Knowledge‐based planning in robotic intracranial stereotactic radiosurgery treatments

Abstract Purpose To develop a knowledge‐based planning (KBP) model that predicts dosimetric indices and facilitates planning in CyberKnife intracranial stereotactic radiosurgery/radiotherapy (SRS/SRT). Methods Forty CyberKnife SRS/SRT plans were retrospectively used to build a linear KBP model which correlated the equivalent radius of the PTV (req_PTV) and the equivalent radius of volume that receives a set of prescription dose (req_Vi, where Vi = V10%, V20% … V120%). To evaluate the model’s predictability, a fourfold cross‐validation was performed for dosimetric indices such as gradient measure (GM) and brain V50%. The accuracy of the prediction was quantified by the mean and the standard deviation of the difference between planned and predicted values, (i.e., ΔGM = GMpred − GMclin and fractional ΔV50% = (V50%pred − V50%clin)/V50%clin) and a coefficient of determination, R2. Then, the KBP model was incorporated into the planning for another 22 clinical cases. The training plans and the KBP test plans were compared in terms of the new conformity index (nCI) as well as the planning efficiency. Results Our KBP model showed desirable predictability. For the 40 training plans, the average prediction error from cross‐validation was only 0.36 ± 0.06 mm for ΔGM, and 0.12 ± 0.08 for ΔV50%. The R2 for the linear fit between req_PTV and req_vi was 0.985 ± 0.019 for isodose volumes ranging from V10% to V120%; particularly, R2 = 0.995 for V50% and R2 = 0.997 for V100%. Compared to the training plans, our KBP test plan nCI was improved from 1.31 ± 0.15 to 1.15 ± 0.08 (P < 0.0001). The efficient automatic generation of the optimization constraints by using our model requested no or little planner’s intervention. Conclusion We demonstrated a linear KBP based on PTV volumes that accurately predicts CyberKnife SRS/SRT planning dosimetric indices and greatly helps achieve superior plan quality and planning efficiency.


| INTRODUCTION
Stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) are advanced and highly precise forms of radiation therapy. They have been clinically used to treat intracranial tumors and functional abnormalities of the brain. [1][2][3][4] In contrast to conventional fractionated radiation therapy; SRS/SRT delivers one or a few fractions of large ablative dose to a relatively smaller target volume with sub-millimeter target localization accuracy. [5][6][7] The normal tissue sparing for the surrounding brain tissues is achieved by a very steep dose falloff outside the target regions. Favorable treatment results for brain tumors, for example, meningioma have been obtained using SRS/ SRT. 4,[8][9][10][11][12][13][14][15] The dedicated machines designed for effective SRS and SRT include Gammaknife, conventional linear accelerator, and Cyber-Knife, which is a compact, image-guided linear accelerator with a robotic manipulator.
Treatment planning system (TPS) of Cyberknife SRS/SRT such as Multiplan (Accuray Inc., Sunnyvale, CA) cooperates optimizes inverse treatment planning with the full function of Cyberknife for the accurate and versatile SRS/ SRT system. Depending on the complexity of the patient case, however, planning can be very time-consuming. 16 Also, the knowledge and experience of the planner in this complex technology is essential for the quality of treatment planning. 17 The variation in Cyberknife manual planning between institutions and planners is a potential issue in terms of a consistent and high treatment quality of SRS/SRT. According to a recent review article, 18  This study evaluates a KBP model for CyberKnife SRS/SRT treatments. We demonstrate a rigorous method to derive the "empirical values" that meets the clinic-specific needs for different clinical settings and plan constraints. Our model predicts dosimetric indices which facilitate the automatic generation of shell constraints for isodose tuning and yield a highly efficient automated planning process.
Here, we aim to extend KBP's clinical benefit to CyberKnife intracranial patients. or overlapping with brainstem. One of the seven patients had right cochlear within 1cm. In the other 33 plans, PTV was more than 5cm away from critical organs at risk (OARs) ( Table 1).

| MATERIALS AND METHODS
All the plans were created with Accuray TPS Multiplan version 4.6.1 using sequential optimization. Per our clinical practice, one to two fixed circular collimators were used according to the TPS con-

2.A | Univariate regressions
A linear model using univariate regression was built for the 40 training plans. The coefficients of determinants, R 2 , were used as a measure of goodness of fit. The model correlated the equivalent radius of the PTVs (r eq_PTV ) and the equivalent radius of volume receiving a set of percentage of the prescription dose (r eq_Vi , where V i = V 10% , where α and β referred to the slope and offset of the fitted line, and r eq_vi and r eq_PTV are the radius of a sphere with geometric volume equals of V i and PTV, respectively. Once α and β are obtained from the model, various dose volumes can be predicted for a given PTV volume.

2.B | Model Validation and Prediction evaluation
The plan quality metrics such as conformity index (CI) and gradient measure (GM) are commonly used to evaluate intracranial stereotactic radiotherapy plans. GM is defined as.
The new conformity index (nCI) used in this study is defined as.
where TV = tumor volume (cc), TV RX = tumor volume receiving prescription dose (cc), and = V RX prescription isodose volume (cc). The brain volume receiving 50% of the prescription dose was also analyzed to investigate the model. To evaluate the predication accuracy of the model, the 40 plans were evaluated as one group first. Then the fourfold cross-validation was applied as following: the 40 plans were randomly assigned to four groups, each with ten plans. In turns, three of the groups were used to build the model and the validation was performed using the rest one group. The accuracy of our model prediction was quantified by the mean and the standard deviation of the difference between actual clinical and model predicted values, that is, GM = GM pred -GM clin and V 50% =V 50%pred -V 50%clin . For the latter, due to the large spread of the absolute PTV volumes, the fractional brain difference of V 50% was used instead and therefore fractional brain 2.C | Clinical application of the model were compared here for target coverage and normal tissue sparing analysis. The unpaired t test with Welch's correction was also used.

3.A | The univariate regression results
For the 40 training plans, the R 2 for the linear fit between r eq_PTV and r eq_vi was 0.985 AE 0.019 for isodose volumes ranging from V 10% to V 120% (Table 3); particularly, for V 50% R 2 = 0.995 and for V 100% R 2 = 0.997 (Fig. 1).

3.B | Prediction accuracy
For the 40 training plans, the mean absolute error of predicted vs actual clinical GM was 0.38 AE 0.25 mm (Fig. 2). For V 50% predication, the mean absolute error of fractional brain V 50% was 0.12 AE 0.08 (Fig. 3). No volume dependence was observed in both GM and fractional brain V 50% prediction.
As to the prediction accuracy analysis using the fourfold crossvalidation method, the results were very similar to the above: the average absolute prediction error for GM was 0.39 AE 0.23 mm, and for fractional brain V 50% was 0.12 AE 0.08.  However, our KBP model for Cyberknife agree with other published KBP models for other modalities in terms of achieving consistent and improved plan quality with higher efficiency.

3.C | Clinical application of KBP model
Our method mainly focuses on PTV coverage and conformity, since not many OARs are usually involved in intracranial SRS/SRT.
Although no OAR data were used for the model generation, our modeled linear regression is not only limited to the patients with simple geometry where no OAR is a concern. As highlighted in We believe that our method helps improve planning efficiency and plan quality in different scenarios. For the cases with close OAR-PTV proximity, using our model parameters for the shell constraints saves planner's time by quickly achieving acceptable PTV coverage.
3. a) the predicted vs. the actual clinical brain V 50% , b) the fractional brain V 50% prediction error vs. the PTV volume, the mean and the standard deviation for the absolute fractional brain V 50% error: 0.12 and 0.08. Due to the large spread of volumes, the x axis was plotted on a log scale for the better illustration. Consequently, it becomes more straightforward for the planner to move on to the fine-tuning the plan in regards to the OAR constraints, which is likely to yield a more desirable OAR sparing. For the cases with no OARs for optimization, our model helps achieve consistent plan quality. There may be a great potential of our KBP model to be directly adopted in other institutions. Here, we provide our model parameters (Table 3) for the reference purpose to the readers who are interested in using this model. On the other hand, the readers are encouraged to fit their own model based on their own training plans. In addition, our methodology is also applicable to other modalities such as Gamma-Knife or Linac-based stereotactic treatments and to other body sites.
Our future work also includes the investigation of the model parameters variations between institutions, modalities, and body sites.

A U T H O R C O N T R I B U T I O N S T A T E M E N T
Suhong Yu was involved in conceptualization, methodology, software, data curation, and draft preparation. Huijun Xu was involved in writing and revising. Yin Zhang was involved in draft preparation.
Xin Zhang was involved in data collection. Michael Dyer, Minh Tam Truong, and, Ariel Hirsh were involved in reviewing and editing.
Heming Zhen was involved in software, methodology, and reviewing and editing.