Author: Serdar Charyyev, Cynthia Fu-Yu Chuang, Veng Jean Heng, Lianli Liu, Lei Xing, Yong Yang 👨🔬
Affiliation: Department of Radiation Oncology, Stanford University 🌍
Purpose: To replace large finite-size photon phase space files with a compact neural network capable of generating an infinite number of particles.
Methods: Three separate models were developed to account for the different types of particles found in photon phase spaces: primary photons, secondary photons, electrons. For each particle type, a neural network was trained to learn the implicit neural representation (INR) of the probabilistic distribution of particles. The probability density function (PDF) of particles energy (E) and position (x,y) was first modeled by a multi-layer perceptron network. For primary particles, the deterministic relationship between particle position and direction cosines (u,v) was further modeled by another network that takes (E,x,y) as inputs and outputs (u,v). To account for the stochastic nature of (u,v) for secondary particles, we adopted two networks to model the PDF of (E, x, u) and (E, y, v) respectively. After INR learning, phase space files of any desired size can be generated, by sampling the PDF implicitly modeled by the neural network. We applied the INR-based modeling strategy to a vendor-provided 6 MV photon phase space. Model accuracy was validated by using the network-sampled particles as input to an EGSnrc Monte Carlo dose calculation in a water phantom.
Results: The vendor phase space of 50GB was represented by neural networks occupying <5MB. Central axis percent depth dose curves and lateral dose profiles of EGSnrc calculated doses show excellent agreement between the dose distribution calculated using the INR-sampled vs. vendor-provided phase space. A global gamma passing rate (2%/0mm) of 98.1% was achieved when comparing the two dose distributions.
Conclusion: Large external beam photon phase space files can be faithfully represented using INR models with much reduced size (>104-fold reduction). The potential for limitless particle sampling also circumvents any latent uncertainty arising from finite size phase spaces.