TY - JOUR
T1 - Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID
AU - Flaschel, Moritz
AU - Yu, Huitian
AU - Reiter, Nina
AU - Hinrichsen, Jan
AU - Budday, Silvia
AU - Steinmann, Paul
AU - Kumar, Siddhant
AU - De Lorenzis, Laura
PY - 2023
Y1 - 2023
N2 - We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of biological tissue and validate it on experimental data stemming from human brain tissue specimens. Following the motive of the recently proposed computational framework EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) and in contrast to conventional parameter calibration methods, we construct an extensive set of candidate hyperelastic models, i.e., a model library including popular models known from the literature, and develop a computational strategy for automatically selecting a model from the library that conforms to the available experimental data while being represented as an interpretable symbolic mathematical expression. This computational strategy comprises sparse regression, i.e., a regression problem that is regularized by a sparsity promoting penalty term that filters out irrelevant models from the model library, and a clustering method for grouping together highly correlated and thus redundant features in the model library. The model selection procedure is driven by data stemming from mechanical tests under different deformation modes, i.e., uniaxial compression/tension and simple torsion. The data is acquired through conventional mechanical tests that deliver labeled one-dimensional data pairs, and thus the method can be interpreted as a supervised counterpart to the originally proposed EUCLID that is informed by full-field displacement data and global reaction forces. The proposed method is verified on synthetical data with artificial noise. In addition, we present for the first time an experimental investigation of the EUCLID framework by validating the proposed method on experimental data acquired through mechanical tests of human brain specimens, proving that the method is capable of discovering hyperelastic models that exhibit both high fitting accuracy to the data as well as concise and thus interpretable mathematical representations.
AB - We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of biological tissue and validate it on experimental data stemming from human brain tissue specimens. Following the motive of the recently proposed computational framework EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) and in contrast to conventional parameter calibration methods, we construct an extensive set of candidate hyperelastic models, i.e., a model library including popular models known from the literature, and develop a computational strategy for automatically selecting a model from the library that conforms to the available experimental data while being represented as an interpretable symbolic mathematical expression. This computational strategy comprises sparse regression, i.e., a regression problem that is regularized by a sparsity promoting penalty term that filters out irrelevant models from the model library, and a clustering method for grouping together highly correlated and thus redundant features in the model library. The model selection procedure is driven by data stemming from mechanical tests under different deformation modes, i.e., uniaxial compression/tension and simple torsion. The data is acquired through conventional mechanical tests that deliver labeled one-dimensional data pairs, and thus the method can be interpreted as a supervised counterpart to the originally proposed EUCLID that is informed by full-field displacement data and global reaction forces. The proposed method is verified on synthetical data with artificial noise. In addition, we present for the first time an experimental investigation of the EUCLID framework by validating the proposed method on experimental data acquired through mechanical tests of human brain specimens, proving that the method is capable of discovering hyperelastic models that exhibit both high fitting accuracy to the data as well as concise and thus interpretable mathematical representations.
KW - Brain tissue
KW - Constitutive models
KW - Hyperelasticity
KW - Interpretable models
KW - Sparse regression
UR - http://www.scopus.com/inward/record.url?scp=85169419381&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2023.105404
DO - 10.1016/j.jmps.2023.105404
M3 - Article
AN - SCOPUS:85169419381
SN - 0022-5096
VL - 180
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
M1 - 105404
ER -