Predictive analysis of Drug concentration in drug release process via two-dimensional mechanistic model and machine learning integrated Grey Wolf optimization

This research develops a machine learning framework to predict the spatial distribution of drug concentration (C) within a specific cylindrical biomaterial matrix at a fixed release time (t = 2400 s), using the radial (r) and axial (z) coordinates as inputs. The predictions are limited to the specific diffusion-reaction system described by the mass transfer equations, and the parameter set defined by Maxwell method, with no extrapolation beyond the training domain of r ∈ [0, 0.006] m and z ∈ [0, 0.009] m. Three distinct models, Kernel Ridge Regression (KRR), eXtreme Gradient Boosting (XGBoost), and Gaussian Process Regression (GPR), were employed to predict C based on the input parameters r and z. The data for machine learning were obtained by solution of mass transfer equations for this specific system. The effectiveness of each model was evaluated by considering essential metrics, such as the R² score, the Mean Squared Error (MSE), and the Root Mean Squared Error (RMSE). The findings suggest that the XGBoost model surpassed both GPR and KRR, attaining an R² score of 0.97322, showcasing its effectiveness in capturing the inherent patterns within the dataset. GPR also demonstrated good performance with an R² score of 0.95911, whereas KRR exhibited lower accuracy with an R² score of 0.75277. To enhance the models’ predictive capabilities, hyperparameter optimization was carried out using Grey Wolf Optimization (GWO). Within the specific simulated system investigated, this study demonstrates the efficacy of ML models with hyperparameter optimization for predicting spatial drug concentration. Extension to other systems requires additional validation.