α/β ratio: A dose range dependence study

Improved Asymptotic Expansions in High- and Low-Dose Ranges for Generalized Multi-Hit Model of Radiation-Induced Cell Survival

By considering an upper bound on the number of radiation-induced potential lethal damages that can be repaired in a cell, we have proposed the generalized multi-hit (GMH) model with a closed-form solution, which can better fit various radiation-induced cell survival curves. Recent analysis shows that the asymptotic expansions that we gave before can be used to approximate the generalized single-hit single-target (GSHST) model rather than the GMH model. To illustrate the asymptotic trends of radiation-induced cell survival curves, in this study, we improve the asymptotic expansions of the GMH model in low- and high-dose ranges based on the limit formula of the incomplete gamma function in the corresponding dose ranges. When the upper limit of the number of radiation-induced potential lethal damages is one, the improved expansions of the GMH model can be reduced to the previous expansions of the GSHST model, and the improved asymptotic expansions of the GMH model also indicate that the GMH model has the generalized linear-quadratic-linear (LQL) feature. The numerical simulations indicate that the improved asymptotic expansions in high- and low-dose ranges agree well with the non-linear fitting of the GMH model in six kinds of cell lines under the corresponding dose ranges. In addition, we analyze the relative errors of the improved expansions of the GMH model in high- and low-dose ranges to demonstrate the accuracy and effectiveness of the improved expansions. Based on the error analysis, we further give the reasonable ranges of radiation dose applicable to the improved asymptotic expansions of the GMH model.

Treating Glioblastoma Multiforme (GBM) with super hyperfractionated radiation therapy: Implication of temporal dose fractionation optimization including cancer stem cell dynamics

PURPOSE

A previously developed ordinary differential equation (ODE) that models the dynamic interaction and distinct radiosensitivity between cancer stem cells (CSC) and differentiated cancer cells (DCC) was used to explain the definitive treatment failure in Glioblastoma Multiforme (GBM) for conventionally and hypo-fractionated treatments. In this study, optimization of temporal dose modulation based on the ODE equation is performed to explore the feasibility of improving GBM treatment outcome.

METHODS

A non-convex optimization problem with the objective of minimizing the total cancer cell number while maintaining the normal tissue biological effective dose (BEDnormal) at 100 Gy, equivalent to the conventional 2 Gy × 30 dosing scheme was formulated. With specified total number of dose fractions and treatment duration, the optimization was performed using a paired simulated annealing algorithm with fractional doses delivered to the CSC and DCC compartments and time intervals between fractions as variables. The recurrence time, defined as the time point at which the total tumor cell number regrows to 2.8×109 cells, was used to evaluate optimization outcome. Optimization was performed for conventional treatment time frames equivalent to currently and historically utilized fractionation schemes, in which limited improvement in recurrence time delay was observed. The efficacy of a super hyperfractionated approach with a prolonged treatment duration of one year was therefore tested, with both fixed regular and optimized variable time intervals between dose fractions corresponding to total number of fractions equivalent to weekly, bi-weekly, and monthly deliveries (n = 53, 27, 13). Optimization corresponding to BEDnormal of 150 Gy was also obtained to evaluate the possibility in further recurrence delay with dose escalation.

RESULTS

For the super hyperfractionated schedules with dose fraction number equivalent to weekly, bi-weekly, and monthly deliveries, the recurrence time points were found to be 430.5, 423.9, and 413.3 days, respectively, significantly delayed compared with the recurrence time of 250.3 days from conventional fractionation. Results show that optimal outcome was achieved by first delivering infrequent fractions followed by dense once per day fractions in the middle and end of the treatment course, with sparse and low dose treatments in the between. The dose to the CSC compartment was held relatively constant throughout while larger dose fractions to the DCC compartment were observed in the beginning and final fractions that preceded large time intervals. Dose escalation to BEDnormal of 150 Gy was shown capable of further delaying recurrence time to 452 days.

CONCLUSION

The development and utilization of a temporal dose fractionation optimization framework in the context of CSC dynamics have demonstrated that substantial delay in GBM local tumor recurrence could be achieved with a super hyperfractionated treatment approach. Preclinical and clinical studies are needed to validate the efficacy of this novel treatment delivery method.

Generalized Multi-Hit Model of Radiation-Induced Cell Survival with a Closed-Form Solution: An Alternative Method for Determining Isoeffect Doses in Practical Radiotherapy

The standard linear-quadratic (LQ) model is currently the preferred model for describing the ionizing radiation-induced cell survival curves and tissue responses. And the LQ model is also widely used to calculate isoeffect doses for comparing different fractionated schemes in clinical radiotherapy. Despite its ubiquity, because the actual dose-response curve may appear linear at high doses in the semilogarithmic plot, the application of the LQ model is greatly challenged in the high-dose region, while the dose employed in stereotactic body radiotherapy (SBRT) is often in this area. Alternatively, the biophysical models of radiation-induced effects with a linear-quadratic-linear (LQL) characteristic can well fit the dose-survival curve of cells in vitro. However, most of these LQL models are phenomenological and have not fully considered the biophysical mechanism of radiation-induced damage and repair, and the fitting quality decreases in some high-dose ranges. In this work, to provide an alternative model to describe the cell survival curves in high-dose ranges and predict the biologically effective dose (BED) for SBRT, we propose a novel generalized multi-hit model with a closed-form solution by considering an upper bound on the number of lethal damages induced by radiation that can be repaired in a cell. This model has a clear biophysical basis and a simple expression, and also has the LQL characteristic under low- and high-dose approximate conditions. The experimental data fitting indicated that compared to the standard LQ model and our previously generalized target model, the current model can better fit the radiation-induced cell survival curves in the high-dose ranges (P < 0.05). The current model parameters and parameter ratios were determined from the fits in different kinds of cell lines irradiated with various dose rates and linear energy transfer (LET), which indicates that the model parameters significantly depend on the dose rate and LET. Based on the current model, we derived two equivalence formulae for the BED calculations in the low- and high-dose ranges, and then calculated the BED for the clinical data of SBRT from 17 selected studies. The correlation analysis showed that there were significant linear correlations between the BED at isocenter and planning target volume (PTV) edge calculated by this model and the LQ model (R > 0.86, P < 0.001). In conclusion, the generalized multi-hit model proposed in this work can be used as an alternative tool to handle in vitro radiation-induced cell survival curves in high-dose ranges, and calculate the in vivo BED for comparing the dose fractionation schemes in clinical radiotherapy.

Correlation between Biological Effective Dose and Radiation-induced Liver Disease from Hypofractionated Radiotherapy

Background

The prevention of radiation-induced liver disease (RILD) is very significant in ensuring a safe radiation treatment and high quality of life.

Aims and Objectives

The purpose of this study is to investigate the correlation of physical and biological effective dose (BED) metrics with liver toxicity from hypo-fractionated liver radiotherapy.

Materials and Methods

41 hypo-fractionated patients in 2 groups were evaluated for classic radiation-induced liver disease (RILD) and chronic RILD, respectively. Patients were graded for effective toxicity (post-treatment minus pre-treatment) using the Common Terminology Criteria for Adverse Events (CTCAE) v4.0. Physical dose (PD) distributions were converted to BED. The V_10Gy, V_15Gy, V_20Gy, V_25Gy and V_30Gy physical dose-volume metrics were used in the analysis together with their respective BED-converted metrics of V_16.7Gy3, V_30Gy3, V_46.7Gy3, V_66.7Gy3 and V_90Gy3. All levels were normalized to their respective patient normal liver volumes (NLV) and evaluated for correlation to RILD. Results were measured quantitatively using R² regression analysis.

Results

The classic RILD group had median follow-up time of 1.9 months and the average PD-NLV normalized V_10Gy, V_15Gy, V_20Gy, V_25Gy and V_30Gy metrics per grade were plotted against RILD yielding R² correlations of 0.84, 0.72, 0.73, 0.65 and 0.70, respectively while the BED-volume metrics of V_16.7Gy3, V_30Gy3, V_46.7Gy3, V_66.7Gy3 and V_90Gy3 resulted in correlation values of 0.84, 0.74, 0.66, 0.78 and 0.74, respectively. BED compared to PD showed a statistically significant (p=.03) increase in R² for the classic RILD group. Chronic RILD group had median follow-up time of 12.3 months and the average PD-NLV normalized V_10Gy, V_15Gy, V_20Gy, V_25Gy and V_30Gy metrics per grade were plotted against RILD grade yielding R² correlations of 0.48, 0.92, 0.88, 0.90 and 0.99 while the BED-volume metrics of V_16.7Gy3, V_30Gy3, V_46.7Gy3, V_66.7Gy3 and V_90Gy3 resulted in correlation values of 0.43, 0.94, 0.99, 0.21 and 0.00, respectively.

Conclusion

The strong correlations of the V_10Gy and V_15Gy PD-volume metrics as well as the V_16.7Gy3 (BED of V_10Gy) to both classic and chronic RILD imply the appropriateness of the current 15_Gy evaluation level for liver toxicity with hypo-fractionated treatments.

Use of 3D biological effective dose (BED) for optimizing multi-target liver cancer treatments

The purpose is to calculate the composite 3D biological effective dose (BED) distribution in healthy liver, when multiple lesions are treated concurrently with different hypo-fractionated schemes and stereotactic body radiation therapy, and to investigate the potential of biological based plan optimization. Two patients, each having two tumors that were treated sequentially with different treatment plans, were selected. The treatment information of both treatment plans of the patients was used and their dose matrices were exported to an in-house MATLAB software, which was used to calculate the composite BED distribution. The composite BED distributions were used to determine if the healthy liver received BED beyond tolerance. When the dose to the minimum critical volume was less than tolerance, an optimization code was used to derive the scaling factors (ScF) that should be applied to the dose matrix of each plan until the minimum critical volume of healthy liver reaches a BED close to tolerance. It was shown that for each patient, there is a margin for dose escalation regarding the doses to the individual targets. More specifically, the ScFs of the doses range between 5.6 and 99 in the first patient, whereas for the second patient, the ScFs of the optimal doses range between 12.7 and 35.6. The present study indicates that there is a significant margin for dose escalation without increasing the radiation toxicity to the healthy liver. Also, the calculation of the composite BED distribution can provide additional information that may lead to a better assessment of the liver's tolerance to different fractionation schemes and prescribed doses as well as more clinically relevant treatment plan optimization.

A comprehensive model for heat-induced radio-sensitisation

Combined radiotherapy (RT) and hyperthermia (HT) treatments may improve treatment outcome by heat induced radio-sensitisation. We propose an empirical cell survival model (AlphaR model) to describe this multimodality therapy. The model is motivated by the observation that heat induced radio-sensitisation may be explained by a reduction in the DNA damage repair capacity of heated cells. We assume that this repair is only possible up to a threshold level above which survival will decrease exponentially with dose. Experimental cell survival data from two cell lines (HCT116, Cal27) were considered along with that taken from the literature (baby hamster kidney [BHK] and Chinese hamster ovary cells [CHO]) for HT and combined RT-HT. The AlphaR model was used to study the dependence of clonogenic survival on treatment temperature, and thermal dose R2 ≥ 0.95 for all fits). For HT survival curves (0-80 CEM43 at 43.5-57 °C), the number of free fit AlphaR model parameters could be reduced to two. Both parameters increased exponentially with temperature. We derived the relative biological effectiveness (RBE) or HT treatments at different temperatures, to provide an alternative description of thermal dose, based on our AlphaR model. For combined RT-HT, our analysis is restricted to the linear quadratic arm of the model. We show that, for the range used (20-80 CEM43, 0-12 Gy), thermal dose is a valid indicator of heat induced radio-sensitisation, and that the model parameters can be described as a function thereof. Overall, the proposed model provides a flexible framework for describing cell survival curves, and may contribute to better quantification of heat induced radio-sensitisation, and thermal dose in general.

Postoperative hypofractionated stereotactic brain radiation (HSRT) for resected brain metastases: improved local control with higher BED10

INTRODUCTION

HSRT directed to large surgical beds in patients with resected brain metastases improves local control while sparing patients the toxicity associated with whole brain radiation. We review our institutional series to determine factors predictive of local failure.

METHODS

In a total of 39 consecutive patients with brain metastases treated from August 2011 to August 2016, 43 surgical beds were treated with HSRT in three or five fractions. All treatments were completed on a robotic radiosurgery platform using the 6D Skull tracking system. Volumetric MRIs from before and after surgery were used for radiation planning. A 2-mm PTV margin was used around the contoured surgical bed and resection margins; these were reviewed by the radiation oncologist and neurosurgeon. Lower total doses were prescribed based on proximity to critical structures or if prior radiation treatments were given. Local control in this study is defined as no volumetric MRI evidence of recurrence of tumor within the high dose radiation volume. Statistics were calculated using JMP Pro v13.

RESULTS

Of the 43 surgical beds analyzed, 23 were from NSCLC, 5 were from breast, 4 from melanoma, 5 from esophagus, and 1 each from SCLC, sarcoma, colon, renal, rectal, and unknown primary. Ten were treated with three fractions with median dose 24 Gy and 33 were treated with five fractions with median dose 27.5 Gy using an every other day fractionation. There were no reported grade 3 or higher toxicities. Median follow up was 212 days after completion of radiation. 10 (23%) surgical beds developed local failure with a median time to failure of 148 days. All but three patients developed new brain metastases outside of the treated field and were treated with stereotactic radiosurgery, whole brain radiation and/or chemotherapy. Five patients (13%) developed leptomeningeal disease. With a median follow up of 226 days, 30 Gy/5 fx was associated with the best local control (93%) with only 1 local failure. A lower total dose in five fractions (ie 27.5 or 25 Gy) had a local control rate of 70%. For three fraction SBRT, local control was 100% using a dose of 27 Gy in three fractions (follow up was > 600 days) and 71% if 24 Gy in three fractions was used. A higher total biologically equivalent dose (BED₁₀) was statistically significant for improved local control (p = 0.04) with a threshold BED₁₀ ≥ 48 associated with better local control.

CONCLUSIONS

HSRT after surgical resection for brain metastasis is well tolerated and has improved local control with BED₁₀ ≥ 48 (30 Gy/5 fx and 27 Gy/3 fx). Additional study is warranted.

Rescue Effect Inherited in Colony Formation Assays Affects Radiation Response

It is well known that nonirradiated cells can exhibit radiation damage (bystander effect), and recent findings have shown that nonirradiated cells may help protect irradiated cells (rescue effect). These findings call into question the traditional view of radiation response: cells cannot be envisioned as isolated units. Here, we investigated traditional colony formation assays to determine if they also comprise cellular communication affecting the radiation response, using colony formation assays with varying numbers of cells, modulated beam irradiation and media transfer. Our findings showed that surviving fraction gradually increased with increasing number of irradiated cells. Specifically, for DU-145 human prostate cancer cells, surviving fraction increased 1.9-to-4.1-fold after 5-12 Gy irradiation; and for MM576 human melanoma cells, surviving fraction increased 1.9-fold after 5 Gy irradiation. Furthermore, increased surviving fraction was evident after modulated beam irradiation, where irradiated cells could communicate with nonirradiated cells. Media from dense cell culture also increased surviving fraction. The results suggest that traditional colony formation assays comprise unavoidable cellular communication affecting radiation outcome and the shape of the survival curve. We also propose that the increased in-field surviving fraction after modulated beam irradiation is due to the same effect.

Equivalence of cell survival data for radiation dose and thermal dose in ablative treatments: analysis applied to essential tremor thalamotomy by focused ultrasound and gamma knife

Thermal dose and absorbed radiation dose have historically been difficult to compare because different biological mechanisms are at work. Thermal dose denatures proteins and the radiation dose causes DNA damage in order to achieve ablation. The purpose of this paper is to use the proportion of cell survival as a potential common unit by which to measure the biological effect of each procedure. Survival curves for both thermal and radiation doses have been extracted from previously published data for three different cell types. Fits of these curves were used to convert both thermal and radiation dose into the same quantified biological effect: fraction of surviving cells. They have also been used to generate and compare survival profiles from the only indication for which clinical data are available for both focused ultrasound (FUS) thermal ablation and radiation ablation: essential tremor thalamotomy. All cell types could be fitted with coefficients of determination greater than 0.992. As an illustration, survival profiles of clinical thalamotomies performed by radiosurgery and FUS are plotted on a same graph for the same metric: fraction of surviving cells. FUS and Gamma Knife have the potential to be used in combination to deliver a more effective treatment (for example, FUS may be used to debulk the main tumour mass, and radiation to treat the surrounding tumour bed). In this case, a model which compares thermal and radiation treatments is valuable in order to adjust the dose between the two.

Radiosensitivity and relative biological effectiveness based on a generalized target model

By considering both cellular repair effects and indirect effects of radiation, we have generalized the traditional target model, and made it have a linear-quadratic-linear characteristic. To assess the repair capacity-dependent radiosensitivity and relative biological effectiveness (RBE), the generalized target model was used to fit the survival of human normal embryonic lung fibroblast MRC-5 cells in the G0 and G1 phases after various types of radiations. The fitting results indicate that the generalized target model works well in the dose ranges considered. The resulting calculations qualitatively show that the parameter ratio (a/V) in the model could represent the cellular repair capacity. In particular, the significant linear correlations between radiosensitivity/RBE and cellular repair capacity are observed for different slopes of the linear regression curves. These results show that the radiosensitivity and RBE depend on the cellular repair capacity and can be regulated by linear energy transfer. These analyses suggest that the ratio a/V in the generalized target model can also be used for radiation damage assessment in radiotherapy.

Hypofractionated stereotactic radiotherapy for brain metastases from lung cancer : Evaluation of indications and predictors of local control

AIM

To evaluate the efficacy and toxicity of hypofractionated stereotactic radiotherapy (HSRT) for brain metastases (BMs) from lung cancer, and to explore prognostic factors associated with local control (LC) and indication.

PATIENTS AND METHODS

We evaluated patients who were treated with linac-based HSRT for BMs from lung cancer. Lesions treated with stereotactic radiosurgery (SRS) in the same patients during the same periods were analysed and compared with HSRT in terms of LC or toxicity. There were 53 patients with 214 lesions selected for this analysis (HSRT: 76 lesions, SRS: 138 lesions). For HSRT, the median prescribed dose was 35 Gy in 5 fractions.

RESULTS

The 1‑year LC rate was 83.6 % in HSRT; on multivariate analysis, a planning target volume (PTV) of <4 cm(3), biologically effective dose (BED10) of ≥51 Gy, and adenocarcinoma were significantly associated with better LC. Moreover, in PTVs ≥ 4 cm(3), there was a significant difference in LC between BED10 < 51 Gy and ≥ 51 Gy (p = 0.024). On the other hand, in PTVs < 4 cm(3), both HSRT and SRS had good LC with no significant difference (p = 0.195). Radiation necrosis emerged in 5 of 76 lesions (6.6 %) treated with HSRT and 21 of 138 (15.2 %) lesions treated with SRS (p = 0.064).

CONCLUSION

Linac-based HSRT was safe and effective for BMs from lung cancer, and hence might be particularly useful in or near an eloquent area. PTV, BED10, and pathological type were significant prognostic factors. Furthermore, in BMs ≥ 4 cm(3), a dose of BED ≥ 51 Gy should be considered.

Incorporating cancer stem cells in radiation therapy treatment response modeling and the implication in glioblastoma multiforme treatment resistance

PURPOSE

To perform a preliminary exploration with a simplistic mathematical cancer stem cell (CSC) interaction model to determine whether the tumor-intrinsic heterogeneity and dynamic equilibrium between CSCs and differentiated cancer cells (DCCs) can better explain radiation therapy treatment response with a dual-compartment linear-quadratic (DLQ) model.

METHODS AND MATERIALS

The radiosensitivity parameters of CSCs and DCCs for cancer cell lines including glioblastoma multiforme (GBM), non-small cell lung cancer, melanoma, osteosarcoma, and prostate, cervical, and breast cancer were determined by performing robust least-square fitting using the DLQ model on published clonogenic survival data. Fitting performance was compared with the single-compartment LQ (SLQ) and universal survival curve models. The fitting results were then used in an ordinary differential equation describing the kinetics of DCCs and CSCs in response to 2- to 14.3-Gy fractionated treatments. The total dose to achieve tumor control and the fraction size that achieved the least normal biological equivalent dose were calculated.

RESULTS

Smaller cell survival fitting errors were observed using DLQ, with the exception of melanoma, which had a low α/β = 0.16 in SLQ. Ordinary differential equation simulation indicated lower normal tissue biological equivalent dose to achieve the same tumor control with a hypofractionated approach for 4 cell lines for the DLQ model, in contrast to SLQ, which favored 2 Gy per fraction for all cells except melanoma. The DLQ model indicated greater tumor radioresistance than SLQ, but the radioresistance was overcome by hypofractionation, other than the GBM cells, which responded poorly to all fractionations.

CONCLUSION

The distinct radiosensitivity and dynamics between CSCs and DCCs in radiation therapy response could perhaps be one possible explanation for the heterogeneous intertumor response to hypofractionation and in some cases superior outcome from stereotactic ablative radiation therapy. The DLQ model also predicted the remarkable GBM radioresistance, a result that is highly consistent with clinical observations. The radioresistance putatively stemmed from accelerated DCC regrowth that rapidly restored compartmental equilibrium between CSCs and DCCs.

The biological effect of large single doses: a possible role for non-targeted effects in cell inactivation

BACKGROUND AND PURPOSE

Novel radiotherapy techniques increasingly use very large dose fractions. It has been argued that the biological effect of large dose fractions may differ from that of conventional fraction sizes. The purpose was to study the biological effect of large single doses.

MATERIAL AND METHODS

Clonogenic cell survival of MCF7 and MDA-MB-231 cells was determined after direct X-ray irradiation, irradiation of feeder cells, or transfer of conditioned medium (CM). Cell-cycle distributions and the apoptotic sub-G1 fraction were measured by flow cytometry. Cytokines in CM were quantified by a cytokine antibody array. γH2AX foci were detected by immunofluorescence microscopy.

RESULTS

The surviving fraction of MCF7 cells irradiated in vitro with 12 Gy showed an 8.5-fold decrease (95% c.i.: 4.4-16.3; P<0.0001) when the density of irradiated cells was increased from 10 to 50×10(3) cells per flask. Part of this effect was due to a dose-dependent transferrable factor as shown in CM experiments in the dose range 5-15 Gy. While no effect on apoptosis and cell cycle distribution was observed, and no differentially expressed cytokine could be identified, the transferable factor induced prolonged expression of γH2AX DNA repair foci at 1-12 h.

CONCLUSIONS

A dose-dependent non-targeted effect on clonogenic cell survival was found in the dose range 5-15 Gy. The dependence of SF on cell numbers at high doses would represent a "cohort effect" in vivo. These results support the hypothesis that non-targeted effects may contribute to the efficacy of very large dose fractions in radiotherapy.

Modelling of cell killing due to sparsely ionizing radiation in normoxic and hypoxic conditions and an extension to high LET radiation

PURPOSE

An approach for describing cell killing with sparsely ionizing radiation in normoxic and hypoxic conditions based on the initial number of randomly distributed DNA double-strand breaks (DSB) is proposed. An extension of the model to high linear energy transfer (LET) radiation is also presented.

MATERIALS AND METHODS

The model is based on the probabilities that a given DNA giant loop has one DSB or at least two DSB. A linear combination of these two classes of damage gives the mean number of lethal lesions. When coupled with a proper modelling of the spatial distribution of DSB from ion tracks, the formalism can be used to predict cell response to high LET radiation in aerobic conditions.

RESULTS

Survival data for sparsely ionizing radiation of cell lines in normoxic/hypoxic conditions were satisfactorily fitted with the proposed parametrization. It is shown that for dose ranges up to about 10 Gy, the model describes tested experimental survival data as good as the linear-quadratic model does. The high LET extension yields a reasonable agreement with data in aerobic conditions.

CONCLUSIONS

A new survival model has been introduced that is able to describe the most relevant features of cellular dose-response postulating two damage classes.

Hypo-fractionated IMRT for patients with newly diagnosed glioblastoma multiforme: a 6 year single institutional experience

OBJECTIVES

Glioblastoma (GBM) is the most common malignant primary brain tumour in adults. Surgery and radiotherapy constitute the cornerstones for the therapeutic management of GBM. The standard treatment today is maximal surgical resection followed by concomitant chemo-radiation therapy followed by adjuvant TMZ according to Stupp protocol. Despite the progress in neurosurgery, radiotherapy and oncology, the prognosis still results poor. In order to reduce the long time of standard treatment, maintaining or improving the clinical results, in our institute we have investigated the effects of hypo-fractionated radiation therapy for patients with GBM.

PATIENTS AND METHODS

Sixty-seven patients affected by GBM who had previously undergone surgical resection (total, subtotal or biopsy) were enrolled between October 2005 and December 2011 in a single institutional study of hypo-fractionated intensity modulated radiation therapy (IMRT) followed or not by adjuvant chemotherapy with TMZ (6-12 cycles). The most important eligibility criteria were: biopsy-proven GBM, KPS ≥ 60, age ≥ 18 years, no previous brain irradiation, informed consensus. Hypo-fractionated IMRT was delivered to a total dose of 25 Gy in 5 fractions prescribed to 70% isodose. Response to treatment, OS, PFS, toxicity and patterns of recurrence were evaluated, and sex, age, type of surgery, Karnofsky performance status, Recursive Partitioning Analysis (RPA) classification, time between surgery and initiation of radiotherapy were evaluated as potential prognostic factors for survival.

RESULTS

All patients have completed the treatment protocol. Median age was 64.5 years (range 41-82 years) with 31 females (46%) and 36 males (54%). Median KPS at time of treatment was 80. The surgery was gross total in 38 patients and subtotal in 14 patients; 15 patients underwent only biopsy. No grade 3-4 acute or late neurotoxicity was observed. With median follow-up of 14.9 months, the median OS and PFS were 13.4 and 7.9 months, respectively.

CONCLUSIONS

The hypo-fractionated radiation therapy can be used for patients with GBM, resulting in favourable overall survival, low rates of toxicity and satisfying QoL. Future investigations are needed to determine the optimal fractionation for GBM.

Stereotactic body radiation therapy in non-small-cell lung cancer: linking radiobiological modeling and clinical outcome

For patients with peripheral, early-stage non-small-cell lung cancer, it has been found feasible to deliver 5 or fewer fractions of large doses through stereotactic body radiation therapy (SBRT) without causing severe early or late injury and with impressive tumor control. In this review, we employ radiobiological modeling with the linear quadratic formulation to explore the adequacy of various dose schedules used for tumor control in the lung as supported by clinical evidence, the influence of dose distribution and delivery time on local control, and how to decrease the likelihood of severe toxicity following SBRT. Furthermore, the validity of the linear quadratic formalism in the high dose range of SBRT for lung cancer is explored.

Tissue radiation response with maximum Tsallis entropy

The expression of survival factors for radiation damaged cells is currently based on probabilistic assumptions and experimentally fitted for each tumor, radiation, and conditions. Here, we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a cutoff hypothesis, motivated by clinical observations. The obtained expression shows a remarkable agreement with the experimental data found in the literature.

The Hug-Kellerer equation as the universal cell survival curve

The Hug-Kellerer (H-K) equation is one of the earliest proposed radiation cell survival curves. We examine this equation in view of the recent perceived need for a universal cell survival curve which would be applicable to single radiation fractions at high doses. We derive relationships between the three parameters of the H-K equation and the parameters alpha and beta of the linear-quadratic equation. Using these relationships we show how the H-K equation can be used to determine single-fraction doses which are equivalent in theory to the dose in a conventional multi-fraction course of radiation therapy.

Choline PET based dose-painting in prostate cancer--modelling of dose effects

BACKGROUND

Several randomized trials have documented the value of radiation dose escalation in patients with prostate cancer, especially in patients with intermediate risk profile. Up to now dose escalation is usually applied to the whole prostate. IMRT and related techniques currently allow for dose escalation in sub-volumes of the organ. However, the sensitivity of the imaging modality and the fact that small islands of cancer are often dispersed within the whole organ may limit these approaches with regard to a clear clinical benefit. In order to assess potential effects of a dose escalation in certain sub-volumes based on choline PET imaging a mathematical dose-response model was developed.

METHODS

Based on different assumptions for alpha/beta, gamma 50, sensitivity and specificity of choline PET, the influence of the whole prostate and simultaneous integrated boost (SIB) dose on tumor control probability (TCP) was calculated. Based on the given heterogeneity of all potential variables certain representative permutations of the parameters were chosen and, subsequently, the influence on TCP was assessed.

RESULTS

Using schedules with 74 Gy within the whole prostate and a SIB dose of 90 Gy the TCP increase ranged from 23.1% (high detection rate of choline PET, low whole prostate dose, high gamma 50/ASTRO definition for tumor control) to 1.4% TCP gain (low sensitivity of PET, high whole prostate dose, CN + 2 definition for tumor control) or even 0% in selected cases. The corresponding initial TCP values without integrated boost ranged from 67.3% to 100%. According to a large data set of intermediate-risk prostate cancer patients the resulting TCP gains ranged from 22.2% to 10.1% (ASTRO definition) or from 13.2% to 6.0% (CN + 2 definition).

DISCUSSION

Although a simplified mathematical model was employed, the presented model allows for an estimation in how far given schedules are relevant for clinical practice. However, the benefit of a SIB based on choline PET seems less than intuitively expected. Only under the assumption of high detection rates and low initial TCP values the TCP gain has been shown to be relevant.

CONCLUSIONS

Based on the employed assumptions, specific dose escalation to choline PET positive areas within the prostate may increase the local control rates. Due to the lack of exact PET sensitivity and prostate alpha/beta parameter, no firm conclusions can be made. Small variations may completely abrogate the clinical benefit of a SIB based on choline PET imaging.

Radiobiological model comparison of 3D conformal radiotherapy and IMRT plans for the treatment of prostate cancer

The main aim of radiotherapy is to deliver a dose of radiation that is high enough to destroy the tumour cells while at the same time minimising the damage to normal healthy tissues. Clinically, this has been achieved by assigning a prescription dose to the tumour volume and a set of dose constraints on critical structures. Once an optimal treatment plan has been achieved the dosimetry is assessed using the physical parameters of dose and volume. There has been an interest in using radiobiological parameters to evaluate and predict the outcome of a treatment plan in terms of both a tumour control probability (TCP) and a normal tissue complication probability (NTCP). In this study, simple radiobiological models that are available in a commercial treatment planning system were used to compare three dimensional conformal radiotherapy treatments (3D-CRT) and intensity modulated radiotherapy (IMRT) treatments of the prostate. Initially both 3D-CRT and IMRT were planned for 2 Gy/fraction to a total dose of 60 Gy to the prostate. The sensitivity of the TCP and the NTCP to both conventional dose escalation and hypo-fractionation was investigated. The biological responses were calculated using the Källman S-model. The complication free tumour control probability (P+) is generated from the combined NTCP and TCP response values. It has been suggested that the alpha/beta ratio for prostate carcinoma cells may be lower than for most other tumour cell types. The effect of this on the modelled biological response for the different fractionation schedules was also investigated.

Some implications of linear-quadratic-linear radiation dose-response with regard to hypofractionation

Recent technological advances enable radiation therapy to be delivered in a highly conformal manner to targets located almost anywhere in the body. This capability has renewed the clinical interest in hypofractionation wherein the tumor is delivered a few fractions of very large dose per fraction. Extrapolating clinical experience from conventional regimens to fractions of high dose is important to designing hypofractionated treatments. The concept of biologically effective dose (BED) based on the linear-quadratic (LQ) formulation e(-(alphaD+betaD2) is a useful tool for intercomparing conventional fractionations but may be hampered if the value of alpha/beta is dose range dependent and/or when extrapolating to fractions of high dose because the LQ curve bends continuously on the log-linear plot. This does not coincide with what is observed experimentally in many clonogenic cell survival studies at high dose wherein radiation dose-response relationships more closely approximate a straight line. Intercomparison of conventional fractionations with hypofractionated regimens may benefit from BED calculations which instead use a dose range independent linear-quadratic-linear (LQ-L) formulation which better fits the experimental data across a wider range of dose. The dosimetric implications of LQ-L are explored using a simple model which requires only the specification of a dose D(T) at which the LQ curve transitions to final linearity and the log(e) cell kill per Gy in the final linear portion of the survival curve at high dose. It is shown that the line tangent to the LQ curve at transition dose D(T) can often be used to approximate the final slope of the dose response curve. When D(T) = 2alpha/ beta Gy, the line tangent to the LQ curve at D(T) intersects the e(-alphaD) and e(-betaD2) curves at dose alpha/ beta Gy and also closely fits the linear response in the high dose region of some classic in vitro cell survival curves for which the value of alpha/beta is low. It is hypothesized that D(T) will increase as the magnitude of alpha/beta increases. Examples are presented illustrating how to recognize LQ-L behavior in multifraction isoeffect studies of late responses such as spinal cord and lung. When planning hypofractionated regimens involving reactions with low alpha/beta, recognizing LQ-L behavior could be important because the dose-response is likely to transition to final linearity within the contemplated range of hypofractional doses.

The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery

The linear-quadratic (LQ) model is widely used to model the effect of total dose and dose per fraction in conventionally fractionated radiotherapy. Much of the data used to generate the model are obtained in vitro at doses well below those used in radiosurgery. Clinically, the LQ model often underestimates tumor control observed at radiosurgical doses. The underlying mechanisms implied by the LQ model do not reflect the vascular and stromal damage produced at the high doses per fraction encountered in radiosurgery and ignore the impact of radioresistant subpopulations of cells. The appropriate modeling of both tumor control and normal tissue toxicity in radiosurgery requires the application of emerging understanding of molecular-, cellular-, and tissue-level effects of high-dose/fraction-ionizing radiation and the role of cancer stem cells.