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

2020 ◽  
Author(s):  
Mark Ka Heng Chan ◽  
Chi-Leung Chiang
Keyword(s):  
Linear Regression ◽  
Stereotactic Body Radiotherapy ◽  
Survival Curve ◽  
Dose Fractionation ◽  
Tumor Control ◽  
Model Parameters ◽  
High Dose ◽  
Linear Quadratic ◽  
Equivalent Uniform Dose ◽  
Prescription Dose

Abstract Purpose To examine the equivalent uniform dose (EUD) formalism using the universal survival curve (USC) applicable to high-dose stereotactic body radiotherapy (SBRT). Materials and methods For 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. Results For 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 $$\alpha /\beta$$ α / β 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. Conclusion A 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.

scholarly journals A simple model for calculating relative biological effectiveness of X-rays and gamma radiation in cell survival

2020 ◽  
Vol 93 (1112) ◽  
pp. 20190949 ◽  
Author(s):  
Oleg N. Vassiliev ◽  
Christine B. Peterson ◽  
David R. Grosshans ◽  
Radhe Mohan
Keyword(s):  
Experimental Data ◽  
Cell Survival ◽  
Relative Biological Effectiveness ◽  
Survival Curve ◽  
Linear Functions ◽  
Model Parameters ◽  
High Dose ◽  
X Rays ◽  
Γ Radiation ◽  
Biological Effectiveness

Objectives: The relative biological effectiveness (RBE) of X-rays and γ radiation increases substantially with decreasing beam energy. This trend affects the efficacy of medical applications of this type of radiation. This study was designed to develop a model based on a survey of experimental data that can reliably predict this trend. Methods: In our model, parameters α and β of a cell survival curve are simple functions of the frequency-average linear energy transfer (LF) of delta electrons. The choice of these functions was guided by a microdosimetry-based model. We calculated LF by using an innovative algorithm in which LF is associated with only those electrons that reach a sensitive-to-radiation volume (SV) within the cell. We determined model parameters by fitting the model to 139 measured (α,β) pairs. Results: We tested nine versions of the model. The best agreement was achieved with [Formula: see text] and β being linear functions of [Formula: see text] .The estimated SV diameter was 0.1–1 µm. We also found that α, β, and the α/β ratio increased with increasing [Formula: see text] . Conclusions: By combining an innovative method for calculating [Formula: see text] with a microdosimetric model, we developed a model that is consistent with extensive experimental data involving photon energies from 0.27 keV to 1.25 MeV. Advances in knowledge: We have developed a photon RBE model applicable to an energy range from ultra-soft X-rays to megaelectron volt γ radiation, including high-dose levels where the RBE cannot be calculated as the ratio of α values. In this model, the ionization density represented by [Formula: see text] determines the RBE for a given photon spectrum.

Stereotactic Body Radiation Therapy in Multiple Organ Sites

2007 ◽  
Vol 25 (8) ◽  
pp. 947-952 ◽  
Author(s):  
Robert D. Timmerman ◽  
Brian D. Kavanagh ◽  
L. Chinsoo Cho ◽  
Lech Papiez ◽  
Lei Xing
Keyword(s):  
Radiation Therapy ◽  
Stereotactic Body Radiation Therapy ◽  
Advanced Technology ◽  
Dose Fractionation ◽  
Tumor Control ◽  
High Dose ◽  
Stereotactic Body Radiation ◽  
Phase Ii Studies ◽  
Prospective Phase ◽  
Prospective Trials

Introduction Stereotactic body radiation therapy (SBRT) uses advanced technology to deliver a potent ablative dose to deep-seated tumors in the lung, liver, spine, pancreas, kidney, and prostate. Methods SBRT involves constructing very compact high-dose volumes in and about the tumor. Tumor position must be accurately assessed throughout treatment, especially for tumors that move with respiration. Sophisticated image guidance and related treatment delivery technologies have developed to account for such motion and efficiently deliver high daily dose. All this serves to allow the delivery of ablative dose fractionation to the target capable of both disrupting tumor mitosis and cellular function. Results Prospective phase I dose-escalation trials have been carried out to reach potent tumoricidal dose levels capable of eradicating tumors with high likelihood. These studies indicate a clear dose-response relationship for tumor control with escalating dose of SBRT. Prospective phase II studies have been reported from several continents consistently showing very high levels of local tumor control. Although late toxicity requires further careful assessment, acute and subacute toxicities are generally acceptable. Patterns of toxicity, both clinical and radiographic, are distinct from those observed with conventionally fractionated radiotherapy as a result of the unique biologic response to ablative fractionation. Conclusion Prospective trials using SBRT have confirmed the efficacy of treatment in a variety of patient populations. Although mechanisms of ablative-dose injury remain elusive, ongoing prospective trials offer the hope of finding the ideal application for SBRT in the treatment arsenal.

scholarly journals Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy

Information ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 313
Author(s):  
Alessandro Bertuzzi ◽  
Federica Conte ◽  
Federico Papa ◽  
Carmela Sinisgalli
Keyword(s):  
Nonlinear Programming ◽  
Treatment Time ◽  
External Beam Radiotherapy ◽  
Dose Fractionation ◽  
Quadratic Model ◽  
Analytical Determination ◽  
Model Parameters ◽  
Linear Quadratic ◽  
Quadratic Constraints

The present work of review collects and evidences the main results of our previous papers on the optimization of fractionated radiotherapy protocols. The problem under investigation is presented here in a unitary framework as a nonlinear programming application that aims to determine the optimal schemes of dose fractionation commonly used in external beam radiotherapy. The radiation responses of tumor and normal tissues are described by means of the linear quadratic model. We formulate a nonlinear, non-convex optimization problem including two quadratic constraints to limit the collateral normal tissue damages and linear box constraints on the fractional dose sizes. The general problem is decomposed into two subproblems: (1) analytical determination of the optimal fraction dose sizes as a function of the model parameters for arbitrarily fixed treatment lengths; and (2) numerical determination of the optimal fraction number, and of the optimal treatment time, in different parameter settings. After establishing the boundedness of the optimal number of fractions, we investigate by numerical simulation the optimal solution behavior for experimentally meaningful parameter ranges, recognizing the crucial role of some parameters, such as the radiosensitivity ratio, in determining the optimality of hypo- or equi-fractionated treatments. Our results agree with findings of the theoretical and clinical literature.

The significance of cell survival parameters for the use of equivalent uniform dose in tumour dose evaluation

2002 ◽  
Vol 3 (1) ◽  
pp. 27-32
Author(s):  
W. Kilby
Keyword(s):  
Cell Survival ◽  
Rank Order ◽  
Treatment Plan ◽  
Survival Models ◽  
Model Parameters ◽  
Linear Quadratic ◽  
Equivalent Uniform Dose ◽  
Tumour Dose ◽  
Treatment Plans ◽  
Treatment Plan Evaluation

Equivalent Uniform Dose (EUD) has been proposed as a means of comparing treatment plans which include large PTV dose heterogeneity. Moreover, it has been suggested that EUD is insensitive to the underlying cell survival model parameters used in its calculation, and that arbitrary values might be used. This dependence of EUD on radiobiological parameters has been studied using different cell survival models (exponential and linear quadratic) and a range of artificially generated and clinical (lung and prostate) treatment plans. EUD was found to be strongly dependent on the variable SF2, but not on α/β, or number of fractions. When clinical treatment plans were ranked in order of EUD, a dependence of rank order on SF2 was observed, suggesting that arbitrary SF2 values are not appropriate for treatment plan evaluation. These results suggest that tumour specific SF2 values should be used for EUD calculation, and this is discussed.

scholarly journals Intermittent radiotherapy as alternative treatment for recurrent high grade glioma: a modeling study based on longitudinal tumor measurements

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sarah C. Brüningk ◽  
Jeffrey Peacock ◽  
Christopher J. Whelan ◽  
Renee Brady-Nicholls ◽  
Hsiang-Hsuan M. Yu ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Treatment Option ◽  
Radiation Treatment ◽  
Phase 1 ◽  
High Grade Glioma ◽  
Patient Specific ◽  
Tumor Control ◽  
Model Parameters ◽  
High Dose ◽  
High Grade

AbstractRecurrent high grade glioma patients face a poor prognosis for which no curative treatment option currently exists. In contrast to prescribing high dose hypofractionated stereotactic radiotherapy (HFSRT, $$\ge 6$$ ≥ 6 Gy $$\times$$ × 5 in daily fractions) with debulking intent, we suggest a personalized treatment strategy to improve tumor control by delivering high dose intermittent radiation treatment (iRT, $$\ge 6$$ ≥ 6 Gy $$\times$$ × 1 every 6 weeks). We performed a simulation analysis to compare HFSRT, iRT and iRT plus boost ($$\ge 6$$ ≥ 6 Gy $$\times$$ × 3 in daily fractions at time of progression) based on a mathematical model of tumor growth, radiation response and patient-specific evolution of resistance to additional treatments (pembrolizumab and bevacizumab). Model parameters were fitted from tumor growth curves of 16 patients enrolled in the phase 1 NCT02313272 trial that combined HFSRT with bevacizumab and pembrolizumab. Then, iRT +/− boost treatments were simulated and compared to HFSRT based on time to tumor regrowth. The modeling results demonstrated that iRT + boost(− boost) treatment was equal or superior to HFSRT in 15(11) out of 16 cases and that patients that remained responsive to pembrolizumab and bevacizumab would benefit most from iRT. Time to progression could be prolonged through the application of additional, intermittently delivered fractions. iRT hence provides a promising treatment option for recurrent high grade glioma patients for prospective clinical evaluation.

scholarly journals Safety and Efficacy of a Five-Fraction Stereotactic Body Radiotherapy Schedule for Centrally Located Non–Small-Cell Lung Cancer: NRG Oncology/RTOG 0813 Trial

2019 ◽  
Vol 37 (15) ◽  
pp. 1316-1325 ◽  
Author(s):  
Andrea Bezjak ◽  
Rebecca Paulus ◽  
Laurie E. Gaspar ◽  
Robert D. Timmerman ◽  
William L. Straube ◽  
...  
Keyword(s):  
Lung Cancer ◽  
Small Cell Lung Cancer ◽  
Cell Lung Cancer ◽  
Stereotactic Body Radiotherapy ◽  
Early Stage ◽  
Main Bronchus ◽  
Small Cell ◽  
Tumor Control ◽  
High Dose ◽  
Small Cell Lung

PURPOSE Patients with centrally located early-stage non–small-cell lung cancer (NSCLC) are at a higher risk of toxicity from high-dose ablative radiotherapy. NRG Oncology/RTOG 0813 was a phase I/II study designed to determine the maximum tolerated dose (MTD), efficacy, and toxicity of stereotactic body radiotherapy (SBRT) for centrally located NSCLC. MATERIALS AND METHODS Medically inoperable patients with biopsy-proven, positron emission tomography–staged T1 to 2 (≤ 5 cm) N0M0 centrally located NSCLC were accrued into a dose-escalating, five-fraction SBRT schedule that ranged from 10 to 12 Gy/fraction (fx) delivered over 1.5 to 2 weeks. Dose-limiting toxicity (DLT) was defined as any treatment-related grade 3 or worse predefined toxicity that occurred within the first year. MTD was defined as the SBRT dose at which the probability of DLT was closest to 20% without exceeding it. RESULTS One hundred twenty patients were accrued between February 2009 and September 2013. Patients were elderly, there were slightly more females, and the majority had a performance status of 0 to 1. Most cancers were T1 (65%) and squamous cell (45%). Organs closest to planning target volume/most at risk were the main bronchus and large vessels. Median follow-up was 37.9 months. Five patients experienced DLTs; MTD was 12.0 Gy/fx, which had a probability of a DLT of 7.2% (95% CI, 2.8% to 14.5%). Two-year rates for the 71 evaluable patients in the 11.5 and 12.0 Gy/fx cohorts were local control, 89.4% (90% CI, 81.6% to 97.4%) and 87.9% (90% CI, 78.8% to 97.0%); overall survival, 67.9% (95% CI, 50.4% to 80.3%) and 72.7% (95% CI, 54.1% to 84.8%); and progression-free survival, 52.2% (95% CI, 35.3% to 66.6%) and 54.5% (95% CI, 36.3% to 69.6%), respectively. CONCLUSION The MTD for this study was 12.0 Gy/fx; it was associated with 7.2% DLTs and high rates of tumor control. Outcomes in this medically inoperable group of mostly elderly patients with comorbidities were comparable with that of patients with peripheral early-stage tumors.

scholarly journals Analytical solution to the radiotherapy fractionation problem including dose bound constraints

2021 ◽  
Author(s):  
Luis Alberto Fernández ◽  
Lucía Fernández
Keyword(s):  
At Risk ◽  
Radiation Effect ◽  
Organs At Risk ◽  
Dose Fractionation ◽  
Quadratic Model ◽  
High Dose ◽  
Bound Constraints ◽  
Linear Quadratic ◽  
Linear Quadratic Model ◽  
Radiotherapy Dose

Abstract This paper deals with the classic radiotherapy dose fractionation problem for cancer tumors concerning the following goals: a) To maximize the effect of radiation on the tumor, restricting the effect produced to the organs at risk (healing approach). b) To minimize the effect of radiation on the organs at risk, while maintaining enough effect of radiation on the tumor (palliative approach). We will assume the linear-quadratic model to characterize the radiation effect and consider the stationary case (that is, without taking into account the timing of doses and the tumor growth between them). The main novelty with respect to previous works concerns the presence of minimum and maximum dose fractions, to achieve the minimum effect and to avoid undesirable side effects, respectively. We have characterized in which situations is more convenient the hypofractionated protocol (deliver few fractions with high dose per fraction) and in which ones the hyperfractionated regimen (deliver a large number of lower doses of radiation) is the optimal strategy. In all cases, analytical solutions to the problem are obtained in terms of the data. In addition, the calculations to implement these solutions are elementary and can be carried out using a pocket calculator.

scholarly journals Intermittent radiotherapy as alternative treatment for recurrent high grade glioma: A modelling study based on longitudinal tumor measurements

2021 ◽  
Author(s):  
Sarah C. Brüningk ◽  
Jeffrey Peacock ◽  
Christopher J. Whelan ◽  
Hsiang-Hsuan M. Yu ◽  
Solmaz Sahebjam ◽  
...  
Keyword(s):  
Treatment Option ◽  
Tumour Growth ◽  
Simulation Analysis ◽  
Phase 1 ◽  
High Grade Glioma ◽  
Patient Specific ◽  
Tumor Control ◽  
Model Parameters ◽  
High Dose ◽  
High Grade

ABSTRACTRecurrent high grade glioma patients face a poor prognosis for which no curative treatment option currently exists. In contrast to prescribing high dose hypofractionated stereotactic radiotherapy (HFSRT, ≥ 6 Gyx5 in daily fractions) with debulking intent, we suggest a personalized treatment strategy to improve tumor control by delivering intermittent high dose treatment (iRT, ≥ 6 Gyx1 every six weeks). We performed a simulation analysis to compare HFSRT, iRT and iRT plus boost (≥ 6 Gyx3 in daily fractions at time of progression) based on a mathematical model of tumour growth, radiation response and patient-specific evolution of resistance to additional treatments (pembrolizumab and bevacizumab). Model parameters were fitted from tumour growth curves of 16 patients enrolled in the phase 1 NCT02313272 trial that combined HFSRT with bevacizumab and pembrolizumab. Then, iRT +/-boost treatments were simulated and compared to HFSRT based on time to tumor regrowth. The modelling results demonstrated that iRT+boost(-boost) treatment was equal or superior to HFSRT in 15(11) out of 16 cases and that patients that remained responsive to pembrolizumab and bevacizumab would benefit most from iRT. Time to progression could be prolonged through the application of additional, intermittently delivered fractions. iRT hence provides a promising treatment option for recurrent high grade glioma patients.

Glucose Calibration Modeling in Blood with Spline Regression Approaching to Non-Invasive Tools

2018 ◽  
pp. 144-149
Author(s):  
Ria Hayatun Nur ◽  
Indahwati A ◽  
Erfiani A
Keyword(s):  
Diabetes Mellitus ◽  
Linear Regression ◽  
Good Health ◽  
Cubic Spline ◽  
The Body ◽  
Spline Regression ◽  
Linear Quadratic ◽  
Important Thing ◽  
Non Invasive

In this globalization era, health is the most important thing to be able to run various activities. Without good health, this will hinder many activities. Diabetes mellitus is one of the diseases caused by unhealty lifestyle.There are many treatments that can be done to prevent the occurrence of diabetes. The treatments are giving the insulin and also checking the glucose rate to the patients.Checking the glucose rate needs the tools which is safety to the body. This research want to develop non invasive tool which is safety and do not injure the patient. The purpose of this research is also finding the best model which derived from Linear, Quadratic, and Cubic Spline Regression. Some respondents were taking to get the glucose measuring by invasive and non invasive tools. It could be seen clearly that Spline Linear Regression was the best model than Quadratic and Cubic Spline Regression. It had 70% and 33.939 for R2 and RMSEP respectively.

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