Efficient simulation of ultrafast magnetic resonance experiments

Abstract

Magnetic resonance spectroscopy and imaging experiments in which spatial dynamics (diffusion and flow) closely coexists with chemical and quantum dynamics (spin-spin couplings, exchange, cross-relaxation, etc.) have historically been very hard to simulate - Bloch-Torrey equations do not support complicated spin Hamiltonians, and the Liouville-von Neumann formalism does not support explicit spatial dynamics. In this paper, we formulate and implement a more advanced simulation framework based on the Fokker-Planck equation. The proposed methods can simulate, without significant approximations, any spatio-temporal magnetic resonance experiment, even in situations when spatial motion co-exists intimately with quantum spin dynamics, relaxation and chemical kinetics.

Frequency-swept pulses for ultrafast spatially encoded NMR

“…All the simulations were carried out with the spinach software library [29], implemented in matlab; version 2.3 was used. spinach uses the Fokker-Planck formalism to account simultaneously for spin and spatial variables, and provides an efficient tool for the simulation of ultrafast NMR experiments [30,31], including relaxation and diffusion effects. The details of the simulation framework are not described here and can be found in Refs [30,31].…”

Separating the coherence transfer from chemical shift evolution in high‐resolution pure shift COSY NMR

“…These effects were further investigated by simulation using the Spinach software package and, in particular, the recently introduced modules to deal with spatial encoding. [21,22] To keep the simulation time to a minimum, we simulated the isolated proton spin system on the right hand side of the molecule, which contains observable couplings in the COSY spectrum arising from 2 J, 3 J, 4 J, and 6 J couplings (see Figure 1). Where values for the relevant coupling constants could be easily measured from the onedimensional proton spectrum, these were used in the simulations.…”

Large‐scaleNMRsimulations in liquid state: A tutorial

“…Time domain NMR simulation packages solve Liouville ‐ von Neumann's equation (the equivalent of Schrödinger's equation for spin ensembles) and calculate the observable magnetisation at each point in time: where is a vector that contains information about spin system state, is a matrix, called Liouvillian, that depends on things such as J ‐couplings and relaxation rates, and is the observable magnetisation projector. To a computer, Equation looks like standard linear algebra; it is solved by calculating the exponential of : Technical details may be found in more specialised reviews of magnetic resonance simulation methods . Spinach is designed to automate this process: the user specifies the spin system and the experiment parameters, and receives a free induction decay at the end of the calculation.…”

“…Many packages can generate a reasonable likeness of a 1D NMR spectrum for large spin systems, but complicated combinations of multidimensional pulse sequences, advanced relaxation and kinetics treatments, shaped pulses and gradients, diffusion, and flow are only available in Spinach . This is the result of very recent theoretical developments, the primary ones being quantum mechanical simulation algorithms that have much lower computational resource requirements than anything previously available, and the Fokker–Planck equation for the spatial degrees of freedom …”