In vivo data-driven discovery of tissue's constitutive relations: proof of concept on a thigh muscle

Motivation: Over simplified constitutive relations limit the applicability of in vivo biomechanical analysis of tissue. Goal(s): To develop a data-driven framework for discovering potentially more accurate in vivo constitutive relations using displacement fields and pressure measurements obtained in a simple acquisition/reconstruction setup. Approach: An inflatable pressure cuff is used to deform the thigh muscle during an MRI scan. Time-resolved images and displacement fields are reconstructed directly from k-space and used to extract strain information. This information allows for the discovery of potentially more accurate constitutive relations. Results: An anisotropic constitutive relation for the hamstring is found. Numerical tests suggest the validity of the method. Impact: Data-driven discovery of tissue’s constitutive relations could help to better characterise its mechanical properties. We demonstrated in this proof of concept study that information acquired during simple dynamic loading experiments allows reconstruction of constitutive relations that include muscle anisotropy.