Quantum mechanical simulations in diffusion MRI

Abstract

Background: Various magnetic resonance imaging simulation packages rely on Bloch equations, Bloch-Torrey equations and the Liouville–von Neumann equation is which a dynamical formulation to simulate a voltage bias across a molecular system and to model a time-dependent current in terms of classical or quantum treatments of magnetic resonance imaging respectively.

Method: The problems in these equations cannot address spin dynamic such as j-coupling and spatial dynamics such as diffusion and flow at the same level. In this study, the Fokker-Planck formalism was used to simulate phantoms that deal with diffusion and flow on the spatial dynamics side and j-coupling in the spin dynamic side using the Spinach simulation package.

Result: The numerical simulation of magnetic resonance imaging has two limits in terms of research. First, a complicated spin system is associated with simple diffusion and flow, such as in spatially encoded NMR experiments. Second, a simple spin system is associated with high dimensional diffusion and flow.

Conclusion: A unique simulation package that deals with the quantum mechanics treatment of spin dynamics and the classical description of diffusion and flow in three dimensions are presented in this work.

Funding Statement: The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this study.