Solvent relaxation by uniformly magnetized solute spheres. The classical-quantal connection

Area of Science:

• Biophysics
• Magnetic Resonance Imaging (MRI)
• Computational Physics

Background:

• Large magnetic entities (4 nm to 4 microns) are crucial for MRI, including iron oxide nanoparticles and deoxygenated blood cells.
• Modeling these systems as magnetized solute spheres in water is a common approach.
• Existing methods include Monte Carlo for larger particles and quantum mechanics for smaller ones.

Purpose of the Study:

• To interrelate classical and quantum mechanical approaches for calculating relaxation times (1/T1 and 1/T2) in MRI.
• To determine the appropriate model (classical or quantum) based on particle size and system conditions.

Main Methods:

• Comparison of published Monte Carlo calculations (classical) with quantum mechanical outer sphere theory.
• Application to dysprosium-(DTPA)2- doped polystyrene spheres in water across various sizes.
• Inclusion of motional narrowing assumption in the quantum mechanical model.

Main Results:

• Both classical and quantum theories provide identical 1/T2 results for particles < 1 micron.
• For larger particles (> 1 micron), quantum theory overestimates 1/T2 due to breakdown of motional narrowing.
• Classical theory accurately models relaxation in dense systems where water molecules have limited interaction time, unlike quantum theory.

Conclusions:

• Classical and quantum approaches offer a trade-off between computational complexity/applicability and mathematical simplicity.
• Quantum theory reveals the intimate relationship between 1/T1 and 1/T2, suggesting extensions for classical 1/T1 computation.
• The choice between classical and quantum models depends on particle size and the specific relaxation dynamics.