On the use of principal component analysis method to optimize sphere packing algorithm for lattice radiotherapy of large/bulky unresectable tumor

Background: Spatially Fractionated Radiotherapy (SFRT) delivers highly heterogenous dose distribution, characterized by an alternating pattern of high- and low-dose regions within the large tumor volume. Lattice SFRT (LRT) achieves this dose distribution via high-dose spheres arranged in a hexagonal pattern throughout the tumor. A major obstacle in LRT planning is optimizing the number of spheres within the tumor while maintaining the geometric constraints to allow for steep dose gradients and preserving normal tissue dose levels. Purpose: We present a novel strategy for lattice deployment for LRT using principal component analysis (PCA) to address the sphere packing problem. The aim of this report is improving sphere packing for LRT treatments will increase the volume of the peak dose the tumor receives from a given lattice configuration, potentially enhancing patient outcomes. Methods: Three lattice deployment methods were investigated. Our proposed method split-PCA (s-PCA), in which the lattice pattern is oriented split between the first and second principal axes, 1-PCA has the lattice pattern oriented based on the first principal axis, and n-PCA which does not utilize PCA to orientate the lattice pattern within the tumor. Thirty-five previously treated SFRT patients (15 Gy in 1 fraction) were replanned using each PCA method. All plans utilized four full VMAT arcs, offset collimator angles of ± 15°, 6MV-FFF energy, and a lattice diameter of 1.5 cm and spacing of 3 cm. The resulting plans were evaluated based on D_50%, D_mean, V_50%, D_10%, D_90%, peak-to-valley dose ratio (PVDR = D_10% ÷ D_90%), D_2cm, and D_max to nearby critical organs. Results: The s-PCA lattice plans had a statistically significant increase in the number of spheres packed within the tumor compared to the 1-PCA (Δ mean = 0.91, p = 0.019) and n-PCA (Δ mean = 1.43, p < 0.001). In addition, the s-PCA method outperformed the n-PCA method in terms of D_50%, D_mean, V_50%, D_10%, and D_90% and statistically outperformed 1-PCA in terms of D_50%, D_10%, and D_90%. However, the s-PCA gave a statistically significant decrease in PVDR in comparison to the 1-PCA (Δ mean = −0.94, p = 0.036) and the n-PCA (Δ mean = −2.21, p < 0.001). Within our study cohort, there were no significant differences between the three deployment methods when analyzing D_2cm or maximum dose to critical organs. Conclusion: This lattice deployment strategy demonstrated enhanced sphere packing, thus improving tumor dose while restricting maximum dose to critical organs. The s-PCA approach may enhance debulking and sensitization of large and unresectable tumors for follow-up treatments. The s-PCA method has been implemented within our clinical practice, with future research focusing on prospective studies to assess clinical outcomes.