Inhomogeneous Magnetization Transfer (IHMT) appears to be myelin-selective^[1,2,3]. In IHMT, images are acquired with four different soft prepulses: no prepulse (S₀), prepulse at offset +Δ (S₊) or -Δ (S_-), and prepulses at both ±Δ simultaneously (S_both). The IHMT Ratio, typically measured from aqueous proton intensity, is

$$\text{IHMTR}=\frac{S_+ + S_- - 2S_{\text{both}}}{2S_0} \le 1$$

IHMTR≠0 in systems with lipid lamellar structures (e.g. myelin, hair conditioner)^[1,2], but ≈0 in many other systems (e.g. gelatin, agarose)^[4].

Lipid hydrocarbon chain spin systems are thermally-averaged, resulting in spectral behaviour dominated by intra-methylene dipolar couplings. These methylenes resemble an ensemble of spin-1 systems^[5,6], and others have suggested this underlies the IHMT mechanism^[1,7]. Recent work has also highlighted IHMT's sensitivity to T_1D, the dipolar order relaxation time^[2]. Nonetheless, the accepted view remains that IHMT's lipid-selectivity results from lipid chains having inhomogeneous lineshapes^[1,2,3,7].

Here, we present experimental results on homogeneously-broadened systems with IHMTR≠0, contradicting the inhomogeneous explanation. The following simple spin-1 model shows how this is possible.

We consider the non-aqueous protons only, since their behaviour under the prepulses determines if IHMT will occur. The Hamiltonian of a dipolar-coupled methylene pair is $$${\cal H} = -\omega_0 I_z -\omega_D I_z^2$$$ (ω₀=Larmor frequency, ω_D=dipolar interaction strength, ω₀»ω_D). The equilibrium density matrix is

$$\rho = M_0 I_z = M_0\, \text{diag}(1,0,-1).$$

Then, assuming the prepulses are calibrated for inversion, S₊ exchanges ρ₁₁/ρ₂₂, S_- exchanges ρ₂₂/ρ₃₃, and S_both exchanges ρ₁₁/ρ₃₃ (using 2× the power to invert both transitions). Following the prepulse, $$$\langle I_z \rangle$$$ is the magnetization, and $$$\langle I_z^2 \rangle$$$ the dipolar order (nonzero only in S₊/S_-).

We form the "non-aqueous IHMTR":

$$\begin{align}\text{non-aqueous IHMTR} &=\frac{(\langle I_z \rangle_+ -\langle I_z \rangle_0)+(\langle I_z \rangle_- -\langle I_z \rangle_0) - (\langle I_z \rangle_{\text{both}} - \langle I_z \rangle_0)}{2\langle I_z \rangle_0} \\&= \frac{ (-\frac{1}{2}) + (-\frac{1}{2}) - (-2) }{2} =\frac{1}{2}.\end{align}$$

We don't multiply $$$(\langle I_z \rangle_0 - \langle I_z \rangle_{\text{both}})$$$ by 2 because we assumed 2× the power was used to invert both transitions.

Following a hard observe pulse of flip angle α, the spectral line amplitudes A_± at ω₀±ω_D are

$$A_\pm = [\frac{1}{2}(\rho_{11}-\rho_{33})]\sin\alpha\pm [\frac{1}{2}(\rho_{11}+\rho_{33}) -\rho_{22}] \cos\alpha \sin\alpha. ~~~~~\text{(1)}$$

Evidently, irradiating one transition affects the other's amplitude, and both amplitudes are equal when α=π/2. The lines cannot be independently saturated, as would be the case in an inhomogeneously-broadened system, yet it has a nonzero IHMTR. This equation's second term produces spectral asymmetry from dipolar order, and can only be observed when α≠nπ/2.

10% (w/w) Prolipid-161 (PL161, Ashland, DE, USA) in 99% D₂O was used for spin-1 model comparison, T_1D, and IHMT measurements. PL161 is a suitable myelin model for IHMT^[4,8]. IHMT and T_1D was also measured in air-dried Douglas Fir wood (sapwood), human hair, and lamb Achilles tendon. Wood and hair have homogeneously-broadened non-aqueous proton spectra, primarily from cellulose and α-keratin crystallites, respectively^[9,10,11]. Both have exchangeable aqueous protons. The NMR experiments utilized a home-built spectrometer (200 MHz / 4.7 T). Figure 1 shows the IHMT and Adiabatic Demagnetization/Remagnetization in the Rotating Frame (ADRF/ARRF) sequences used.

The PL161 and fir non-aqueous proton spectra following IHMT prepulses (Figure 2) showed no evidence of hole-burning. However, with α=33^o, the characteristic spectral asymmetry from dipolar order in S₊/S_- is obvious.

As a function of α, the ω>0/ω<0 spectral integrals of PL161 were fit to (1) (Figure 3). Inhomogeneously-broadened spectra would only have a sin(α) dependence, but we clearly see more complex behaviour consistent with dipolar order.

Our samples' non-aqueous and aqueous IHMTRs vs. Δ and their T_1Ds are given in Figures 4 and 5, respectively. Fir and hair have IHMTR≠0, despite being homogeneously-broadened systems. Also, although PL161's T_1D is 20-40× larger than the fir and hair's, the corresponding IHMTRs are only 2-3× larger. Consequently, T_1D is likely not the only relevant non-aqueous timescale.

Many tissues and phantoms in which IHMTR≈0 are highly dynamic systems, so dipolar couplings are transient. For IHMT to occur, we believe the coupling lifetime must be long enough for dipolar order to develop: τ_D$$$\gtrsim$$$1/(4ν₁) (τ_D = dipolar coupling correlation time, ν₁ = prepulse nutation frequency). ν₁ must be small enough to only excite one side of the spectrum, setting a lower limit for τ_D. In a system with transient dipolar couplings, T_1D is constrained to be no greater than τ_D.

We have given evidence that IHMT doesn't rely upon inhomogeneously-broadened non-aqueous proton lines. Our nonzero IHMTR results in homogeneously-broadened systems are explained with a simple spin-1 model. Furthermore, we have proposed that nonzero IHMTRs depend upon the dipolar coupling correlation time (≈T_1D in motionally-dynamic systems), which must be long enough for appreciable dipolar order development during the prepulse.