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Optimal Treatment Planning in Radiotherapy Based on Boltzmann Transport Equations

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Trends in PDE Constrained Optimization

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 165))

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Abstract

We look at the optimization of radiotherapy treatment planning. By using a deterministic model of dose deposition in tissue derived from the Boltzmann transport equations, we can improve on the accuracy of existing models near tissue inhomogeneities while also making use of adjoint calculus for developing necessary conditions for optimality. We describe the relevant model and consider the planning problem in an optimal control framework. Two versions of the problem are discussed, optimality conditions are derived, and numerical methods are described. Numerical examples are presented.

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Author information

Authors and Affiliations

  1. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, A-8010, Graz, Austria

    Richard C. Barnard

  2. MATHCCES, Department of Mathematics, RWTH Aachen University, Schinkelstr. 2, D-52062, Aachen, Germany

    Martin Frank

  3. IGPM, Department of Mathematics, RWTH Aachen University, Templergraben 55, D-52062, Aachen, Germany

    Michael Herty

Authors
  1. Richard C. Barnard
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  2. Martin Frank
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  3. Michael Herty
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Corresponding author

Correspondence to Richard C. Barnard .

Editor information

Editors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Günter Leugering

  2. Institut für Dynamik komplexer technisch, Max-Planck-Institut, Magdeburg, Germany

    Peter Benner

  3. Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Dortmund, Germany

    Sebastian Engell

  4. Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

    Andreas Griewank

  5. Mathematisches Institut, Universität Basel, Basel, Switzerland

    Helmut Harbrecht

  6. Fachbereich Mathematik Optimierung und Approximation, Universität Hamburg, Hamburg, Germany

    Michael Hinze

  7. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

    Rolf Rannacher

  8. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Stefan Ulbrich

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Barnard, R.C., Frank, M., Herty, M. (2014). Optimal Treatment Planning in Radiotherapy Based on Boltzmann Transport Equations. In: Leugering, G., et al. Trends in PDE Constrained Optimization. International Series of Numerical Mathematics, vol 165. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-05083-6_28

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