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  • 1Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA.

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We developed a new computational method for simulating spin dynamics in liquids, accounting for the distant dipolar field (DDF) on complex shapes. This approach enables more accurate modeling of magnetic resonance imaging (MRI) contrast in bounded samples.

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Area of Science:

  • Physics, Computational Physics, Magnetic Resonance Imaging

Background:

  • The distant dipolar field (DDF) significantly impacts spin dynamics in liquids, influencing multiple-quantum coherences and magnetic resonance imaging (MRI) contrast.
  • Standard Fast Fourier Transform (FFT) methods for DDF calculations are limited to periodic or Cartesian grids, posing challenges for bounded, complex geometries.
  • Accurate simulation of Bloch-DDF dynamics on bounded domains with realistic diffusion boundary conditions is crucial for advanced MRI applications.

Purpose of the Study:

  • To develop and validate a robust computational framework for simulating Bloch-DDF dynamics on bounded domains with complex geometries and Neumann diffusion conditions.
  • To provide an analyzable and reproducible method for understanding spin dynamics influenced by DDF in realistic sample environments.

Main Methods:

  • Derived a conforming finite-element weak formulation for Bloch-DDF equations, incorporating spatially varying diffusion/relaxation and short-distance regularization of the DDF kernel.
  • Proved operator boundedness and established an L2 energy balance, demonstrating the dissipative nature of diffusion and relaxation.
  • Employed a matrix-free near/far scheme for real-space DDF evaluation and an implicit-explicit splitting method for time integration, with explicit precession treatment using Rodrigues rotations.

Main Results:

  • Established local well-posedness and continuous dependence on data for the Bloch-DDF model under specific conditions.
  • Validated the finite-element method against three closed-form benchmarks, confirming its accuracy in isolating model components.
  • Quantified curved-boundary effects by comparing finite-element results with finite-difference methods on a spherical domain.

Conclusions:

  • The developed finite-element method provides a stable, accurate, and reproducible approach for simulating Bloch-DDF dynamics on bounded domains with complex geometries.
  • This framework supports multi-cycle, lab-frame calculations and offers a pathway for more precise modeling of MRI contrast in diverse sample types.