Pareto Surface Algorithm for Non-Convex Radiation Planning

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Solution Overview

Problem

Conventional radiation therapy planning methods rely on a time-consuming 'human iteration loop' to find the best compromise between radiation dosage for targets and sparing healthy tissue, particularly failing when dealing with non-convex Pareto surfaces in intensity modulated radiotherapy and volumetric arc therapy.

Innovation Solution

An algorithm that uses a feasible set and objective functions within a linear programming environment to determine and develop a multi-dimensional Pareto surface, allowing for systematic exploration of treatment options by iteratively selecting reference points and directions to build up a model of the Pareto surface, even in non-convex cases, using multi-kernel computers to execute the code.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of operation

If conventional planning methods use a single objective function with weighted objectives, then the planning process can be simplified, but the time-consuming human iteration loop is required to find optimal weighting factors

Engineering Contradiction:

Improveplanning process simplicityVSAvoidhuman iteration loop time

Core Design Contradiction:

Ease of operationVSLoss of time

Solution Approach 1:

The system automatically generates and presents multiple treatment plans with different weightings and Pareto optimal points without requiring human iteration. The optimization algorithm self-determines the Pareto front by solving multiple objective functions simultaneously, eliminating the need for planners to manually adjust weights and iterate through solutions.

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The system pre-calculates and presents multiple Pareto optimal treatment plans before the planner makes a final selection. By generating the full Pareto front in advance, the system eliminates the need for iterative human adjustment of weighting factors, allowing planners to directly review and select from pre-computed optimal solutions.

Inventive Principle:

Principle #10Preliminary action

2Ease of manufacture

If conventional methods use triangle-based iteration to define Pareto surface, then the method is simple to implement, but it fails when the surface has concave portions

Engineering Contradiction:

Improvemethod implementation simplicityVSAvoidPareto surface accuracy

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The method segments the Pareto surface approximation into multiple linear programming problems, each solved with different weighting vectors. This segmentation allows the algorithm to handle both convex and concave portions of the Pareto surface by systematically exploring different weight combinations, ensuring complete coverage of the Pareto front without relying on single-triangle iteration approaches.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The system changes the weighting parameters of multiple objective functions to systematically explore the Pareto surface. By varying the weights of different objectives (target coverage, organ sparing, etc.), the algorithm can identify Pareto optimal points across the entire surface, including concave regions, thereby improving reliability while maintaining implementation simplicity through standard linear programming techniques.

Inventive Principle:

Principle #35Parameter changes

3Adaptability or versatility

If the Pareto surface is non-convex due to non-convex objective functions or feasible set, then more treatment options are available, but conventional approximation methods fail

Engineering Contradiction:

Improvetreatment option rangeVSAvoidPareto surface approximation

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The optimization system is designed to universally handle both convex and non-convex Pareto surfaces by using multiple linear programming problems with different weighting vectors. This multi-functional approach allows the same algorithm to accurately approximate the Pareto front regardless of whether the underlying objective functions or feasible set are convex, thereby maintaining reliability while capturing the full range of treatment options.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS10431333B2Systems and method for developing radiation dosage control plans using a paretofront (pareto surface)

Publication Date: 2019.10.01 FRAUNHOFER GESELLSCHAFT ZUR FORDERUNG DER ANGEWANDTEN FORSCHUNG EV

AI summary

System, method, and computer program product to select a desired portion of a subject to receive a radiation dose, including: determining a plurality of Pareto points on a Pareto surface (PS); selecting a first reference point (p1) on a back side of an assumed Pareto surface (PS′) and first direction (q1) emerging therefrom towards PS′ from behind; selecting a first starting adjustment (x10) and iteratively developing forward a minimum criterion in steps until a final adjustment (x11) is reached that still is implementable in the radiation apparatus; stopping the forward development, thereby determining x11 represented by a final front point (y11) as a real Pareto point of PS′; and along q1, dismissing undetermined portions of the objective space in front of and behind y11 as not containing parts of the PS, and continuing with other remaining more determined portions that are assumed to each contain a part of PS′.