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Optimization models for needle placement in 3D-printed masks for high dose rate brachytherapy

Nasim Mirzavand Boroujeni, Jean-Philippe P. Richard, David Sterling, Christopher Wilke

TL;DR

This paper tackles the challenge of placing HDR-BT needles in 3D-printed masks for skin cancers, aiming to deliver homogeneous dose distributions while avoiding critical structures. It introduces two modeling paradigms—fixed and free needles—with a three-phase workflow for the latter: Phase 1 identifies promising dwell positions, Phase 2 selects a nonintersecting set of needles via a maximum-coverage or clustering approach, and Phase 3 derives a final dose plan using a line-source model. Across a nose-cancer case, the proposed methods yield more uniform DVHs and improved dosimetric indices compared to a Freiburg flap clinical plan, while offering potential reductions in planning time, particularly with the clustering-based approach. The work provides rigorous geometric constraints for needle-needle and needle-structure nonintersection using conic dual formulations, and it demonstrates practical applicability through detailed experimental procedures and comparative analyses. Overall, the study advances patient-specific, mask-based HDR-BT planning by combining computational optimization with clinically relevant dose objectives and feasibility constraints.

Abstract

High dose rate brachytherapy (HDR-BT) is an appealing treatment option for superficial cancers that permits the delivery of higher local doses than other radiation modalities without a significant increase in toxicity. In order for HDR-BT to be used in these situations, needles through which the radiation source is passed must be strategically placed in close proximity to the patient's body. Currently, this crucial step is performed manually by physicians or medical physicists. The use of 3D-printed masks customized for individual patients has been advocated as a way to more precisely and securely position these needles, with the potential of producing better and safer treatment plans. In this paper, we propose optimization approaches for positioning needles within 3D-printed masks for HDR-BT, focusing on skin cancers. We numerically show that the models we propose efficiently generate more homogeneous plans than those derived manually and provide an alternative to manual placement that can save planning time and enhance plan quality.

Optimization models for needle placement in 3D-printed masks for high dose rate brachytherapy

TL;DR

This paper tackles the challenge of placing HDR-BT needles in 3D-printed masks for skin cancers, aiming to deliver homogeneous dose distributions while avoiding critical structures. It introduces two modeling paradigms—fixed and free needles—with a three-phase workflow for the latter: Phase 1 identifies promising dwell positions, Phase 2 selects a nonintersecting set of needles via a maximum-coverage or clustering approach, and Phase 3 derives a final dose plan using a line-source model. Across a nose-cancer case, the proposed methods yield more uniform DVHs and improved dosimetric indices compared to a Freiburg flap clinical plan, while offering potential reductions in planning time, particularly with the clustering-based approach. The work provides rigorous geometric constraints for needle-needle and needle-structure nonintersection using conic dual formulations, and it demonstrates practical applicability through detailed experimental procedures and comparative analyses. Overall, the study advances patient-specific, mask-based HDR-BT planning by combining computational optimization with clinically relevant dose objectives and feasibility constraints.

Abstract

High dose rate brachytherapy (HDR-BT) is an appealing treatment option for superficial cancers that permits the delivery of higher local doses than other radiation modalities without a significant increase in toxicity. In order for HDR-BT to be used in these situations, needles through which the radiation source is passed must be strategically placed in close proximity to the patient's body. Currently, this crucial step is performed manually by physicians or medical physicists. The use of 3D-printed masks customized for individual patients has been advocated as a way to more precisely and securely position these needles, with the potential of producing better and safer treatment plans. In this paper, we propose optimization approaches for positioning needles within 3D-printed masks for HDR-BT, focusing on skin cancers. We numerically show that the models we propose efficiently generate more homogeneous plans than those derived manually and provide an alternative to manual placement that can save planning time and enhance plan quality.

Paper Structure

This paper contains 36 sections, 10 theorems, 26 equations, 13 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Literature review
  4. Problem features and modeling constructs
  5. Exiting planes
  6. Intersection between two needles
  7. Intersection between a needles and a body structure
  8. Models and methods
  9. Fixed needles model
  10. Free needles model
  11. Phase 1: Finding candidate dwell positions.
  12. Phase 2: Finding needles associated with candidate dwell positions.
  13. Method 1: Maximum coverage model.
  14. Method 2: Clustering approach.
  15. Step 1 (Assigning dwell positions to needles).
  16. ...and 21 more sections

Key Result

Proposition 2.0

Let $({\color{black}x}^i,{\color{black}d}^i,{\color{black}l}^i,{\color{black}u}^i)$ and $({\color{black}x}^j,{\color{black}d}^j,{\color{black}l}^j,{\color{black}u}^j)$ be the parameters of two finite needles ${\color{black}\ell}^i$ and ${\color{black}\ell}^j$. Also let ${\color{black}p} \ge 1$ and $ in variables ${\color{black}v}=({\color{black}v^0};{\color{black}v^0_+};{\color{black}v^1},{\color{

Figures (13)

  • Figure 1: Case study of a patient with skin cancer on the nose
  • Figure 2: 3D representation of body structures included in DVHs computations
  • Figure 3: Clinical results
  • Figure 4: Fixed needles model results
  • Figure 5: 3D representation of candidate dwell positions
  • ...and 8 more figures

Theorems & Definitions (14)

  • Proposition 2.0
  • Proposition 2.0
  • Proposition 2.0
  • Proposition 6.0
  • proof
  • Corollary 6.1
  • Proposition 6.1
  • proof
  • Lemma 6.2
  • proof
  • ...and 4 more