RT Journal Article
SR Electronic
T1 Quantum mechanical MRI simulations: Solving the matrix dimension problem
JF Science Advances
JO Sci Adv
FD American Association for the Advancement of Science
SP eaaw8962
DO 10.1126/sciadv.aaw8962
VO 5
IS 7
A1 Allami, Ahmed J.
A1 Concilio, Maria Grazia
A1 Lally, Pavan
A1 Kuprov, Ilya
YR 2019
UL http://advances.sciencemag.org/content/5/7/eaaw8962.abstract
AB We propose a solution to the matrix dimension problem in quantum mechanical simulations of MRI (magnetic resonance imaging) experiments on complex molecules. This problem is very old; it arises when Kronecker products of spin operators and spatial dynamics generators are taken—the resulting matrices are far too large for any current or future computer. However, spin and spatial operators individually have manageable dimensions, and we note here that the action by their Kronecker products on any vector may be computed without opening those products. This eliminates large matrices from the simulation process. MRI simulations for coupled spin systems of complex metabolites in three dimensions with diffusion, flow, chemical kinetics, and quantum mechanical treatment of spin relaxation are now possible. The methods described in this paper are implemented in versions 2.4 and later of the Spinach library.