Essential Concepts in MRI. Yang Xia

or much longer) while T₂ becomes short (tens of milliseconds or much shorter). This random field model is valid in the “weak collision” case where τc < T₂; the theory will fail at the situation in relatively rigid materials. Some of the longest T₁ are commonly found in solids, on the order of tens of minutes; some of the shortest T₂ are on the order of 10 µs, which occurs in solids as well as well-organized connective tissues such as tendon and ligaments. Typical ranges of T₁ and T₂ for biological tissues are marked in Figure 3.4.

Figure 3.4 Schematic log/log trends of relaxation times on the correlation time τ_c, which also depend upon the resonance frequency and temperature (not shown). T₁ relaxation time has a minimum, occurring when ω ~ 1/τ_c. This minimum separates two regimes of relaxation. On the left of the minimum is the extreme narrowing regime (ω ≪ 1/τ_c) where T₁ ~ T₂, where one can find the reduction of the homogeneous line width (1/πT₂); one commonly finds simple and less viscous liquids of small molecules in this regime. On the right of the minimum there is a regime (ω ≫ 1/τ_c) where T₁ and T₂ diverge significantly; one can find in this regime viscous liquids and polymers of relatively large and complex molecules, as well as a variety of biological tissues.

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      Notes

      1 1 The Zeeman effect is named after Dutch physicist Pieter Zeeman for his 1896 observation of splitting of the optical spectral lines in a magnetic field.