Sparsity Constrained Linear Tangent Space Alignment Model (LTSA) for 3d Cardiac Extracellular Volume Mapping

Cardiac longitudinal relaxation time (T
1
) and extracellular volume (ECV) are valuable bio-markers used for the quantitative characterization of cardiac tissue properties, showing great potential in many clinical applications such as diffuse fibrosis. However, cardiac T
1
and ECV mapping is difficult because of respiratory and cardiac motions. A unique challenge for post-contrast T
1
mapping is that the concentration of contrast agent also changes over time. Recently, a linear tangent space alignment (LTSA) model-based fast MRI method has been proposed to enable high-resolution, high-frame-rate dynamic MR with sparsely sampled (k, t)-space data by leveraging the intrinsic low-dimensional manifold structure of dynamic MR images, showing superior performance over the low-rank model-based methods. This work extends the LTSA method by imposing an additional sparsity constraint on the subspace alignment matrix of the LTSA model for improved image reconstruction. The performance of the proposed method is validated in 3D free-breathing, pre- and post-contrast cardiac T
1
mapping as well as ECV mapping using in vivo data acquired on healthy volunteers at 3T.