Data-driven discovery of mechanical models directly from MRI spectral data

TL;DR

This paper introduces a novel framework that combines MRI spectral data reconstruction with data-driven discovery of biomechanical models, enabling the identification of interpretable dynamical models without relying on periodic motion.

Contribution

It presents a new integrated method that jointly reconstructs displacement fields and identifies biomechanical models directly from undersampled MRI spectral data, improving over traditional two-step approaches.

Findings

Framework successfully validated on a dynamic phantom

Outperforms two-step reconstruction and modeling approach

Does not rely on periodic motion assumptions

Abstract

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.