Compressed radiotherapy treatment planning: A new paradigm for rapid and high-quality treatment planning optimization

Radiotherapy treatment planning involves solving large-scale optimization problems that are often approximated and solved sub-optimally due to time constraints. Central to these problems is the dose influence matrix-also known as the dij matrix or dose deposition matrix-which quantifies the radiation dose delivered from each beamlet to each voxel. Our findings demonstrate that this matrix is highly compressible, enabling a compact representation of the optimization problems and allowing them to be solved more efficiently and accurately.

To develop a compressed radiotherapy treatment planning framework based on a sparse-plus-low-rank matrix compression technique. This approach circumvents conventional sparsification methods that discard small matrix elements-often representing scattering components-and may compromise the quality of the treatment plan.

We precompute the primary ( $S$ ) and scattering ( $L$ ) dose contributions of the dose influence matrix $A$ separately for photon therapy, expressed as: $A=S+L$ . Our analysis reveals that the singular values of the scattering matrix $L$ exhibit exponential decay, indicating that $L$ is a low-rank matrix. This allows us to compress $L$ into two smaller matrices: $L^{m\times n}\approx H^{m\times r}{W}^{r\times n}$ , where $r$ is relatively small (approximately 5-10). Since the primary dose matrix $S$ is sparse, this supports the use of the well-established "sparse-plus-low-rank" decomposition technique for the influence matrix $A$ , approximated as: $A\approx S+H\times W$ . We introduce an efficient algorithm for sparse-plus-low-rank matrix decomposition, even without direct access to the scattering matrix. This algorithm is applied to optimize treatment plans for ten lung and ten prostate patients, using both compressed and sparsified versions of matrix $A$ . We then evaluate the dose discrepancy between the optimized and final plans. We also integrate this compression technique with our in-house automated planning system, ECHO, and evaluate the dosimetric quality of the generated plans with and without compression.

Compressed planning offers superior trade-offs between accuracy and computational efficiency, adjustable through algorithm parameters. For example, we achieved average reductions in dose discrepancy and optimization time of 73% and 20%, respectively, for 10 prostate patients, and 83% and 13% for lung patients. By using the compressed matrix within our automated ECHO planning system, we maintained comparable PTV coverage while significantly enhancing the sparing of organs at risk. Specifically, mean doses to the bladder and rectum for prostate patients were reduced by 8.8% and 12.5%, respectively. For lung patients, mean doses to the lungs (left and right, excluding GTV) and heart were reduced by 10.8% and 11.2%, respectively, compared to plans generated with the sparsified matrix.

The proposed framework enables rapid, high-quality treatment planning without compromising data integrity and plan quality. By integrating that with recent advancements in AI-driven influence matrix calculations, this platform has the potential to facilitate fast and efficient online adaptive radiotherapy treatment planning, enhancing both speed and accuracy in clinical workflows.