Application of Recursive Convolutional Layers to a 3D U-Net for Microbeam Radiotherapy dose prediction

Background and aim: Microbeam Radiotherapy (MRT) is a spatially fractionated radiotherapy modality consisting of high and low dose regions called peaks and valleys. It has been demonstrated that the prohibitively long computational time required for Monte Carlo dose calculation can be addressed effectively via the application of 3D U-Nets, but these networks can be inaccurate, especially for the valley dose. Recursive Convolutional Layers (RCL) have been shown to improve the performance of neural networks, however have never been applied to MRT dose prediction. This work applies RCLs to the problem of predicting Geant4 simulated MRT dose in rats, with the aim of increasing the dose prediction accuracy. Methods: An existing 3D U-Net architecture for MRT is modified to contain RCLs. The effect of RCLs with five recursions is investigated for every location of the 3D U-Net, for peak and valley dose. To investigate the effect of RCLs increasing the model's virtual depth, parts of the 3D U-Net are replaced with five sequential blocks of the same type. Results: The RCLs improved the model accuracy for both peak and valley dose. The valley dose prediction had the greatest improvement, with the greatest increase from 70.6% phantom voxels agreeing within 3% of the Geant4 dose to 84.9% when using the RCLs. The five sequential blocks performed worse in predicting valley dose in bone and at tissue boundaries. It is further found that it is best to place RCLs immediately after the input and before the output within the same model.