Inference of deformation mechanisms and constitutive response of soft material surrogates of biological tissue by full-field characterization and data-driven variational system identification

We present a novel, fully three-dimensional approach to soft material characterization and constitutive modeling with relevance to soft biological tissue. Our approach leverages recent advances in experimental techniques and data-driven computation. The experimental component of this approach involves in situ mechanical loading in a magnetic field (using MRI), yielding the entire deformation tensor field throughout the specimen regardless of the possible irregularities in its three-dimensional shape. Characterization can therefore be accomplished with data at a reduced number of deformation states. We refer to this experimental technique as MR-u. Its combination with powerful approaches to inverse modeling, specifically methods of model inference, would open the door to insightful mechanical characterization for soft materials. In recent computational advances that answer this need, we have developed new, data-driven inverse techniques to infer the model that best explains the physics governing observed phenomena from a spectrum of admissible ones, while maintaining parsimony of representation. This approach is referred to as Variational System Identification (VSI). In this communication, we apply the MR-u approach to characterize soft polymers regarding them as surrogates of soft biological tissue, and using VSI, we infer the physically best-suited and parsimonious mathematical models of their mechanical response. We demonstrate the performance of our methods in the face of noisy data with physical constraints that challenge the identification of mathematical models, while attaining high accuracy in the predicted response of the inferred models.

Automated summary

This study introduces an innovative three-dimensional approach to characterize and model soft materials, particularly soft biological tissues. By using MRI for mechanical loading experiments and data-driven computation, the complete deformation tensor field of specimens can be obtained, allowing for characterization through a reduced number of deformation states. The combination of MRI-u with inverse modeling methods enables the inference of physically best-suited and parsimonious mathematical models for the mechanical response of soft polymers, which can serve as surrogate models for soft biological tissues.