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.

scholarly journals Estimation of cell response in fractionation radiotherapy using different methods derived from linear quadratic model

2015 ◽  
Vol 49 (4) ◽  
pp. 347-356 ◽  
Author(s):  
Safoora Nikzad ◽  
Bijan Hashemi ◽  
Golshan Mahmoudi ◽  
Milad Baradaran-Ghahfarokhi
Keyword(s):  
Cell Response ◽  
Treatment Time ◽  
Theoretical Models ◽  
Accurate Method ◽  
Quadratic Model ◽  
Breast Adenocarcinoma ◽  
Linear Quadratic ◽  
Overall Treatment Time ◽  
Simple Method ◽  
Theoretical Methods

Abstract Background. The aim of this study was to use various theoretical methods derived from the Linear Quadratic (LQ) model to calculate the effects of number of subfractions, time intervals between subfractions, dose per subfraction, and overall fraction time on the cells’ survival. Comparison of the results with experimental outcomes of melanoma and breast adenocarcinoma cells was also performed. Finally, the best matched method with experimental outcomes is introduced as the most accurate method in predicting the cell response. Materials and methods. The most widely used theoretical methods in the literature, presented by Keall et al., Brenner, and Mu et al., were used to calculate the cells’ survival following radiotherapy with different treatment schemes. The overall treatment times were ranged from 15 to 240 minutes. To investigate the effects of number of subfractions and dose per subfraction, the cells’ survival after different treatment delivery scenarios were calculated through fixed overall treatment times of 30, 60 and 240 minutes. The experimental tests were done for dose of 4 Gy. The results were compared with those of the theoretical outcomes. Results. The most affective parameter on the cells’ survival was the overall treatment time. However, the number of subfractions per fractions was another effecting parameter in the theoretical models. This parameter showed no significant effect on the cells’ survival in experimental schemes. The variations in number of subfractions per each fraction showed different results on the cells’ survival, calculated by Keall et al. and Brenner methods (P<0.05). Conclusions. Mu et al. method can predict the cells’ survival following fractionation radiotherapy more accurately than the other models. Using Mu et al. method, as an accurate and simple method to predict the cell response after fractionation radiotherapy, is suggested for clinical applications.

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 Free Educational Android Mobile Application for Radiobiology

2021 ◽  
Vol 28 (3) ◽  
pp. 315-319
Author(s):  
Camil Ciprian MIRESTEAN ◽  
◽  
Alexandru Dumitru ZARA ◽  
Roxana Irina IANCU ◽  
Dragos Petru Teodor IANCU ◽  
...  
Keyword(s):  
Target Volume ◽  
Tnm Staging ◽  
Dose Fractionation ◽  
Quadratic Model ◽  
Smart Devices ◽  
Smart Device ◽  
Linear Quadratic ◽  
Altered Fractionation ◽  
Linear Quadratic Model ◽  
Volume Delineation

The use of mobile devices and applications dedicated to different medical fields has improved the quality and facilitated medical care, especially in the last 10 years. The number of applications running on the software platforms of smart phones or other smart devices is constantly growing. Radiotherapy also benefits from applications (apps) for TNM staging of cancers, for target volume delineation and toxicity management but also from radiobiological apps for calculating equivalent dose schemes for different dose fractionation regimens. In the context of the increasingly frequent use of altered fractionation schemes, the use of radiobiological models and calculations based on the linear quadratic model (LQ) becomes a necessity. We aim to evaluate free radiobiology apps for the Android software platform. Given the global educational deficit, the lack of experts and the concordance between radiobiology education and the need to use basic clinical notions of modern radiotherapy, the existence of free apps for the Android platform running on older generation processors can transform even an old smart device in a powerful “radiobiology station.” Apps for radiobiology can help the radiation oncologist and medical physicist with responsibilities in radiotherapy treatment planning in the context of accelerated adoption of hypo-fractionation regimens and calculation of the effect of treatment gaps, a topic of interest in the COVID-19 pandemic context. Radiobiology apps can also partially fill the educational gap in radiobiology by arousing the interest of young radiation oncologists to deepen the growing universe of fundamental and clinical radiobiology.

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.

Linear-Quadratic Model for Planning Neutron Therapy with the Use of U-120 Cyclotron

2018 ◽  
pp. 41-47
Author(s):  
Валерий Лисин ◽  
V. Lisin
Keyword(s):  
Dose Fractionation ◽  
Quadratic Model ◽  
Time Interval ◽  
Skin Damage ◽  
Linear Quadratic ◽  
Standard Regimen ◽  
Neutron Therapy ◽  
Linear Quadratic Model ◽  
Radiation Induced ◽  
Early Radiation

Purpose: To estimate the feasibility of using linear-quadratic model (LQM) for planning neutron therapy regimens by the criterion of early radiation-induced reactions. Material and methods: The LQM, which described the reaction of tissues to fractionated irradiation, was used. The results obtained were compared with similar results found on the basis of the TDF model successfully used for neutron therapy planning. Results: The LQM parameters αn and βn for radiation induced skin damage were found. The dependence of a single dose of neutrons on the number of therapy sessions was obtained. This dependence was in good agreement with the analogous dependence found by the TDF model, which indicated the correctness of the method for calculating it. When using LQM for planning neutron therapy, the issue related with the time intervals between sessions was considered. For this purpose, the comparative calculations of the ratio of the total effect, determined by the LQM, and the TDF factor were carried out. The difference between the compared values did not exceed 6 %, thus allowing the time interval for planning neutron therapy using LQM to be excluded. Two methods to control the damage to normal tissue using LQM were considered. The first method was based on the evaluation of part of the used tolerance of the irradiated tissue, and the second one was carried out by transferring the applied dose fractionation regimen of neutron therapy to the isoeffective standard regimen of photon therapy. Conclusion: It was shown that LQM can be used for planning neutron therapy regimens in cancer patients by the criterion of early radiation-induced reactions. The results obtained extend the potential of radiobiological planning of neutron therapy and can serve as a basis for the development of the method of using LQM in prediction of late radiation-induced complications.

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