Mathematical Biosciences and Engineering, 2016, 13(6): 1131-1142. doi: 10.3934/mbe.2016034.

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Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization

1. Silesian University of Technology, Institute of Automatic Control, Akademicka 16, 44-100 Gliwice
2. Silesian University of Technology, ul.Akademicka 16, 44-100, Gliwice

We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.
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Keywords partial differential equations; spatial systems; Sensitivity analysis; difference equations; tumor growth.

Citation: Krzysztof Fujarewicz, Krzysztof Łakomiec. Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization. Mathematical Biosciences and Engineering, 2016, 13(6): 1131-1142. doi: 10.3934/mbe.2016034


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This article has been cited by

  • 1. Krzysztof Fujarewicz, Estimation of initial functions for systems with delays from discrete measurements, Mathematical Biosciences and Engineering, 2016, 14, 1, 165, 10.3934/mbe.2017011
  • 2. Krzysztof Łakomiec, Karolina Kurasz, Krzysztof Fujarewicz, , Information Technology in Biomedicine, 2019, Chapter 42, 481, 10.1007/978-3-319-91211-0_42
  • 3. Krzysztof Fujarewicz, Krzysztof Łakomiec, Spatiotemporal sensitivity of systems modeled by cellular automata, Mathematical Methods in the Applied Sciences, 2018, 10.1002/mma.5358
  • 4. Krzysztof Fujarewicz, Krzysztof Łakomiec, , Advanced, Contemporary Control, 2020, Chapter 48, 567, 10.1007/978-3-030-50936-1_48

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Copyright Info: 2016, Krzysztof Fujarewicz, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

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