Exploring hyperelastic material model discovery for human brain cortex: Multivariate analysis vs. artificial neural network approaches

The human brain, characterized by its intricate architecture, exhibits complex mechanical properties that underpin its critical functional capabilities. Traditional computational methods, such as finite element analysis, have been instrumental in uncovering the fundamental mechanisms governing the brain's physical behaviors. However, accurate predictions of brain mechanics require effective constitutive models to represent the nuanced mechanical properties of brain tissue. In this study, we aimed to identify well-suited material models for human brain tissue by leveraging artificial neural network and multiple regression techniques. These methods were applied to a generalized framework of widely accepted classic models, and their respective outcomes were systematically compared. To evaluate model efficacy, all setups were maintained consistent across both approaches, except for strategies employed to mitigate potential overfitting. Our findings reveal that artificial neural networks are capable of automatically identifying accurate constitutive models from given admissible estimators. However, the five-term and two-term neural network models trained under single-mode and multi-mode loading scenarios, respectively, were found to be suboptimal. These models could be further simplified into two-term and single-term formulations using multiple regression, achieving even higher predictive accuracy. This refinement underscores the importance of rigorous cross-validations of regularization parameters in neural network-based methods to ensure globally optimal model selection. Additionally, our study demonstrates that traditional multivariable regression methods, when combined with appropriate information criterion, are also highly effective in discovering optimal constitutive models. These insights contribute to the ongoing development of advanced material constitutive models, particularly for complex biological tissues.