Patient and treatment characteristics
All MBM-SRS cases treated between 11/2011 and 08/2017 were retrospectively selected. This group consisted of 18 patients with 143 metastases treated in 22 SRS sessions (4–20 metastases/session). After adding the OBM-SRS treatments of the same patients (n = 3), OBM-SRS cases were randomly added from the matched tumor volume and dose range treatment database until 2:1 session split between MBM and OBM was reached. The OBM cohort then consisted of eight patients with 19 brain metastases treated in 11 SRS sessions (1–3 metastases/session). Overall, 23 patients with 162 brain metastases treated in 33 SRS sessions were analyzed. Primary tumor histology was NSCLC (n = 10), MLA (n = 8), BC (n = 4) and RCC (n = 1).
Median single and cumulative PTV/session (GTV + 0–1 mm) were 0.10 cc (0.01–4.64 cc) and 1.77cc (0.17–13.66 cc) for MBM and 0.49cc (0.11–3.58 cc) and 0.83 cc (0.11–4.07 cc) for OBM, respectively. PTV D98% ranged from 16 to 20 Gy (median, OBM = 20 Gy and MBM = 18 Gy) prescribed to the median 70% (59–83%) isodose line. For all cases between one and four fixed cylindrical collimators of 5–15 mm diameter were used depending on size, shape, location and number of metastases. Treatment plan optimization was performed according to best practice guidelines [22, 23], which included GTV mean dose optimization [24] wherever necessary and dedicated minimization of healthy brain volume receiving 3–12 Gy [25] in a trade-off against treatment time. Session treatment times as captured by log files were median 104 min (36–226 min) for MBM and 60 min (23–123 min) for OBM, respectively.
Additional WBRT was given prior to nine sessions (40.9%) for MBM and five sessions (45.4%) for OBM, respectively, yet not within 3 months of SRS. Additional TT/IT [8], chemotherapy and no additional therapy within 30 days of SRS was given for 11, 12 and 10 SRS sessions, respectively (Table 1).
Table 1 Patient and treatment characteristics Tumor-dose-rate calculation
To calculate TDR, the treatment data (system calibration files, treatment planning files including planning CT and beam configurations, and treatment log files including specific beam-on times) was imported into an in-house planning system (eCKP, version 2.1) [21, 26]. The authors then recalculated the accumulative dose for each PTV voxel for every minute over the whole treatment course.
For time span s (in minutes) and voxel v and any time point t (in minutes) during treatment the TDR is defined as:
$$TDR\left(s,v,t\right)=\frac{\textit{ACCDOSE}\left(v,t\right)-\textit{ACCDOSE}\left(v,t-s\right)}{s}$$
(1)
(in Gy/min)where ACCDOSE(v,t) is the accumulative dose of voxel v at time point t. For time span s and each voxel v the maximum TDR is defined as:
$$TDR(s,v)=\mathit{\max }_{s\leq t\leq T}\left(TDR\left(s,v,t\right)\right)$$
(2)
where T is the total treatment time (in minutes). Since it is difficult to assess each voxel separately, the authors further calculated the maximum TDR for a percentage of the PTV (i.e., 50% or 98%). In other words, they calculated the TDR for which 50% or 98% of the voxels reach at least a certain TDR at any time span during treatment. For time span s and PTV percentage p (range, 0–1) the TDR is defined as:
$$TDR\left(s,p\right)=TDR\mathrm{'}(s,\left| PTV\right| *\left(1-p\right))$$
(3)
with TDR′(s,vi) ≤ TDR′(s,vi + 1) and |PTV| is the amount of PTV voxels v. If the TDR is sorted according to its values as demanded by Eq. 3 one can also display the TDR as a tumor-dose-rate histogram for any given time span s. Specific clinical relevant time spans (s = 20, 40, 60, 80, 100, 120 min) [15,16,17,18,19,20] and PTV percentages (p = 0.50, 0.98) were then considered for TDR analysis. For simplicity the authors refer herein to tumor-dose-rate always as TDRs,p in combination with time span s and PTV percentage p of specific brain metastases. For all TDRs,p with time spans s > T they specified:
$$\mathrm{TDR}_{\mathrm{s}>\mathrm{T},\mathrm{p}}=\mathrm{TDR}_{\mathrm{T},\mathrm{p}}$$
(4)
Technical and clinical treatment parameters
The authors analyzed TDRs,p dependence on: (a) treatment time and sub-parameter (treated lesions, beam directions, beams/metastasis and monitor units [MU]), (b) prescription dose and sub-parameter (absolute dose, prescription isodose and maximum dose) and (c) metastasis properties and sub-parameter (total or single metastasis volume and average radiologic depth/beam to metastasis). Furthermore, two parameters were introduced to describe the relation of the selected collimators to each treated metastasis. A volume parameter was specified according to the effective dose sphere of each collimator based on its diameter in the center of the metastasis treated in relation to the PTV and defined wVolume as:
$$w_{\text{Volume}}=\frac{PTV}{\sum _{c}\left(\frac{\pi {d_{c}}^{3}}{6}\right)}$$
(5)
where c is the collimator targeting the PTV with diameter dc (in millimeters). Furthermore, a treatment planning parameter was specified according to the mean number of lesions targeted per collimator for collimators c targeting the specific PTV and defined wCollimator as:
$$w_{\text{Collimator}}=\frac{\sum _{c}\left(|\mathrm{PTV}_{c}|\right)}{|c|}$$
(6)
where |PTVc| is the number of PTVs targeted by collimator c and |c| is the number of collimators used for the PTV. In order to correlate TDRs,p to clinical outcome, TDRs,p combinations were analyzed as described above in relation to the RECIST (Response Evaluation Criteria in Solid Tumors) classifications during first (3 months) and overall follow-up under consideration of clinical parameters potentially influencing local control such as simultaneous TT/IT or chemotherapy, prior WBRT and dose [8, 27, 28].
Follow-up and statistical analysis
All patients received magnetic resonance imaging (MRI) identical to treatment planning according to best practice at 6–8 weeks and 3/6/9/12 months after treatment and every 6 months thereafter [1]. For this work, the final follow-up was performed 04/2019 to capture long-term TDR effects. Local response assessment was performed using RECIST, classified into complete response (CR), partial response (PR), local stable disease (SD) and local progressive disease (PD). Local response assessment included the differentiation of PD and radiation necrosis (RN) according to standard practice [27].
Local control (LC) and overall survival (OS) were estimated using the Kaplan-Meier method with SPSS (v20.0, IBM, Armonk, USA). For modeling dependencies between TDR and plan parameters, Spearman’s rank correlation coefficients (ρ) using SPSS and coefficients of determination (R2) from linear and power regression using Excel (v2007, Microsoft, Seattle, USA) were calculated. Univariate analyses using Cox proportional hazard regression models were performed to investigate the patient disease characteristics and dosimetric parameters as predictors of OS, LC (CR or PR or SD), local tumor response (CR or PR) and RN. For Cox regression censoring was done at last follow-up and for LC, local tumor response and RN also at time of death. Stepwise forward conditional methods were further performed in multivariate analysis incorporating variables that were found to be significant (p ≤ 0.05) in univariate analyses.