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Quantum mechanical MRI simulations: Solving the matrix dimension problem

Quantum mechanical MRI simulations: Solving the matrix dimension problem
Quantum mechanical MRI simulations: Solving the matrix dimension problem

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.

2375-2548
Allami, Ahmed J.
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Concilio, Maria Grazia
a28efff1-e031-475b-afbc-10129875c879
Lally, Pavan
ec4b89d9-3afe-4003-9ae0-7ff096aad776
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065
Allami, Ahmed J.
28371dc0-6ccb-4e08-80a4-c35f499fdc03
Concilio, Maria Grazia
a28efff1-e031-475b-afbc-10129875c879
Lally, Pavan
ec4b89d9-3afe-4003-9ae0-7ff096aad776
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065

Allami, Ahmed J., Concilio, Maria Grazia, Lally, Pavan and Kuprov, Ilya (2019) Quantum mechanical MRI simulations: Solving the matrix dimension problem. Science Advances, 5 (7), [eaaw8962]. (doi:10.1126/sciadv.aaw8962).

Record type: Article

Abstract

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.

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Accepted/In Press date: 14 June 2019
e-pub ahead of print date: 19 July 2019
Published date: 19 July 2019

Identifiers

Local EPrints ID: 433132
URI: http://eprints.soton.ac.uk/id/eprint/433132
ISSN: 2375-2548
PURE UUID: 5144e0a6-ba66-45a8-b8eb-618126529ee6
ORCID for Ilya Kuprov: ORCID iD orcid.org/0000-0003-0430-2682

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Date deposited: 09 Aug 2019 16:30
Last modified: 07 Oct 2020 02:01

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Contributors

Author: Ahmed J. Allami
Author: Maria Grazia Concilio
Author: Pavan Lally
Author: Ilya Kuprov ORCID iD

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