Nonaqueous magnetization following adiabatic and selective pulses in brain: T1 and cross‐relaxation dynamics

Abstract

Inversion pulses are commonly employed in MRI for $T_1$‐weighted contrast and relaxation measurements. In the brain, it is often assumed that adiabatic pulses saturate the nonaqueous magnetization. We investigated this assumption using solid‐state NMR to monitor the nonaqueous signal directly following adiabatic inversion and compared this with signals following hard and soft inversion pulses. The effects of the different preparations on relaxation dynamics were explored. Inversion recovery experiments were performed on ex vivo bovine and porcine brains using 360‐MHz (8.4 T) and 200‐MHz (4.7 T) NMR spectrometers, respectively, using broadband rectangular, adiabatic, and sinc inversion pulses as well as a long rectangular saturation pulse. Analogous human brain MRI experiments were performed at 3 T using single‐slice echo‐planar imaging. Relaxation data were fitted by mono‐ and biexponential decay models. Further fitting analysis was performed using only two inversion delay times. Adiabatic and sinc inversion left much of the nonaqueous magnetization along $B_0$ and resulted in biexponential relaxation. Saturation of both aqueous and nonaqueous magnetization components led to effectively monoexponential $T_1$ relaxation. Typical adiabatic inversion pulses do not, as has been widely assumed, saturate the nonaqueous proton magnetization in white matter. Unequal magnetization states in aqueous and nonaqueous ¹H reservoirs prepared by soft and adiabatic pulses result in biexponential $T_1$ relaxation. Both pools must be prepared in the same magnetization state (e.g., saturated or inverted) in order to observe consistent monoexponential relaxation.

We use solid‐state NMR to monitor both aqueous and nonaqueous signals directly during inversion recovery using multiple preparation pulses in vivo and ex vivo. In contradiction to the common assumption, we show that applying typical adiabatic inversion pulses to white matter leaves substantial nonaqueous proton signal aligned along $B_0$. This leads to biexponential $T_1$ relaxation during inversion recovery, resembling that following a selective inversion pulse.

1. INTRODUCTION

Longitudinal relaxation is widely used as a contrast mechanism in brain tissue. As quantitative MRI methods are translated into clinical use, it is critical to characterize fully the relaxation dynamics leading to key parameters such as $T_1$. There is great interest in developing an unambiguous measurement protocol to obtain a “true” $T_1$ in vivo, which is immune to variations in external factors such as scan parameters or B‐field inhomogeneity. Reported $T_1$ values in white matter show substantial variation ¹ , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ of the order of 50%, which is concerning if $T_1$ is to be used as a quantitative metric.

Previous work ³ , ⁵ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ has shown that magnetization transfer by means of ¹H (proton) exchange between neighboring populations in water and myelin lipid structures plays a significant role in the longitudinal relaxation of white matter. Relaxation of separate but exchanging “aqueous” and “nonaqueous” protons in a two‐pool tissue model (or binary spin‐bath model) yields biexponential relaxation dependent upon the initial conditions of the pools' bulk magnetization. ⁷ , ¹² , ¹⁴ This effect makes measured $T_1$ strongly dependent on the inversion pulse characteristics when fitting a typical monoexponential model to this generally multiexponential relaxation.

Adiabatic pulses are useful in numerous areas of NMR and MRI due to their unique properties compared with conventional soft pulses. With low power deposition and independently scalable excitation bandwidths, these pulses yield constant flip angles over relatively large sample volumes, which would typically suffer from $B_1$ inhomogeneity. ¹⁵ , ¹⁶ , ¹⁷ In MRI it has frequently been assumed that the application of typical adiabatic pulses to brain tissue will saturate the nonaqueous proton magnetization in white matter. ⁵ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ However, signals from the nonaqueous tissue components decay quickly with $T_2\sim$ 50  $\mu \mathrm{s}$, ²⁷ which is too fast to be measured directly by most MRI sequences, so direct measurements to validate this assumption on clinical instrumentation are not straightforward.

Our work interrogates the common assumption that nonaqueous protons are saturated by typical adiabatic pulses in MRI and compares the magnetization state and relaxation dynamics following an adiabatic pulse with those found following other inversion pulses. Using solid‐state NMR spectroscopy, we measure the nonaqueous signal directly in ex vivo brain samples. We performed saturation recovery (SR) and inversion recovery (IR) experiments using adiabatic pulses alongside broadband (hard) and frequency selective (soft) shaped pulses on two different ex vivo brain samples with analogous experiments in vivo on human brain in order to examine the form of the longitudinal relaxation resulting from each class of pulse. Clear deviation from monoexponential relaxation in white matter in both NMR and MRI settings under selective and adiabatic inversion was observed.

The ex vivo results presented here provide a new window to compare and understand the effects of these different preparation pulses, as the behavior of the nonaqueous signal in some cases has only been assumed in vivo. Human results in this study act as a validation of the NMR methods and demonstrate the clinical relevance. We also explore a method to measure $T_1$ in vivo that produces recoveries consistent with a monoexponential model. Finally, we show the precariousness of commonly used methodology that relies on just two IR or SR data points to measure $T_1$.

2. METHODS

2.1. NMR measurements

2.1.1. Experiments

A bovine brain was obtained unfrozen from a cow under 30 months old (Innovative Research—Novi, MI, USA) approximately 30 hours after harvest following transport in a refrigerated container. Two samples were collected from the splenium of the corpus callosum with masses 53.6 mg (WM1‐b) and 45.9 mg (WM2‐b) and one from frontal white matter with mass 67.7 mg (WM3‐b). A porcine brain was harvested from a five‐month‐old Yucatan pig obtained from Premier BioSource (Rensselaer, IN, USA) approximately 3 hours after death. Two samples were collected from the corpus callosum with masses 144 mg (WM1‐p) and 243 mg (WM2‐p) and one from the pons with mass 170 mg (WM3‐p). Tissue samples were immediately sealed in separate 5‐mm NMR tubes with proton‐free o‐rings and caps, and all experiments were performed within 60 hours. All animal protocols and procedures used for this study were approved by the Animal Care Committee of the University of British Columbia and were in accordance with the policies of the Canadian Council on Animal Care.

Bovine experiments were performed in a 360‐MHz (8.4 T) Oxford Instruments superconducting magnet using a home‐built NMR spectrometer at room temperature, $21.9\pm$ ${0.5}^{\circ }\mathrm{C}$. Porcine experiments were performed in a 200‐MHz (4.7 T) Oxford Instruments superconducting magnet using the same spectrometer with temperature regulated to $37.0\pm {0.5}^{\circ }\mathrm{C}$. A standard inversion recovery sequence was performed with free induction decay (FID) acquisition (IR‐FID: 180°–TI–90°) and 40 inversion delay times (TI), defined here as the time between pulses, logarithmically spaced from 10 μs–10 s. A 10‐s recycle time was used in each experiment, and each TI acquisition was repeated eight times.

Four types of preparation pulse were used: (1) a broadband, or “hard”, $\sim$ 8  $\mu \mathrm{s}$ rectangular pulse inverted all proton populations; (2) an adiabatic hyperbolic secant inversion pulse was matched to typical clinical parameters (10 ms pulse length, 750 Hz (17.6 μT) maximum amplitude, $\beta ={730\mathrm{s}}^{-1}$, ¹⁵ and 4 kHz bandwidth frequency modulation); (3) a frequency‐selective, or “soft”, 3‐ms three‐lobe sinc pulse (1.1 kHz excitation bandwidth), representative of a clinical MR pulse, inverted the aqueous protons while affecting the nonaqueous protons minimally; and (4) a 500‐ms rectangular saturation pulse with an amplitude of 63 Hz was used for saturation recovery experiments.

2.1.2. Analysis

Relaxation data were extracted from the IR series by summing phased time‐domain data from 1.5–2.5 ms (bovine) or 2–3 ms (porcine) for each delay time, which ensured that the nonaqueous signal was well decayed and only the aqueous signal was analyzed. This was done in order to mimic the signals that would be observed in conventional MRI measurements where the nonaqueous components are not visible. The data were then fitted with the equation

$$M_z(TI)=M_0\left(1-\sum _{i=\text{L,S}}{a}_i{e}^{-TI/T_{1,i}}\right).$$ (1)

This equation reflects the exact solution of an exchanging two‐pool model, ²⁸ , ²⁹ where the time constants $T_{1,i}$ depend on the exchange rate, pool sizes, and intrinsic relaxation times of the two pools. The subscripts $i=$ L,S refer to the “long” and “short” biexponential components respectively. The $a_i$ amplitude coefficients depend on the initial conditions following the inversion pulse. For perfect inversion of all magnetization, $\sum a_i=2$. A nonlinear least‐squares (NLLS) fitting routine (lsqcurvefit) native to MATLAB (MathWorks, Natick, MA) was used to obtain $M_0$, $a_i$, and $T_{1,i}$ in Equation 1. The fitting method accommodated negative $a_i$ factors, as can occur in the canonical two‐pool system when the initial pool states are unequal. ⁷ , ¹⁰ , ²⁸ , ²⁹

To compute the inversion efficiencies of aqueous and nonaqueous components, their respective contributions were first separated from fits to FIDs as follows: a standard exponential was first fitted to a section of the FID attributed to the aqueous signal, $\sim$ 2–15 ms, extracting an estimate of $T_2^{\ast }$, $\sim$ 5 ms at 200 MHz, $\sim$ 2.5 ms at 360 MHz, across samples. The fitted exponential was subtracted from the total FID with the resulting difference deemed the nonaqueous signal. A brief section of this decay, S( $t\approx$ 10–30  $\mu$s) was then fitted to a moment expansion function, ³⁰

$$S(t)=S(0)\left[1-\frac{M_2{t}^2}{2!}+\frac{M_4{t}^4}{4!}-\frac{M_6{t}^6}{6!}\right].$$ (2)

Both the exponential (representing the aqueous component) and the moment expansion (representing the nonaqueous component) were extrapolated to $t=$ 0 to account for the $\sim$ 5  $\mu$s dead time. Inversion efficiencies were computed from the ratios of these extrapolations for the shortest and longest TI times.

2.2. MRI measurements

2.2.1. Experiments

One healthy subject (female, age 41) participated. All experiments were performed with a Philips Ingenia Elition 3 T clinical MRI scanner with a 32‐channel head coil receive array. First, a 3D $T_1$‐MPRAGE (TR/TE/TI = 3000/3.6/984 ms, $1\times 1\times 5$ mm voxel size) scan was performed to be used as a reference image for registration. Three longitudinal relaxation experiments analogous to the NMR study were performed using a single‐slice echo‐planar imaging (EPI) readout sampling one transverse 5‐mm slice through the base of the genu and splenium of the corpus callosum. The image matrix size was $128\times 128$ and the scan duration was $\sim$ 80 s. The preparation pulses used were as follows: (1) an adiabatic hyperbolic secant inversion pulse with 10 ms length, 13.5 μT (575 Hz) maximum amplitude, $\beta ={730s}^{-1}$, and 1.34 kHz bandwidth frequency modulation; (2) a 3‐ms sinc–Gauss inversion pulse, the “soft” pulse; and (3) a 500‐ms rectangular pulse with 0.23  $\mu \mathrm{T}$ (10 Hz) amplitude (i.e., 5 $\times$ 100 ms pulses tuned to flip angle = 5 $\times$ 360°), producing a saturation recovery. Twelve TI times were selected from those used in the NMR IR experiments: TI = 5.5, 10.2, 35.8, 66.9, 125, 234, 598, 818, 1118, 1529, 3910, and 5348 ms, where TI is defined as above as the time from the end of the preparation pulse to the start of the EPI excitation pulse. Repetition times, TR, were chosen as (TI + 5 s) to allow for full population equilibration between each repetition. Ethical approval for this scanning, considered under methods development, was granted by the Clinical Research Ethics Board at the University of British Columbia.

2.2.2. Analysis

The 3D $T_1$ scan data were used to create global white matter and region of interest (ROI) masks for the single‐slice IR data. First, using FSL6.0 (Analysis Group, FMRIB, Oxford, UK), ³¹ the data were registered nonlinearly to a standard brain (MNI152) using a 12‐parameter model with FMRIB's linear image registration tool (FLIRT) ³² , ³³ and then FMRIB's nonlinear image registration tool (FNIRT). ROIs of the internal capsules, splenium and genu of the corpus callosum, major forceps, and minor forceps from the JHU DTI‐based White‐Matter Labels, ³⁴ , ³⁵ as well as cerebral white matter, thalamus, putamen, and caudate from the Harvard–Oxford subcortical structural atlas, ³⁶ were then thresholded in intensity at 90% probability and transformed into the data space. Finally, binary masks were transferred from the transformed ROIs onto the single‐slice IR data and adjusted manually to avoid partial volume effects to generate the ROIs seen in Figure 1. All images showed a Nyquist ghost in the anterior region stemming from the EPI readout, which had negligible effect on results. In addition, an elliptical anterior region of $B_0$ inhomogeneity above the sinuses was prevalent in the saturation recovery data. This precluded reliable analysis of the genu of the corpus callosum, minor forceps, caudate, and anterior cerebral white matter ROIs.

FIGURE 1.

ROI masks generated from data registration to standard MNI152 brain. ROIs are displayed on data from the sinc–Gauss inversion at TI=237 ms for optimal white/gray matter contrast. (A) ROIs from the JHU White Matter Labels. ³⁴ , ³⁵ Yellow: minor forceps, cyan: genu of corpus callosum, blue: internal capsules, red: splenium of corpus callosum, green: major forceps. (B) Cerebral white matter. (C) Yellow: putamen, red: thalamus, cyan: caudate identified by the Harvard–Oxford subcortical structural atlas. ³⁶ Note that an anterior region of the cerebral matter ROI, (B), is omitted, due to $B_0$ inhomogeneity above the sinuses.

Masked ROI data from each experiment were fitted voxel‐wise to the mono‐ and biexponential Equation 1, again using NLLS in Matlab. The resulting fit parameters, $T_{1,i}$, and corresponding component amplitudes, $a_i$, were collected into histograms and are reported as mean $\pm$ standard error $\left(\sigma /\sqrt{\text{\# of voxels}}\right)$, assuming a Gaussian distribution and common true values across all voxels of a region. For the saturation data, voxel amplitudes were also averaged across an ROI before fitting. A “two‐point” fitting analysis used the same method while choosing all permutations of two TI times to fit and holding the monoexponential amplitude factor, $a$ (Equation 1), fixed at the result of the full data set's monoexponential fit (which is not generally known in typical practice).

The Bayesian Information Criterion (BIC) was found for both mono‐ and biexponential models by first averaging the signal intensity across each ROI, then computing:

$$\text{BIC}=n\ln (\widehat{{\sigma }_{\mathrm{e}}^2})+k\ln (n),$$ (3)

where $k$ is the number of free parameters, $\widehat{{\sigma }_{\mathrm{e}}^2}$ is the error variance, and $n$ is the number of data points. The BIC statistic was used to compare the goodness of fit of the different models, including a penalty for overfitting or using more parameters than necessary. When models are compared using the BIC, the model yielding the lower value represents the data better. A difference of >10 is generally considered as very strong evidence to support the use of the model with the lower BIC value. ³⁷

3. RESULTS

3.1. Preparation pulse efficiency and initial magnetization state

Spectra from the bovine WM‐3b sample following a short delay, TI = 68  $\mu \mathrm{s}$ (Figure 2), show the narrow aqueous Lorentzian signal and the overlapping broad nonaqueous super‐Lorentzian line shape ³⁸ , ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ in differing states of inversion for each preparation. The hard pulse (Figure 2A) effectively inverted both populations (solid black curve), i.e., the full line shape is of opposite sign but similar in magnitude to the equilibrium spectrum (red dashed curve). The integrals of these two spectra showed that, following hard inversion, the nonaqueous signal amplitude was −94% of the fully relaxed signal on average in bovine samples, similar to the average of −95% found for the porcine samples. It is clear that the adiabatic inversion left much of the dipolar broadened nonaqueous magnetization along $B_0$, seen in Figure 2B as the portion of the solid black curve above the $x$‐axis. A significant portion of the nonaqueous signal, 24% (bovine) and an average of 22% (porcine), remains along $B_0$. The same result is clear in the time domain (inset in Figure 2), where the initial slopes of the nonaqueous ( $t\lesssim 50\mu \mathrm{s}$) and aqueous (0.4 ms $\lesssim t\lesssim$ 1 ms) contributions to the FIDs are opposite in sign. This means that, directly following the adiabatic inversion, the bulk magnetization states (i.e., spin temperatures) of aqueous and nonaqueous proton populations are unequal: the aqueous pool is almost fully inverted, while the nonaqueous pool remains partly aligned along $B_0$, and is not, as has been widely assumed, saturated. As a comparison, an even larger portion of the nonaqueous magnetization, 82% (bovine) and 79% (porcine), remained along $B_0$ directly following the soft sinc inversion (Figure 2C), which is also clear in the decreased initial FID amplitude (Figure 2C inset). The nonaqueous intensity visible after the saturation pulse was 4.0% of the fully relaxed signal across porcine samples (data not shown).

FIGURE 2.

Spectra collected from WM3‐b sample during IR experiments at a fully relaxed state (red dashed) and directly following the following (black solid): (A) a hard, (B) adiabatic, or (C) sinc inversion pulse. Insets show the first millisecond of the FID with TI = 68  $\mu$s, that is, the inverse Fourier transform of the black curves, from each inversion case where the hard inversion case sets the normalization. Horizontal bars at the bottom of (B) and (C) indicate the approximate bandwidths of the inversion pulses.

3.2. Monoexponential fitting

Monoexponential recovery‐curve fits to porcine relaxation data are shown in Figure 3. Quantitative results from these fits are reported in Table 1, and fitting results from all samples may be found in Supplementary Material Tables S1 and S2. While a noticeable residual trend exists in the hard inversion and saturation cases, a much more significant deviation (of opposite sign) from the fit is seen in the adiabatic case. This trend continues in the sinc inversion case with a greater root‐mean‐square (RMS) misfit and shorter $T_1$. The adiabatic inversion evidently drives relaxation behavior more similar to that resulting from selective sinc inversion than that from hard inversion or saturation.

FIGURE 3.

Representative recovery curves in porcine white matter (sample WM2‐p) from relaxation experiments with (A) hard, (B) saturation, (C) adiabatic, and (D) sinc preparation pulses. The solid red and dashed blue lines show monoexponential and biexponential best‐fitting curves to relaxation data, respectively (black circles). The corresponding residuals (green +, orange x, respectively) have been overlaid and multiplied by a factor of 10. Note that the amplitude is scaled such that the equilibrium value $M_0$ = 100.

TABLE 1.

Example mono‐ and biexponential fit parameters from the WM2‐p ex vivo porcine IR data analysis. Statistical uncertainties (68% confidence intervals) from the fitting routine are reported in parentheses. X marks in the rightmost column indicate cases where the less appropriate model has been applied.

	Porcine Corpus Callosum (WM2‐p)
Monoexponential
	$T_1$ (s)		$a$		RMS misfit*
Hard	1.436(7)		1.961(4)		0.58%
Saturation	1.407(5)		1.0412(5)		0.22%
Adiabatic	1.23(3)		1.92(2)		2.73%	X
Sinc	1.11(5)		1.94(3)		4.70%	X

Biexponential
	$T_{1,\mathrm{L}}$ (s)	$a_{\mathrm{L}}$	$T_{\text{1,S}}$ (ms)	$a_{\mathrm{S}}$	RMS misfit*
Hard	1.400(4)	1.990(4)	110(20)	‐0.030(3)	0.19%	X
Saturation	1.362(3)	1.063(2)	260(20)	‐0.022(2)	0.038%	X
Adiabatic	1.368(7)	1.820(4)	40(3)	0.108(3)	0.35%
Sinc	1.36(1)	1.755(7)	42(3)	0.191(5)	0.62%

^*Computed as percentage of max amplitude.

Results from fitting the analogous in vivo experiments to a monoexponential relaxation model are shown in Figure 4 and summarized in Table 2 for the cerebral WM ROI. Full ROI results for both the white and gray matter regions examined are listed in Supplementary Table S3 and Figure S1. Maps showing $T_1$ fit parameters alongside the goodness of fit of the relaxation measurements to the monoexponential model are shown in Figures 5A–C and F–H, respectively. The in vivo results display the same trends as the ex vivo NMR results: the sinc–Gauss inversion leads to the shortest apparent $T_1$ followed by the adiabatic inversion, while the saturation recovery sequence yields the longest $T_1$. Using the RMS misfit as a metric, Figures 5F–H demonstrate that the relaxation following the long saturation pulse is the most nearly monoexponential. White matter structures are discernible in the adiabatic and sinc–Gauss misfit maps.

FIGURE 4.

Representative recovery curves from in vivo cerebral white matter from relaxation experiments with (A) saturation, (B) adiabatic, and (C) sinc–Gauss preparation pulses. The solid red and dashed blue lines show monoexponential and biexponential best‐fitting curves to relaxation data, respectively (black circles), where the intensity across the ROI was averaged before fitting. The corresponding residuals (green +, orange x, respectively) have been overlaid and multiplied by a factor of 10. Note that the amplitudes have been scaled such that the equilibrium value $M_0$ = 100, and that magnitudes before the zero crossing in (B) and (C) have been flipped to the negative axis for display purposes.

TABLE 2.

Mono‐ and biexponential fit parameters from in vivo data analysis from human cerebral white matter in Figure 1B. $\mathrm{\Delta }$BIC = BIC BIC , the difference in computed Bayesian Information Criteria (BIC) between each fitting method. Reported uncertainties (in parentheses) are standard errors. Uncertainties are omitted in the ROI averaged fit parameters because the fit is ill‐conditioned. The RMS misfit is averaged across the ROI. X marks in the rightmost column indicate cases where the less appropriate model has been applied.

	Human Cerebral WM
Monoexponential
	$T_1$ (s)		$a$		RMS misfit*
Saturation	1.013(3)		0.888(4)		0.19%
Adiabatic	0.905(3)		1.913(1)		2.59%		X
Sinc‐Gauss	0.861(2)		1.891(1)		3.32%		X

Biexponential
	$T_{1,\mathrm{L}}$ (s)	$a_{\mathrm{L}}$	$T_{\text{1,S}}$ (ms)	$a_{\mathrm{S}}$	RMS misfit*	$\mathrm{\Delta }$ BIC
Saturation	1.67(5)	0.42(1)	870(10)	0.47(1)	0.19%	‐5.0	X
Saturation †	1.01	0.44	1010	0.44	0.19%	‐5.0	X
Adiabatic	0.996(6)	1.784(4)	92(3)	0.165(4)	0.83%	22.3
Sinc‐Gauss	0.983(3)	1.719(2)	94(2)	0.216(2)	0.53%	38.9

^*Computed as percentage of max amplitude.

^†Signal amplitude averaged across ROI before fitting.

FIGURE 5.

(A–E) $T_1$ and $T_{1,\mathrm{L}}$ (s) parameters from voxelwise mono‐ and biexponential fitting, respectively, and (F–K) the RMS misfit, computed as a percentage of the maximum signal amplitude, maps of the slice in each inversion case when fitted to (A–C, F–H) monoexponential or (D–E, I–K) biexponential recovery models.

3.3. Biexponential fitting

Results from fitting the biexponential recovery model to the porcine relaxation data are summarized in Figure 3 with fit parameters listed in Table 1 and additional parameters shown in Figure S3. Complete sets of fit parameters are reported in Supplementary Tables S1 and S2. While the hard inversion and saturation recovery data were reasonably well fitted with a monoexponential, a small reduction in RMS misfit was found with a biexponential, albeit with very small and negative $a_{\mathrm{S}}$ components. The improvement in fitting with biexponentials was much more drastic for the adiabatic and sinc inversion experiments, where the misfit values decreased by factors of $\sim$ 8. With an improved fit, the resulting $T_{1,\mathrm{L}}$ parameters in these cases lengthen and coalesce toward the monoexponential $T_1$ values found in the hard inversion and saturation cases. The $T_{\text{1,S}}$ components found for adiabatic and soft inversions are similar within samples, but appear with differing amplitude factors, $a_{\mathrm{S}}$.

Voxelwise fitting of the in vivo IR data to a biexponential relaxation model generated the cerebral WM fit parameters listed in Table 2, ROI‐averaged recovery curves reported in Figure 4, and $T_{1,\mathrm{L}}$ maps in Figures 5D–E. Since the saturation data are well described with one component, adding a second component introduces a wide variety of ill‐defined possible fits (Table 2). While the biexponential fit significantly reduces the RMS misfit in the adiabatic and sinc cases (Figure 5J–K), little improvement is seen in the saturation case, where the two $T_1$ values are both >750 ms. However, in the sinc–Gauss and adiabatic inversion experiments we recover trends resembling the NMR results where, notably, the $T_{1,\mathrm{L}}$ components are similar to the saturation recovery monoexponential result. Table 2 also lists the difference in Bayesian Information Criteria, $\mathrm{\Delta }\text{BIC}={\text{BIC}}_{\text{mono}}-{\text{BIC}}_{\text{bi}}$. Saturation recovery yields negative $\mathrm{\Delta }\text{BIC}$ values, meaning the BIC was lower in the monoexponential fitting, which suggests that the biexponential fit is unnecessary in this case.

3.3.1. Two‐point fitting

Figure 6 illustrates the results from our examination using only two IR or SR data points (TI times) to calculate $T_1$ relaxation. The axes of TI times in Figure 6 align at each possible pairing. We used white in the diverging color scale to represent the corresponding monoexponential $T_1$ fit parameter from saturation recovery in Tables 1 and S3 to allow for a simple relative comparison. The NMR maps are more homogeneous than those of the MRI data, likely owing to the significantly larger signal‐to‐noise ratio (SNR) in the NMR experiment. Note that fitting the in vivo sinc–Gauss and adiabatic recovery data only allows fitting the absolute value of the right side of Equation 1, which permits two possible solutions. We ensured the “correct” recovery solution was used simply by providing a relatively long initial guess for $T_1$ (1 s).

FIGURE 6.

$T_1$ results from monoexponential fitting to recovery curves from each inversion/saturation case with two TI times in (A–C) NMR and (D–F) MRI experiments. Axes represent all pairings of available TI times, and the color scale indicates the $T_1$ value in seconds, where white is centered at the monoexponential $T_1$ fit parameter listed in Tables 1 and S3. The displayed results are characteristic examples from a porcine corpus callosum matter (WM2‐p) sample and human in vivo splenium of the corpus callosum ROI in Figure 1A in the NMR and MRI cases, respectively.

4. DISCUSSION

The aim of this work was to investigate the initial magnetization state and form of longitudinal relaxation in white matter following a variety of excitations, notably adiabatic, using both ex vivo NMR and in vivo MRI. The fact that NMR experiments at two field strengths (8.4 and 4.7 T) produced similar results, but with generally longer $T_1$ times at the higher field, provides confidence that the phenomena observed are comparable with those expected at the lower field strength (3 T) used for imaging. The hard/saturation pulses and soft sinc/sinc–Gauss pulses were implemented to generalize our results to common types of pulse class and to serve as limiting cases, where monoexponential relaxation is expected in the former and biexponential behavior has previously been well documented in the latter. ³ , ⁵ , ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ⁴⁸

4.1. Adiabatic pulses do not saturate nonaqueous magnetization

Because of the short $T_2$ ( $\sim$ 50  $\mu \mathrm{s}$ ²⁷ ) of the nonaqueous component in white matter stemming from restricted proton mobility, ⁴² , ⁴⁹ typical MRI scanners cannot measure the nonaqueous spectrum directly even with ultrashort TE (UTE) sequences. ²⁰ , ⁴² , ⁵⁰ , ⁵¹ , ⁵² Solid‐state NMR avoids this issue with a short dead time ( $\sim$ 5  $\mu \mathrm{s}$) and short pulse widths (90° pulse $\sim$ 4  $\mu \mathrm{s}$) so that the nonaqueous signal may be efficiently excited and observed. Spectra obtained (Figure 2) from short inversion delays, TI, in the NMR experiments demonstrate that typical adiabatic inversion pulses do not saturate the nonaqueous proton magnetization in white matter. This result contrasts with assumptions made in numerous previous studies ⁵ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ and elucidates previous findings of incomplete inversion in a single pool model. ⁵³ , ⁵⁴ , ⁵⁵ , ⁵⁶ , ⁵⁷

Due to the strength of interproton dipolar interactions, adiabatic pulses typically used in vivo do not meet the adiabatic condition for nonaqueous protons. This results in the partial saturation of the nonaqueous signals seen in Figure 2. From the (incorrect) assumption that adiabatic pulses “cause saturation” of semisolid spins that has often been made in the literature, one might expect that increasing the $B_1$ of the adiabatic pulses might simply cause more effective saturation. However, if $B_1$ is increased to become larger than the dipolar coupling strength, adiabatic behavior is recovered for these dipolar coupled spins. Such adiabatic inversion of semisolid spins would require a $B_1$ far beyond that available in typical high‐field MRI instruments.

4.2. Unequal initial magnetization states between pools results in biexponential relaxation

Aqueous and nonaqueous bulk magnetizations are prepared in different initial nonequilibrium states with adiabatic and soft pulses. In the two‐pool framework, ²⁸ , ²⁹ , ⁵⁸ magnetization and chemical exchange rapidly equalize the pools' spin polarizations, producing an apparent $T_1$ component much shorter than the $T_1$ found following full inversion. Some previous studies have attributed this short component to a separable signal from a distinct NMR visible water pool. ⁴ , ⁵⁹ However, our characterization of the nonaqueous signal directly following inversion aligns with the established explanation of magnetization transfer induced biexponentiality, which has not been well described when adiabatic pulses are used. ⁶⁰ , ⁶¹ , ⁶² , ⁶³

The apparent short component distorts the $T_1$ obtained from fitting the relaxation to a monoexponential. While a particular $T_1$ cannot be linked to a specific tissue pool, ⁷ , ¹⁰ it may, under consistent excitation conditions, be considered a qualitative measure of the semisolid pool abundance. In both the ex vivo and in vivo experiments, the adiabatic inversion pulse produced a significant $T_{\text{1,S}}$ component. The distortion of the monoexponential fitting in the adiabatic case lies between that of the hard inversion/saturation and soft pulse inversion. In the in vivo measurements, one component was deemed adequate in fitting the saturation recovery data, whereas biexponential fitting resulted in agreeing $T_{\text{1,S}}$ parameters for the soft (sinc–Gauss) and adiabatic cases, with a lower amplitude in the latter. The $T_{1,\mathrm{L}}$ components in the soft and adiabatic cases also tended toward the hard inversion/saturation monoexponential result, showing that monoexponential fitting underestimates the tissue's actual $T_1$. Biexponential fitting of the in vivo SR data yielded very long $T_{1,\mathrm{L}}$ values (Tables 2 and S3); however, the negative $\mathrm{\Delta }\text{BIC}$ values associated with these fits illustrate that these inconsistent values are the result of overfitting and do not improve the fit significantly over the monoexponential. The sinc–Gauss and adiabatic values show a significant improvement from mono‐ to biexponential fitting. Even with this improvement in modeling, the residuals of the biexponential fits to soft and adiabatic inversions in Figures 3 and 4 retain a systematic character. This suggests the presence of more $T_1$ components, perhaps exceeding 100 ms, ⁴ , ⁷ , ¹⁰ or a more complex function needed to describe the recovery curve.

To summarize, when both pools are excited with the same initial magnetization conditions (as with the hard inversion or long‐SR preparation), nearly monoexponential relaxation is observed. Other preparation conditions give rise to biexponential relaxation, where the shorter time constant reflects equilibration between the pools while the longer time constant approaches the monoexponential $T_1$ seen in the uniform excitation case.

4.3. Biexponential relaxation is more pronounced in white matter than gray matter

Fitted gray matter $T_1$ parameters (Supplementary Figure S1) are longer than those measured in white matter, with the relation between ROIs resembling that of Gelman et. al. ⁶⁴ More pertinent is the noticeable white/gray contrast found in the monoexponential misfit maps (Figures 5G–H), which is largely due to the differences in myelin content between the two tissue types. In white matter, the larger nonaqueous fraction and the close proximity of aqueous/nonaqueous protons in myelin leads to a substantial distortion of the relaxation when the magnetizations in the aqueous and nonaqueous components are prepared in different states. The lower relative nonaqueous spin abundance in gray matter allows for more accurate fitting with a monoexponential function in each case, creating the contrast in Figures 5G–H. However, the initial magnetization state preparation still plays a significant role; sinc–Gauss and adiabatic pulses led to an underestimated $T_1$ compared with the saturation recovery result. The $\mathrm{\Delta }\text{BIC}$ statistic for the gray matter ROIs reinforces this conclusion, with $\mathrm{\Delta }{\text{BIC}}_{\text{saturation}}$ negative in each ROI and $\mathrm{\Delta }{\text{BIC}}_{\text{sinc‐gauss}}>\mathrm{\Delta }{\text{BIC}}_{\text{adiab}}>$ 10 (Supplementary Table S3). The misfit in gray matter is smaller but still nonzero, agreeing with previous findings. ¹² , ⁴⁵ As in white matter, the Bayesian information criteria suggest that a biexponential model is appropriate in cases of soft and adiabatic inversion.

4.4. Exchange hinders $T_1$ reproducibility?

Previous studies have reported widespread discrepancies in $T_1$ when comparing IR with other techniques like variable flip angle (VFA) and Look‐Locker (LL). These discrepancies have been attributed to incomplete spoiling and inaccurate $B_1$ mapping, ² , ⁶ which can impact these latter measurements. Our NMR measurements are free of these issues, as there is no spoiling and $B_1$ is precise (inhomogeneity measured at 1 part in 120 at 360 MHz). We suggest that the seemingly method‐dependent or site‐dependent $T_1$ variations may stem, at least in part, from the inherent multiexponential character of the longitudinal relaxation resulting from unequal aqueous and nonaqueous magnetizations prepared in different states. While our measurements do not attempt to explore these effects for VFA or LL sequences, it is clear that future work is needed in this area.

Valid and robust $T_1$ mapping methodology has been demonstrated in prior work using more complex multiparameter fitting procedures, ⁶⁵ multipool modeling, ⁴ , ⁷ , ¹⁰ , ¹³ , ⁶⁶ , ⁶⁷ , ⁶⁸ , ⁶⁹ , ⁷⁰ , ⁷¹ or simply judicious selection of TIs (i.e., setting a minimum TI) and knowledge of $T_{\text{1,S}}$. ³ , ⁷² We report that a “long” saturation recovery, as used in this work, is an alternate concept for assessing a consistent $T_1$ in vivo through monoexponential recovery. Because the magnetization exchange time between semisolid protons (e.g., bound to myelin lipid headgroups) and water protons is of the order of 100 ms, ⁷ , ¹⁰ the 500‐ms saturation time used ensures that, in regions where the RF irradiation is on resonance, the aqueous and nonaqueous components are both thoroughly saturated. This (nearly) monoexponential relaxation curve is easily reproducible between sites from a physical standpoint, and the requisite sequence is straightforward to implement. The concept of maintaining uniform pool magnetizations during recovery has been pointed out previously in an alternate variable flip‐angle implementation by Teixeira et al. ⁴⁷ Their controlled saturation magnetization transfer protocol for measuring $T_1$ showed good mapping reproducibility across sites and vendors. ⁴⁸

We recognize that the relatively long timescale for complete saturation makes for lengthy experiments: acquiring one slice using this saturation recovery sequence took approximately 81 s, making full brain coverage appear to be challenging. With reliable single exponential behavior, however, it is likely that the number of TI points needed could be reduced to accelerate the measurements somewhat. Saturation‐recovery measurements also suffer from a reduced dynamic range compared with inversion‐recovery methods (i.e., recovery from 0 to $M_0$ instead of $-M_0$ to $M_0$). The improved robustness of the technique might make this a justifiable concession. The major limitation of the saturation recovery sequence used here was vulnerability to $B_0$ inhomogeneity leading to poor saturation, which then created more instability in fitting with few TI points. This, as well as a long sequence time, may make clinical full brain application impractical.

4.5. Fast two‐point $T_1$ methods are precarious

Quantitative MRI demands reproducibility, which must compromise with speed for clinical feasibility. This prompted us to assess the minimum number of TI times needed to capture $T_1$ relaxation in tissue accurately. Often the bare minimum, two TI times, is chosen, as in MP2RAGE (e.g., TI = 800/2200 ms ⁵⁷ ), to fit a monoexponential IR curve. Figure 6 shows that drawing quantitative conclusions through this compromise is risky. Figure 6A suggests that, if the preparation of initial magnetization states (through 500‐ms saturation) yields very nearly monoexponential relaxation, then most reasonable choices of TI, in the upper portion of the plots, will produce similar $T_1$ values, as would be expected from a pure exponential. In both soft and adiabatic inversion cases, using two TI points will almost certainly give an underestimated $T_1$ because the two‐point fitting produces a $T_1$ based on the ratio of the two signal intensities. The apparent short component stemming from cross‐relaxation in these inversions causes a larger recovery of magnetization at short TI than would otherwise be measured, leading to an underestimated $T_1$. Figures 6E and 6F display potentially deceiving fit results at TI = 598 ms. In the adiabatic case, $T_1$ at this point seems to agree well with the monoexponential saturation result. This point is most near the zero crossing of the recovery curve and should generally be avoided because, with magnitude measurements, both of the possible relaxation times consistent with the data will have values that might be considered reasonable with no way to resolve the ambiguity.

The results of Figure 6 were obtained by holding the amplitude factor, a, fixed at a non‐ideal value (i.e., <2 for IR) found from analysis of the full data sets, which is not usually an available option in vivo. $T_1$ determined from the two‐point method is highly dependent on the choice of a, because a small fluctuation in the signal at an early TI may cause a large change in the fitted relaxation trajectory. It is clear that fitting a recovery curve with two points does not establish a reliable quantitative analysis and is only useful for qualitative mapping. Because clinical sequences such as MP2RAGE are generally not simple two‐point IR techniques, but rather based on steady‐state small flip‐angle pulses, our results likely do not precisely reflect the distortions that may be produced clinically. However, we expect it is unlikely that these complications would resolve the kinds of distortions we have found.

Rioux et al. ³ and Liu et al. ⁷³ have previously suggested mitigating the influence of $T_{\text{1,S}}$ by choosing TI values sufficiently long for monoexponential fitting (e.g., TI $\gtrsim$ 150 ms at 3 T), noting that this minimum time should depend on field strength, as does $T_1$. Determining a short time cutoff with only two recovery points may be difficult to define according to the results in Figure 6. In addition, component times from the four‐pool model of the order of 150 ms have been reported previously. ⁴ , ⁷ , ¹⁰ The saturation recovery method used in this work takes the same precaution of attempting to remove the magnetization transfer timescale from the overall relaxation, but instead applies this to the experiment rather than the analysis. Omitting short time data limits the effective signal range in a fashion somewhat similar to the dynamic range limitation of saturation recovery methods, and makes estimating the extrapolated $t=$ 0 point more ambiguous in fitting.

Another precarious practice to mention is that quantitative in vivo measurement sequences are commonly first validated by application to water‐based phantoms, where the exchange effects discussed here are insignificant. The misfit measured in both white and gray matter then illuminates the potential for issues in this type of validation, as seen by Stikov et al., ² due to the lack of accounting for partial nonaqueous saturation effects.

4.6. Outlook

The theoretical background that is usually used to understand both soft and adiabatic pulses, such as the two‐pool model employed here, does not account for dipolar‐coupled spins in the system. We plan to study the effects of these kinds of pulses in two‐component systems with Redfield–Provotorov theory. ⁷⁴

The main limiting factor of the “long” saturation recovery sequence used here was the susceptibility to $B_0$ inhomogeneity due to the long, low‐amplitude saturation pulse. In future implementations, we will explore options to replace the continuous‐wave saturation method with more broadband methods, such as a saturation pulse train, which may lead to a more robust sequence and more spatially uniform saturation. This would allow the initial magnetization state to be known accurately and allow for more consistent measurement across scanner sites. A faster, more robust measurement might allow for clinical implementation.

5. CONCLUSIONS

We have examined longitudinal relaxation in brain tissue following hard, adiabatic, and soft inversion and long saturation in order to illuminate how these different preparations yield different initial magnetization states and change the magnetization recovery dynamics. By directly monitoring the state of nonaqueous protons with solid‐state NMR in multiple ex vivo samples, we have shown that a typical adiabatic pulse does not saturate the proton population completely, contrary to common assumption. Through both in vivo and ex vivo experiments, we demonstrated that preparation of aqueous/nonaqueous magnetization in unequal states via soft or adiabatic pulses results in biexponential relaxation due to cross‐relaxation between pools. When biexponential relaxation is observed, measurement of $T_1$ using only two TI points will underestimate the measured $T_1$ due to the apparent short $T_1$ component. Accordingly, we introduced the concept of a “long” saturation recovery sequence as a straightforward, if impractical, means of producing monoexponential relaxation in vivo.

Supporting information

nbm4936‐sup‐0001‐supp‐mat‐resub.pdf

Reynolds LA, Morris SR, Vavasour IM, et al. Nonaqueous magnetization following adiabatic and selective pulses in brain: T1 and cross‐relaxation dynamics. NMR in Biomedicine. 2023;36(8):e4936. doi: 10.1002/nbm.4936