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					                                                                      Prioritized optimization for IMRT treatment planning

                                                                                      Konstantin Zakarian, Joseph Deasy and James Alaly
       Heading                                                                 Dept. of Radiation Oncology, Washington University, St. Louis, MO

                                                                                                                 As the linear-quadratic solver, we used the Mosek's quadratic programming                                                 CERR screen shots for Prioritized Optimization example 2
                                                                                                                 (QP) optimization toolbox to test IMRT plans on PIV 2.6 GHz. IMRT plans were
IMRT treatment planning (IMRTP) typically entails trade-offs between goals associated                            created and calculated inside CERR. The Mosek's routines allow for linear or
with tumor control (such as a high D95) and goals associated with low normal tissue                              quadratic terms in either the objective function or the constraints. This allows
complication rates (such as spinal cord dose less than 45 Gy). Previously proposed                               us to convert objective functions to inequality constraints based on the best
IMRT algorithms attempt to control such tradeoffs either by changing numerical weights                           performance of the objective function during the priority iteration.
of terms in a single objective function, or by introducing a priori inequalities on dose or
dose-volume characteristics. In both cases, the user is required to provide significant
quantitative information prior to running the treatment plan. Much of this data (e.g.,                         Examples:
dose-volume constraints) is based on estimated behavior of the best plan possible. Our
previously discussed proposal [1] is to prioritize the planning goals according to their                       Example 1. IMRT plan with 7 equally spaced 18MV beams,
clinical significance, and to iteratively re-state and solve the treatment planning problem                    Start angle 0 degrees (from patient‟s left).
taking into account the next-lower priority treatment goal at each problem re-statement.
At each problem re-statement iteration, the solver improves the plan with respect to the
                                                                                                               Total number of PB‟s – 3456 with 0.5 x 0.5 cm2 size at isocenter
stated goal, without violating the higher priority goals which have been converted to                          Structures: Cord, CTV5940, LP (left parotid), RP (right parotid), Anchor zone.
constraints. This algorithm has been implemented within our treatment planning                                 QP Mosek‟s optimizer                                                                                     Prioritized optimization test for head and heck                DVH‟s: PTV – dark green, spinal
research system (CERR) [2] and several plans based on realistic patient data have been                         Total optimization time: 3 min (5 problem statement iterations)                                          IMRT plan with 10 equally spaced beams                         cord - red, left parotid - light green,
produced. We call this approach Prioritized Radiotherapy Optimization (PRO), and we                                                                                                                                     (example 2)                                                    right parotid, brown.
conclude based on early experience that PRO is a promising approach to making IMRTP                            Example 2. IMRT plan with 10 equally space 18MV beams
more straightforward and responsive to the clinical goals of the treatment planners.
We are developing a fast implementation of PRO within CERR, based on efficient interior
                                                                                                               Start angle degrees (from patient‟s left).
point linear-quadratic programming routines.                                                                   Total number of PB‟s – 1986 with 1 x 1 cm2 size at isocenter
                                                                                                               Structures: Cord, CTV4950, LP (left parotid), RP (right parotid), Anchor zone.
                                                                                                               QP Mosek‟s optimizer                                                                                                                  Two more CERR Prioritized Optimization Examples
                                                                                                               Total optimization time: 4 min

  The prioritized radiotherapy optimization (PRO) process implemented
                                  in CERR                                                                                        Prioritized planning example input prescription

                                                                                                               1) Constraint: dose to spinal cord (with 3 mm margin) < 45 Gy

                                                                                                               2) Constraint: dose to brain stem (with 3 mm margin) < 55 Gy

                                                                                                               3) Constraint: dose to PTV < 75 Gy.

                                                                                                               4) Priority I goal: minimize quadratic variation in dose over the target (PTV) versus prescription
                                                                                                                  dose of 60 Gy.

                                                                                                               5) Priority II goal: minimize mean dose to both parotid glands.
                                                                                                                                                                                                                      IMRT head and neck plan for 7 equally angle                 IMRT head and neck plan for 9 equally angle
                                                                                                                                                                                                                      spaced 18MV beams                                           spaced 18MV beams
                                                                                                               6) Priority III goal: minimize quadratic dose in the anchor zone
                                                                         (Deasy, 2002)

                                                                                                                                        The goal is to spare the parotid glands
 1. Create fluence matrices (beamlet dose contribution matrices) for the                                                                without compromising the target dose
    structures involved in the prescription                                                                                             distribution.
 2. Formulate the prescription vectors for each of these structure (typically,
                                                                                                                                        Note the lack of ad hoc parameters or
    prescribed target dose or zero dose for normal structures)                                                                          weights.
                                                                                                                                                                                                                                                          Summary and conclusions
 3. Construct the Hessian matrix
 4. Set the priority constraints                                                                                                                                                                                    The formulation of IMRTP presented here has several advantages:
 5. Run linear-quadratic solver                                                                                                                                                                                       • Prioritized optimization allows physicians and other planners to state the
 6. For the next-lower priority objective, convert current priority objective as                                           CERR screen shots for prioritized optimization example 1                                      problem in clinically meaningful terms.
    a constraint                                                                                                                                                                                                      • Lower priority goals do not adversely affect higher priority goals. Conflicts
                                                                                                                                                                                                                         between goals are well-controlled.
                                                                                                                                                                                                                      • The ‘best performance’ of each goal is determined before converting that
         The “anchor zone” technique as a part of prioritized                                                                                                                                                            goal to a constraint for lower priority goal problem statement iterations.
                            optimization                                                                                                                                                                                 Therefore, the user does not need to know the best performance of any
                                                                                                                                                                                                                         individual plan metric before using it as a plan goal. In particular, prioritized
The “anchor zone” technique is a simple method of controlling dose characteristics                                                                                                                                       optimization does not require guesses of what the appropriate dose-volume
near the edge of a target volume which still allows for fast optimization. We introduce
                                                                                                                                                                                                                         constraints may be.
an 'anchor' structure, which is a strip region which surrounds the target at a fixed
margin. The anchor zone has a finite width (typically 1-2 cm). Between the anchor
                                                                                                                                                                                                                      • Prioritized optimization allows for the use of dose-based objectives in place
zone and the target lies the „transition zone‟, also typically 1 to 2 cm in width. The                                                                                                                                   of radiobiologically-based objectives, as each objective function is not
anchor zone is included in the objective function inside prioritized optimization as a                                                                                                                                   competing with another term representing a dissimilar outcome endpoint.
structure which should receive low doses. It thereby serves to control the dose falloff                                                                                                                             • The linear-quadratic formulation is an efficient way to formulate prioritized
behavior outside and near the target. Typically, it is a low priority goal as it is meant                                                                                                                             optimization, with single problem statement iterations requiring only 30
                                                                                                                                     Prioritized optimization test for the head and heck
merely to ensure smooth and rapid dose falloff. An extra benefit is that is tends to                                                 IMRT plan with 7 equally spaced beams (example                                   seconds to one minute, and total problem solutions are returned in less than 5
smooth beam weights as well.                                                                                                         1)                                                                               minutes.
                                                                                                                                                                                                                    • We hypothesize that prioritized radiotherapy optimization (PRO) could enable a
                                                                                                                                                                                                                      straightforward and nearly automated approach to IMRTP.

                                                                                                                                                                                                                       This research was supported by NCI grants R29 CA85181 and R01 90445.

                                                                                                                                                                                                                       CERR can be downloaded from and links. CERR is free for non-commercial research use.
                                                                                                                                                                                                                          Use of CERR for clinical patient care is prohibited.

Figure 1 (a) – transverse slice for IMRT plan with uniform         Figure 2 Magnified (4:1) images of                                                                                                                  References
beam weights (all weights equal to 1); (b) –transverse slice for   transverse slice: (a) - IMRT plan with
IMRT plan with 'anchor' optimization and 1 cm transition zone;     'anchor' optimization and 1 cm transition                                                                                                           1. Deasy, J., Prioritized treatment planning for radiotherapy optimization, Proceedings of Chicago 2000 World
(c) –transverse slice for IMRT plan 'anchor' optimization and      zone; (b) - IMRT plan with 'anchor'                                                                                                                    Congress on Medical Physics and Biomedical Engineering (proceedings on CDROM) 2000.
1.5 cm transition zone.                                            optimization and 1.5 cm transition zone.                                                                                                            2. J. O. Deasy, A. I. Blanco, and V. H. Clark “CERR: A Computational Environment for Radiotherapy
                                                                   The thinner transition zone (1 cm) is too                         DVH‟s: PTV – red (prescription 60 Gy), spinal                                        Research,” Med Phys 30:979-985 (2003).
                                                                   small.                                                                                                                                              3. J. O. Deasy, “IMRT Software Design Goals” Workshop on operations research applied to radiation therapy
                                                                                                                                     cord - purple, left parotid - magenta, right parotid
                                                                                                                                     – cyan.                                                                              (ORART) (2002)

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