Determining Alpha Dart (224Ra) Source Requirements for Ellipsoidal Tumors Using a 3D Close Packing Algorithm
Abstract
Purpose
Diffusing alpha-emitters Radiation Therapy (Alpha DaRT) requires accurate placement of radioactive sources to ensure full coverage of the Gross Tumor Volume (GTV) while minimizing the required total number and length of implanted sources. We proposed a 3D close-packing algorithm to optimally determine the number, positions, and lengths of cylindrical sources within ellipsoidal tumors.
Methods
In this work, the great circle of a spherical tumor or the central elliptical cross-section of an ellipsoidal tumor was discretized into small circles of radius r0. We set r0 = 2 mm, corresponding to a lattice spacing of 4 mm as used by Heger et al. [1]. Cylinders with radius r0 (representing therapeutic dose surrounding Alpha DaRT sources) were placed at these centers, perpendicular to the base plane, and their heights from the base to the tumor surface were computed. The source configuration S(h) assigned to each cylinder was based on a combination of 10 mm and 20 mm cylindrical sources: 10 mm for h ≤ 10 mm, 20 mm for 10 < h ≤ 20 mm, 10 + 20 mm for 20 <h ≤ 30 mm, and so on. This ensured full geometric coverage while minimizing total source length.
Results
A Python code was implemented to calculate the number and combination of 10 mm and 20 mm sources for tumors of arbitrary dimensions. For a representative 7.54 cc tumor (24.32 mm diameter sphere and a 20 mm x 24 mm x 30 mm ellipsoid), the Python code rapidly determined the optimal source allocation. The results demonstrate that tumor shape and orientation of implantation have a significant influence on source allocation and the total source length required.
Conclusion
The proposed algorithm is immediately applicable for rapid estimations in simple ellipsoidal geometries, aiding in initial case assessment and source ordering.