A Nomogram for Predicting the Expected Seed Count for Diffusing Alpha-Emitters Radiation Therapy (Alpha DaRT) Treatment Planning
Abstract
Purpose
To develop, compare, and validate a nomogram that uses tumor shape and size to predict seed density for Diffusing Alpha-emitters Radiation Therapy (Alpha DaRT) treatment planning with flexible and needle applicators.
Methods
DaRT seed densities were evaluated using four geometry-based nomogram models differing by tumor shape (cuboid or ellipsoid) and needle row offset pattern (cubic or hexagonal lattice). All models assumed parallel needle insertion with uniform inter-needle spacing. A seed was counted as included if its geometric center lay within the tumor volume. Tumor volumes ranging from 1 to 40 cm³ were generated by independently varying each tumor axis dimension from 1 mm upward in 0.5 mm increments. Seed density was compared for: (1) cubic needle lattice in a cuboid volume, (2) hexagonal needle lattice in a cuboid volume, (3) cubic needle lattice in an ellipsoidal volume, and (4) hexagonal needle lattice in an ellipsoidal volume.
Results
The highest seed density was observed for the hexagonal needle lattice within an ellipsoidal treatment volume (7.2 ± 1.0 seeds/cm³), whereas the lowest occurred for the cubic needle lattice within a cuboidal treatment volume (4.7 ± 1.0 seeds/cm³). The remaining two configurations yielded comparable densities (6.6 ± 2.1 and 6.8 ± 1.1 seeds/cm³). These values agree with the first-in-human Alpha DaRT clinical trial by Popovtzer et al., which reported approximately 7 seeds/cm³. For our first clinical case (CTV = 3.14 cm³), both the pre-implant plan (25 seeds) and post-implant outcome (21 seeds) were most consistent with ellipsoidal treatment volumes using either a cubic (21.5 ± 5.8 seeds) or a hexagonal needle lattice (23.6 ± 4.5 seeds).
Conclusion
This work demonstrates that geometry-based nomograms capture the influence of tumor shape and packing geometry on achievable seed distributions, enabling more reproducible and personalized Alpha DaRT treatment planning quality assurance prior to seed order placement.