Exploring hyperelastic material model discovery for human brain cortex:
  multivariate analysis vs. artificial neural network approaches
Jixin Hou Nicholas Filla Xianyan Chen Mir Jalil Razavi Tianming Liu Xianqiao Wang
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.