Principal-stretch-based constitutive neural networks autonomously discover a subclass of Ogden models for human brain tissue

Abstract

The soft tissue of the brain deforms in response to external stimuli, which can lead to traumatic brain injury. Constitutive models relate the stress in the brain to its deformation and accurate constitutive modeling is critical in finite element simulations to estimate injury risk. Traditionally, researchers first choose a constitutive model and then fit the model parameters using tension, compression, or shear experiments. In contrast, constitutive artificial neural networks enable automated model discovery without having to choosing a specific model a priori before learning the model parameters. Here we reverse engineer a constitutive artificial neural network that uses the principal stretches, raised to a wide range of exponential powers, as activation functions for the hidden layer. Upon training, the network autonomously discovers a subclass of models with multiple Ogden terms that outperform popular constitutive models including neo Hooke, Blatz Ko, and Mooney Rivlin. While invariant-based networks fail to capture the pronounced tension-compression asymmetry of brain tissue, our principal-stretch-based network can simultaneously explain tension, compression, and shear data for the cortex, basal ganglia, corona radiata, and corpus callosum. Without fixing the number of terms a priori, our model self-selects the best subset of terms out of more than a million possible combinations, while simultaneously discovering the best model parameters and best experiment to train itself. Eliminating user-guided model selection has the potential to induce a paradigm shift in soft tissue modeling and democratize brain injury simulations. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.