Patient characteristics, SBRT doses, and grading of radiation induced brachial plexopathy are compared in Table 2 for both studies. There was a total of 89 patients included in the study with the median age of 72 and 73 for Karolinska University and Indiana University, respectively. 93 tumors were treated in total with 22 patients having metastases.
Dose, fractionation, and volume of the brachial plexus
At Indiana University, the median prescribed treatment dose was 57 Gy in 3-4 fractions and the maximum brachial plexus dose ranged from 6 to 83 Gy (median, 26 Gy) in 3-4 fractions. The Indiana University dataset had 37 brachial plexus maximum point dose (Dmax) values (for 36 patients) that were all included in the model. The paper did not report which patients received 3 or 4 fractions, or volume information, and these are the main limitations of the study (1). Both published datasets (1, 2) used biological conversions with α/β=3 Gy, thus the biological effective dose is denoted as BED3. According to the linear quadratic model (14-15), the 2 Gy per day equivalent EQD2 = 60 Gy Emami brachial plexus limit (5) corresponds to BED3 = 100 Gy. In 3 fractions, LQ equates this to 26 Gy, which also was the median brachial plexus Dmax of the 37 cases, and this was initially used as a cutoff point of risk analysis (1).
The Karolinska group used 45 Gy in 3 fractions for 80% of the cases, therefore that also was the median prescription. One patient was treated with 60 Gy in 10 fractions, six were treated with 56 Gy in 8 fractions, and the rest were in 3-5 fractions. The authors performed analysis with both USC and LQ models and found no major difference between the two for their data, so presented the data in terms of BED3 with the LQ model. Brachial plexus maximum point dose (Dmax) ranged from BED3 = 0.10–524 Gy, which we converted to 3-fraction equivalent dose since the median number of fractions in both studies was 3. The Karolinska dataset presented model parameters for Dmax, in addition to dose to hottest X cc (Dx) for D0.1cc, D1cc and D3cc, but the Indiana dataset only had Dmax. Therefore, the pooled model has no volume information, and consists of maximum point doses only.
Endpoint, Follow-up time, and estimated risk of the endpoint occurring within the follow-up time
Median range of follow up was longer in Karolinska with 30 months (range 6.1-72.2) while Indiana had a median of 13 months (range 1-71). Among the 89 patients included in both studies, 14 of them developed CTCAE grade 2 or higher RIBP, acknowledging the differences among the endpoint definitions in Table 1. Among the 14, the most common complications were grade 2, comprising 7 patients. Only 1 patient from Indiana University was recorded with grade 4 disabling RIBP described as shoulder ache progressing to paresthesia and further worsening to arm and hand wasting. This case corresponded to brachial plexus Dmax of 76 Gy. One patient from Karolinska also noted signs of RIBP 13 months post SBRT further progressing to total paralysis of the arm, but was scored as grade 3 since CTCAE 4.0 is without grade 4 RIBP; LENT-SOMA is a useful point of comparison in this regard as shown in Table 1, because it does include a definition of grade 4.
It is also important to note that in the Karolinska study, 13 patients underwent additional radiotherapy to the lung ipsilateral to the tumor site that is not included in the model in Fig. 1. Out of the 13, 10 of the patients had very low additional brachial plexus dose, Dmax BED3 ≤ 3.1 Gy. The remaining 3 had a prior conventional dose of Dmax BED3 = 90-123 Gy with only 1 patient from this subset developing RIBP. Therefore, for the Karolinska study, 6 out of 7 patients developed RIBP strictly only from the SBRT.
Dose-response model and DVH Risk Map
Given the approximation of the 6 elements needed for a dose-response model (13), and considering their limitations, caveats, and confounding factors as enumerated above and described in the discussion, a pooled dose-response model was created. According to the fitted probit model (17, 18- 20), the dose corresponding to 50% risk of complications was 70.2 Gy (95% CI: 55-116 Gy), and the slope parameter at this dose was 0.49 (95% CI: 0.35-0.74). The probit model and 95% confidence intervals are depicted in Fig. 1 (17-20). Significance was assessed via the Fisher Exact Test (25, 26) split at the median dose of the combined dataset (Dmax=27 Gy), yielding p-value = 0.0035. The 5% and 10% risk levels were 13.7 Gy and 26 Gy, respectively, in 3-4 fractions. Appendix Fig. A2 shows that for this dataset, probit and logistic models are within +/- 1.6% of their average, up to 60 Gy in 3-4 fractions, and diverge from each other above this dose where the data is very sparse.
The connection between dose/volume, fractionation, and incidence of complications for the endpoint of grade 2 or higher brachial plexopathy is summarized in the form of a DVH Risk Map (13) in Fig. 2. This map includes a graph of published dose constraints in the upper portion of the figure, as well as a numerical summary of low- and high-risk constraints in the lower portion of the figure, with the resultant estimates of risk from the pooled model from Fig. 1. Appendix Fig. A1 shows how the 5% and 50% risk levels at 5 years (TD 5/5 and TD 50/5) in the Emami paper (5) were obtained from expert opinion and models in the Burman paper (6). Similarly, risk levels in the DVH Risk Map in Fig. 2 are interpolated from the dose-response model of Fig. 1. A more complete description of the DVH Risk Map may be found for several other organs-at-risk in the literature (27- 29).
The DVH Risk Map in Fig. 2 shows the number of fractions on the x-axis and the raw total physical dose without any BED conversion on the y-axis. Each of the five panels specifies a dose/volume metric including dose for the 50% and 10% volumes, as well as D3cc, D1cc, and Dmax. Published dose constraints from Appendix Table A1 are plotted as blue diamond marks on the map (Fig. 2). These constraints were partitioned into low- and high-risk categories from among the more established limits, represented as the circled selected limits with labels. The red X represents the dose at which a published Adverse Event (AE) occurred, as may be seen in Appendix Table A1. For visualization, a trendline of low- and high-risk are drawn as the dashed green and solid red lines in this map. Although the partitioning is somewhat arbitrary, this is approximately analogous to the TD5/5 and TD 50/5 Emami limits for conventional fractionation, but now customized to the published limits in a more useful clinical range of practice. Based on the pooled dataset, as may be seen from the tabular portion of Fig. 2, the low-risk trend of brachial plexus Dmax in 3-4 fractions is about 10% risk and the high-risk trend is about 15% risk.