's formula. To meet the first 90PP-95D dosimetric criterion after 10min of treatment, margins of 1.5, 3.2 and 6.2 mm were calculated in LR, SI and AP directions, respectively. In order to meet the targeted dosimetry criterion of 95PP-99D, the margin was increased by 0.2, 0.5 and 1 mm, in the LR, SI and AP directions, respectively (Table 1).

Since the evaluation of the trajectories revealed a directional dependence of the intrafraction prostate motion, with important displacements in inferior and posterior directions, NI-AS and time-dependent margins were first calculated using the van Herk's formula and then retrieved using the voxel shifting method. Hence, after 10 min of treatment, using van Herk's formula, a margin of 0.5 and 0.6 mm was needed in left and right directions, respectively, 1.7 and 0.7 mm in inferior and superior, respectively, and 0.9 and 3.5 mm in anterior and posterior directions, respectively, to meet the 90PP-95D dosimetric criterion (Table 1). To achieve the targeted criterion of 95PP-99D, after 10 min of treatment, a margin of 0.5 and 0.7 mm was needed in left and right directions, respectively, 1.9 and 0.8 mm in inferior and superior directions, respectively and 1.1 and 4.6 in anterior and posterior directions, respectively.

Using the voxel shifting method, margins needed to meet the 95PP-99D dosimetric criterion were generally more important, except in left-right direction.

Hence, after 10 min of treatment, a margin of 0 and 1 mm was needed in left and right directions, respectively, 4 and 3 mm in inferior and superior directions, respectively and 4 and 8 mm in anterior and posterior directions, respectively (Table2).

Finally, to evaluate the corresponding shifted dose distribution, 18 treatment plans (one for each patient of the cohort) were automatically re-computed using the non-isotropic margins found at 7 min treatment (Table 2) to take into account both the physicians' margin recommendations [START_REF] Brand | Intensity-modulated fractionated radiotherapy versus stereotactic body radiotherapy for prostate cancer (PACE-B): acute toxicity findings from an international, randomised, open-label, phase 3, non-inferiority trial[END_REF], where a posterior CTV-to-PTV expansion between 3 and 5 mm is needed, and the average duration of an HF treatment (2 min of pre-treatment imaging phase plus 5 min of treatment delivery). Boxplots in Fig. 3 report the CTV coverage depending on time. After 5 and 7 min of treatment the prescription constraints on CTV coverage were achieved for 96% of fractions. The same median target coverage as a homogeneous margin of 5 mm was achieved, but with drastically reduced margins in LR, SI and anterior directions.

Discussions

In this study, intrafraction prostate motion was monitored in 46 patients (876 total fractions) that underwent moderate HF radiation therapy, with prostate monitoring phase ranging between 200 and 600 s. This involved pretreatment imaging and treatment phase. To deliver 3 Gy per fraction in VMAT with flattening filter (FF) photon beams generally takes about 3 min 30 s, whereas delivering hypofractionated treatment of 6 to 7 Gy per fraction generally takes 6 to 7 min. The use of flattening filter free (FFF) beams is likely to divide by 2 the delivery time, thus reducing the probability of prostate motion. Hence, using FFF beams could also lead to a reduction of the treatment margins required compared to FF beams. The large observation time provided in this study enabled us to have a sufficiently large observation period to mimic both moderately and highly hypofractionated treatment delivered with FF or FFF beams.

Similar to other studies, some of which using other monitoring devices, the detected intrafraction displacements were generally small (> 3 mm in 16% of treatment time and > 5 mm in 5% of treatment time) but larger displacements (≥ 8 mm) occurred with a frequency less than 1%, as also reported elsewhere [START_REF] Langen | Observations on Real-Time Prostate Gland Motion Using Electromagnetic Tracking[END_REF][START_REF] Sihono | Determination of Intrafraction Prostate Motion During External Beam Radiation Therapy With a Transperineal 4-Dimensional Ultrasound Real-Time Tracking System[END_REF][START_REF] Richardson | Intrafraction monitoring of prostate motion during radiotherapy using the Clarity® Autoscan Transperineal Ultrasound (TPUS) system[END_REF][START_REF] Richter | Evaluation of intrafraction prostate motion tracking using the Clarity Autoscan system for safety margin validation[END_REF]. The smallest displacements were observed in LR directions and the largest ones in inferior and posterior directions [START_REF] Li | Reduction of prostate intrafractional motion from shortening the treatment time[END_REF][START_REF] Langen | Observations on Real-Time Prostate Gland Motion Using Electromagnetic Tracking[END_REF][START_REF] Sihono | Determination of Intrafraction Prostate Motion During External Beam Radiation Therapy With a Transperineal 4-Dimensional Ultrasound Real-Time Tracking System[END_REF][START_REF] Pang | Analysis of intra-fraction prostate motion and derivation of duration-dependent margins for radiotherapy using real-time 4D ultrasound[END_REF][START_REF] Xie | Intrafractional Motion of the Prostate During Hypofractionated Radiotherapy[END_REF][START_REF] Li | Gains From Real-Time Tracking of Prostate Motion During External Beam Radiation Therapy[END_REF].

Hence, even if Li et al. [START_REF] Li | Prefraction displacement and intrafraction drift of the prostate due to perineal ultrasound probe pressure[END_REF] showed that the monitoring probe can affect prostate displacements, based on our observations, we can assume that there was no impact of the probe pressure on intrafraction prostate displacement. Possibly, the shift in AP direction was due to a patient relaxation or a change in bladder and rectal fullness. In this direction further research is taking place in our institution to better understand the relationship between the daily anatomical variations and the relative prostate displacements.

Similarly to this work, an increased variance of prostate displacements for longer observation times was found in the literature [START_REF] Langen | Observations on Real-Time Prostate Gland Motion Using Electromagnetic Tracking[END_REF]. Generally, using conventional treatment protocols, large target displacements appear to be acceptable if occurring for a short period of time during irradiation. However, during HF treatments such displacements become much more relevant because of the risk of late radiation effects. This makes the calculation of appropriate margins even more important. The analysis of the impact of intrafraction motion on target coverage using homogeneous CTV-to-PTV margins around the CTV showed a general loss in target coverage because of increased treatment times even using up to 6 mm CTV-to-PTV margins. Conversely, analyzing the median shifted dose distribution, for a daily routine HF fraction lasting approximately 5 min, a homogeneous margin of 5 mm should guarantee sufficient target coverage during all treatment.

In the recent literature, there has been a growing interest in finding non-homogeneous minimum margins for considering intrafraction motion as a function of treatment time. A summary of the most recent studies is given in Table 3. In all the studies van Herk's formula was used to calculate time dependent NI-AS margins. An innovative feature of our work is that we compared two different margin calculation strategies over a large cohort of patients. We also proposed an objective analysis of CTV coverage in function of time using increased CTV-to-PTV margins, without operator dependence, by using an auto planning system to perform the treatment plans.

As a comparison with recent studies, non-isotropic margins were first derived using the van Herk's formula and considering the 90PP-95D dosimetric criterion. The margins obtained in our work were similar in LR and SI directions compared to Pang et al [START_REF] Pang | Duration-dependent margins for prostate radiotherapy-a practical motion mitigation strategy[END_REF], considering an observation time of 8 min.

Conversely, margin obtained in AP direction was double (5.20 vs 2.65 mm). While after only 4 min of treatment, Sihono et al. [START_REF] Sihono | Determination of Intrafraction Prostate Motion During External Beam Radiation Therapy With a Transperineal 4-Dimensional Ultrasound Real-Time Tracking System[END_REF] achieved higher margins in LR direction than other studies, they also found smaller margins in AP direction than in our study (1.33 vs 2.40 mm). Steiner et al. [START_REF] Steiner | Prostate and patient intrafraction motion: Impact on treatment time-dependent planning margins for patients with endorectal balloon[END_REF] obtained the same AP margin of 6.2 mm but after 15 min of observation time versus 10 min for this study.

Therefore, the difference could result in the procedures for patient's preparation before treatment delivery. In our case, the diet suggested to the patients was maybe less respected. In addition, most patients of the cohort were treated between 14-16 pm, which might have a connection with anatomical movements and subsequent prostate movements.

Since prostate displacements observed were more important in posterior and inferior directions, it was relevant to calculate NI-AS margins. Using van Herk's method, margins obtained were smaller than Pang et al. [START_REF] Pang | Analysis of intra-fraction prostate motion and derivation of duration-dependent margins for radiotherapy using real-time 4D ultrasound[END_REF] in all directions except in posterior direction, after 8 min of treatment. By adapting the dosimetric criteria to HF treatment (95PP-99D), margins were increased by 0.1 mm in left, right and superior directions, 0.2 mm in inferior and anterior directions, and 0.5 mm in posterior direction, after 8 min of treatment. However, van Herk's formula loses accuracy during HF treatments because of the reduced number of fractions ( 14) and because of non-homogeneous dose distribution. Additionally, patient population cannot be assumed as homogeneous and therefore systematic and random errors are not constant across all population. Systematic errors are also minimized if daily IGRT is performed, which is the case for all SBRT treatments.

By using the voxel shifting method, we made the assumption that the effect of intrafraction motion could be approximated as a shift of the voxel relative to the planning position.

Moreover, considering the asymmetry of prostate movements, this method could be more effective in retrieving NI-AS margins. Considering a 7 min HF treatment (taking also into account the pre-treatment phase), greater margins were found using the voxel shifting method compared to van Herk's margins, except in left and right directions.

Hence, even if the margins found differed between studies, they were all agreed that posterior margins should be more important than in other directions to take into account intrafraction motion. Note that this is contrary to most international protocols which recommend a reduction of the margins in the posterior direction, to reduce the risk of toxicity to the rectum [START_REF] Brand | Intensity-modulated fractionated radiotherapy versus stereotactic body radiotherapy for prostate cancer (PACE-B): acute toxicity findings from an international, randomised, open-label, phase 3, non-inferiority trial[END_REF].

To validate the robustness of the new CTV-to-PTV margins found with the voxel shifting method, automatic plans were recomputed for a 7 min HF treatment. The evaluation of the dosimetric CTV coverage after 5 and 7 min of treatment was equivalent to the dosimetric coverage obtained with a 5 mm homogeneous margin but with drastically reduced margins in all directions except in posterior.

A possible limitation of our study is that rotations of the prostate were not considered in evaluating non-isotropic margins, as the Clarity 4D TPUS workstation does not support rotations shifts. In the context of our clinical interest in prostate intra-fractional motion, this does not constitute a major drawback.

Finally, similarly to another work, no interplay effect arising from the interaction between intrafraction organ motion and the multileaf collimator position for each particular segment was considered in this study [START_REF] Sumida | Robust plan optimization using edge-enhanced intensity for intrafraction organ deformation in prostate intensity-modulated radiation therapy[END_REF]. According to the literature, one method to account for this effect consists in using a segmentbased convolution method, which involves in convolving the static dose distribution attributed to each segment with the probability density function (PDF)

of motion during delivery of the segment [START_REF] Li | Quantifying the interplay effect in prostate IMRT delivery using a convolution-based method[END_REF]. Other method consists in using the set of leaf sequences obtained from an electronic portal imaging device to construct the dose distribution [START_REF] Lee | The use of EPID-measured leaf sequence files for IMRT dose reconstruction in adaptive radiation therapy[END_REF]. Machine log files in combination with Monte Carlo dose calculations have also been widely used [START_REF] Schreibmann | Patient-specific quality assurance method for VMAT treatment delivery[END_REF][START_REF] Litzenberg | Synchronized dynamic dose reconstruction[END_REF]. Finally, the MR-linac technology allows now combining the linac machine log files with motion information obtained from the intrafraction 3D cine-MR dynamics [START_REF] Kontaxis | Delivered dose quantification in prostate radiotherapy using online 3D cine imaging and treatment log files on a combined 1.5 T magnetic resonance imaging and linear accelerator system[END_REF].

Conclusions

To conclude, we reported here our experience in deriving NI-AS duration-dependent margins to generate the required planning target volume for prostate HF radiotherapy treatments. The objective was to propose minimum margin for taking into account intrafraction motion during HF treatment of prostate cancer for centers who do not have the possibility to monitor in real time prostate motion. Similarly to other works, we found that margins should not be reduced in posterior direction, as regularly done in many protocols to minimize the rectal toxicity. Using the voxel shifting method, a 5 mm homogeneous margin was found to be sufficient to ensure a correct CTV dosimetric coverage. NI-AS margin calculation showed that this margin could be reduced in all but posterior direction.

The use of reduced treatment margins in HF treatment could allow to considerably reduce the dose to the OARs, as shown elsewhere [START_REF] Zelefsky | Incidence of Late Rectal and Urinary Toxicities After Three-Dimensional Conformal Radiotherapy and Intensity-Modulated Radiotherapy for Localized Prostate Cancer[END_REF]. However, to ensure a sufficient CTV coverage without increasing posterior margins, and to minimize the treatment toxicity, a monitoring tool to control prostate's movements seems essential. In our institution, a 5 mm homogeneous CTV-to-PTV margin is used for highly HF prostate treatments. With the results obtained and with the use of the TP-US monitoring modality we should be able to reduce margins to 3 mm. Further work is in progress to assess the dosimetric consequences of these margins on the OARs, as a function of radiotherapy treatment's length.

Fig. 1 Fig. 2 :Fig. 3

 123 Fig. 1 Distribution of the observed intrafractional prostate displacement for 46 patients (876 sessions)

  Dosimetric criterion: 95PP -99D

Table 1 :

 1 Necessary non-isotropic and asymmetric margins (mm) obtained by van Herk's margin recipe using two different dosimetric criteria. The considered patient population is of 46 patients (876 sessions).

	Non-isotropic margins
	90PP-95D

Table 2 :

 2 Necessary non-isotropic and asymmetric margins (mm) for meeting 95PP-99D coverage criteria for 46 patients (876 sessions).

Table 3 :

 3 Comparison between different studies to retrieve asymmetric and non-isotropic CTV-to-PTV margins

	Non-isotropic margins
	Authors	# of patients	Observation	Margins LR	Margins SI	Margins AP	Notes
			time (min)	(mm)	(mm)	(mm)
	Pang et al. (23) -2020	55	8	1.02	2.41	2.65	Prostate monitoring: Clarity 4D TPUS
			15	1.84	4.29	4.63	Margins calculation: van Herk's formula
	Sihono et al. (11) -2018	38	4	1.25	1.10	1.33	Prostate monitoring: Clarity 4D TPUS
							Margins calculation: van Herk's formula
	Steiner et al. (30) -2013	17	15	2.3	3.9	6.2	Prostate monitoring: Fiducials
							Margins calculation: Van Herk's formula
	di Franco et al. -2021	46	4	0.6	1.3	2.4	Prostate monitoring: Clarity 4D TPUS
	(this study)		8	1.2	2.7	5.2	Margins calculation: van Herk's formula
			10	1.5	3.2	6.2
	Non-isotropic and asymmetric margins
	Pang et al. (19) -2018	60	8	0.8 left	1.7 sup	1.7 ant
				0.8 right	2.7 inf

Acknowledgements

This work was performed within the framework of the SIRIC LYriCAN Grant INCa-INSERM-DGOS-12563, and the LABEX PRIMES(ANR-11-LABX-0063) of Université de Lyon, within the program Investissements d'Avenir (ANR-11-IDEX-0007) operated by the ANR. We are grateful to Sophie King for her involvement in this work.

Conflicts of interest statement

This work was performed in the framework of a research cooperation agreement with Elekta AB.