Correlation of clinical outcome, radiobiological modeling of tumor control, normal tissue complication probability in lung cancer patients treated with SBRT using Monte Carlo calculation algorithm

Abstract Purpose/Background We analyzed the predictive value of non‐x‐ray voxel Monte Carlo (XVMC)‐based modeling of tumor control probability (TCP) and normal tissue complication probability (NTCP) in patients treated with stereotactic body radiotherapy (SBRT) using the XVMC dose calculation algorithm. Materials/Methods We conducted an IRB‐approved retrospective analysis in patients with lung tumors treated with XVMC‐based lung SBRT. For TCP, we utilized tumor size‐adjusted biological effective dose (s‐BED) TCP modeling validated in non‐MC dose calculated SBRT to: (1) verify modeling as a function of s‐BED in patients treated with XVMC‐based SBRT; and (2) evaluate the predictive potential of different PTV dosimetric parameters (mean dose, minimum dose, max dose, prescription dose, D95, D98, and D99) for incorporation into the TCP model. Correlation between observed local control and TCPs was assessed by Pearson's correlation coefficient. For NTCP, Lyman NTCP Model was utilized to predict grade 2 pneumonitis and rib fracture. Results Eighty‐four patients with 109 lung tumors were treated with XVMC‐based SBRT to total doses of 40 to 60 Gy in 3 to 5 fractions. Median follow‐up was 17 months. The 2‐year local and local‐regional control rates were 91% and and 78%, respectievly. All estimated TCPs correlated significantly with 2‐year actuarial local control rates (P < 0.05). Significant corelations between TCPs and tumor control rate according to PTV dosimetric parameters were observed. D99 parameterization demonstrated the most robust correlation between observed and predicted tumor control. The incidences of grade 2 pneumonitis and rib fracture vs. predicted were 1% vs. 3% and 10% vs. 13%, respectively. Conclusion Our TCP results using a XVMC‐based dose calculation algorithm are encouraging and yield validation to previously described TCP models using non‐XVMC dose methods. Furthermore, D99 as potential predictive parameter in the TCP model demonstrated better correlation with clinical outcome.

implemented in clinical practice. 17 In this study, we sought to analyze the correlation between clinical outcome and previously described non-MC-based modeling of local TCP and NTCP in patients treated with SBRT using the x-ray voxel MC (XVMC) dose calculation algorithm. Compared to other MC methods, XVMC algorithm in Brainlab iPlan was configured for more accurate dose calculation in heterogeneous tissues through the kernels were allowed to change with the local electron density variations and significantly reducing calculation time by using the multigrid superposition method. [6][7][8] Very useful for patient dose calculation in clinically realistic time. In addition, we evaluated the predictive potential of various PTV dosimetric parameters [mean dose, minimum dose, max dose, prescription dose, and dose to 95% (D95) /98% (D98)/ 99% (D99) of the target volume] after incorporation into the predictive TCP model. Observed local control rates were subsequently compared to those predicted by previously described 2 years TCP modeling as a function of biological effective dose (BED) and tumor size. 17

2.A | Study population and treatment
We conducted an IRB-approved retrospective analysis of clinical outcomes and treatment planning data from patients treated with XVMC-based lung SBRT at our institution from 2013 to 2016. The XVMC was based on the XVMC algorithm implemented in the Brainlab iPlan RT treatment planning system (Version, 4.1.2, Brainlab AG, Feldkirchen, Germany). All treatment plans were calculated on the MeanIP (average intensity projections of 4D-CT) images using XVMC algorithm for heterogeneity corrections with 2.0 × 2.0 × 2.0 mm 3 dose grid sizes, 2% variance (relative standard deviation of the mean), dose to medium and accuracy optimized for MLC modeling, whereas the MLC is modeled with full tongue-and-groove design.
Our study population consisted of patients who underwent imageguided lung SBRT for either T1-T3 lung cancer or metastatic lung tumors from different primary subsites. Treatment schedules included total prescription doses of 40 to 60 Gy delivered in 3 to 5 fractions. Both peripheral and centrally treated lung tumors were included.
Follow-up examination was conducted with regular interval CT scans to assess response to treatment. Eighteen FDG PET scans were performed, when clinically warranted, for patients with followup CT scans which were indicative of possible disease progression.
Local recurrence was defined as disease progression in the treated lung parenchyma based upon imaging and/or histologic confirmation.

2.B | Tumor control probability modeling
For TCP modeling, we utilized the size-adjusted biological effective dose (s-BED) modeling described by Ohri et al. which defines 2 years TCP as an exponential function of dose and assumes a linear inverse relationship between tumor size and BED in patients treated with SBRT using non-MC-based dose calculation. 17 The equation is: where BED10 is the BED calculated using the Linear Quadratic Model with an alpha/beta of 10 Gy, TCD50 is the dose required to achieve 50% tumor control, where k = 31Gy corresponding to TCD50 = 0 Gy, c is a constant (10 Gy/cm) used to define the shape of the curve, and L is tumor diameter in centimeters. This model was chosen as it reflected data from a large multi-institution study set in which 504 tumors treated with hypofractionated radiation therapy.

2.C | TCP model parameterization and evaluation
Due to relatively shorter follow-up interval (median of 17 months),  19 Patients evaluated for rib fracture included a subset population with peripherally treated tumors in which the PTV overlapped the ribs. Predicted toxicity rates were compared to observed clinically and statistically analyzed via the Chi-squared test-two sided. The equation is: Gy for normal lung (DVH for total lung minus ITV, that was v i ), TD50 = 45 Gy, γ 50 = 1.2; the parameter, and a = 1.0. TD50 represents the 50% probability of complication in 5 years after irradiation. For parallel organs such as lung and ribs "a = 1" parameter was based on already validated parameter from a multi-institutional study by Sonke et al.. 19

2.E | Clinical outcome and predictors of recurrence
Local recurrence and local-regional recurrence free survival rates were obtained for each patient. Predictors of local tumor recurrence were evaluated by cox regression analysis and stratified primary site  Table 2. Treatment characteristics are outlined in Table 3.

3.B | Clincal outcomes and predictors of recurrence
Median follow-up time was 17 months (range, 6-39 months). A total of ten local recurrence were identified, and local and regional control rates were 91% and and 78%, respectievly. The 2-year actuarial local control rate was 87%. Median time to local progression was 15 months (range, 10-36 months), and median time to regional progression was 17 months (range, 5-36 months). Patient and tumor predictors of local recurrence are outlined in Table 4. Cox regression analysis revealed larger target volume (P = 0.001) and the absence of COPD comordbidity (P = 0.007) to be significant predictors of local recurrence. Histology, tumor location, and primary vs. metastatic tumor status did not significantly predict for local recurrence.

3.D | NTCP parameterization
Observed normal tissue complication rate did not significantly differ from those estimated by modeling (P > 0.05). The incidence of grade 2 pneumonitis vs. predicted was 1%(n = 1) vs. 3%, and the incidence of rib fracture (n = 21) was observed in 10% (n = 2) vs. predicted  tumor size into the model to more accurately predict observed local control rates but also determined that the probability of tumor control was significantly overestimated without taking into account tumor size. 17 Results of multivariable analysis in our study further reinforced local control rates to be dependent on target volume size (P = 0.001), and the importance of tumor size on treatment outcome after SBRT has been echoed clinically by several other authors. [20][21][22] Although symptomatic COPD statistically correlated to local recurrent rate in this study, the similar finding has not been demonstrated in the literatures. In general patient's COPD status is not a contraindication for SBRT. However, it could be a risk factor for development of radiation-induced pneumonitis (RIP In the paper by Ohri et al., 17  All of TCPs estimated with size-adjusted BED parameterization did significantly correlate with clincal outcome. Among all of the size-adjusted BED parameters, quantitatively TCP generated with D95, D98, and D99 seemed to more accurately predict than the other variables. Conversely, quantitatively minimum PTV dose and max PTV dose seemed to under and over predict TCP, respectively.
We attempted to isolate the predictive potential of one parameter over the others by analyzing the Pearson's correlation coefficient.
TCP generated with D99 demonstrated the highest correlation amongst all the variables. This was in accordance with our initial hypothesis and reflects the need to inocoporate actual dose delivered to the PTV for more robust probability modeling.
Our overall incidence of normal tissue toxicity was low, including one patient with clinically observed grade 2 pneumonitis and two patients with rib fracture. Our estimated complication probablity did not significantly differ from clinically observed rates of toxicity. While this is encouraging, our low incidence of events is a limiting factor and certainly these results must be validated in larger data sets.

4.C | Future directions
Certainly, validation of our predictive modeling experience in larger advanced dose calculation SBRT data sets is necessary to confirm our observations. Subsequently, comparison to alternative predictive models may help generate the optimal predictive model tool. In an effort to improve the therapeutic ratio in patients treated with lung SBRT, refinement of tumor control modeling may help facilitate bridging between modeling and clinical implementation with the end goal of biologically based treatment plan optimization.
In the future, we hope to further evaluate normal tissue complication probability modeling in patients who undergo MC-based lung SBRT looking specifically at both lung parenchymal and rib toxicity.

| CONCLUSION
Despite a relatively shorter follow-up interval, our tumor control probability results using a MC-based dose calculation algorithm are encouraging and yield validation to previously described predictive models using non-MC dose calculation methods. Our results verify TCP modeling for lung SBRT as a function of BED and tumor size.
Furthermore, we present for consideration D99 as another potential predictive parameter in the TCP model for better correlation with clinical outcome. Longer follow-up interval and larger data sets are needed to validate our observations.

CONFLI CT OF INTEREST
The authors have no conflict of interest.