Exploring hyperelastic material model discovery for human brain cortex: multivariate analysis vs. artificial neural network approaches
This work addresses the need for precise mechanical models in brain tissue analysis, offering incremental improvements in model selection and simplification for computational biomechanics.
The study tackled the problem of identifying accurate constitutive material models for human brain tissue by comparing artificial neural networks (ANNs) and multiple regression methods, finding that ANNs can automatically discover models but require careful regularization, while regression simplified models to two-term and single-term forms with higher accuracy.
Traditional computational methods, such as the finite element analysis, have provided valuable insights into uncovering the underlying mechanisms of brain physical behaviors. However, precise predictions of brain physics require effective constitutive models to represent the intricate mechanical properties of brain tissue. In this study, we aimed to identify the most favorable constitutive material model for human brain tissue. To achieve this, we applied artificial neural network and multiple regression methods to a generalization of widely accepted classic models, and compared the results obtained from these two approaches. To evaluate the applicability and efficacy of the model, all setups were kept consistent across both methods, except for the approach to prevent potential overfitting. Our results demonstrate that artificial neural networks are capable of automatically identifying accurate constitutive models from given admissible estimators. Nonetheless, the five-term and two-term neural network models trained under single-mode and multi-mode loading scenarios, were found to be suboptimal and could be further simplified into two-term and single-term, respectively, with higher accuracy using multiple regression. Our findings highlight the importance of hyperparameters for the artificial neural network and emphasize the necessity for detailed cross-validations of regularization parameters to ensure optimal selection at a global level in the development of material constitutive models. This study validates the applicability and accuracy of artificial neural network to automatically discover constitutive material models with proper regularization as well as the benefits in model simplification without compromising accuracy for traditional multivariable regression.