Applicability of the linear-quadratic model to single and fractionated radiotherapy schedules: an experimental study

Volume prediction for large brain metastases after hypofractionated gamma knife radiosurgery through artificial neural network

The effectiveness of single-session gamma knife radiosurgery (GKRS) for small metastatic brain tumors has been proven, but hypofractionated GKRS (hfGKRS) for large brain metastases (BM) from the linear quadratic (LQ) model is uncertain. The purpose of this study was to investigate volume changes large BM after hfGKRS from the LQ model and predict volume changes using artificial neural network (ANN). We retrospectively investigated the clinical findings of 28 patients who underwent hfGKRS with large BM (diameter >3 cm or volume >10 cc). A total of 44 tumors were extracted from 28 patients with features. We randomly divided 30 large brain tumors as training set and 14 large brain tumors as test set. To predict the volume changes after hfGKRS, we used ANN models (single-layer perceptron (SLP) and multi-layer perceptron (MLP)). The volume reduction was 96% after hfGKRS for large BM from the LQ model. ANN model predicted volume changes with 70% and 80% accuracy for SLP and MLP, respectively. Even in large BM, hfGKRS from the LQ model could be a good treatment option. Additionally, the MLP model could predict volume changes with 80% accuracy after hfGKRS for large BM.

Variability of α/β ratios for prostate cancer with the fractionation schedule: caution against using the linear-quadratic model for hypofractionated radiotherapy

BACKGROUND

Prostate cancer (PCa) is known to be suitable for hypofractionated radiotherapy due to the very low α/β ratio (about 1.5-3 Gy). However, several randomized controlled trials have not shown the superiority of hypofractionated radiotherapy over conventionally fractionated radiotherapy. Besides, in vivo and in vitro experimental results show that the linear-quadratic (LQ) model may not be appropriate for hypofractionated radiotherapy, and we guess it may be due to the influence of fractionation schedules on the α/β ratio. Therefore, this study attempted to estimate the α/β ratio in different fractionation schedules and evaluate the applicability of the LQ model in hypofractionated radiotherapy.

METHODS

The maximum likelihood principle in mathematical statistics was used to fit the parameters: α and β values in the tumor control probability (TCP) formula derived from the LQ model. In addition, the fitting results were substituted into the original TCP formula to calculate 5-year biochemical relapse-free survival for further verification.

RESULTS

Information necessary for fitting could be extracted from a total of 23,281 PCa patients. A total of 16,442 PCa patients were grouped according to fractionation schedules. We found that, for patients who received conventionally fractionated radiotherapy, moderately hypofractionated radiotherapy, and stereotactic body radiotherapy, the average α/β ratios were 1.78 Gy (95% CI 1.59-1.98), 3.46 Gy (95% CI 3.27-3.65), and 4.24 Gy (95% CI 4.10-4.39), respectively. Hence, the calculated α/β ratios for PCa tended to become higher when the dose per fraction increased. Among all PCa patients, 14,641 could be grouped according to the risks of PCa in patients receiving radiotherapy with different fractionation schedules. The results showed that as the risk increased, the k (natural logarithm of an effective target cell number) and α values decreased, indicating that the number of effective target cells decreased and the radioresistance increased.

CONCLUSIONS

The LQ model appeared to be inappropriate for high doses per fraction owing to α/β ratios tending to become higher when the dose per fraction increased. Therefore, to convert the conventionally fractionated radiation doses to equivalent high doses per fraction using the standard LQ model, a higher α/β ratio should be used for calculation.

The long-term outcome of CyberKnife-based stereotactic radiotherapy for central skull base meningiomas: a single-center experience

Few reports exist demonstrating the effects of stereotactic radiotherapy (SRT) on the central skull base meningiomas (CSMs). A retrospective analysis of 113 patients was performed. The median age was 62 (IQR 50-72) years old, and 78 patients (69%) were female. Upfront SRT was performed in 41 (36%), where 17 (15%) patients were asymptomatic. The other SRT was for postoperative adjuvant therapy in 32 (28%), and for the recurrent or relapsed tumors in 40 (35%) patients. Previous operation was done in 74 patients (66%). Among the available pathology in 46 patients, 37 (80%) were WHO grade I, 8 (17%) were grade II, and 1 (2%) was grade III. The median prescribed dose covered 95% of the planning target volume was 25 (IQR 21-25) Gy, and the median target volume was 9.5 (IQR 3.9-16.9) cm³. The median progression-free survival (PFS) was 48 (IQR 23-73) months and 84% and 78% were free of tumor progression at 5 and 10 years respectively. The median follow-up was 49 (IQR 28-83) months. PFS was better in grade I than grade II (p = 0.02). No other baseline factors including the history of previous operation were associated with PD or PFS. Adverse events of radiation therapy were radiation-induced optic neuropathy (0.9%), and cerebral edema (4.4%). Asymptomatic cavernous carotid stenosis was found in three (2.7%), five (4.4%) underwent ventriculoperitoneal shunt placement for normal pressure hydrocephalus, and five (4.4%) died. SRT is useful for the management of CSMs with a low rate of adverse events.

Establishment of a New Three-Dimensional Dose Evaluation Method Considering Variable Relative Biological Effectiveness and Dose Fractionation in Proton Therapy Combined with High-Dose-Rate Brachytherapy

Purpose:

The purpose of this study is to evaluate the influence of variable relative biological effectiveness (RBE) of proton beam and dose fractionation has on dose distribution and to establish a new three-dimensional dose evaluation method for proton therapy combined with high-dose-rate (HDR) brachytherapy.

Materials and Methods:

To evaluate the influence of variable RBE and dose fractionation on dose distribution in proton beam therapy, the depth-dose distribution of proton therapy was compared with clinical dose, RBE-weighted dose, and equivalent dose in 2 Gy fractions using a linear-quadratic-linear model (EQD2_LQL). The clinical dose was calculated by multiplying the physical dose by RBE of 1.1. The RBE-weighted dose is a biological dose that takes into account RBE variation calculated by microdosimetric kinetic model implemented in Monte Carlo code. The EQD2_LQL is a biological dose that makes the RBE-weighted dose equivalent to 2 Gy using a linear-quadratic-linear (LQL) model. Finally, we evaluated the three-dimensional dose by taking into account RBE variation and LQL model for proton therapy combined with HDR brachytherapy.

Results:

The RBE-weighted dose increased at the distal of the spread-out Bragg peak (SOBP). With the difference in the dose fractionation taken into account, the EQD2_LQL at the distal of the SOBP increased more than the RBE-weighted dose. In proton therapy combined with HDR brachytherapy, a divergence of 103% or more was observed between the conventional dose estimation method and the dose estimation method we propose.

Conclusions:

Our dose evaluation method can evaluate the EQD2_LQL considering RBE changes in the dose distribution.

Comparison of treatment results between 3- and 2-stage Gamma Knife radiosurgery for large brain metastases: a retrospective multi-institutional study

OBJECTIVE

In order to obtain better local tumor control for large (i.e., > 3 cm in diameter or > 10 cm3 in volume) brain metastases (BMs), 3-stage and 2-stage Gamma Knife surgery (GKS) procedures, rather than a palliative dose of stereotactic radiosurgery, have been proposed. Here, authors conducted a retrospective multi-institutional study to compare treatment results between 3-stage and 2-stage GKS for large BMs.

METHODS

This retrospective multi-institutional study involved 335 patients from 19 Gamma Knife facilities in Japan. Major inclusion criteria were 1) newly diagnosed BMs, 2) largest tumor volume of 10.0-33.5 cm3, 3) cumulative intracranial tumor volume ≤ 50 cm3, 4) no leptomeningeal dissemination, 5) no more than 10 tumors, and 6) Karnofsky Performance Status 70% or better. Prescription doses were restricted to between 9.0 and 11.0 Gy in 3-stage GKS and between 11.8 and 14.2 Gy in 2-stage GKS. The total treatment interval had to be within 6 weeks, with at least 12 days between procedures. There were 114 cases in the 3-stage group and 221 in the 2-stage group. Because of the disproportion in patient numbers and the pre-GKS clinical factors between these two GKS groups, a case-matched study was performed using the propensity score matching method. Ultimately, 212 patients (106 from each group) were selected for the case-matched study. Overall survival, tumor progression, neurological death, and radiation-related adverse events were analyzed.

RESULTS

In the case-matched cohort, post-GKS median survival time tended to be longer in the 3-stage group (15.9 months) than in the 2-stage group (11.7 months), but the difference was not statistically significant (p = 0.65). The cumulative incidences of tumor progression (21.6% vs 16.7% at 1 year, p = 0.31), neurological death (5.1% vs 6.0% at 1 year, p = 0.58), or serious radiation-related adverse events (3.0% vs 4.0% at 1 year, p = 0.49) did not differ significantly.

CONCLUSIONS

This retrospective multi-institutional study showed no differences between 3-stage and 2-stage GKS in terms of overall survival, tumor progression, neurological death, and radiation-related adverse events. Both 3-stage and 2-stage GKS performed according to the aforementioned protocols are good treatment options in selected patients with large BMs.

Comparison of the average surviving fraction model with the integral biologically effective dose model for an optimal irradiation scheme

In this paper, we compare two radiation effect models: the average surviving fraction (ASF) model and the integral biologically effective dose (IBED) model for deriving the optimal irradiation scheme and show the superiority of ASF. Minimizing the effect on an organ at risk (OAR) is important in radiotherapy. The biologically effective dose (BED) model is widely used to estimate the effect on the tumor or on the OAR, for a fixed value of dose. However, this is not always appropriate because the dose is not a single value but is distributed. The IBED and ASF models are proposed under the assumption that the irradiation is distributed. Although the IBED and ASF models are essentially equivalent for deriving the optimal irradiation scheme in the case of uniform distribution, they are not equivalent in the case of non-uniform distribution. We evaluate the differences between them for two types of cancers: high α/β ratio cancer (e.g. lung) and low α/β ratio cancer (e.g. prostate), and for various distributions i.e. various dose-volume histograms. When we adopt the IBED model, the optimal number of fractions for low α/β ratio cancers is reasonable, but for high α/β ratio cancers or for some DVHs it is extremely large. However, for the ASF model, the results keep within the range used in clinical practice for both low and high α/β ratio cancers and for most DVHs. These results indicate that the ASF model is more robust for constructing the optimal irradiation regimen than the IBED model.

[Hypofractionated radiotherapy for glioblastoma: changing the radiation treatment paradigm]

Hypofractionation has the dual advantage of increased cell death with a higher dose per fraction and a reduced effect of accelerated tumor cell repopulation due to a shorter overall treatment time. However, the potential advantage may be offset by increased toxicity in the late-responding neural tissues. Recently, investigators have attempted delivering radical doses of HFRT by escalating the dose in the immediate vicinity of the enhancing tumor and postoperative surgical cavity and reported reasonable outcomes with acceptable toxicity levels. Three different studies of high-dose HFRT have reported on the paradoxical phenomenon of improved survival in patients developing radiation necrosis at the primary tumor site. The toxicity criteria of RTOG and EORTC have defined clinically or radiographically suspected radionecrosis as Grade 4 toxicity. However, most patients diagnosed with radiation necrosis in the above studies remained asymptomatic. Furthermore, the probable association with improved survival would strongly argue against adopting a blind approach for classifying radiation necrosis as Grade 4 toxicity. The data emerging from the above studies is encouraging and strongly argues for further research. However, the majority of these studies are predominantly retrospective or relatively small single-arm prospective series that add little to the overall quality of evidence. Notwithstanding the above limitations, HFRT appears to be a safe and feasible strategy for glioblastoma patients.

The impact of different stereotactic radiation therapy regimens for brain metastases on local control and toxicity

Purpose

Stereotactic radiation therapy (SRT) enables focused, short course, high dose per fraction radiation delivery to brain tumors that are less ideal for single fraction treatment because of size, shape, or close proximity to sensitive structures. We sought to identify optimal SRT treatment regimens for maximizing local control while minimizing morbidity.

Methods and materials

We performed a retrospective review of patients treated with SRT for solid brain metastases using variable dose schedules between 2001 and 2011 at 3 academic hospitals. Endpoints included (1) local control, (2) acute toxicity (Common Toxicity Criteria for Adverse Events v3.0), and (3) symptomatic radionecrosis. Kaplan-Meier and a competing risks methodology were used to estimate the actuarial rate of local failure and assess the association of clinical and treatment covariates with time to local failure.

Results

A total of 156 patients was identified. Common tumor histologies included breast (21%), non-small cell lung (32%), melanoma (22%), small cell lung (9%), and renal cell carcinoma (6%). The majority of lesions were supratentorial (57%). Median target volume was 3.99 mL (range, 0.04-58.42). Median total SRT dose was 25 Gy (range, 12-36), median fractional dose was 5 Gy (range, 2.5-11), and median number of fractions was 5 (range, 2-10). Cumulative incidence of local progression at 3, 6, 12, 18, and 24 months was 11%, 22%, 29%, 34%, and 36%. Total prescription dose was the only factor significantly associated with time to local progression on univariate (P = .02) and multivariable analysis (P = .01, adjusted hazards ratio, 0.87). Five patients experienced seizures within 10 days of SRT and 5 patients developed radionecrosis. All patients with documented radionecrosis received prior radiation to the index lesion.

Conclusions

Our series of SRT for brain metastases found total prescription dose to be the only factor associated with local control. Both acute and long-term toxicity events from SRT were modest.

Radiobiology of hypofractionated stereotactic radiotherapy: what are the optimal fractionation schedules?

In hypofractionated stereotactic radiotherapy (SRT), high doses per fraction are usually used and the dose delivery pattern is different from that of conventional radiation. The daily dose is usually given intermittently over a longer time compared with conventional radiotherapy. During prolonged radiation delivery, sublethal damage repair takes place, leading to the decreased effect of radiation. In in vivo tumors, however, this decrease in effect may be counterbalanced by rapid reoxygenation. Another issue related to hypofractionated SRT is the mathematical model for dose evaluation and conversion. The linear-quadratic (LQ) model and biologically effective dose (BED) have been suggested to be incorrect when used for hypofractionation. The LQ model overestimates the effect of high fractional doses of radiation. BED is particularly incorrect when used for tumor responses in vivo, since it does not take reoxygenation into account. Correction of the errors, estimated at 5-20%, associated with the use of BED is necessary when it is used for SRT. High fractional doses have been reported to exhibit effects against tumor vasculature and enhance host immunity, leading to increased antitumor effects. This may be an interesting topic that should be further investigated. Radioresistance of hypoxic tumor cells is more problematic in hypofractionated SRT, so trials of hypoxia-targeted agents are encouraged in the future. In this review, the radiobiological characteristics of hypofractionated SRT are summarized, and based on the considerations, we would like to recommend 60 Gy in eight fractions delivered three times a week for lung tumors larger than 2 cm in diameter.

Downregulation of MDC1 and 53BP1 by short hairpin RNA enhances radiosensitivity in laryngeal carcinoma cells

DNA double-strand breaks (DSBs) induced by ionizing radiation (IR) are among the most cytotoxic types of DNA damage. The DNA damage response (DDR) may be a reason for the cancer cell resistance to radiotherapy using IR. Identified as critical upstream mediators of the phosphorylation of ataxia telangiectasia-mutated (ATM) pathway, mediator of DNA damage checkpoint 1 (MDC1) and p53-binding proteins 1 (53BP1) may affect the radiosensitivity of tumor cells. In the present study, we generated two HEP-2 cell lines with a stable knockdown of MDC1 or 53BP1 with short hairpin RNA (shRNA), respectively, and investigated the effect of MDC1 and 53BP1 on cell radiosensitivity, cell cycle distribution and the formation of cell foci. Downregulation of the two proteins reduced the number of clonogenic cells that treated with IR. Accumulation of G2/M phase cells was detected after the MDC1 and 53BP1 downregulation. These results indicated that the expression of MDC1 or 53BP1 limited tumor cell sensitivity to radiotherapy and may play an important role in the DNA repair progression. Furthermore, the MDC1 foci was identified and presented in the 53BP1-inhibited cells. By contrast, the 53BP1 foci was absent from the MDC1-inhibited cells. The results confirmed that the recruitment of 53BP1 into the foci occurred in an MDC1-dependent manner.

Track-event theory of cell survival with second-order repair

When fractionation schemes for hypofractionation and stereotactic body radiotherapy are considered, a reliable cell survival model at high dose is needed for calculating doses of similar biological effectiveness. In this work, a simple model for cell survival which is valid also at high dose is developed from Poisson statistics. It is assumed that a cell is killed by an event that is defined by two double-strand breaks on the same or different chromosomes. Two different mechanisms can produce events. A one-track event is always represented by two simultaneous double-strand breaks. A two-track event results in one double-strand break. Therefore, at least two two-track events on the same or different chromosomes are necessary to produce an event. It is assumed that two double-strand breaks can be repaired with a certain repair probability. Both the one-track events and the two-track events are statistically independent. From the stochastic nature of cell killing which is described by the Poisson distribution, the cell survival probability was derived. The model was fitted to experimental data. It was shown that a solution based on Poisson statistics exists for cell survival. It exhibits exponential cell survival at high dose and a finite gradient of cell survival at vanishing dose, which is in agreement with experimental cell studies. The model fits the experimental data as well as the LQ model and is based on two free parameters. It was shown that cell survival can be described with a simple analytical formula on the basis of Poisson statistics. This solution represents in the limit of large dose the typical exponential behavior and predicts cell survival as well as the LQ model.