Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms.

The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumour as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighbouring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard multileaf collimator (MLC) delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modelled mathematically as a system of linear inequalities. We show that using this method allows us to arrive at a smoother intensity pattern. Including nonlinear terms in the simultaneous projection algorithm to deal with dose-volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and the gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.

[1]  Y. Censor,et al.  Inherently parallel algorithms in feasibility and applications , 1997 .

[2]  Y. Censor,et al.  Block-iterative projection methods for parallel computation of solutions to convex feasibility problems , 1989 .

[3]  Y. Censor,et al.  On the use of Cimmino's simultaneous projections method for computing a solution of the inverse problem in radiation therapy treatment planning , 1988 .

[4]  Y. Censor,et al.  A computational solution of the inverse problem in radiation-therapy treatment planning , 1988 .

[5]  G Starkschall,et al.  A constrained least-squares optimization method for external beam radiation therapy treatment planning. , 1984, Medical physics.

[6]  Richard Barakat,et al.  Algorithms for reconstruction of partially known, band-limited Fourier-transform pairs from noisy data , 1985 .

[7]  J. Galvin,et al.  An optimized forward-planning technique for intensity modulated radiation therapy. , 2000, Medical physics.

[8]  M D Altschuler,et al.  Semi-automated radiotherapy treatment planning with a mathematical model to satisfy treatment goals. , 1989, International journal of radiation oncology, biology, physics.

[9]  J Höffner,et al.  Development of a fast optimization preview in radiation treatment planning. , 1996, Strahlentherapie und Onkologie : Organ der Deutschen Rontgengesellschaft ... [et al].

[10]  Yair Censor,et al.  Proximity Function Minimization Using Multiple Bregman Projections, with Applications to Split Feasibility and Kullback–Leibler Distance Minimization , 2001, Ann. Oper. Res..

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

[12]  Heinz H. Bauschke,et al.  On Projection Algorithms for Solving Convex Feasibility Problems , 1996, SIAM Rev..

[13]  Ying Xiao,et al.  The use of mixed-integer programming for inverse treatment planning with pre-defined field segments. , 2002, Physics in medicine and biology.

[14]  F Nüsslin,et al.  Intensity modulated photon beams subject to a minimal surface smoothing constraint. , 2000, Physics in medicine and biology.

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

[16]  L. Xing,et al.  Iterative methods for inverse treatment planning. , 1996, Physics in medicine and biology.

[17]  J. Hiriart-Urruty,et al.  Fundamentals of Convex Analysis , 2004 .

[18]  Olivier C.L. Haas.  Radiotherapy Treatment Planning , 1999 .

[19]  Yair Censor,et al.  The dose–volume constraint satisfaction problem for inverse treatment planning with field segments , 2004, Physics in medicine and biology.

[20]  T Lahtinen,et al.  Use of the Cimmino algorithm and continuous approximation for the dose deposition kernel in the inverse problem of radiation treatment planning. , 1998, Physics in medicine and biology.

[21]  J Yang,et al.  Smoothing intensity-modulated beam profiles to improve the efficiency of delivery. , 2001, Medical physics.

[22]  P S Cho,et al.  Conformal radiotherapy computation by the method of alternating projections onto convex sets. , 1997, Physics in medicine and biology.

[23]  David J. Evans,et al.  Medical image reconstruction using a multi-objective genetic local search algorithm , 2000, Int. J. Comput. Math..

[24]  S. Spirou,et al.  A gradient inverse planning algorithm with dose-volume constraints. , 1998, Medical physics.

[25]  P S Cho,et al.  Hardware-sensitive optimization for intensity modulated radiotherapy. , 2000, Physics in medicine and biology.

[26]  S. Webb,et al.  Inverse planning with constraints to generate smoothed intensity-modulated beams. , 1998, Physics in medicine and biology.

[27]  Weiguo Lu,et al.  Fast treatment plan modification with an over-relaxed Cimmino algorithm. , 2004, Medical physics.

[28]  S. Sutlief,et al.  Optimization of intensity modulated beams with volume constraints using two methods: cost function minimization and projections onto convex sets. , 1998, Medical physics.

[29]  Y. Censor,et al.  Parallel Optimization: Theory, Algorithms, and Applications , 1997 .

[30]  P. Xia,et al.  Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments. , 1998, Medical physics.

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

[32]  T. Bortfeld,et al.  The Use of Computers in Radiation Therapy , 2000, Springer Berlin Heidelberg.

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

[34]  Yongyi Yang,et al.  Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics , 1998 .

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