An Optimization Framework for Conformal Radiation Treatment Planning

An optimization framework for three-dimensional conformal radiation therapy is presented. In conformal therapy, beams of radiation are applied to a patient from different directions, where the aperture through which the beam is delivered from each direction is chosen to match the shape of the tumor, as viewed from that direction. Wedge filters may be used to produce a gradient in beam intensity across the aperture. Given a set of equispaced beam angles, a mixed-integer linear program can be solved to determine the most effective angles to be used in a treatment plan, the weight (exposure time) to be used for each beam, and the type and orientation of wedges to be used. Practical solution techniques for this problem are described; they include strengthening of the formulation and solution of smaller approximate problems obtained by a reduced parametrization of the treatment region. In addition, techniques for controlling the dose-volume histogram implicitly for various parts of the treatment region using hot-and cold-spot control parameters are presented. Computational results are given that show the effectiveness of the proposed approach on practical data sets.

[1]  J. Kereiakes,et al.  The method of linear programming applied to radiation treatment planning. , 1968, Radiology.

[2]  B Legras,et al.  Software for linear and non-linear optimization in external radiotherapy. , 1982, Computer programs in biomedicine.

[3]  M. Goitein,et al.  Multi-dimensional treatment planning: II. Beam's eye-view, back projection, and projection through CT sections. , 1983, International journal of radiation oncology, biology, physics.

[4]  David Sonderman,et al.  Radiotherapy Treatment Design Using Mathematical Programming Models , 1985, Oper. Res..

[5]  M. Langer,et al.  Optimization of beam weights under dose-volume restrictions. , 1987, International journal of radiation oncology, biology, physics.

[6]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[7]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[8]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[9]  S. Webb.  Optimisation of conformal radiotherapy dose distributions by simulated annealing. , 1989, Physics in medicine and biology.

[10]  I. Rosen,et al.  The influence of dose constraint point placement on optimized radiation therapy treatment planning. , 1990, International journal of radiation oncology, biology, physics.

[11]  T. Bortfeld,et al.  Methods of image reconstruction from projections applied to conformation radiotherapy. , 1990, Physics in medicine and biology.

[12]  J. Shapiro,et al.  Large scale optimization of beam weights under dose-volume restrictions. , 1990, International journal of radiation oncology, biology, physics.

[13]  E. T. Quinto,et al.  The mathematics and physics of radiation dose planning using X-rays , 1990 .

[14]  S. Shalev,et al.  The objective evaluation of alternative treatment plans: II. Score functions. , 1991, International journal of radiation oncology, biology, physics.

[15]  S. Webb.  Optimization by simulated annealing of three-dimensional conformal treatment planning for radiation fields defined by a multileaf collimator. , 1991, Physics in medicine and biology.

[16]  I. Rosen,et al.  Treatment plan optimization using linear programming. , 1991, Medical physics.

[17]  C. Pelizzari,et al.  The use of beam's eye view volumetrics in the selection of non-coplanar radiation portals. , 1992, International journal of radiation oncology, biology, physics.

[18]  C. Pelizzari,et al.  Beam's eye view volumetrics: an aid in rapid treatment plan development and evaluation. , 1992, International journal of radiation oncology, biology, physics.

[19]  S. Webb.  Optimization by simulated annealing of three-dimensional, conformal treatment planning for radiation fields defined by a multileaf collimator: II. Inclusion of two-dimensional modulation of the x-ray intensity. , 1992, Physics in medicine and biology.

[20]  T. Bortfeld,et al.  Optimization of beam orientations in radiation therapy: some theoretical considerations. , 1993, Physics in medicine and biology.

[21]  G. Sherouse.  A mathematical basis for selection of wedge angle and orientation. , 1993, Medical physics.

[22]  P. C. Williams,et al.  The design and performance characteristics of a multileaf collimator , 1994, Physics in medicine and biology.

[23]  T. Bortfeld,et al.  Realization and verification of three-dimensional conformal radiotherapy with modulated fields. , 1994, International journal of radiation oncology, biology, physics.

[24]  E. Hussein,et al.  Determination of beam orientation in radiotherapy planning. , 1994, Medical physics.

[25]  Anders Brahme,et al.  Few‐field radiation therapy optimization in the phase space of complication‐free tumor control , 1995, Int. J. Imaging Syst. Technol..

[26]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[27]  S. Webb.  The Physics of Conformal Radiotherapy: Advances in Technology , 1997 .

[28]  S. Webb.  The Physics of Conformal Radiotherapy , 1997 .

[29]  C. Pelizzari,et al.  Optimization of relative weights and wedge angles in treatment planning. , 1997, Medical physics.

[30]  C G Rowbottom,et al.  Improvements in prostate radiotherapy from the customization of beam directions. , 1998, Medical physics.

[31]  S. Webb.  Configuration options for intensity-modulated radiation therapy using multiple static fields shaped by a multileaf collimator. , 1998, Physics in medicine and biology.

[32]  K. Burnham,et al.  Optimization of beam orientation in radiotherapy using planar geometry. , 1998, Physics in medicine and biology.

[33]  C. Pelizzari,et al.  A three-dimensional algorithm for optimizing beam weights and wedge filters. , 1998, Medical physics.

[34]  C G Rowbottom,et al.  Beam-orientation customization using an artificial neural network. , 1999, Physics in medicine and biology.

[35]  A L Boyer,et al.  Clinical implementation of wedge filter optimization in three-dimensional radiotherapy treatment planning. , 1999, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[36]  Michael C. Ferris,et al.  Optimizing the Delivery of Radiation Therapy to Cancer Patients , 1999, SIAM Rev..

[37]  B. Murray,et al.  The development of target-eye-view maps for selection of coplanar or noncoplanar beams in conformal radiotherapy treatment planning. , 1999, Medical physics.

[38]  Weldon A. Lodwick,et al.  Optimization Methods for Radiation Therapy Plans , 1999 .

[39]  J. Tervo,et al.  A model for the control of a multileaf collimator in radiation therapy treatment planning , 2000 .

[40]  Eva K. Lee,et al.  Optimization of radiosurgery treatment planning via mixed integer programming. , 2000, Medical physics.

[41]  J. Dai,et al.  Selecting beam weight and wedge filter on the basis of dose gradient analysis. , 2000, Medical physics.

[42]  J. Dai,et al.  Optimizing beam weights and wedge filters with the concept of the super-omni wedge. , 2000, Medical physics.

[43]  C G Rowbottom,et al.  Simultaneous optimization of beam orientations and beam weights in conformal radiotherapy. , 2001, Medical physics.

[44]  James A. Purdy,et al.  Intensity-modulated radiotherapy: current status and issues of interest. , 2001, International journal of radiation oncology, biology, physics.

[45]  L. Xing,et al.  Pseudo beam's-eye-view as applied to beam orientation selection in intensity-modulated radiation therapy. , 2001, International journal of radiation oncology, biology, physics.

[46]  Xing Wu,et al.  A global optimization method for three-dimensional conformal radiotherapy treatment planning , 2001, Physics in medicine and biology.

[47]  L. Xing,et al.  Examination of the effect of increasing the number of radiation beams on a radiation treatment plan , 2002, Physics in medicine and biology.

[48]  Yan Chen,et al.  A deterministic iterative least-squares algorithm for beam weight optimization in conformal radiotherapy. , 2002, Physics in medicine and biology.

[49]  D M Shepard,et al.  Direct aperture optimization: a turnkey solution for step-and-shoot IMRT. , 2002, Medical physics.

[50]  Michael C. Ferris,et al.  An Optimization Approach for Radiosurgery Treatment Planning , 2002, SIAM J. Optim..

[51]  L. Xing,et al.  Incorporating prior knowledge into beam orientation optimization in IMRT. , 2002, International journal of radiation oncology, biology, physics.

[52]  Horst W. Hamacher,et al.  Inverse Radiation Therapy Planning: A Multiple Objective Optimisation Approach , 1999 .

[53]  Yair Censor,et al.  The Least-Intensity Feasible Solution for Aperture-Based Inverse Planning in Radiation Therapy , 2003, Ann. Oper. Res..

[54]  M Earl,et al.  Inverse planning for intensity-modulated arc therapy using direct aperture optimization , 2003, Physics in medicine and biology.

[55]  A. Holder.  Designing Radiotherapy Plans with Elastic Constraints and Interior Point Methods , 2003, Health care management science.

[56]  C. Yu,et al.  Inverse planning for intensity-modulated arc therapy using direct aperture optimization. , 2001, Physics in Medicine and Biology.

[57]  M. Ehrgott,et al.  Radiation Therapy Planning by Multicriteria Optimisation , 2003 .

[58]  Eva K. Lee,et al.  Integer Programming Applied to Intensity-Modulated Radiation Therapy Treatment Planning , 2003, Ann. Oper. Res..

[59]  Michael C. Ferris,et al.  Radiosurgery Treatment Planning via Nonlinear Programming , 2003, Ann. Oper. Res..

[60]  Matthias Ehrgott,et al.  Optimisation of beam directions in intensity modulated radiation therapy planning , 2003, OR Spectr..

[61]  Ronald L. Rardin,et al.  A coupled column generation, mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer , 2004, Math. Program..

[62]  Allen Holder.  Radiotherapy Treatment Design and Linear Programming , 2005 .

[63]  Michael C. Ferris,et al.  Sampling issues for optimization in radiotherapy , 2006, Ann. Oper. Res..

[64]  A. Holder.  Partitioning multiple objective optimal solutions with applications in radiotherapy design , 2006 .

[65]  Robert R. Meyer,et al.  Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches , 2006 .