Aqueous and Non-aqueous T1 relaxation in brain under six diverse initial conditions
Alan Manning1, Carl Michal1, and Alex MacKay1,2

1Physics, University of British Columbia, Vancouver, BC, Canada, 2Radiology, University of British Columbia, Vancouver, BC, Canada


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.


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 τR 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<mi<1, 0=thermal equilibrium, 0.5=zero magnetization, 1=inverted magnetization), Cj depends on initial conditions, vj is the jth eigenvector, 1/T1,j* is the jth 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 τR, 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 mR) for myelin water, IE water, and the sum of both non-aqueous pools. The unrestricted FPM was fit to mR) and the restricted FPM was fit to the CPMG curves, giving a fitted mR) indirectly.

Results and Discussion

Fig. 3 shows an example of the FID and spectral data when the system is in equilibrium (τR=10 s, panel A,C) and shortly after a soft inversion pulse (τR=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.


Observation of the aqueous and non-aqueous magnetizations using NMR spectroscopy can yield detailed insights into the T1 relaxation behavior of white matter. Unrestricted multi-pool analysis offers a way to analyze T1 relaxation data in a general way. Because the observed T1 relaxation behavior is in general multi-component, and depends sensitively on the initial conditions of the different pools, great care must be taken in interpreting T1 relaxation measurements.


APM was supported by an NSERC doctoral scholarship. ALM and CAM were supported by NSERC Discovery Grants. This research was enabled in part by support provided by WestGrid (www.westgrid.ca) and Compute Canada (www.computecanada.ca).


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Figure 1. The unrestricted multi-pool model (A) and the restricted four pool model (FPM, B). The multi-pool model makes no assumptions about the kind of pool or their connectivity (magnetization exchange) to each other. The restricted FPM is based on physiological constraints and the measurable separation between myelin water and IE water based on their T2 times.

Figure 2. The pulse sequences used in this work. (A) General scheme of pulse sequences. (B) The hard inversion pulse inverts both aqueous and non-aqueous magnetization. (C) The soft inversion pulse inverts the aqueous magnetization only. (D) The four Goldman-Shen sequences separate proton populations with distinct T2s.20,21 The echo or filter time, τf, is either 1 ms (nulling the non-aqueous magnetization) or 50 ms (nulling both non-aqueous and myelin water magnetization). After the filter, the remaining magnetization is flipped along the +z (“up”) or -z (“down”) direction.

Figure 3. Fitting the 1H FID signal for sample WM-sp1. The spectrum (A,B) of WM tissue consists of a broad contribution from the non-aqueous components and an intense, narrow line from the aqueous components. Although their signal timescales in the FID (C,D) differ by 103-104, we are able to fit both components. The insets show the long-time FID behavior. The non-equilibrium spectrum for IR-Soft in (B) shows the inversion of the aqueous protons only. The spikes around 2.25 kHz and 4.25 kHz are environmental noise.

Figure 4. The effective longitudinal relaxation times, T1* for all samples. The unrestricted FPM was fit to the measured pool amplitudes. The restricted FPM was fit to the CPMG curves. The T1* times from both methods are similar. The origin of the T1* was determined from the restricted FPM’s fitted eigenvectors.

Figure 5. Measured pool amplitudes and the fits from the unrestricted four-pool model for sample WM-fr. The four pool model fits the total aqueous and non-aqueous amplitudes well. The relative contribution of the eigenvalues, and the resulting T1 relaxation behavior, depends on the initial conditions. From these plots, the diversity of the six experiments’ initial conditions is clear, as is the multi-component relaxation behavior.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)