# Sparsity constrained split feasibility for dose-volume constraints in inverse planning of intensity-modulated photon or proton therapy

## TL;DR

This paper introduces a novel sparsity-constrained split feasibility approach for inverse planning in intensity-modulated radiation therapy, effectively incorporating dose-volume constraints using continuous methods, demonstrated through proton therapy case studies.

## Contribution

It presents a new split feasibility formulation with sparsity constraints for dose-volume constraints in IMRT planning, enabling continuous optimization methods and improved treatment plans.

## Key findings

- Successfully applied to 2D and clinical proton therapy cases
- Achieved dose distributions satisfying dose-volume constraints
- Performed as well as or better than existing treatment planning systems

## Abstract

A split feasibility formulation for the inverse problem of intensity-modulated radiation therapy (IMRT) treatment planning with dose-volume constraints (DVCs) included in the planning algorithm is presented. It involves a new type of sparsity constraint that enables the inclusion of a percentage-violation constraint in the model problem and its handling by continuous (as opposed to integer) methods. We propose an iterative algorithmic framework for solving such a problem by applying the feasibility-seeking CQ-algorithm of Byrne combined with the automatic relaxation method (ARM) that uses cyclic projections. Detailed implementation instructions are furnished. Functionality of the algorithm was demonstrated through the creation of an intensity-modulated proton therapy plan for a simple 2D C-shaped geometry and also for a realistic base-of-skull chordoma treatment site. Monte Carlo simulations of proton pencil beams of varying energy were conducted to obtain dose distributions for the 2D test case. A research release of the Pinnacle3 proton treatment planning system was used to extract pencil beam doses for a clinical base-of-skull chordoma case. In both cases the beamlet doses were calculated to satisfy dose-volume constraints according to our new algorithm. Examination of the dose-volume histograms following inverse planning with our algorithm demonstrated that it performed as intended. The application of our proposed algorithm to dose-volume constraint inverse planning was successfully demonstrated. Comparison with optimized dose distributions from the research release of the Pinnacle3 treatment planning system showed the algorithm could achieve equivalent or superior results.