Accuracy and performance analysis for Bloch and Bloch-McConnell simulation methods.

Area of Science:

• Physics
• Computational Science
• Medical Imaging

Background:

• The Bloch and Bloch-McConnell equations are fundamental to understanding nuclear magnetic resonance (NMR) phenomena.
• Efficient and accurate numerical solutions are crucial for advancing magnetic resonance imaging (MRI) techniques.

Purpose of the Study:

• To introduce novel solution methodologies for the Bloch and Bloch-McConnell equations.
• To quantitatively compare these new methods against existing approaches for solving these equations.

Main Methods:

• A new exact solution per time step was derived using eigenvalues and generalized eigenvectors.
• Fast numerical methods, including asymmetric and symmetric operator splitting, were extended to the Bloch-McConnell equations.
• Comparison involved various numerical techniques: spin domain, one-step, multi-step methods, and matrix exponential, with error metrics based on the exact solution.

Main Results:

• Nine distinct solution methods were analyzed for accuracy and performance across diverse numerical experiments.
• Results demonstrated significant variations in accuracy among methods, particularly with short relaxation times and long pulse durations.
• Extensive numerical experiments covered both non-selective and slice-selective MR imaging scenarios.

Conclusions:

• The rotation matrices approach is confirmed as accurate and efficient for Bloch equations without relaxation effects.
• Symmetric operator splitting methods are recommended for both Bloch and Bloch-McConnell equations due to superior numerical accuracy and runtime efficiency.
• These findings provide valuable guidance for selecting optimal numerical solvers in MRI applications.