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

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.

Free-breathing motion compensated 4D (3D+respiration) T2-weighted turbo spin-echo MRI for body imaging

Purpose: To develop and evaluate a free-breathing respiratory motion compensated 4D (3D+respiration) $T_2$-weighted turbo spin echo sequence with application to radiology and MR-guided radiotherapy. Methods: k-space data are continuously acquired using a rewound Cartesian acquisition with spiral profile ordering (rCASPR) to provide matching contrast to the conventional linear phase encode ordering and to sort data into multiple respiratory phases. Low-resolution respiratory-correlated 4D images were reconstructed with compressed sensing and used to estimate non-rigid deformation vector fields, which were subsequently used for a motion compensated image reconstruction. rCASPR sampling was compared to linear and CASPR sampling in terms of point-spread-function (PSF) and image contrast with in silico, phantom and in vivo experiments. Reconstruction parameters for low-resolution 4D-MRI (spatial resolution and temporal regularization) were determined using a grid search. The proposed motion compensated rCASPR was evaluated in eight healthy volunteers and compared to free-breathing scans with linear sampling. Image quality was compared based on visual inspection and quantitatively by means of the gradient entropy. Results: rCASPR provided a superior PSF (similar in ky and narrower in kz) and showed no considerable differences in images contrast compared to linear sampling. The optimal 4D-MRI reconstruction parameters were spatial resolution=$4.5 mm^3$ and $\lambda_t=10^{-4}$. The groupwise average gradient entropy was 22.31 for linear, 22.20 for rCASPR, 22.14 for soft-gated rCASPR and 22.02 for motion compensated rCASPR. Conclusion: The proposed motion compensated rCASPR enables high quality free-breathing T2-TSE with minimal changes in image contrast and scan time. The proposed method therefore enables direct transfer of clinically used 3D TSE sequences to free-breathing.