Nibbling toward optimal sphere packing for lattice spatially fractionated radiotherapy of large and bulky unresectable tumors

Abstract

Background
The Spatially Fractionated Radiotherapy (SFRT) treatment technique is characterized by its highly heterogeneous dose distribution, with an alternating pattern of high‐ and low‐dose areas inside large tumors. For lattice SFRT, a technique that utilizes high‐dose spheres, a common obstacle is maximizing the number of high‐dose spheres within the tumor while maintaining spacing rules to preserve the low‐dose regions.


Purpose
We propose a novel algorithm that uses the Rödl nibble methodology to optimize the number of lattice vertices placement for SFRT planning. By increasing the number of vertices, tumor dose metrics can be enhanced, potentially improving patient outcomes.


Materials and methods

Our new proposed algorithm, which utilizes the Rödl nibble technique, was benchmarked against the standard lattice deployment method, where the lattice centers are placed onto a rigid grid within the tumor. Both techniques used a 1.5 cm diameter lattice sphere, with center‐to‐center spacing of 3√2 cm. Twenty patients previously treated with MLC‐based 3D‐conformal SFRT were included in this cohort. All replans utilized four full VMAT arcs, with collimator angles in increments of 15°, 6 MV‐FFF beams, and were to be delivered on a C‐arm LINAC. Both sets of replans used the same optimization objectives and priorities and were prescribed a nominal dose of 15 Gy to the GTV. Several benchmarking metrics were evaluated, including GTV D
mean
, D
10%
, D
50%
, D
90%
, V
50%
, peak‐to‐valley ratio (PVDR = D
10%
÷ D
90%
), D
2cm
, as well as the D
max
of nearby critical organs were evaluated.



Results

The Rödl nibble algorithm substantially increased the number of spheres (Δ mean = 9.2 vertices), with an algorithm execution time of 71.26 ± 74.43 s (12.89–246.30 s). This resulted in a statistically significant increase in D
mean
(Δ mean = 2.61 Gy), D
5%
(Δ mean = 2.22 Gy), D
10%
(Δ mean = 2.19 Gy), D
50%
(Δ mean = 2.68 Gy), D
90%
(Δ mean = 3.52 Gy), and V
50%
(Δ mean = 27.0%); however, this led to decreased PVDR (Δ mean = −6.41) and an increase in D
2cm
(Δ mean = 1.11 Gy). An increased D
max
to nearby critical organs was also observed. Overall, all Rödl nibble replans were clinically acceptable for SFRT treatments. An end‐to‐end example clinical case is provided to demonstrate the utility of this method.



Conclusion
Our novel nibble algorithm significantly increased the number of lattice spheres packed within the tumor volume, resulting in enhanced dose metrics while being computationally efficient. The enhanced tumor dose metrics come with the cost of increased dose outside the tumor. As we implement this method in our clinic, further research will be directed toward site‐specific optimal beam geometry to minimize dose spillage and increase the dose heterogeneity.