A neural network embedding the linear-quadratic model for improved prediction of cellular response to ion beam...

Predicting biological responses to ionizing radiation is challenging due to the complex, multi-scale mechanisms involved. Traditional machine learning (ML) models that fit experimental data on cell survival can be sensitive to experimental uncertainties and lack theoretical consistency. This study developed and validated a neural network (NN) framework that integrates established radiobiological constraints directly into its architecture and training process. The objective was to predict cell surviving fractions (SF) and key radiosensitivity parameters for various cell types and radiation qualities in a manner that remains consistent with known dose-response behaviour. A multi-branch feedforward NN was developed to simultaneously predict SF and derived parameters including the linear-quadratic model (LQM) parameters α and β, the mean inactivation dose (MID), the dose at 10% survival (D₁₀), and the relative biological effectiveness at 10% survival (RBE₁₀). The model architecture explicitly embeds the LQM formula and the calculations of radiosensitivity parameters within dedicated custom layers. A custom loss function penalizes deviations from known ranges and balances multiple prediction objectives. Trained and validated using the Particle Irradiation Data Ensemble (PIDE) via ten-fold cross-validation, the NN achieved high prediction accuracy. Predicted SF values were in excellent agreement with experimental data (R² ≈ 0.95). The model also robustly predicted D₁₀ and MID values (R² ≈ 0.80) and RBE₁₀ value (R² ≈ 0.75). Predictions of LQM's α parameter were reasonably correlated (R² ≈ 0.65), whereas β parameter predictions exhibited greater uncertainty. The integration of the LQM formalism into the NN architecture yielded a model that produces consistent predictions parameterized by mechanistically relevant variables across diverse radiation qualities. Constraining the model with established radiobiological constraints improved its ability to link input features to cellular outcomes, ensuring accurate dose-response modeling and valid extrapolations.