Synopsis

A consistent view of T₁ relaxation in white matter remains elusive. We use an NMR spectrometer to observe white matter T₁ relaxation behavior in both aqueous and non-aqueous protons following six diverse initial magnetizations. The data is analyzed in the context of both an unrestricted and restricted four pool model. We show how the observed multi-component T₁ relaxation behavior depends sensitively on the initial conditions of the different pools, suggesting that great care must be taken in interpreting T₁ relaxation measurements.

Introduction

T₁ relaxation of white matter is the source of much disagreement regarding: the measured T₁ value,^1,2 whether one T₁ component is sufficient,^3,4,5,6,7,8 and whether T₁ components can be associated with specific protons pools.^{5,6,7,8,9,10,11,12,13} To clarify some of these issues, here we use NMR spectroscopy to observe T₁ relaxation in aqueous and non-aqueous protons (typically invisible to MRI scanners) during recovery from six different non-equilibrium states. We then analyze our data in both general and model-specific ways.

If longitudinal relaxation in an arbitrary system (Fig 1A) is modeled by coupled, first-order differential equations, then the general solution as a function of recovery time τ_R is ^13,14: $$\mathbf{m}(\tau_R)=\sum_{j=1}^N C_j\mathbf{v}_j \exp(-\tau_R/T_{1,j}^{*}).$$Here, m is a vector whose components are each pool’s reduced magnetizations (0<m_i<1, 0=thermal equilibrium, 0.5=zero magnetization, 1=inverted magnetization), C_j depends on initial conditions, v_j is the j^th eigenvector, 1/T_1,j^* is the j^th effective T₁ time, and N the number of pools. This equation also describes measured data that is the sum of two or more pools.

The above equation implies an unrestricted multi-pool analysis, since no assumptions about pool connectivity are made. We also fit a specific four-pool model,^{7,13,15,16,17,18} henceforth called the restricted FPM. In this model for WM (Fig. 1B), the proton pools are 1) non-aqueous myelin, 2) myelin water, 3) intra/extra-cellular (IE) water, 4) non-aqueous non-myelin, and exchange only occurs between pools 1↔2, 2↔3, and 3↔4.

Materials and Methods

A chilled bovine brain was obtained about 30 hours after harvesting (Innovative Research, Novi, MI, USA). Samples of white (WM) and grey matter (GM) were excised, sealed in short sections of 5 mm NMR tubes between Teflon spacers, and chilled until use (samples: WM-sp1 and WM-sp2 are splenium WM, WM-fr is frontal WM, GM-bg is basal ganglia grey matter). A 4.7 T homebuilt NMR spectrometer with a broadband solenoidal probe was used. The sample temperature was regulated at 37 ^oC.

Six pulse sequences were used to prepare unique initial longitudinal magnetization states. Each sequence follows the general scheme shown in Fig. 2A: preparation pulses were followed by a recovery delay of time τ_R, and then an FID or CPMG echo train was acquired. The six preparation pulses were: 1) hard or 2) soft inversion-recovery, and 3-6) four kinds of Goldman Shen (GS) sequences.

FIDs were fit with a sum of super-Lorentzian and Gaussian lineshapes for the non-aqueous signal¹⁹ and with a template from the equilibrium aqueous spectrum for the aqueous signal. CPMG curve fits used three exponentials to account for the myelin water and two distinct (~60 ms and ~110 ms) IE water components. Together, this gives measured pool amplitudes m(τ_R) for myelin water, IE water, and the sum of both non-aqueous pools. The unrestricted FPM was fit to m(τ_R) and the restricted FPM was fit to the CPMG curves, giving a fitted m(τ_R) indirectly.

Results and Discussion

Fig. 3 shows an example of the FID and spectral data when the system is in equilibrium (τ_R=10 s, panel A,C) and shortly after a soft inversion pulse (τ_R=2.7 ms, panel B,D). We are able to fit the signal from the non-aqueous and aqueous protons separately.

When the restricted and unrestricted FPM were fit to the data, the resulting T₁^*s and their associated eigenvectors were similar, as shown in Fig. 4 for all samples. This shows the assumptions leading to the restricted FPM are valid. Whether the T₁^*s originate from exchange between pools or from spin-lattice relaxation can be determined by analyzing the eigenvectors. The GM sample was fit well with only two pools, due to its low myelin content.

Comparisons of the restricted FPM fit with the measured total aqueous and total non-aqueous amplitudes are shown in Fig. 5. The diverse initial conditions from the six experiments are evident, as is its multi-component behavior. The restricted FPM describes the data well, although not as well as the unrestricted FPM (not shown), which deviates negligibly from the data. Future work will focus on modifications to the restricted FPM to more fully describe the data.

Conclusion

Acknowledgements

References

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