Data-driven discovery of mechanical models directly from MRI spectral data
This proof-of-concept study addresses the problem of modeling in vivo tissue dynamics for biomechanical insights, but it is incremental as it builds on existing spectro-dynamic and SINDy methods.
The authors tackled the challenge of identifying interpretable biomechanical models from undersampled MRI spectral data by proposing a reconstruction framework that combines displacement field reconstruction with data-driven model discovery using SINDy, and validated it on a dynamic phantom, showing it outperformed a two-step approach.
Finding interpretable biomechanical models can provide insight into the functionality of organs with regard to physiology and disease. However, identifying broadly applicable dynamical models for in vivo tissue remains challenging. In this proof of concept study we propose a reconstruction framework for data-driven discovery of dynamical models from experimentally obtained undersampled MRI spectral data. The method makes use of the previously developed spectro-dynamic framework which allows for reconstruction of displacement fields at high spatial and temporal resolution required for model identification. The proposed framework combines this method with data-driven discovery of interpretable models using Sparse Identification of Non-linear Dynamics (SINDy). The design of the reconstruction algorithm is such that a symbiotic relation between the reconstruction of the displacement fields and the model identification is created. Our method does not rely on periodicity of the motion. It is successfully validated using spectral data of a dynamic phantom gathered on a clinical MRI scanner. The dynamic phantom is programmed to perform motion adhering to 5 different (non-linear) ordinary differential equations. The proposed framework performed better than a 2-step approach where the displacement fields were first reconstructed from the undersampled data without any information on the model, followed by data-driven discovery of the model using the reconstructed displacement fields. This study serves as a first step in the direction of data-driven discovery of in vivo models.