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  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)  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
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 http://deasylab.info 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) http://www.isye.gatech.edu/nci-nsf.orart.2002/pdf-files/deasy.pdf (2002)