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A fluence map optimization model for restoring traditional fractionation in IMRT treatment planning

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Abstract

One of the core problems in intensity modulated radiation therapy (IMRT) treatment planning is the fluence map optimization (FMO) problem, which determines a fluence map (or profile) for each beam used in the delivery of treatment. Radiation therapy is administered in multiple so-called daily fractions to allow for healthy tissue to recover from damage caused by the treatment. Before the advent of IMRT, the treatment was designed to ensure a constant dose to cells in the target (the areas in the patient where cancerous cells are present or suspected). In the presence of multiple targets with different prescribed doses, this design meant that treatment had to be delivered in a sequence of unequal fractions, one per prescription dose level. For example, in case of two targets treatment would consist of an initial plan aimed at treating both targets to a lower total dose, followed by a so-called boost plan aimed at delivering the additional dose at the target with higher prescribed dose. In contrast, IMRT treatment plans are often delivered with equal treatment plan for each fraction, which means that the dose per fraction cannot be the same for all targets. The important problem of restoring traditional fractionation to IMRT treatments has not yet received much attention in the literature. In this paper we propose a new optimization model that explicitly restores fractionation into the FMO problem, yielding an optimal set of fluence maps for each fraction. We illustrate the capabilities of our approach on clinical head-and-neck cancer cases.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada

    Dionne M. Aleman

  2. Division of Optimization and Systems Theory, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Johan Wallgren

  3. Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI, 48109, USA

    H. Edwin Romeijn

  4. ViewRay Inc., 2 Thermo Fisher Way, Oakwood Village, OH, 44146, USA

    James F. Dempsey

Authors
  1. Dionne M. Aleman
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  2. Johan Wallgren
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  3. H. Edwin Romeijn
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  4. James F. Dempsey
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Corresponding author

Correspondence to Dionne M. Aleman.

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National Science Foundation Alliance for Graduate Education and the Professoriate; National Science Foundation Graduate Research Fellowship.

Appendices

Appendix A: Parameter weights

See Table 5.

Table 5 Values of \(\underline{w}_{s}\) and \(\overline{w}_{s}\) for all structures in FMO-traditional and FMO-fractionation models
Full size table

Appendix B: DVHs and axial slices for all cases

See Figs. 4, 5, 6, 7, 8 and 9.

Fig. 4
figure 4

Target DVHs and axial slices in Fractions 1 (left) and 2 (right) for Case 1. Total dose DVHs for saliva glands and unspecified tissue is shown as well. In the target DVH figures the prescription dose and 93 % thereof are indicated by vertical dashed lines while 95 % target volume is marked by a horizontal dashed line. In the critical structure DVH figures the sparing criterion for saliva glands is marked by a dot

Full size image
Fig. 5
figure 5

Target DVHs and axial slices in Fractions 1 (left) and 2 (right) for Case 2. Total dose DVHs for saliva glands and unspecified tissue is shown as well. In the target DVH figures the prescription dose and 93 % thereof are indicated by vertical dashed lines while 95 % target volume is marked by a horizontal dashed line. In the critical structure DVH figures the sparing criterion for saliva glands is marked by a dot

Full size image
Fig. 6
figure 6

Target DVHs and axial slices in Fractions 1 (left) and 2 (right) for Case 3. Total dose DVHs for saliva glands and unspecified tissue is shown as well. In the target DVH figures the prescription dose and 93 % thereof are indicated by vertical dashed lines while 95 % target volume is marked by a horizontal dashed line. In the critical structure DVH figures the sparing criterion for saliva glands is marked by a dot

Full size image
Fig. 7
figure 7

Target DVHs and axial slices in Fractions 1 (left) and 2 (right) for Case 4. Total dose DVHs for saliva glands and unspecified tissue is shown as well. In the target DVH figures the prescription dose and 93 % thereof are indicated by vertical dashed lines while 95 % target volume is marked by a horizontal dashed line. In the critical structure DVH figures the sparing criterion for saliva glands is marked by a dot

Full size image
Fig. 8
figure 8

Target DVHs and axial slices in Fractions 1 (left) and 2 (right) for Case 5. Total dose DVHs for saliva glands and unspecified tissue is shown as well. In the target DVH figures the prescription dose and 93 % thereof are indicated by vertical dashed lines while 95 % target volume is marked by a horizontal dashed line. In the critical structure DVH figures the sparing criterion for saliva glands is marked by a dot

Full size image
Fig. 9
figure 9

Target DVHs and axial slices in Fractions 1 (left) and 2 (right) for Case 6. Total dose DVHs for saliva glands and unspecified tissue is shown as well. In the target DVH figures the prescription dose and 93 % thereof are indicated by vertical dashed lines while 95 % target volume is marked by a horizontal dashed line. In the critical structure DVH figures the sparing criterion for saliva glands is marked by a dot

Full size image

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Aleman, D.M., Wallgren, J., Romeijn, H.E. et al. A fluence map optimization model for restoring traditional fractionation in IMRT treatment planning. Optim Lett 8, 1453–1473 (2014). https://doi.org/10.1007/s11590-013-0672-z

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