Purpose: Pre-calculation of accurate dose deposition kernels for GammaKnife (GK) and GammaPod (GP) treatment planning can be very time consuming with an enormous number of candidate shots. To address this issue, we propose a novel decomposition model of dose deposition kernels for GK and GP treatment planning.
Methods: The dose deposition kernel for an arbitrary shot position is modeled as the product of a shift-invariant kernel and spatially variant scale factor. The shift-invariant kernels, one for each collimator, are pre-calculated on the commissioning phantom using the Monte Carlo (MC) method. The spatially variant scale factor is defined as the ratio of the mean tissue maximum ratio (TMR) at the candidate shot to that at the commissioning shot. The scale factors or normalized mean TMRs can be calculated on the whole treatment volume through parallel-beam ray tracing followed by averaging over all source directions. The proposed dose calculation was compared with the MC calculation for various shot locations and spot sizes on the phantom and twelve clinical plans.
Results: The kernel decomposition (KD) model achieved similar doses to those calculated by the MC method. The Gamma index passing rates in 2%, 2 mm criteria were greater than 99% for the phantom study and clinical plans. The calculation time of the KD approach was within sub-seconds, which was several orders of magnitude faster than the MC method.
Conclusion: The scale factors can be calculated very efficiently when implemented in GPU and only needs to be calculated once before treatment planning. The proposed dose calculation can provide accurate dose and is very fast with kernel shifting and scaling. In addition, both dose and derivatives can be calculated in real-time without pre-calculating the dose deposition kernels, which is critical to efficient search of optimal plans for GK and GP.
Funding Support, Disclosures, and Conflict of Interest: This work was supported in part by NIH grants (R01 CA235723, R01 CA218402).