System and method of obtaining spatially-encoded NMR parameters from arbitrarily-shaped compartments and linear algebraic modeling

An NMR system for acquiring and reconstructing a value of an NMR parameter spatially localized to at least one compartment of interest, said NMR system employing an applied static magnetic field B0, and NMR excitation and detection systems, and comprising an MRI apparatus configured to accommodate a sample of interest,

• wherein said MRI apparatus is configured to:
• perform a first magnetic resonance imaging (MRI) of at least a portion of said sample with a first MRI pulse sequence using said NMR system and using at least one of a set of k-space spatial encoding gradients or coil sensitivity encoding maps to obtain a first magnetic resonance image to identify at least one compartment of interest;
• generate a second MRI pulse sequence that encodes said NMR parameter with a subset of said at least one of said set of k-space spatial encoding gradients or said coil sensitivity encoding maps;
• apply said second MRI pulse sequence using said NMR system to acquire spatial information relating to said NMR parameter from said at least one compartment of interest;
• segment said first magnetic resonance image into a plurality of compartments that includes said at least one compartment of interest;
• and
• reconstruct a value of said NMR parameter in said at least one compartment of interest,
• wherein said NMR parameter is one of a nuclear spin density, a relaxation time T1, T1ρ, T2, or T2*, a diffusion coefficient, a perfusion measure, a functional measure, a spectral parameter, a chemical reaction rate, or a chemical exchange saturation transfer (CEST) index.