The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy
Radiation therapy is one of the important treatment procedures of cancer. The day-to-day delivered dose to the tissue in radiation therapy often deviates from the planned fixed dose per fraction. This day-to-day variation of radiation dose is stochastic. Here, we have developed the mathematical form...
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AIMS Press
2015-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.159 |
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| author | Subhadip Paul Prasun Kumar Roy |
| author_facet | Subhadip Paul Prasun Kumar Roy |
| author_sort | Subhadip Paul |
| collection | DOAJ |
| description | Radiation therapy is one of the important treatment procedures of cancer. The day-to-day delivered dose to the tissue in radiation therapy often deviates from the planned fixed dose per fraction. This day-to-day variation of radiation dose is stochastic. Here, we have developed the mathematical formulation to represent the day-to-day stochastic dose variation effect in radiation therapy. Our analysis shows that that the fixed dose delivery approximation under-estimates the biological effective dose, even if the average delivered dose per fraction is equal to the planned dose per fraction. The magnitude of the under-estimation effect relies upon the day-to-day stochastic dose variation level, the dose fraction size and the values of the radiobiological parameters of the tissue. We have further explored the application of our mathematical formulation for adaptive dose calculation. Our analysis implies that, compared to the premise of the Linear Quadratic Linear (LQL) framework, the Linear Quadratic framework based analytical formulation under-estimates the required dose per fraction necessary to produce the same biological effective dose as originally planned. Our study provides analytical formulation to calculate iso-effect in adaptive radiation therapy considering day-to-day stochastic dose deviation from planned dose and also indicates the potential utility of LQL framework in this context. |
| format | Article |
| id | doaj-art-de9d172d390444af927ee552ec01e353 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-de9d172d390444af927ee552ec01e3532025-01-24T02:34:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-0113115917010.3934/mbe.2016.13.159The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapySubhadip Paul0Prasun Kumar Roy1National Brain Research Centre, Manesar, Gurgaon, Haryana-122051National Brain Research Centre, Manesar, Gurgaon, Haryana-122051Radiation therapy is one of the important treatment procedures of cancer. The day-to-day delivered dose to the tissue in radiation therapy often deviates from the planned fixed dose per fraction. This day-to-day variation of radiation dose is stochastic. Here, we have developed the mathematical formulation to represent the day-to-day stochastic dose variation effect in radiation therapy. Our analysis shows that that the fixed dose delivery approximation under-estimates the biological effective dose, even if the average delivered dose per fraction is equal to the planned dose per fraction. The magnitude of the under-estimation effect relies upon the day-to-day stochastic dose variation level, the dose fraction size and the values of the radiobiological parameters of the tissue. We have further explored the application of our mathematical formulation for adaptive dose calculation. Our analysis implies that, compared to the premise of the Linear Quadratic Linear (LQL) framework, the Linear Quadratic framework based analytical formulation under-estimates the required dose per fraction necessary to produce the same biological effective dose as originally planned. Our study provides analytical formulation to calculate iso-effect in adaptive radiation therapy considering day-to-day stochastic dose deviation from planned dose and also indicates the potential utility of LQL framework in this context.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.159stochasticbiological effectjensen's inequalityradiation therapy.daily dose |
| spellingShingle | Subhadip Paul Prasun Kumar Roy The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy Mathematical Biosciences and Engineering stochastic biological effect jensen's inequality radiation therapy. daily dose |
| title | The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy |
| title_full | The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy |
| title_fullStr | The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy |
| title_full_unstemmed | The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy |
| title_short | The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy |
| title_sort | consequence of day to day stochastic dose deviation from the planned dose in fractionated radiation therapy |
| topic | stochastic biological effect jensen's inequality radiation therapy. daily dose |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.159 |
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