Universal Survival Curve Models Research Articles

Development of a tumor control probability model for boron neutron capture therapy of head and neck cancer.

The tumor control probability (TCP) model has been used for estimating the response of the radiation (photon) therapy for a given treatment dose (distribution). In Taiwan, boron neutron capture therapy (BNCT) is still at the stage of the clinical trials without standard dose prescription. In this study, universal survival curve (USC) model was selected as the TCP model for BNCT. The tumor response and dose distribution from protocol I of the clinical trial of the recurrent head and neck (H&N) cancer conducted by Taipei Veterans General Hospital and National Tsing Hua University were used to verify the TCP model established in this study. The results showed that, using the USC model as a biological model of dose conversion, the TCP calculated by the generalized Equivalent Uniform Dose (gEUD)-based TCP model can be used to well correlate the relationship between the tumor response and dose distribution of the patients of recurrent H&N cancer. The result shows that 25% and 60% of TCP correspond to partial response and complete response of H&N cancer, respectively. This study also indicated that, when BNCT was used to treat recurrent H&N cancer, the minimum dose was an important factor on the efficacy of the treatment. Minimum dose of 18 Gy-w corresponds to at least 60% of TCP.

Radiobiological evaluation of organs at risk for electronic high-dose-rate brachytherapy in uveal melanoma: a radiobiological modeling study.

PurposeThe objective of this study was to examine feasibility of single- or hypo-fraction of high-dose-rate (HDR) electronic brachytherapy (eBT) in uveal melanoma treatment.Material and methodsBiologically effective doses (BED) of organs at risk (OARs) were compared to those of iodine-125-based eye plaque low-dose-rate brachytherapy (125I LDR-BT) with vitreous replacement (VR). Single- or hypo-fractionated equivalent physical doses (SFEDs or HFEDs) for tumor were calculated from tumor BED of 125I LDR-BT using linear-quadratic (LQ) and universal survival curve (USC) models. BED OARs doses to retina opposite the implant, macula, optic disc, and lens were calculated and compared among SFED, HFED, and 125I LDR-BT. Electronic BT of 50 kVp was considered assuming dose fall-off as clinically equivalent to 125I LDR-BT. All OARs BEDs were analyzed with and without silicone oil VR.ResultsFor a single-fraction incorporating VR, the median/interquartile range of LQ (USC)-based BED doses of the retina opposite the implant, macula, optic disc, and lens were 16%/1.2% (33%/4%), 35%/19.5% (64%/17.7%), 37%/19% (75%/17.8%), and 27%/7.9% (68%/23.2%) of those for 125I LDR-BT, respectively. SFED tumor values were 29.8/0.2 Gy and 51.7/0.5 Gy when using LQ and USC models, respectively, which could be delivered within 1 hour. SFED can be delivered within 1 hour using a high-dose-rate eBT. Even four-fraction delivery of HFED without VR resulted in higher OARs doses in the macula, optic disc, and lens (135 ~ 159%) than when using 125I LDR-BT technique. A maximum p-value of 0.005 was observed for these distributions.ConclusionsThe simulation of single-fraction eBT, including vitreous replacement, resulted in significantly reduced OARs doses (16 ~ 75%) of that achieved with 125I LDR-BT.

Revisiting the formalism of equivalent uniform dose based on the linear-quadratic and universal survival curve models in high-dose stereotactic body radiotherapy

PurposeTo examine the equivalent uniform dose (EUD) formalism using the universal survival curve (USC) applicable to high-dose stereotactic body radiotherapy (SBRT).Materials and methodsFor nine non-small-cell carcinoma cell (NSCLC) lines, the linear-quadratic (LQ) and USC models were used to calculate the EUD of a set of hypothetical two-compartment tumor dose–volume histogram (DVH) models. The dose was varied by ±5%, ±10%, and ±20% about the prescription dose (60 Gy/3 fractions) to the first compartment, with fraction volume varying from 1% and 5% to 30%. Clinical DVHs of 21 SBRT treatments of NSCLC prescribed to the 70–83% isodose lines were also considered. The EUD of non-standard SBRT dose fractionation (EUDSBRT) was further converted to standard fractionation of 2 Gy (EUDCFRT) using the LQ and USC models to facilitate comparisons between different SBRT dose fractionations. Tumor control probability (TCP) was then estimated from the LQ- and USC-EUDCFRT.ResultsFor non-standard SBRT fractionation, the deviation of the USC- from the LQ-EUDSBRT is largely limited to 5% in the presence of dose variation up to ±20% to fractional tumor volume up to 30% in all NSCLC cell lines. Linear regression with zero constant yielded USC-EUDSBRT = 0.96 × LQ-EUDSBRT (r2 = 0.99) for the clinical DVHs. Converting EUDSBRT into standard 2‑Gy fractions by the LQ formalism produced significantly larger EUDCFRT than the USC formalism, particularly for low alpha /beta ratios and large fraction dose. Simplified two-compartment DVH models illustrated that both the LQ- and USC-EUDCFRT values were sensitive to cold spot below the prescription dose with little volume dependence. Their deviations were almost constant for up to 30% dose increase above the prescription. Linear regression with zero constant yielded USC-EUDCFRT = 1.56 × LQ-EUDCFRT (r2 = 0.99) for the clinical DVHs. The clinical LQ-EUDCFRT resulted in median TCP of almost 100% vs. 93.8% with USC-EUDCFRT.ConclusionA uniform formalism of EUD should be defined among the SBRT community in order to apply it as a single metric for dose reporting and dose–response modeling in high-dose-gradient SBRT because its value depends on the underlying cell survival model and the model parameters. Further investigations of the optimal formalism to derive the EUD through clinical correlations are warranted.

Optimization of the accelerated partial breast brachytherapy fractionation considering radiation effect on planning target and organs at risk

The same fractionation scheme of accelerated partial breast irradiation (APBI) with brachytherapy is usually applied to APBI patients without considering the radiaton effect on the planning target and organs at risk (OARs) for an individual patient. The purpose of this study is to report the results of optimization of the fractionation scheme by evaluating the radiation effect on target and OARs with a modified linear-quadratic model, universal survival curve (USC), based on dose-volume histograms (DVHs). Ten breast patients treated with multilumen balloon brachytherapy were selected. The minimum skin and chest wall/rib (CW/rib) spacing ranged from 2.5 to 14.3 mm and from 0.5 to 25.0 mm, respectively. The USC model parameters were set as: (1) breast:α = 0.3, β = 0.05; (2) skin: acute reaction α = 0.101, β = 0.009; late reaction α = 0.064, β = 0.029; (3) CW/rib: α = 0.3, β = 0.12. Boundary dose Dt was 6 Gy for both target and OARs. The relation between radiation effects on the target (ET) and OARs (EOAR) were plotted for fraction numbers (N) from 1 to 20. If ET is set at a certain value, the fractionation that results in a minimum EOAR value corresponds to the optimal fractionation. The results show that the optimal fractionation is different for different OAR damage effects. For most of the patients, N = 2 is best for minimizing skin acute reactions while N = 20 is best for minimizing skin late reactions. N varies from 3 to 20 among patients for minimizing CW/rib toxicity. The determined unique optimal N for treatment delivery was found to vary from 1 to 20 among these 10 patients resulted from balancing the different damage effects considering the spatial dose for a given patient geometry. Optimal fractionation can be achieved for an individual patient by evaluating the radiation effect on tumor and OARs with the USC model based on the patient specific DVHs with APBI brachytherapy.

Comparison of Three Radiobiological Models in Stereotactic Body Radiotherapy for Non-Small Cell Lung Cancer.

Objective: The applicability of the linear quadratic (LQ) model to local control (LC) modeling after hypofractionated radiotherapy to treat lung cancer is highly debated. To date, the differences in predicted outcomes between the LQ model and other radiobiological models, which are characterized by additional dose modification beyond a certain transitional dose (dT), have not been well established. This study aims to compare the outcomes predicted by the LQ model with those predicted by two other radiobiological models in stereotactic body radiotherapy (SBRT) for non-small cell lung cancer (NSCLC).Methods: Computer tomography (CT) simulation data sets for 20 patients diagnosed with stage Ⅰ primary NSCLC were included in this study. Three radiobiological models, including the LQ, the universal survival curve (USC) and the modified linear quadratic and linear (mLQL) model were employed to predict the tumor control probability (TCP) data. First, the dT values for the USC and mLQL models were determined. Then, the biologically effective dose (BED) and the predicted TCP values from the LQ model were compared with those calculated from the USC and mLQL models.Results: The dT values from the USC model were 29.6 Gy, 33.8 Gy and 44.5 Gy, whereas the values were 90.2 Gy, 84.0 Gy and 57.3 Gy for the mLQL model for 1-year, 2-year and 3-year TCP prediction. The remarkable higher dT values obtained from the mLQL model revealed the same dose-response relationship as the LQ model in the low- and high-dose ranges. We also found that TCP prediction from the LQ and USC models differed by less than 3%, although the BED values for the two models were significantly different.Conclusion: Radiobiological analysis reveals small differences between the models and suggested that the LQ model is applicable for modeling LC using SBRT to treat lung cancer, even when an extremely high fractional dose is used.

Tumor Control Probability Analysis for Single-Fraction Carbon-Ion Radiation Therapy of Early-Stage Non-small Cell Lung Cancer

To investigate the suitability of the linear-quadratic (LQ) and universal survival curve (USC) models in describing the 3-year tumor control probability data of patients with stage I non-small cell lung cancer treated with carbon-ion radiation therapy. Carbon-ion radiation therapy was given at a total dose of 59.4 to 95.4Gy (relative biological effectiveness [RBE]) in 18 fractions, at 72Gy[RBE] in 9 fractions, at 52.8 to 60Gy[RBE] in 4 fractions, and at 28 to 50Gy[RBE] in a single fraction. A meta-analysis of published clinical data from 394 patients presenting with early-stage non-small cell lung cancer was conducted. Tumor control probability modeling based on the LQ and USC models was performed by simultaneously fitting the clinical data obtained from the different fractionation schedules while considering several spread-out Bragg peak (SOBP) sizes. Radiobiological parameters were derived from the fit. On the basis of the results, a novel SOBP was created for the single-fraction regimen that was optimized with respect to the USC model and aimed at achieving a 95% local control. The USC model gave a better fit to the 3-year local control data than the LQ modeldid. The fit using various SOBP sizes yielded transition doses between 5.6 and 7.0Gy. The results also revealed α/β ratios between 7.4 and 9.1Gy for the LQ model and between 7.4 and 9.4Gy for the USC model. The USC model provided a better estimate of the local control rate for the single-fraction course. For the schemes with a greater number of fractions, the local control rate estimates from the LQ and USC models were comparable. A USC-based SOBP design was then created for the single-fraction schedule. The updated design resulted in a flatter RBE profile compared with the conventional SOBP design. It also gave a better clinical dose prediction to optimize the tumor control rate.

SU‐F‐T‐02: Estimation of Radiobiological Doses (BED and EQD2) of Single Fraction Electronic Brachytherapy That Equivalent to I‐125 Eye Plaque: By Using Linear‐Quadratic and Universal Survival Curve Models

Purpose:To test the radiobiological impact of hypofractionated choroidal melanoma brachytherapy, we calculated single fraction equivalent doses (SFED) of the tumor that equivalent to 85 Gy of I125‐BT for 20 patients. Corresponding organs‐at‐risks (OARs) doses were estimated.Methods:Twenty patients treated with I125‐BT were retrospectively examined. The tumor SFED values were calculated from tumor BED using a conventional linear‐quadratic (L‐Q) model and an universal survival curve (USC). The opposite retina (α/β = 2.58), macula (2.58), optic disc (1.75), and lens (1.2) were examined. The % doses of OARs over tumor doses were assumed to be the same as for a single fraction delivery. The OAR SFED values were converted into BED and equivalent dose in 2 Gy fraction (EQD2) by using both L‐Q and USC models, then compared to I125‐BT.Results:The USC‐based BED and EQD2 doses of the macula, optic disc, and the lens were on average 118 ± 46% (p < 0.0527), 126 ± 43% (p < 0.0354), and 112 ± 32% (p < 0.0265) higher than those of I125‐BT, respectively. The BED and EQD2 doses of the opposite retina were 52 ± 9% lower than I125‐BT. The tumor SFED values were 25.2 ± 3.3 Gy and 29.1 ± 2.5 Gy when using USC and LQ models which can be delivered within 1 hour. All BED and EQD2 values using L‐Q model were significantly larger when compared to the USC model (p < 0.0274) due to its large single fraction size (> 14 Gy).Conclusion:The estimated single fraction doses were feasible to be delivered within 1 hour using a high dose rate source such as electronic brachytherapy (eBT). However, the estimated OAR doses using eBT were 112 ∼ 118% higher than when using the I125‐BT technique. Continued exploration of alternative dose rate or fractionation schedules should be followed.

SU‐C‐BRA‐07: Virtual Bronchoscopy‐Guided IMRT Planning for Mapping and Avoiding Radiation Injury to the Airway Tree in Lung SAbR

Purpose:Post‐treatment radiation injury to central and peripheral airways is a potentially important, yet under‐investigated determinant of toxicity in lung stereotactic ablative radiotherapy (SAbR). We integrate virtual bronchoscopy technology into the radiotherapy planning process to spatially map and quantify the radiosensitivity of bronchial segments, and propose novel IMRT planning that limits airway dose through non‐isotropic intermediate‐ and low‐dose spillage.Methods:Pre‐ and ∼8.5 months post‐SAbR diagnostic‐quality CT scans were retrospectively collected from six NSCLC patients (50–60Gy in 3–5 fractions). From each scan, ∼5 branching levels of the bronchial tree were segmented using LungPoint, a virtual bronchoscopic navigation system. The pre‐SAbR CT and the segmented bronchial tree were imported into the Eclipse treatment planning system and deformably registered to the planning CT. The five‐fraction equivalent dose from the clinically‐delivered plan was calculated for each segment using the Universal Survival Curve model. The pre‐ and post‐SAbR CTs were used to evaluate radiation‐induced segmental collapse. Two of six patients exhibited significant segmental collapse with associated atelectasis and fibrosis, and were re‐planned using IMRT.Results:Multivariate stepwise logistic regression over six patients (81 segments) showed that D0.01cc (minimum point dose within the 0.01cc receiving highest dose) was a significant independent factor associated with collapse (odds‐ratio=1.17, p=0.010). The D0.01cc threshold for collapse was 57Gy, above which, collapse rate was 45%. In the two patients exhibiting segmental collapse, 22 out of 32 segments showed D0.01cc >57Gy. IMRT re‐planning reduced D0.01cc below 57Gy in 15 of the 22 segments (68%) while simultaneously achieving the original clinical plan objectives for PTV coverage and OAR‐sparing.Conclusion:Our results indicate that the administration of lung SAbR can Result in significant injury to bronchial segments, potentially impairing post‐SAbR lung function. To our knowledge, this is the first investigation of functional avoidance based on mapping and minimizing dose to individual bronchial segments.The presenting author receives research funding from Varian Medical Systems, Elekta, and VisionRT.

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>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>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>6Gy) have significant difference than USC values. BED matching for designing SBRT treatment should consider comprehensive calculations to include BED of USC model.

Incorporating Cancer Stem Cells in Radiation Therapy Treatment Response Modeling and the Implication in Glioblastoma Multiforme Treatment Resistance

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. 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. 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. 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.

Survival and tumour control probability in tumours with heterogeneous oxygenation: A comparison between the linear-quadratic and the universal survival curve models for high doses

Background. The validity of the linear-quadratic (LQ) model at high doses has been questioned due to a decreasing agreement between predicted survival and experimental cell survival data. A frequently proposed alternative is the universal survival curve (USC) model, thought to provide a better fit in the high-dose region. The comparison between the predictions of the models has mostly been performed for uniform populations of cells with respect to sensitivity to radiation. This study aimed to compare the two models in terms of cell survival and tumour control probability (TCP) for cell populations with mixed sensitivities related to their oxygenation.Methods. The study was performed in two parts. For the first part, cell survival curves were calculated with both models assuming various homogeneous populations of cells irradiated with uniform doses. For the second part, a realistic three-dimensional (3D) model of complex tumour oxygenation was used to study the impact of the differences in cell survival on the modelled TCP. Cellular response was assessed with the LQ and USC models at voxel level and a Poisson TCP model at tumour level.Results. For hypoxic tumours, the disputed continuous bend of the LQ survival curve was counteracted by the increased radioresistance of the hypoxic cells and the survival curves started to diverge only at much higher doses than for oxic tumours. This was also reflected by the TCP curves for hypoxic tumours for which the difference in D50 values for the LQ and USC models was reduced from 5.4 to 0.2 Gy for 1 and 3 fractions, respectively, in a tumour with only 1.1% hypoxia and from 9.5 to 0.4 Gy in a tumour with 11.1% hypoxia.Conclusions. For a large range of fractional doses including hypofractionated schemes, the difference in predicted survival and TCP between the LQ and USC models for tumours with heterogeneous oxygenation was found to be negligible.

A Comparative Analysis of Radiobiological Models for Cell Surviving Fractions at High Doses

For many years the linear-quadratic (LQ) model has been widely used to describe the effects of total dose and dose per fraction at low-to-intermediate doses in conventional fractionated radiotherapy. Recent advances in stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) have increased the interest in finding a reliable cell survival model, which will be accurate at high doses, as well. Different models have been proposed for improving descriptions of high dose survival responses, such as the Universal Survival Curve (USC), the Kavanagh-Newman (KN) and several generalizations of the LQ model, e.g. the Linear-Quadratic-Linear (LQL) model and the Pade Linear Quadratic (PLQ) model. The purpose of the present study is to compare a number of models in order to find the best option(s) which could successfully be used as a fractionation correction method in SRT. In this work, six independent experimental data sets were used: CHOAA8 (Chinese hamster fibroblast), H460 (non-small cell lung cancer, NSLC), NCI-H841 (small cell lung cancer, SCLC), CP3 and DU145 (human prostate carcinoma cell lines) and U1690 (SCLC). By detailed comparisons with these measurements, the performance of nine different radiobiological models was examined for the entire dose range, including high doses beyond the shoulder of the survival curves. Using the computed and measured cell surviving fractions, comparison of the goodness-of-fit for all the models was performed by means of the reduced χ (2)-test with a 95% confidence interval. The obtained results indicate that models with dose-independent final slopes and extrapolation numbers generally represent better choices for SRT. This is especially important at high doses where the final slope and extrapolation numbers are presently found to play a major role. The PLQ, USC and LQL models have the least number of shortcomings at all doses. The extrapolation numbers and final slopes of these models do not depend on dose. Their asymptotes for the cell surviving fractions are exponentials at low as well as high doses, and this is in agreement with the behaviour of the corresponding experimental data. This is an important improvement over the LQ model which predicts a Gaussian at high doses. Overall and for the highlighted reasons, it was concluded that the PLQ, USC and LQL models are theoretically well-founded. They could prove useful compared to the other proposed radiobiological models in clinical applications for obtaining uniformly accurate cell surviving fractions encountered in stereotactic high-dose radiotherapy as well as at medium and low doses.

The impact of fractionation in SBRT: Analysis with the linear quadratic model and the universal survival curve model

Background. Since the impact of fractionation in SBRT has not been systematically investigated, this modelling study was performed to see how the therapeutic window is affected for a range of fractions at target doses commonly administered in SBRT. Material and methods. Isoeffective tumour-doses (constant cell survival) were calculated with the linear quadratic (LQ) and the universal survival curve (USC) models for 2–20 fractions. The isoeffective tumour-regimes (with α/β = 10 Gy) were used to calculate the sparing of normal tissues (with α/β = 3 Gy) for an increasing number of fractions. Sparing was calculated as an increase in cell survival and decrease in normal tissue complication probability (NTCP) as compared to a common scheme with 3 fractions of 22 Gy to the centre of the target [(15 Gy to the periphery of the planning target volume (PTV)]. Results. At a high dose per fraction, above about 15 Gy, the USC model predicted much lower fractionation sensitivity than the LQ model. This holds true for both tumour and normal tissues. The USC model also predicted greater sparing of normal tissues outside the PTV as compared to the LQ model. Especially at dose levels of the order of 30–50% to that in the centre of the target. The decrease in NTCP predicted by the USC model was of the order of 30% for 10 fractions as compared to the NTCP for 3 fractions. With the LQ model the corresponding decrease was of the order of 10%. Conclusion. The USC model generally predicts a larger therapeutic window than the LQ model for an increasing number of fractions than today's practice in SBRT.

Stereotactic body radiation therapy and 3-dimensional conformal radiotherapy for stage I non-small cell lung cancer: A pooled analysis of biological equivalent dose and local control

PurposeTo determine the relationship between tumor control probability (TCP) and biological effective dose (BED) for radiation therapy in medically inoperable stage I non-small cell lung cancer (NSCLC). Methods and MaterialsForty-two studies on 3-dimensional conformal radiation therapy (3D-CRT) and SBRT for stage I NSCLC were reviewed for tumor control (TC), defined as crude local control ≥ 2 years, as a function of BED. For each dose-fractionation schedule, BED was calculated at isocenter using the linear quadratic (LQ) and universal survival curve (USC) models. A scatter plot of TC versus BED was generated and fitted to the standard TCP equation for both models. ResultsA total of 2696 patients were included in this study (SBRT: 1640; 3D-CRT: 1056). Daily fraction size was 1.2-4 Gy (total dose: 48-102.9) with 3D-CRT and 6-26 (total dose: 20-66) with SBRT. Median BED was 118.6 Gy (range, 68.5-320.3) and 95.6 Gy (range, 46.1-178.1) for the LQ and USC models, respectively. According to the LQ model, BED to achieve 50% TC (TCD50) was 61 Gy (95% confidence interval, 50.2-71.1). TCP as a function of BED was sigmoidal, with TCP ≥ 90% achieved with BED ≥ 159 Gy and 124 Gy for the LQ and USC models, respectively. ConclusionsDose-escalation beyond a BED 159 by LQ model likely translates into clinically insignificant gain in TCP but may result in clinically significant toxicity. When delivered with SBRT, BED of 159 Gy corresponds to a total dose of 53 Gy in 3 fractions at the isocenter.

SU‐FF‐T‐491: Cell Survival Curve Fitting Techniques in High Dose Region for Use in Stereotactic Body Radiation Therapy (SBRT)

Purpose: To select a cell survival curve model that is capable of fitting cell survival at high dose region used in stereotactic body radiation therapy. Materials and Methods: Data from fourteen cell lines were examined. These include a Chinese hamster cell line, a human glioblastoma cell line, two prostate cell lines and ten lung cancer cell lines. Each of these cell lines were fitted to eight different models (4 with 2 parameters and 4 with three parameters) for cell survival. These models included among others the well known linear quadratic model and the single hit multi target model; and the more recent McKenna‐Ahmad repair model, Kavanagh‐Newman model and universal survival curve model. The χ2/df of each fit was compared to determine the model most appropriate for that survival curve. Results: No single model provided the best fit for all the cell lines. For all cell lines there were models that were superior to the linear quadratic. Two recent models (McKenna‐Ahmad repair model, Kavanagh‐Newman model) provided the best fits for many cell lines. These models have low dose quadratic behavior which changes to linear behavior at high doses. The McKenna‐ Ahmad and Kavanagh‐Newman formulas for cell survival are respectively as follows: urn:x-wiley:00942405:media:mp1989:mp1989-math-0001 Conclusion: We recommend that one of the two recent two parameter models be used for fitting cell survival curves if one is primarily interested in cell survival into or past the shoulder region of the cell survival curve.

Universal Survival Curve and Single Fraction Equivalent Dose: Useful Tools in Understanding Potency of Ablative Radiotherapy

Overprediction of the potency and toxicity of high-dose ablative radiotherapy such as stereotactic body radiotherapy (SBRT) by the linear quadratic (LQ) model led to many clinicians' hesitating to adopt this efficacious and well-tolerated therapeutic option. The aim of this study was to offer an alternative method of analyzing the effect of SBRT by constructing a universal survival curve (USC) that provides superior approximation of the experimentally measured survival curves in the ablative, high-dose range without losing the strengths of the LQ model around the shoulder. The USC was constructed by hybridizing two classic radiobiologic models: the LQ model and the multitarget model. We have assumed that the LQ model gives a good description for conventionally fractionated radiotherapy (CFRT) for the dose to the shoulder. For ablative doses beyond the shoulder, the survival curve is better described as a straight line as predicted by the multitarget model. The USC smoothly interpolates from a parabola predicted by the LQ model to the terminal asymptote of the multitarget model in the high-dose region. From the USC, we derived two equivalence functions, the biologically effective dose and the single fraction equivalent dose for both CFRT and SBRT. The validity of the USC was tested by using previously published parameters of the LQ and multitarget models for non-small-cell lung cancer cell lines. A comparison of the goodness-of-fit of the LQ and USC models was made to a high-dose survival curve of the H460 non-small-cell lung cancer cell line. The USC can be used to compare the dose fractionation schemes of both CFRT and SBRT. The USC provides an empirically and a clinically well-justified rationale for SBRT while preserving the strengths of the LQ model for CFRT.