Linear algebraic methods applied to intensity modulated radiation therapy.

Methods of linear algebra are applied to the choice of beam weights for intensity modulated radiation therapy (IMRT). It is shown that the physical interpretation of the beam weights, target homogeneity and ratios of deposited energy can be given in terms of matrix equations and quadratic forms. The methodology of fitting using linear algebra as applied to IMRT is examined. Results are compared with IMRT plans that had been prepared using a commercially available IMRT treatment planning system and previously delivered to cancer patients.

[1]  B. R. Hunt,et al.  The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer , 1973, IEEE Transactions on Computers.

[2]  B G Fallone,et al.  An active set algorithm for treatment planning optimization. , 1997, Medical physics.

[3]  Steve Webb.  Optimizing radiation therapy inverse treatment planning using the simulated annealing technique , 1995, Int. J. Imaging Syst. Technol..

[4]  Tariq S. Durrani,et al.  Conformal therapy using maximum entropy optimization , 1995, Int. J. Imaging Syst. Technol..

[5]  D M Shepard,et al.  Application of constrained optimization to radiotherapy planning. , 1999, Medical physics.

[6]  T R Mackie,et al.  An iterative filtered backprojection inverse treatment planning algorithm for tomotherapy. , 1995, International journal of radiation oncology, biology, physics.

[7]  S. Webb.  Optimizing the planning of intensity-modulated radiotherapy. , 1994, Physics in medicine and biology.

[8]  J. Varah.  A Practical Examination of Some Numerical Methods for Linear Discrete Ill-Posed Problems , 1979 .

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

[10]  I I Rosen,et al.  Dose-volume considerations with linear programming optimization. , 1991, Medical physics.

[11]  T. Mackie,et al.  Iterative approaches to dose optimization in tomotherapy. , 2000, Physics in medicine and biology.

[12]  G T Chen,et al.  Fast iterative algorithms for three-dimensional inverse treatment planning. , 1998, Medical physics.

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

[14]  B G Fallone,et al.  A continuous penalty function method for inverse treatment planning. , 1998, Medical physics.

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

[16]  J. Llacer.  Inverse radiation treatment planning using the Dynamically Penalized Likelihood method. , 1997, Medical physics.