Alpha particle microdosimetry calculations using a shallow neural network

A shallow neural network was trained to accurately calculate the microdosimetric parameters, 〈z₁〉 and 〈z₁²〉 (the first and second moments of the single-event specific energy spectra, respectively) for use in alpha-particle microdosimetry calculations. The regression network of four inputs and two outputs was created in MATLAB and trained on a data set consisting of both previously published microdosimetric data and recent Monte Carlo simulations. The input data consisted of the alpha-particle energies (3.97-8.78 MeV), cell nuclei radii (2-10μm), cell radii (2.5-20μm), and eight different source-target configurations. These configurations included both single cells in suspension and cells in geometric clusters. The mean square error (MSE) was used to measure the performance of the network. The sizes of the hidden layers were chosen to minimize MSE without overfitting. The final neural network consisted of two hidden layers with 13 and 20 nodes, respectively, each with tangential sigmoid transfer functions, and was trained on 1932 data points. The overall training/validation resulted in a MSE = 3.71 × 10^-7. A separate testing data set included input values that were not seen by the trained network. The final test on 892 separate data points resulted in a MSE = 2.80 × 10^-7. The 95th percentile testing data errors were within ±1.4% for 〈z₁〉 outputs and ±2.8% for 〈z₁²〉 outputs, respectively. Cell survival was also predicted using actual versus neural network generated microdosimetric moments and showed overall agreement within ±3.5%. In summary, this trained neural network can accurately produce microdosimetric parameters used for the study of alpha-particle emitters. The network can be exported and shared for tests on independent data sets and new calculations.