Linear-quadratic-linear Research Articles

Obtaining organ-specific radiobiological parameters from clinical data for radiation therapy planning of head and neck cancers

Objective. Different radiation therapy (RT) strategies, e.g. conventional fractionation RT (CFRT), hypofractionation RT (HFRT), stereotactic body RT (SBRT), adaptive RT, and re-irradiation are often used to treat head and neck (HN) cancers. Combining and/or comparing these strategies requires calculating biological effective dose (BED). The purpose of this study is to develop a practical process to estimate organ-specific radiobiologic model parameters that may be used for BED calculations in individualized RT planning for HN cancers. Approach. Clinical dose constraint data for CFRT, HFRT and SBRT for 5 organs at risk (OARs) namely spinal cord, brainstem, brachial plexus, optic pathway, and esophagus obtained from literature were analyzed. These clinical data correspond to a particular endpoint. The linear-quadratic (LQ) and linear-quadratic-linear (LQ-L) models were used to fit these clinical data and extract relevant model parameters (alpha/beta ratio, gamma/alpha, d T and BED) from the iso-effective curve. The dose constraints in terms of equivalent physical dose in 2 Gy-fraction (EQD2) were calculated using the obtained parameters. Main results. The LQ-L and LQ models fitted clinical data well from the CFRT to SBRT with the LQ-L representing a better fit for most of the OARs. The alpha/beta values for LQ-L (LQ) were found to be 2.72 (2.11) Gy, 0.55 (0.30) Gy, 2.82 (2.90) Gy, 6.57 (3.86) Gy, 5.38 (4.71) Gy, and the dose constraint EQD2 were 55.91 (54.90) Gy, 57.35 (56.79) Gy, 57.54 (56.35) Gy, 60.13 (59.72) Gy and 65.66 (64.50) Gy for spinal cord, optic pathway, brainstem, brachial plexus, and esophagus, respectively. Additional two LQ-L parameters d T were 5.24 Gy, 5.09 Gy, 7.00 Gy, 5.23 Gy, and 6.16 Gy, and gamma/alpha were 7.91, 34.02, 8.67, 5.62 and 4.95.Significance. A practical process was developed to extract organ-specific radiobiological model parameters from clinical data. The obtained parameters can be used for biologically based radiation planning such as calculating dose constraints of different fractionation regimens.

Brain Re-Irradiation Robustly Accounting for Previously Delivered Dose.

(1) Background: The STRIDeR (Support Tool for Re-Irradiation Decisions guided by Radiobiology) planning pathway aims to facilitate anatomically appropriate and radiobiologically meaningful re-irradiation (reRT). This work evaluated the STRIDeR pathway for robustness compared to a more conservative manual pathway. (2) Methods: For ten high-grade glioma reRT patient cases, uncertainties were applied and cumulative doses re-summed. Geometric uncertainties of 3, 6 and 9 mm were applied to the background dose, and LQ model robustness was tested using α/β variations (values 1, 2 and 5 Gy) and the linear quadratic linear (LQL) model δ variations (values 0.1 and 0.2). STRIDeR robust optimised plans, incorporating the geometric and α/β uncertainties during optimisation, were also generated. (3) Results: The STRIDeR and manual pathways both achieved clinically acceptable plans in 8/10 cases but with statistically significant improvements in the PTV D98% (p < 0.01) for STRIDeR. Geometric and LQ robustness tests showed comparable robustness within both pathways. STRIDeR plans generated to incorporate uncertainties during optimisation resulted in a superior plan robustness with a minimal impact on PTV dose benefits. (4) Conclusions: Our results indicate that STRIDeR pathway plans achieved a similar robustness to manual pathways with improved PTV doses. Geometric and LQ model uncertainties can be incorporated into the STRIDeR pathway to facilitate robust optimisation.

Radiobiological Meta-Analysis of the Response of Prostate Cancer to Different Fractionations: Evaluation of the Linear-Quadratic Response at Large Doses and the Effect of Risk and ADT.

The purpose of this work was to investigate the response of prostate cancer to different radiotherapy schedules, including hypofractionation, to evaluate potential departures from the linear-quadratic (LQ) response, to obtain the best-fitting parameters for low-(LR), intermediate-(IR), and high-risk (HR) prostate cancer and to investigate the effect of ADT on the radiobiological response. We constructed a dataset of the dose-response containing 87 entries/16,536 patients (35/5181 LR, 32/8146 IR, 20/3209 HR), with doses per fraction ranging from 1.8 to 10 Gy. These data were fit to tumour control probability models based on the LQ model, linear-quadratic-linear (LQL) model, and a modification of the LQ (LQmod) model accounting for increasing radiosensitivity at large doses. Fits were performed with the maximum likelihood expectation methodology, and the Akaike information criterion (AIC) was used to compare the models. The AIC showed that the LQ model was superior to the LQL and LQmod models for all risks, except for IR, where the LQL model outperformed the other models. The analysis showed a low α/β for all risks: 2.0 Gy for LR (95% confidence interval: 1.7-2.3), 3.4 Gy for IR (3.0-4.0), and 2.8 Gy for HR (1.4-4.2). The best fits did not show proliferation for LR and showed moderate proliferation for IR/HR. The addition of ADT was consistent with a suppression of proliferation. In conclusion, the LQ model described the response of prostate cancer better than the alternative models. Only for IR, the LQL model outperformed the LQ model, pointing out a possible saturation of radiation damage with increasing dose. This study confirmed a low α/β for all risks.

Extracting Organ-Specific Radiobiological Model Parameters of Abdominal Organs from Clinical Outcome Data for Biological Radiation Treatment Planning

<h3>Purpose/Objective(s)</h3> It is desirable to consider organ-specific treatment response in a variety of biological radiotherapy (RT) planning scenarios, e.g., adaptive RT with varying daily dose, reirradiation, multi-modality RT, varying fractionation. This study aims to extract organ-specific radiobiological model parameters for selected abdominal organs and to demonstrate their applications in determining OAR dose constraints using biologically effective dose (BED) and equivalent dose in 2Gy fractions (EQD2). <h3>Materials/Methods</h3> Available clinical studies from the literature reporting dose volume constraints for abdominal organs, e.g., duodenum, stomach, small bowel, and rectum, along with the compiled data in available sources such as TG101, QUANTEC, HyTEC, national and institutional trial protocols were analyzed. The data ranging from conventional fractionation RT (CFRT) to stereotactic body RT (SBRT) were analyzed to determine the maximum point doses (MPD) corresponding to no more than 5% grade ≥ 3 toxicity. The endpoints were selected according to toxicity scales (e.g., CTCAE (v3 or v4), RTOG). Iso-effect fittings (e.g., MPD vs. fractional dose) on the data collected for each organ were performed using both the linear quadratic (LQ) and the linear-quadratic-linear (LQL) models to extract the organ-specific radiobiological parameters. The dose constraint MPD in terms of BED and EQD2 for each OAR was calculated using the obtained organ-specific parameters. The use of the obtained MPD constraints was demonstrated in reirradiation planning. <h3>Results</h3> More than 50 studies were screened to find an average of 10 to 20 relevant studies for each OAR. The LQL and LQ models fit the clinical data from CFRT to SBRT reasonably well, although the LQL model showed a better fit compared to the LQ model. The table below shows the obtained LQ and LQL model parameters and the MPD constraints in terms of BED and EQD2 for selected abdominal organs, where χ²/df is the reduced chi-square. Using the data in the table, the MPD in the small bowel for a vaginal tumor case re-irradiated with 4 × 5Gy after one year from the initial RT of 10 × 3Gy was estimated as 50.2 Gy EQD2, below the constraint of 53.1 Gy. <h3>Conclusion</h3> We developed a robust method to successfully extract abdominal organ-specific radiobiological parameters from clinical data. These parameters can be used to convert OAR dose constraints from different RT fractionations/techniques for biologically optimized RT planning.

Tumor Control Probability After Radiosurgery of Brain Metastases With and Without Retreatment

To develop and compare tumor-control probability (TCP) models for single-fraction stereotactic radiosurgery (SRS) for brain metastasis (BMs) with and without retreatment. We developed three different schemas to model TCP of BMs treated with linear accelerator-based SRS. Dose to 99% of each planning target volume (PTV D99) and 6-month local control were fit using linear-quadratic-linear (LQ-L) models based on equivalent-dose conversions in 2 Gy (EQD2). The M1 schema had separate LQ-L TCP models for initial dose (M1-initial) and retreatment dose (M1-retreat), and the M2 schema had an LQ-L model using the sum of 50% of the initial SRS dose plus the retreatment SRS dose. The M1-initial and M1-retreat schema modeled local control after first SRS to 48 lesions (patients=22) and second SRS to 46 lesions (patients=21). The M0 schema included a whole data set of 349 lesions (patients=136) receiving first SRS (no retreatment and M1-initial). LQ-L models fitted the data well (χ2=0.059-0.525 and P=0.999-1.000). For M0 and M1-retreat, the fitted models EQD250 and γ50 parameters were similar. The LQ-L fitted EQD250 was ∼8.0 Gy for M0 and M1-retreat, ∼24 Gy for M1-initial, and ∼19 Gy for M2. The model fitted γ50 was 0.1 Gy for M0, M1-retreat, and M2 and 0.5 for M1-initial. For the PTV D99 of 10 and 20 Gy, the steepest to shallowest dose-response or largest change in TCP, that is, TCP20Gy - TCP10Gy, was observed in M1-initial (0.49) and M2 (0.17). M0 and M1-retreat showed a similar change in TCP of 0.21. The model-fitted parameters predicted the recurrent BMs required a higher threshold dose and had a steeper dose-response for first SRS versus second SRS and M0. Alternatively, the recurrent BMs required ∼2 Gy higher predicted PTV D99 dose for first SRS to achieve the same TCP of 0.75 compared with second SRS and M0. Further investigations on larger patient cohorts are needed for validating our findings in predictive modeling of recurrent BMs.

Volumetric reduction of brain metastases after stereotactic radiotherapy: Prognostic factors and effect on local control.

Few reports include volumetric measurements as endpoints after stereotactic radiotherapy (SRT) despite the importance of such measurements. This study aimed to (1) investigate the impact of the volumetric response (specifically, an over 65% and over 90% volume reduction in brain metastases) at 6months post-SRT on local control and (2) identify the predictive factors for a volumetric response of over 65% and over 90%. This study included 250 unresected brain metastases (>0.3cc) treated with SRT. Doses were stratified according to the biological effective dose (BED). The BED was calculated using four models: linear-quadratic (LQ): α/β=10; LQ: α/β=20; LQ cubic: α/β=12; and LQ linear: α/β=10. The median prescription dose was 30 Gy/3 fractions (BED20, 45). The median follow-up time after SRT was 18.6months (range, 6.4-81.8months). In the multivariate analysis, over 65% volume reduction and over 90% volume reduction were prognostic factors for local control (hazard ratio: 2.370, p=0.011 and hazard ratio: 3.161, p=0.014, respectively). A dose of 80% of the gross tumor volume (GTV) D80 > BED20 58 was a predictive factor for over 65% and over 90% volume reductions (odds ratio: 1.975, p=0.023; odds ratio: 3.204, p < 0.001, respectively). Robust volume reduction of brain metastases at 6months post-SRT can predict local control. GTV D80 in the LQ model: α/β=20 may be warranted for good volume reduction.

A Practical Workflow to Calculate 3D BED Composite Plan Using Organ-Specific Radiobiological Parameters

Biological effective dose (BED) distribution calculation is desirable for combining multiple treatments based on image sets at different times and/or with different fractionations, e.g., re-irradiation. In addition, the composite BED plan needs to be converted back to a physical dose plan in a common fractionation for plan evaluation and/or comparison. The purpose of this work is to develop a practical workflow to composite 3D BED plan and to convert it back to a physical dose plan.The workflow was developed using contouring software. The organ-specific radiobiological parameters (e.g., α/β, γ/α and dt) for different organs at risk (OAR) were obtained by fitting available clinical dose volume constraint data using a linear-quadratic-linear (LQ-L) model and were stored in the software. The BEDs in each voxel for two separate treatments were calculated using the LQ-L model for each OAR. By contour-based deformable image registration (DIR) algorithm in the software, the two images were registered to obtain a 3D composite BED. Using the rearranged LQ-L model in the software extension, the physical dose was calculated for a given fractionation scheme voxel by voxel from the 3D composite BED.The contouring software workflow along with the organ-specific BED parameters was implemented and successfully tested with two head and neck cancer re-irradiation cases. Case I was initially treated with 36 Gy in 6 fractions in 2017 and was re-irradiated with 35 Gy in 5 fractions in 2020. The case II had the first treatment of 70 Gy in 35 fractions in 2008 and the second treatment with 40 Gy in 5 fractions in 2020. The composite BED distributions calculated by the contouring software workflow were converted back to physical dose distributions with 2 Gy per fraction. The total physical doses received by the OARs after second treatments were all within acceptable clinical dose limits, consistent with the fact that no radiation related toxicity was reported for both patients. The obtained organ-specific parameters and the calculation results for these two cases are tabulated below.A practical workflow along with organ-specific radiobiological parameters was developed to generate BED composite plan and to convert it back into physical dose distribution. This study provides an additional tool to evaluate overall dose for each OAR in re-irradiation or iso-toxic adaptive radiation therapy.

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.

Evaluation of indirect damage and damage saturation effects in dose–response curves of hypofractionated radiotherapy of early-stage NSCLC and brain metastases

Background and purposeTo investigate the possible contribution of indirect damage and damage saturation to tumour control obtained with SBRT/SRS treatments for early-stage NSCLC and brain metastases. Methods and materialsWe have constructed a dataset of early-stage NSCLC and brain metastases dose–response. These data were fitted to models based on the linear-quadratic (LQ), the linear-quadratic-linear (LQL), and phenomenological modifications of the LQ-model to account for indirect cell damage. We use the Akaike-Information-Criterion formalism to compare performance, and studied the stability of the results with changes in fitting parameters and perturbations on dose/TCP values. ResultsIn NSCLC, a modified LQ-model with a beta-term increasing with dose yields the best-fits for α/β = 10 Gy. Only the inclusion of very fast accelerated proliferation or low α/β values can eliminate such superiority. In brain, the LQL model yields the best-fits, and the ranking is not affected by variations of fitting parameters or dose/TCP perturbations. ConclusionsFor α/β = 10 Gy, a modified LQ-model with a beta-term increasing with dose provides better fits to NSCLC dose–response curves. For brain metastases, the LQL provides the best fit. This might be interpreted as a hint of indirect damage in NSCLC, and damage saturation in brain metastases. The results for NSCLC are strongly dependent on the value of α/β and may require further investigation, while those for brain seem to be clearly significant. Our results can assist in the design of improved radiotherapy for NSCLC and brain metastases, aiming at avoiding over/under-treatment.

Voxel based evaluation of sequential radiotherapy treatment plans with different dose fractionation schemes.

This study presents a methodology for voxel-based evaluation of two phase sequential radiotherapy treatment plans having conventional dose scheme in the first phase and subsequent hypofractionation dose scheme in the second phase based upon different priority [planning target volume (PTV), clinical target volume (CTV) and organs at risk (OAR)] of display modes. A case of carcinoma prostate was selected for demonstration. Varian Eclipse treatment planning system (TPS) was used for contouring and planning. In the first phase, a dose of 52 Gy in 26 fractions to the PTV and in the second phase, a dose of 19.5 Gy in 3 fractions to the PTV Boost was planned on the same CT data set. Both the plans (Phase 1 and Phase 2) were exported and processed using "Voxel-based radiobiology display (VRb) tool". Plan Sum for Biologically effective dose (BED)-Cube and equivalent dose of 2Gy (EQD2)-Cube was reconstructed using a combination of linear quadratic (LQ) and linear quadratic-linear (LQ-L) radiobiological models. Tumor control probability (TCP) and normal tissue complication probability (NTCP) for different target volumes and organs were also calculated using EQD2-volume histograms of the Plan Sum. An in-house graphical user interface (GUI) is developed to present the qualitative and quantitative evaluation of the multiphase treatment plans with different display modes and dose regimens. The voxel based TCP obtained for the combined target volume was 90.56%. NTCP for the bladder and rectum was calculated from the Plan Sum histograms and found to be 0.33% and ~0.0% respectively. The proposed methodology using the VRb tool offers superior plan evaluation for multiphase sequential radiotherapy treatment plans over the existing methods. PTV, CTV and OAR priority based display modes in VRb tool offers better understanding of radiobiological evaluation of sequential radiotherapy treatment plans.

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.

Fitting the Generalized Target Model to Cell Survival Data of Proton Radiation Reveals Dose-Dependent RBE and Inspires an Alternative Method to Estimate RBE in High-Dose Regions.

The imprecise estimation of the relative biological effectiveness (RBE) of proton radiation has been one of the main challenges for further calculating the biologically effective dose in proton therapy. Since dose levels can greatly influence the proton RBE, the relationship between the two should be clarified first. In addition, since the dose-response curves are usually too complex to readily assess RBE in high-dose regions, a reliable and simple method is needed to predict the RBE of proton radiation accurately in clinically relevant doses. The standard linear-quadratic (LQ) model is widely used to determine the RBE of particles for clinical applications. However, there has been some debate over its use when modeling the cell survival curves in high-dose regions, since those survival curves usually show linear behavior in the semilogarithmic plot. By considering both cellular repair effects and indirect effects of radiation, we have proposed a generalized target model with linear-quadratic linear (LQL) characteristics. For the more accurate evaluation of proton RBE in radiotherapy, here we used this generalized target model to fit the cell survival data in V79 and C3H 10T1/2 cells exposed to proton radiation with different LETs. The fitting results show that the generalized target model works as well as the LQ model in general. Based on the fitting parameters of the generalized target model, the RBE of six given doses DT (RBET) could be calculated in the corresponding cell lines with different LETs. The results show that the RBET gradually decreases with increased dose in both cell types. In addition, inspired by the calculation method of the maximum values of RBE (RBEM) in the low-dose region, a novel method was proposed for estimating the RBE in the high-dose region (RBEH) based on the slope ratio of the dose-response curves in this region. Linear regression analysis indicated a significant linear correlation between the proposed RBEH and the RBET in high-dose regions, which suggests that the current method can be used as an alternative tool, which is both simple and robust, to estimate RBE in high-dose regions.

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 (EQD2LQL). 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 EQD2LQL 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 EQD2LQL 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 EQD2LQL considering RBE changes in the dose distribution.

A Unified Dose Response Relationship to Predict High Dose Fractionation Response in the Lung Cancer Stereotactic Body Radiation Therapy.

Aim:This study is designed to investigate the superiority and applicability of the model among the linear-quadratic (LQ), linear-quadratic-linear (LQ-L) and universal-survival-curve (USC) models by fitting published radiation cell survival data of lung cancer cell lines.Materials and Method:The radiation cell survival data for small cell (SC) and non-small cell (NSC) lung cancer cell lines were obtained from published reports, and were used to determine the LQ and cell survival curve parameters, which ultimately were used in the curve fitting of the LQ, LQ-L and USC models.Results:The results of this study demonstrate that the LQ-L(Dt-mt) model, compared with the LQ and USC models, provides best fit with smooth and gradual transition to the linear portion of the curve at transition dose Dt-mt, where the LQ model loses its validity, and the LQ-L(Dt-2α/β) and USC(Dt-mt) models do not transition smoothly to the linear portion of the survival curve.Conclusion:The LQ-L(Dt-mt) model is able to fit wide variety of cell survival data over a very wide dose range, and retains the strength of the LQ model in the low-dose range.

Isobio software: biological dose distribution and biological dose volume histogram from physical dose conversion using linear-quadratic-linear model.

PurposeTo develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL) model.Material and methodsThe Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR), and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2) was calculated using biological effective dose (BED) based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit).ResultsTwo and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS) in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV) determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT) and 0.240, 0.320, and 0.849 for brachytherapy (BT) in HR-CTV, bladder, and rectum, respectively.ConclusionsThe Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

Advances of radiobiology in stereotactic body radiation therapy

RT can not only give the tumor a high dose of irradiation, but also protect the surrounding normal tissue as much as possible. SBRT is consistent with the general law of the dose-effect of tumor radiation biology, which the high dose radiation will increase the damage to the tumor. Compared to conventional radiation therapy, SBRT has less fractions (1-5), and higher single dose (8-30 Gy). The LQ (Linear-Quadratic) model which applied in the multi-fractions conventional radiation therapy may not evaluate the biological effect accurately in large dose radiation. Some scholars proposed USC (universal survival curve), LQL (linear-quadratic-linear), gLQ (generalized-linear-quadratic) modified models to intent to predict the radiobiology better in SBRT.SBRT has become one of the important methods to treat the tumor in Lung, Live, Spine and other organs. Advances in radiation biology can further explore the clinical application of SBRT, which contributes to improve the therapeutic effect of tumor radiotherapy Key words: Stereotactic body radiation therapy; Radiobiology; Advance

Challenges in radiobiological modeling: can we decide between LQ and LQ-L models based on reviewed clinical NSCLC treatment outcome data?

AimTo study the dose-response of stage I non-small-cell lung cancer (NSCLC) in terms of long-term local tumor control (LC) after conventional and hypofractionated photon radiotherapy, modeled with the linear-quadratic (LQ) and linear-quadratic-linear (LQ-L) approaches and to estimate the clinical α/β ratio within the LQ frame.Material and methodsWe identified studies of curative radiotherapy as single treatment through MedLine search reporting 3-year LC as primary outcome of interest. Logistic models coupled with the biologically effective dose (BED) at isocenter and PTV edge according to both the LQ and LQ-L models with α/β = 10 Gy were fitted. Additionally, α/β was estimated from direct LQ fits.ResultsThirty one studies were included reporting outcome of 2319 patients. The LQ-L fit yielded a significant value of 11.0 ± 5.2 Gy for the dose threshold (Dt) for BED10 at the isocenter. The LQ and LQ-L fits did not differ substantially. Concerning the estimation of α/β, the value obtained from the direct LQ fit for the complete fractionation range was 3.9 [68 % CI: 2.2–9.0] Gy (p > 0.05).ConclusionBoth LQ and LQ-L fits can model local tumor control after conventionally and hypofractionated irradiation and are robust methods for predicting clinical effects. The observed dose-effect for local control in NSCLC is weaker at high doses due to data dispersion. For BED10 values of 100–150 Gy in ≥3 fractions, the differences in isoeffects predicted by both models can be neglected.Electronic supplementary materialThe online version of this article (doi:10.1186/s13014-016-0643-5) contains supplementary material, which is available to authorized users.

Strategy for stochastic dose-rate induced enhanced elimination of malignant tumour without dose escalation.

The efficacy of radiation therapy, a primary modality of cancer treatment, depends in general upon the total radiation dose administered to the tumour during the course of therapy. Nevertheless, the delivered radiation also irradiates normal tissues and dose escalation procedure often increases the elimination of normal tissue as well. In this article, we have developed theoretical frameworks under the premise of linear-quadratic-linear (LQL) model using stochastic differential equation and Jensen's inequality for exploring the possibility of attending to the two therapeutic performance objectives in contraposition-increasing the elimination of prostate tumour cells and enhancing the relative sparing of normal tissue in fractionated radiation therapy, within a prescribed limit of total radiation dose. Our study predicts that stochastic temporal modulation in radiation dose-rate appreciably enhances prostate tumour cell elimination, without needing dose escalation in radiation therapy. However, constant higher dose-rate can also enhance the elimination of tumour cells. In this context, we have shown that the sparing of normal tissue with stochastic dose-rate is considerably more than the sparing of normal tissue with the equivalent constant higher dose-rate. Further, by contrasting the stochastic dose-rate effects under LQL and linear-quadratic (LQ) models, we have also shown that the LQ model over-estimates stochastic dose-rate effect in tumour and under-estimates the stochastic dose-rate effect in normal tissue. Our study indicates the possibility of utilizing stochastic modulation of radiation dose-rate for designing enhanced radiation therapy protocol for cancer.

SU‐E‐T‐712: Study of the Linear‐Quadratic‐Linear and Universal‐Survival‐ Curve Models for Lung SBRT Using BED and EQD2 Concepts

Purpose:Linear‐quadratic‐linear(LQ‐L) and Universal‐Survival‐Curve(USC) models are investigated for the changes in biologically effective dose(BED) and equivalent dose at 2Gy/fraction(EQD2) for SBRT.Method:Survival data were extracted from published reports for 5 small‐cell(SC) and 6 non‐small cell(NSC) lung cancer cell lines. The best‐fit regression and chi‐square fit used to compute α and β of LQ, D0, and n of multitarget(MT) and y of LQ‐L models, and used to calculate BED and EQD2 for lung SBRT.Results:The value of parameters α and β was determined by best‐fit regression for low dose survival data(R2≥0.97) and by interactive‐inspection and chi‐square best‐fit to initial curvature points for LQ model, respectively. D0 and n were calculated by best‐fit regression to final slope points. Mean value of α, α/β, D0 and n with 95%CI was 0.756±0.152Gy‐1, 16.31±7.78Gy, 1.014±0.308Gy and 1.688±0.696, respectively, for SC; and 0.18±0.081Gy‐1, 7.74±5.893Gy, 2.90±1.704Gy and 3.69±3.36, for NSC, respectively. Mean value of α, α/β, D0 and n for lung tumors, averaging parameter values for all cell lines, was 0.442±0.194Gy‐1, 11.63±5.241Gy, 1.28±1.07Gy and 2.78±1.88, respectively. BED and EQD2 for LQ, LQ‐L and USC models calculated for dose levels I‐IX of RTOG0813 protocol were 67.52–121.59Gy and 57.61–104.02Gy, 78.25–132.55Gy and 66.77–113.10Gy, 59.14–94.49Gy and 50.46–80.62Gy, respectively. USC curves closely overlap to survival data. For transition dose Dt=2α/β (α/β&gt;6Gy) LQ‐L curves have significant difference at higher doses than USC and survival data. When Dt(LQ‐L)‐Dt(USC), LQ‐L curves exceptionally close to USC and experimental data. In SBRT doses, BED and EQD2 calculated by LQ and LQ‐L(α/β&gt;6Gy) are higher than that of USC model.Conclusion:USC curves closely match with experimental data. BED and EQD2 for dose levels of RTOG0813 protocol for LQ and LQ‐L(α/β&gt;6Gy) have significant difference than USC values. BED matching for designing SBRT treatment should consider comprehensive calculations to include BED of USC model.

SU‐E‐P‐52: Dose‐Volume Toxicity Analysis of Stereotactic Body Radiation Therapy for Hepatocellular Carcinoma

Purpose:To investigate the relationship between physical and biological effective dose (BED) to liver toxicity for SBRT fractionations.Methods:A total of 16 patients (13–10×3Gy, 2–5×10Gy and 1–3×15Gy were selected. Physical dose distributions were converted to voxel based BED values using the linear‐quadratic (LQ) and linear‐quadratic linear (LQ‐L) models for doses per fraction larger than 6Gy. Patients were graded for effective toxicity (post‐treatment minus pre‐treatment grades) using the RTOG Late Radiation Morbidity Scoring Schema associated with Radiation Induced Liver Disease (RILD). Evaluated physical dose‐volume levels consisted of V10Gy, V15Gy, V20Gy, V25Gy and V30Gy which were then converted to BED values corresponding to V16.7Gy3, V30Gy3, V46.7Gy3, V66.7Gy3 and V90Gy3, respectively. All levels were normalized to their respective patient normal liver volumes (NLV) and evaluated for correlation to RILD. Results were measured quantitatively using R‐squared regression analysis.Results:Mean Dose Tolerable to Normal Liver (MDTNL) against RILD grade resulted in an R‐squared value of 0.0104. NLV‐normalized physical dose linear regression fit of V10Gy, V15Gy, V20Gy, V25Gy and V30Gy against RILD yielded R‐squared values of 0.1041, 0.0895, 0.0698, 0.0398 and 0.0009 while BED levels of V16.7Gy3, V30Gy3, V46.7Gy3, V66.7Gy3 and V90Gy3 resulted in values of 0.0002, 0.0153, 0.0533, 0.0427 and 0.0072, respectively. The average NLV‐normalized V10Gy, V15Gy, V20Gy, V25Gy and V30Gy per grade plotted against RILD grade yielded R‐squared correlations of 0.8092, 0.6362, 0.5899, 0.5846 and 0.0224 while the BED levels of V16.7Gy3, V30Gy3, V46.7Gy3, V66.7Gy3 and V90Gy3 resulted in R‐squared correlations of 0.0003, 0.3831, 0.8476, 0.678 and 0.076, respectively.Conclusion:Regression analysis between physical dose, BED and RILD showed strong correlation for the V30Gy and V46.7Gy3 dose‐levels. Average BED and physical dose per grade both exhibit strong correlations to RILD however, a lack of statistical significance exists due to small patient sample size.