Comparison of two close-packing methods for vertex placement in lattice radiotherapy (LRT).
- 1Department of Radiation Oncology, National Cancer Center, National Clinical Research Center for Cancer, Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China.
Abstract
Background
Lattice Radiation Therapy (LRT) is characterized by its 3D-mouldated spatial dose distribution of vertices inside the lattice volume with high peak-to-valley dose ratio (PVDR) for enhancing tumor control and reducing normal tissue toxicity. While face-centered cubic (FCC) and hexagonal close-packed (HCP), both achieving maximum spatial packing density, have been used for vertex placement, a direct comparative analysis of their dosimetric performance is lacking.Purpose
This study aimed to systematically compare FCC and HCP methods for vertex placement under identical conditions to determine which yields superior dosimetric outcomes, specifically regarding the peak-to-valley dose ratio (PVDR), and to provide data supporting the standardization of LRT planning.Materials and methods
This study was retrospectively conducted on 10 patients with large gross tumor volumes (GTV) (GTV; median [IQR] GTV volume: 916.59[609.37] cm³). For each patient, an identical inward margin was applied to the GTV to create the lattice volume for placing LRT vertices. Within this lattice volume, two sets of spherical vertices were generated: one arranged in a HCP lattice and the other in a FCC lattice, both vertices of same diameter. The initial diameter and volume of vertices were determined based on GTV volume. Vertex positions were optimized using an Adaptive Simulated Annealing (ASA) algorithm to maximize inter-vertex distance, with the total volume of all vertices constrained to approximately 1% of the GTV. All plans were optimized using identical dose-volume objectives. Plan quality was evaluated using GTV dose metrics (D₅%, D₁₀%, D₅₀%, D₉₀%, Dmean, V₅₀%), normal tissue mean dose (NT Dmean), maximum point doses (Dmax) to serial organs at risk and PVDR defined by both GTVD₁₀/D₉₀ and lattice volume D₁₀/D₉₀ ratios.Results
Vertex parameters (number, volume, spacing) showed no significant difference between Plan_FCC and Plan_HCP (P > 0.05). Dosimetric analysis revealed a statistically significant increase in PVDR (lattice volume D₁₀/D₉₀) for Plan_FCC compared to Plan_HCP (median [IQR]: 6.95 [3.38] vs. 4.48 [2.00], p = 0.019). No other evaluated metrics demonstrated significant differences, including other GTV metrics NT Dmean or the maximum point doses to serial OARs.Conclusions
Under matched radiation delivery technique, geometric constraints and identical dose-volume objectives, the FCC vertex arrangement yields a statistically significantly higher peak-to-valley dose ratio (lattice volume D₁₀/D₉₀), compared to the HCP arrangement, without compromising other dosimetric indices. This finding suggests that FCC may be a preferred starting configuration for LRT vertex placement in large tumors and we recommend that the FCC arrangement be prioritized in clinical practice.
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BibTeX
@article{song2026comparison,
title = {{Comparison of two close-packing methods for vertex placement in lattice radiotherapy (LRT).}},
author = {Yingjie Song and Pan Ma and Jianrong Dai},
journal = {Journal of applied clinical medical physics},
year = {2026},
month = oct,
doi = {10.1002/acm2.70850},
url = {https://europepmc.org/article/MED/42905958},
note = {CC BY},
}
RIS
TY - JOUR
TI - Comparison of two close-packing methods for vertex placement in lattice radiotherapy (LRT).
AU - Yingjie Song
AU - Pan Ma
AU - Jianrong Dai
PY - 2026
DA - 2026/10/30
JO - Journal of applied clinical medical physics
DO - 10.1002/acm2.70850
UR - https://europepmc.org/article/MED/42905958
AB - Background Lattice Radiation Therapy (LRT) is characterized by its 3D-mouldated spatial dose distribution of vertices inside the lattice volume with high peak-to-valley dose ratio (PVDR) for enhancing tumor control and reducing normal tissue toxicity. While face-centered cubic (FCC) and hexagonal close-packed (HCP), both achieving maximum spatial packing density, have been used for vertex placement, a direct comparative analysis of their dosimetric performance is lacking.Purpose This study aimed to systematically compare FCC and HCP methods for vertex placement under identical conditions to determine which yields superior dosimetric outcomes, specifically regarding the peak-to-valley dose ratio (PVDR), and to provide data supporting the standardization of LRT planning.Materials and methods This study was retrospectively conducted on 10 patients with large gross tumor volumes (GTV) (GTV; median [IQR] GTV volume: 916.59[609.37] cm³). For each patient, an identical inward margin was applied to the GTV to create the lattice volume for placing LRT vertices. Within this lattice volume, two sets of spherical vertices were generated: one arranged in a HCP lattice and the other in a FCC lattice, both vertices of same diameter. The initial diameter and volume of vertices were determined based on GTV volume. Vertex positions were optimized using an Adaptive Simulated Annealing (ASA) algorithm to maximize inter-vertex distance, with the total volume of all vertices constrained to approximately 1% of the GTV. All plans were optimized using identical dose-volume objectives. Plan quality was evaluated using GTV dose metrics (D₅%, D₁₀%, D₅₀%, D₉₀%, Dmean, V₅₀%), normal tissue mean dose (NT Dmean), maximum point doses (Dmax) to serial organs at risk and PVDR defined by both GTVD₁₀/D₉₀ and lattice volume D₁₀/D₉₀ ratios.Results Vertex parameters (number, volume, spacing) showed no significant difference between Plan_FCC and Plan_HCP (P > 0.05). Dosimetric analysis revealed a statistically significant increase in PVDR (lattice volume D₁₀/D₉₀) for Plan_FCC compared to Plan_HCP (median [IQR]: 6.95 [3.38] vs. 4.48 [2.00], p = 0.019). No other evaluated metrics demonstrated significant differences, including other GTV metrics NT Dmean or the maximum point doses to serial OARs.Conclusions Under matched radiation delivery technique, geometric constraints and identical dose-volume objectives, the FCC vertex arrangement yields a statistically significantly higher peak-to-valley dose ratio (lattice volume D₁₀/D₉₀), compared to the HCP arrangement, without compromising other dosimetric indices. This finding suggests that FCC may be a preferred starting configuration for LRT vertex placement in large tumors and we recommend that the FCC arrangement be prioritized in clinical practice.
SN - 1526-9914
ER -