History of Multi-criteria (or Multiobjective) Optimization in Radiation Therapy

Michael Lahanas


Plan: To bother about the best method of accomplishing an accidental result.
Ambrose Bierce, The Enlarged Devil’s Dictionary

Radiotherapy treatment planning in our days is still a trial and error process. The treatment planner has to protect, according to the case, a specific number of organs at risk (OAR) by excessive radiation. The planner has a list of dose values and fraction of volumes for each OAR that should if possible not receive a dose larger than the specific critical dose value. The problem is that radiation from outside the patient has to pass through the body and a specific dose should be delivered to the tumor. The protection of OARs and the planning target volume PTV coverage are objectives that are in conflict. A possibility to reduce the dose in the OARs is to increase the number of beams that allows reducing the intensity of each beam but this increases also the complexity of the treatment plan.

An important problem is the optimal number of beams and their orientation. For these beams we need to know the optimal fluence distribution. There are many different ways to protect a specific OAR but all OARs together in an optimal way is not possible. The planner has some possibilities with current treatment planning systems to modify the dose distribution. A Parameter, weight or importance factor, can be assigned to each objective for the OARs and the PTV that represents to some extent the importance of the objective. Additional critical dose values and volume fractions can be given by the planner. Based on experience a specific beam setup (number and orientation) is selected and the optimization procedure optimizes the beam fluence distribution for the specific set of weights and other parameters selected by the planner. This so called inverse optimization of beam fluences is fast enough and takes 1 minute or even only a few seconds. The optimization result cannot satisfy all the objectives and the treatment planner requires modifying the parameters to calculate the dose distribution, compare the previous results. In a trial and error process the search is repeated until the planner considers that it is difficult to improve further the resulting dose distribution or if the criteria are such that the dose distribution is acceptable.

This approach used today assumes an a priori knowledge of the planner that is expressed by the weights and critical dose values. The decision process is made before the optimization. That such knowledge does not exist, and we do not know if we will obtain such knowledge, is seen by the fact that the optimization is repeated multiple times. In this way the inverse planning is rather a mixed process where decision and optimization are iterated until a solution is selected for which we do not know its actual quality. One has to consider that actually pairs of solutions are compared and it becomes more difficult the more iterations are used to know the quality of the current solution and that of the finally selected.

Only in the last years a inverse planning method is considered that decouples the decision and the optimization process. This coupling is a consequence of trade-off between the objectives in conflict. We therefore have a multiobjective optimization problem. While radiotherapy is applied for almost a century only in the last 5 years the multiobjective character of inverse planning has been recognized. It is probably because an optimum solution by scientists is considered as something unique such as a minimum energy configuration or a minimum of a function. For multiobjective problems usually it is not possible to satisfy simultaneously all objectives in an optimal possible way with the same set of parameters. The multiobjective problem was solved by transforming it into a single objective problem using a specific set of weights for each objective. This is the current practice. Real life problems that consider not only a single objective are more probably real multiobjective problems. Mathematicians almost at the same time when radiotherapy was invented considered what an optimum is in the case of a multi-valued function.

Especially in economics such functions are often considered and Vilfredo Pareto extended the definition of optimality to such multi-valued functions. The result is that for such functions more likely a single optimum solution does not exist but rather a set of finite or even infinite set of optima, the so-called Pareto optimal solutions or Pareto set.

The purpose of multiobjective optimization is to obtain a representative set of the entire Pareto set. This set is used to analyze the trade-offs between the objectives in conflict and then to select a solution that satisfies simultaneously at best all objectives. This is the decision making process performed after the optimization. The optimization is not required to be repeated again. We say that the optimization precedes the decision making process and that optimization and decision are decoupled.

One may ask why one does not try to find the solution that finally is selected? Finally we have a single solution and not many, but the problem is that this requires a knowledge that is obtained only after the representative set is analyzed. The problem is that treatment planning systems try to be as simple as possible and having a large number of solutions is something that makes the planning not easier. It was recognized by S. Webb who said that we do not expect a car to be driven by just a using button which was suggested in some reports in the past about future technology where the driver just has to enter in the vehicle and to press the button (saying the destination).

Actually technology is the possibility to have a better control and a larger possibility and less the simplification of processes. Can we not expect a planner to be able to work with many solutions and to select from these the best? Should we not expect a planner to be educated enough for this purpose? The multiobjective optimization has some important benefits. It provides a coherent view of all possibilities. It presents a complete view of the problem and the potential solutions. Such a possibility is not offered by any system even a system that has been patented in that multiple solutions can be saved and compared. The multiobjective approach offers another important possibility. In that it decouples the decision and optimization process it provides information that is better than all the previous knowledge that has been acquired though experimentation using the trial and error methods of the past that have been presented in thousand of studies. The most important aspect of multiobjective inverse planning is that it allows to obtain solutions that provide a best possible protection for the patient and simultaneously a maximum as possible coverage of the dose required to be delivered to the cancerous region. It allows to understand and compare the limitations and differences of different methods (IMRT, hadron therapy).

Three strategies can be used for solving MO optimization problems.

Method 1 is the conventional approach. The problem is that there is no a priori knowledge and the planner blindly has to repeat the optimization with different parameters, constraints, importance factors until the result is acceptable. Of course there is no possibility really to understand the trade-off between the competing objectives. Therefore the more realistic approach is method 2. Also method 3 is considered but it does not provide really a trade-off information rather a satisfaction of constraints if possible that are relaxed if they cannot be satisfied. Approach 2 provides more insight of the dose optimization problem and has been actually developed in the last 5 years after more than 100 years application of radiotherapy.

The MO approach requires the calculation of a relative large number of solutions to obtain a representative set of solutions. Further studies have to consider the possibilities of reducing this set to the minimum possible size. Additional tools should be provided that help to analyze this set more efficiently. Can a method be used that does an automatic analysis of this set and provides the final solution? The answer is not known as long as there is no systematic comparison of the automatic selected solution using a representative set of efficient solutions. This was never done actually with some exceptions such as in Phys. Med. Biol. 48 pages 399-415 and 2843-2871 (2003). Even if so as Steve Webb says: “Would it be a good thing if a genuinely automated customization technique could be created? At first sight the answer might seem to be affirmative. However, after a while, the skills of human judgment would cease to propagate. Planners might even forget what controls the goodness of outcome. The planning task could become a turnkey. It could become dangerous. Hence I would argue that complete automation is not a desirable objective.” He also says that “automation of treatment planning should not remove the human from key decision making”. Multiobjective optimization is considering exactly this important aspect.

TIMELINE


1906




1997

Haas et al use the first true MO optimization method (a posteriori) in radiotherapy



Yan Yu proposes a decision theoretic steered multiobjective optimization algorithm which can be considered as a mixture of an apriori and a posteriori methods (Method 3). The aim is the satisfaction of constraints. If not then these are relaxed. The method is applied in LDR brachytherapy, neurosurgery and radiation therapy in general. Only one solution is obtained. PIPER a planning system by Yan Yu and others is a result of this work.

1998

Oliver Haas uses the first true multiobjective or multicriteria optimization algorithm: The algorithm is applied in conformal 2 dimensional radiation therapy using only geometrical constraints. The trade-off is obtained.



O. Haas present the first true multiobjective optimization approach for radiotherapy. The algorithm considers only the optimization of geometric objectives to obtain the tradeoff between various geometric objectives used to determine an optimal arrangement of beam directions. A evolutionary algorithm is used.

1999

Haas extends in this monograph the MO approach to dose optimization in conformal beam radiotherapy


This is the first paper of a multiobjective optimization of dwell times for high-dose rate brachytherapy. The optimization and decision making process are decoupled. A Pareto optimal set is obtained and a selection is selected. The results are compared with that Nucletron's planning system. The conformity index COIN is used for the objectives of the PTV and the NT in combination.

2000





2001


The EUROGEN 2001 and EMO2001 papers compare the performance of deterministic and evolutionary MO optimization algorithms. The result is a hybrid version of an MOEA algorithm initialized by a deterministic algorithm.

2002


The paper considers multi-criteria optimization with the deterministic algorithm BFGS. The square root of weights is used as optimization parameter that avoids negative weights commonly found in planning systems such as PLATO by Nucletron which are removed by setting these to 0 which reduces the quality of the solution. The objectives is the dose variance on the PTV surface. Since a correlation exists between COIN and dose variance on the PTV surface the variance is used. It provides a convex set of objectives and provides global optimal solutions.



2003


This paper compares 3 deterministic algorithms for MO optimization in HDR brachytherapy. Although the objectives are convex some failure is observed. This is the first paper that considers global convergence properties. The L-BFGS algorithm is found to provide global optimal solutions.

This paper considers DVH based objectives and constraints for HDR MO inverse planning with evolutionary algorithm as the objective space and constraints are not necessary convex and therefore local minima and concave regions do not allow weighted sums. The algorithm is applied in the planning system SWIFT. The first treatment planning system with a true MO optimization that provides a tradeoff information and a non-dominated set of solutions.


This paper considers methods to avoid dose calculations and allows a very fast MO optimization of dwell times for HDR brachytherapy. The optimization time is almost independent on the number of sampling points.



A multiobjective evolutionary library IMRTOPT for IMRT dose optimization was developed by Kostas Karouzakis and Eduard Schreibmann. The basic library is MOMHLIB of A. Jaskiewicz. This includes the possibility of a deterministic weighted multiobjective optimization with L-BFGS.

This paper considers method considers a multiobjective optimization of beam fluences for IMRT. The global convergence properties of LBFGS are studied. The paper compares 2 set of objectives and suggests the use of Pareto optimality and Pareto fronts as the only correct approach to compare the limitations and differences between different algorithms and set of objectives and constraints. A mechanism is proposed to avoid a 1-2% failure of global convergence of L-BFGS. This is the first approach that is not disturbed by negative weights that other algorithms avoid by constraints or that are eliminating by setting negative fluences to 0 thus distrorting the optimization approach. The paper considers realistic 3D cases.





SWIFTTM

The Treatment planning system SWIFT™ with optimization algorithms developed in Offenbach first in WinOPT-HDR that have been further improved is the first brachytherapy planning system that uses multiobjective optimization methods in clinical routine. It is the first system that decouples optimization and decision in that it presents the trade-off information. Multiobjective algorithms are now used every day in clinical practice in radiotherapy using this system for HDR prostate treatment, developed by Pi-Medical and MedCom, now available by Nucletron.

The Nucletron SWIFT™ system provides the user with a dedicated 3D planning system for HDR Prostate Treatment. Transversal ultrasound images are captured, using a standard stepper unit and ultrasound system, and transformed into 3D information. This is used to determine the optimal implant geometry and to guide the user during the insertion of the needles. The optimal treatment plan is created while the patient is still in the operating room!


Pre-Plan / Live Plan / Optimization

Nucletron SWIFT™ is a unique and exciting brachytherapy treatment planning system ideal for Prostate treatment using the microSelectron© HDR remote afterloading system.

U Lutz, F van Krieken, Effective treatment of prostate cancer, Nucletron BV, THE INTERNATIONAL REVIEW OF PATIENT CARE



2004

Schreibmann et al extend the IMRT study to 3D cases including as objectives the number of beams and a beam orientation. For computational reasons the algorithm is limited to 2D cases. This is the first multiobjective inverse planning method study for IMRT that considers orientation, number of beams and weights independent of any importance factors. It provides the trade-off information necessary to select a optimal solution and replaces the guesswork of single objective optimization algorithms.

The paper considers the history of inverse planning in HDRand LDR brachytherapy from 1930 to the MO approach era.

This work describes in details an MO inverse planning algorithm for HDR brachytherapy. Additional to dosimetric objectives the number of catheters are considered and the algorithm determines optimal position and number of catheters from the analysis of the trade-off of the efficient algorithm that is obtained by a hybrid version of a deterministic and evolutionary algorithm.