Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy
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 sch...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Information |
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| Online Access: | https://www.mdpi.com/2078-2489/11/6/313 |
| _version_ | 1797565629693165568 |
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| author | Alessandro Bertuzzi Federica Conte Federico Papa Carmela Sinisgalli |
| author_facet | Alessandro Bertuzzi Federica Conte Federico Papa Carmela Sinisgalli |
| author_sort | Alessandro Bertuzzi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T19:14:48Z |
| format | Article |
| id | doaj.art-3ae326ace682482eb44b9a79f1d5954a |
| institution | Directory Open Access Journal |
| issn | 2078-2489 |
| language | English |
| last_indexed | 2024-03-10T19:14:48Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Information |
| spelling | doaj.art-3ae326ace682482eb44b9a79f1d5954a2023-11-20T03:26:19ZengMDPI AGInformation2078-24892020-06-0111631310.3390/info11060313Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer RadiotherapyAlessandro Bertuzzi0Federica Conte1Federico Papa2Carmela Sinisgalli3Institute for Systems Analysis and Computer Science—National Research Council of Italy, Via dei Taurini 19, 00185 Rome, ItalyInstitute for Systems Analysis and Computer Science—National Research Council of Italy, Via dei Taurini 19, 00185 Rome, ItalyInstitute for Systems Analysis and Computer Science—National Research Council of Italy, Via dei Taurini 19, 00185 Rome, ItalyInstitute for Systems Analysis and Computer Science—National Research Council of Italy, Via dei Taurini 19, 00185 Rome, ItalyThe 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.https://www.mdpi.com/2078-2489/11/6/313cancer radiotherapy optimizationlinear-quadratic modelnonlinear programming |
| spellingShingle | Alessandro Bertuzzi Federica Conte Federico Papa Carmela Sinisgalli Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy Information cancer radiotherapy optimization linear-quadratic model nonlinear programming |
| title | Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy |
| title_full | Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy |
| title_fullStr | Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy |
| title_full_unstemmed | Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy |
| title_short | Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy |
| title_sort | applications of nonlinear programming to the optimization of fractionated protocols in cancer radiotherapy |
| topic | cancer radiotherapy optimization linear-quadratic model nonlinear programming |
| url | https://www.mdpi.com/2078-2489/11/6/313 |
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