A Plan Robustness Qualification Method of Volumetric Arc Radiotherapy (VMAT) of Set Up Uncertainty in Nasopharyngeal Carcinoma (NPC) Radiotherapy


 Purpose: To evaluate the set-up sensitivity of VMAT plans for Nasopharyngeal carcinoma (NPC) treatment by proposing a plan robustness evaluation method. Methods: 10 patients were selected for this study. A 2-arc volumetric-modulated arc therapy (VMAT) plan was generated for each patient using Varian Eclipse (13.6 Version) treatment planning system (TPS). 5 uncertainty plans (U-plans) were calculated based on the first 5 times set-up errors acquired from cone beam comuter tomography (CBCT). The dose differences and plan robustness of all the PTVs, CTVs, GTVs, and organs at risk (OARs) were analyzed. Tumor control probability (TCP) and normal tissues complication probability (NTCP) were calculated for biological evaluation. Results: The mean dose differences of D98 and D95 (△D98 and△D95) of PTVnx were respectively 3.30 Gy and 2.02 Gy. The △D98 and△D95 of CTVnx were 1.12 Gy and 0.58 Gy. The △D98 and△D95 of GTVnx were 0.56 Gy and 0.33 Gy. The dose coverage of GTVnx and CTVnx was guaranteed with minor dose variation. GTVnd exhibited strong robustness with little variation of D98 (0.5%) and D95 (0.9%). The △D98 and△D95 of CTVnd were 1.39 Gy and 1.03 Gy, distinctively lower than those in PTVnd (2.8 Gy and 2.0 Gy). No marked mean dose variations of Dmean were seen. The mean reduction of TCP (△TCP) in GTVnx and CTVnx were respectively 0.4% and 0.3%. The mean △TCP of GTVnd and CTVnd were 0.92 % and 1.3 % respectively. The CTV exhibited the largest △TCP (2.2 %). In OARs, the optical nerve chiasma was the one with the highest change, with a mean dose variation of 8.81 Gy. The Dmean of bilateral parotids varied in a large range. The mean reduction of NTCP (△NTCP) in the left parotid gland was 13.30%, which sharply increased the risk of parotid gland dysfunction. Conclusion: VMAT plans had a strong sensitivity to set-up uncertainty in NPC radiotherapy, due to the high degree of modulation. We proposed an effective method to evaluate the plan robustness of VMAT plans. Plan robustness and complexity should be taken into account in photon radiotherapy.


Introduction
Nasopharyngeal carcinoma (NPC) is one of the major invasive malignant neoplasms of the head and neck. The main strategy against NPC is radiotherapy for its sensitiveness to radiotherapy (RT) [1]. With larger irradiation volumes, complex and intricate anatomical structures, precision dose coverage, and organ at risk (OAR) sparing were crucial in NPC radiotherapy [2].
Volumetric arc radiotherapy (VMAT) had been widely used in NPC radiotherapy, for VMAT performed optimized dose distribution and OAR sparing by continuous variation of the instantaneous dose rate, MLC leaf positions, and gantry rotational speed [3]. In addition, The concept of precision radiotherapy had been proposed and promoted by taking advantage of physics, engineering, and computational and mathematical oncology to reach the goal of lower complications and better quality of life without compromising of targets. However, more complex plans, such as VMAT and IMRT plans, have higher risks Loading [MathJax]/jax/output/CommonHTML/jax.js of dose calculation and delivery, compared to 3D-CRT plans [4]. Subtle errors in VMAT plans may exert an ampli ed effect on dosimetric errors. A more complete description of dose delivery for complex plans was needed. Treatment plan robustness is the degree of resiliency of the required dose distribution to these uncertainties and varies with the treatment site, technique and method [5]. The concept of robustness had been widely used in proton treatment plans for the sharp distal fall-off and scattering characteristics make proton dose distributions more sensitive to inter-and intra-fractional anatomy variations [6]. Plan robustness quanti cation is a viable quantitative way to evaluate treatment plan sensitivity to uncertainties [7].
Set-up error was one of the main challenges in NPC radiotherapy. In 2000, Van Herk [14][15][16] proposed the method of CTV-PTV margin to treat the clinical target volume (CTV) to 95% of the prescribed dose for 90% of the patients based on the systematic and random isocentric uncertainty. The CTV-PTV margin method had been in use ever since. The cone beam computed tomography (CBCT) has been widely used in position veri cation by correcting online set-up errors according to the registration results [8]. However, the CBCT images were not acquired before each treatment for insu cient and unequally distributed medical resources. It is di cult to evaluate the dose difference due to the random set-up uncertainty. Thus, the sensitivity of VMAT plans to set-up uncertainty should be taken into consideration.
In this study, we aim to evaluate the set-up sensitivity of VMAT plans for Nasopharyngeal carcinoma treatment by proposing a plan robustness evaluation method. The Tumor control probability (TCP) and normal tissues complication probability (NTCP) models were applied to evaluate the potential biological dose differences.

Patient selection and delineation
We retrospectively evaluated treatment plans for 10 NPC patients treated in our institution. The clinical characteristics of the patients enrolled in this study were shown in Table 1. All the patients were immobilized by a thermoplastic mask in a supine position. The CT image with a 2.5 mm slice thickness was acquired using a 16-slice CT scanner (GE Discovery RT, GE Healthcare, Chicago, IL, USA). The target volumes and organs at risk (OARs) were delineated by the same clinician. The gross tumor volume (GTV) included the primary tumor sites and their invasion range (GTVnx) and cervical metastatic lymph node (GTVnd). Clinical target volumes (CTVs) induced CTVnx, CTVnd, and CTV. PTVs included PGTVnx, PTVnd, and PTV.

Robustness Quanti cation Methods
There are 1 treatment plan and 5 perturbated plans for each patient. The dose-volume histogram band (DVHB) quanti cation method was adopted. The DVHB method [9] is one of the classical robustness quanti cation methods. The dose values in 1 treatment plan and 5 U-plans were displayed in Dosevolume histogram (DVH) curves. 6 values could be found when choosing different DVH parameters. In this study, the DVH parameters were chosen to be at D 95 , D 98 , D 2cc , and D mean for CTVs, GTVs, and PTVs.
For serial OARs, the D max was chosen. For the bilateral parotid gland, the V 20Gy , V 30 Gy , V 40 Gy , D mean were chosen. D x represented the dose (in Gy) received by x% of the volume, V y the volume (in percentage) received by y Gy. D 2cc the dose (in Gy) received by a volume of 2 cm 2 . Absolute differences △D x and △V y represented the width, which could be calculated by the absolute value of the minimum value subtracted from the maximum value, and corresponded to the plan robustness for the structure.
Tcp And Ntcp Evaluation (Dup: Abstract ?) Many TCP models have been proposed to predict radiobiological response to dose after irradiation [10,11]. Dose variation brought changes in the physical dose as well as the biological dose, which is directly affected clinical signi cance. We use TCP and NTCP modelings to evaluate the biological effects.
Schultheiss logit model, which is a logic function used to describe the sigmoid dose-response curve, was widely used in clinical. We use the Schultheiss logit model proposed by Niemierko [12]. We calculated the TCP according to Eq. (1) with the parameters: TCD 50 = 61.59 Gy, γ 50 = 3.38 [13].
The σ was calculated by Eq. (3) TD 50 is the tolerance dose yielding a 50% complication rate in the normal organ. V i is the volume at dose D i . Parameter m and n are speci c dose-response constants [14].

Statistical Analysis
The dose differences were calculated by the absolute value of the minimum value subtracted from the maximum value and were explicit by mean value (minimum value to maximum value).

Results
Targets dose coverage  Fig. 3. The maximum dose discrepancies were observed in marginal zones of PTVs. The dose changes of OARs were also greater in the vicinity of marginal zones and lesser distal to these areas.
We performed the DVHB method to evaluate plan robustness. The average dose difference was shown in Table 3. No obvious differences were found in D 2cc .   Table 4 showed the width of DVH bands of OARs. The △D max of the brain stem and its PRV were 4.34Gy (1.50Gy-11.10Gy) and 6.21Gy (2.40Gy- 10.19Gy  A sample of dose-volume histograms (DVHs) of PTVs, CTVs, and GTVs was shown in Fig. 4. The solid line represented the DVH of the treatment plan, and the 5 dashed lines represented the DVH of U-plans.
As to OARs (Fig. 5), the brain stem (Fig. 5A) and its PRV (Fig. 5B) had widened the DVH envelope, indicated weak robustness due to their locations in the vicinity of PTVs. The spinal cord (Fig. 5C) and its PRV (Fig. 5D) had stronger robustness for lesser distance to targets. Bilateral parotid glands (Fig. 5E,5F) were sensitive to set-up uncertainty for their being partially enclosed PTVs. The D max of bilateral optical nerves (Fig. 5G,5H,5I) and lens (Fig. 5J,5K) varied slightly. Apparent dose differences were seen in optical nerve chiasma.

Tcp And Ntcp Evaluation
We performed TCP modeling analysis to evaluate the dose variation and plan robustness induced by setup uncertainty in NPC radiotherapy. The TCP reduction (△TCP) was the mean absolute value of the minimum value subtracted from the maximum value. For GTVnx and CTVnx, the △TCP value was less than 1% (Fig. 6) We performed NTCP modeling analysis to evaluate the dose variation of OARs (Fig. 7A). The NTCP reduction (△NTCP) was obtained as the mean absolute value of the minimum value subtracted from the maximum value. The NTCP values showed minor variations in OARs, except for the left optical nerve (Fig.  7A) and left parotid gland (Fig. 7B). No signi cant biological dose changes were found in OARs.

Discussion
Plan robustness quanti cation is a viable quantitative way to evaluate treatment plan sensitivity to uncertainties and had been widely used in proton treatment [7]. Yock A.D.'s [5]report reviewed robustness analysis methods and their dosimetric effects, to promote reliable plan evaluation and dose reporting, particularly during clinical trials conducted across institutions and treatment modalities. We aim to adopt the plan robustness quanti cation method to evaluate and visualize the plan sensitivity and robustness of the VMAT plan in NPC radiotherapy. We chose the set-up uncertainty for set-up error was one of the main challenges in NPC photon radiotherapy. 5 perturbed plans were calculated based on actual treatment data acquired from CBCT. The dose differences in perturbed plans were analyzed as representative scenarios.
The mean dose differences of D 98 and D 95 of PTVnx were respectively 3.30 Gy (4.7% ) and 2.02 Gy The maximum difference of D mean of PTVs could reach 1.5 Gy. Improved plan robustness of photon radiotherapy should be taken into consideration.
The physical dose changes could be presented in DVH (Fig. 4). As a consequence, the biological dose changed, which was closely linked to clinical outcomes. The TCP and NTCP evaluations were adopted in this research. The △TCP in GTVnx and CTVnx were respectively 0.4% and 0.3% (Fig. 6). However, △TCP of GTVnd and CTVnd were 0.92 % and 1.3 % respectively. The CTV had the largest mean variation of Loading [MathJax]/jax/output/CommonHTML/jax.js △TCP (2.2%). Under dosage in the targets may result in the likelihood of tumor recurrence [17], for TCP predominately correlates with the minimum dose of tumor [12]. TCP evaluation was a referential method to make dose delivery description. However, randomized control trials were needed to be determined supplementation.
Weak robustnesses and large dose variations were observed in the OARs in the vicinity locations of PTVs. The actual irradiation dose of vicinal OAR may be biased upwards due to the set-up uncertainty. For brain stem and spinal cord, mean dose differences reached 1.34Gy and 2.86 Gy. Previous research reported that brain stem necrosis, MIR-based evidence of injury, or neurologic toxicities were related to photon radiotherapy [18][19][20]. Using conventional fractionation of 1.8-2 Gy/fraction to the full-thickness cord, the estimated risk of myelopathy is < 1% and < 10% at 54 Gy and 61 Gy, respectively [21]. For bilateral optic nerves and chiasm, the mean dose differences were 8.0 Gy, 8.7Gy, and 8.Gy. Optic nerve injury typically results in monocular visual loss, except if it occurs very close to the optic chiasm, where bers looping up from the contralateral medial eye/retina can be affected [22]. There is a shred of strong evidence that evidence radiation tolerance is increased with a reduction in the dose per fraction [23]. In radiotherapy of NPC, the bilateral parotids are often under irradiation. The dose variation of D mean of bilateral parotids reached 4.5 Gy (Left) and 4.1Gy (Right). Salivary dysfunction has been correlated to the mean parotid gland dose, with recovery occurring with time [24]. The gland function reduction increased at radiation doses of 20 ~ 40 Gy, with a severe reduction at > 40 Gy [25,26]. Slight reductions of NTCP were observed in the brainstem, spinal cord, optical nerves. However, the maximum △NTCP in the left parotid gland exceeded 20%, which sharply increased the risk of parotid gland dysfunction. Thus, set-up uncertainty exhibits a potential impact on OARs in the vicinity locations of PTVs.
Plan robustness quali cation was always considered in proton therapy. In this study, we applied the robustness quali cation method in photon radiotherapy, to illustrate its sensitivity to uncertainties. The risk of inaccurate dose delivery has been a concern for there is currently no widely applied standard to quantify and report on plan robustness or the effects of uncertainties [27]. Guerreiro, F. [28] evaluated the robustness against inter-fraction anatomical changes between photon and proton dose distributions and found that daily anatomical changes proved to affect the target coverage of VMAT dose distributions to a higher extent. Strong robustness was needed in precision radiotherapy, especially like dose painting which put forward non-uniform prescribed dose in CTV to escalate the dose to regions of high risk and meanwhile de-escalate the dose of the low-risk region. Recently, The robustness optimization methods had been developed by incorporating uncertainty in plan optimization, for CTV should receive the prescribed dose depended on desired dose distribution and dose fall-off near the target rather than geometric margin [29]. Lowe, M. et al [30] believed robustness optimization was an effective method to reduce dose to normal tissues that would be unnecessarily irradiated with the PTV-margin concept. TCP and NTCP models are widely used in clinical evaluation and maybe a new role in treatment plan optimization in the future. Further studies evaluating the clinical outcome and long-term risk should be addressed. Among the limitation of the study, the perturbed plans were calculated with 5-time set-up errors and evaluated by 33 fractions. The dose difference may be magni ed for the set-up error is systematic and random. We aim to evaluate the sensitivity of VMAT plans to set-up errors by adopting the actual set-up error as speci c scenarios. Further investigations are needed for this case.

Conclusions
VMAT plans had a strong sensitivity to set-up uncertainty in NPC radiotherapy, due to the high degree of modulation. We proposed an effective method to evaluate the plan robustness of VMAT plans. Plan robustness and complexity should be taken into account in photon radiotherapy. The robust optimization may have the potential and could be considered in complex plans with a reliable evaluation of long-term clinical outcomes. The patients gave their informed consent for use of the data for research purposes.

Competing interests
The authors state that they have no competing interests.

Figure 1
Steps in robustness and biological evaluation of volumetric arc radiotherapy (VMAT) of NPC. U1~ U5 represented 5 set-up uncertainties acquired from the rst 5 times daily CBCT. T-plan: Treatment plan; Uplan: Uncertainty plan.     Box plot showed the △TCP of all targets due to set-up uncertainties. The △TCP was the mean reduction of TCP.