R_1ρ relaxation functions for weak, intermediate and strong collision models, revisited for frequency swept RF pulses.

Area of Science:

• Magnetic Resonance Spectroscopy
• Relaxometry
• Physical Chemistry

Background:

• Rotating frame T1ρ relaxation is crucial for understanding molecular dynamics.
• Existing models often fail to cover the full range of molecular motion regimes.
• Homonuclear dipole-dipole interactions are key drivers of relaxation.

Purpose of the Study:

• To develop and validate expressions for T1ρ relaxation across strong, intermediate, and weak collision regimes.
• To extend T1ρ formalism to time-dependent relaxation during modulated radiofrequency pulses.
• To assess the theory's applicability to experimental data and potential in vivo use.

Main Methods:

• Integral-based expressions for R1ρ were formulated using effective spectral density functions.
• Continuous wave spin-lock formalism was expanded to time-dependent T1ρ(t) under hyperbolic secant pulses.
• Effective spectral density terms were propagated through modulated RF pulses.

Main Results:

• Derived expressions accurately represent T1ρ relaxation across the entire correlation time range.
• The theory aligns with previous findings for weak collision regimes during hyperbolic secant pulses.
• Experimental T1ρ data for polyacetal (Delrin) in the strong collision regime were well-described.
• The theory successfully explained off-resonance T1ρ relaxation data for glycogen.

Conclusions:

• The developed formalism provides a unified description of T1ρ relaxation across all motional regimes.
• The theory demonstrates excellent agreement with experimental data for diverse materials.
• The formalism's validity for ultra-slow to fast motions suggests potential for in vivo magnetic resonance applications.