Spectral characteristics of semi-solid protons in human brain white matter at 7 T

Abstract

Purpose

To inform quantification of MRI magnetization transfer contrast at high field by measuring the spectral characteristics of ¹H protons in semi-solids in human brain at 7 T, while avoiding prohibitive RF tissue heating and confounding effects from chemical exchange.

Methods

Saturation-recovery type experiments were performed using brief, frequency-specific RF pulses that saturate semi-solid proton magnetization. Analysis of the subsequent recovery of water proton magnetization with a two-pool model of exchange allowed studying spectral characteristics of semi-solid protons.

Results

We show that in white matter, the semi-solid proton spectrum can be approximated with a symmetric, super-Lorentzian line at −2.58±0.05 ppm from the water resonance and an average transverse relaxation time constant (T₂) of 9.6±0.6 µs.

Conclusion

These results are consistent with studies at lower field that have indicated a major contribution from methylene protons to magnetization transfer contrast and will facilitate the design and quantification of magnetization transfer studies at 7 T.

Introduction

In MRI of human brain, Magnetization Transfer (MT) contrast (1) has been used extensively to study tissue composition, specifically the fraction of hydrogen (¹H) protons with restricted mobility, often referred to as semi-solid protons or macromolecular protons (MPs) (2–6). These protons, having a short T₂, are generally not directly detectable by MRI but, through MT, exert an influence on ¹H protons in water (WPs), the primary contributors to the MRI signal. Measures of the magnitude of this MT effect have been used to study MP content in brain tissue (4–6) and characterize alterations in brain myelin content in multiple sclerosis (7, 8) and other pathology (9–11).

The mechanisms underlying MT contrast are complex (12, 13), often rendering interpretation and quantification difficult. Generally, the strongest contributions to MT come from MPs such as proteins and lipids, whose protons can affect WP magnetization through dipolar coupling and chemical exchange (2, 12, 14, 15). However, chemical exchange effects of smaller molecules may contribute as well (16, 17). And chemical exchange effects can be enhanced by using long RF irradiation as is done in so called chemical exchange saturation transfer (CEST) techniques (18). While MT generally contributes to MRI contrast to some extent, this contribution is amplified by differentially perturbing WP and MP magnetization levels from their thermal equilibrium values (2). Because of this, MT contrast is not only dependent on dipolar coupling strength and exchange rate between WP and MP, but also on specifics of the MRI pulse sequence (2). It is the latter principle that has been exploited to highlight certain contributions to MT, rendering a contrast that emphasizes either MPs (4–6, 19, 20) or exchangeable protons (16, 18) with some chemical specificity (18). On the other hand, MP magnetization levels are often not well known and difficult to control, due to the short transverse relaxation time (T₂) of MPs. Therefore, for proper quantification of MT, and avoid unintended contribution of MT in general (non-MT) MRI applications, MP magnetization levels need to be estimated.

Apart from the exchange rate between MPs and WPs, MT contrast is dependent on the characteristics of the radiofrequency (RF) irradiation, the spectral characteristics of MPs and WPs, and T₁ relaxation. Of these factors, the MP spectrum may be the most critical and most difficult to measure, because of MPs extremely short transverse relaxation time constant (T₂). Direct measurements with NMR spectrometers on ex-vivo brain tissue samples and various membrane model systems, including myelin extracts and lecithin, have shown that MPs have complex lineshapes with varying width and off-resonance frequency, dependent on the host molecules and strength of dipolar coupling with neighboring MPs (20–25). Typically, at field strengths up to 9.4 T, super-Lorentzian (SL) and Lorentzian lineshapes have been reported over a spectral range of about 6 ppm and T₂ values of 20–100 µs (20–26). The general understanding is that in membrane-rich white matter, lipid methylene and methyl groups are the major contributors to these spectra (20, 24, 26, 27).

Because MP spectral characteristics may be quite different in-vivo, and at higher field strengths, various attempts have been made to infer the MP spectrum from their effect on the easier detectable WP signal using steady state MT experiments. Studies at clinical field strengths up to 3 T have reported a SL lineshape with a T₂ of in the range of 9–15 µs for white matter (WM) in-vivo (5, 28, 29), similar to the range of 9–13 µs found for tissue samples using this approach (6, 14, 30, 31), but below the 20–100 µs range directly measured by NMR spectroscopy. In addition, several studies have found the MP spectrum to be shifted by about −3 ppm relative to the WP resonance (28, 32–34), consistent with the chemical shift of lipid methylene protons. However this has proven difficult to reproduce, in particular at high field, due to confounding CEST effects (35), and increased tissue heating associated with RF irradiation. Currently, most quantitative MT methods assume the MP spectrum to be centered on the water resonance.

To further investigate MP spectral characteristics, with the ultimate purpose of better quantifying MT contrast in MRI of brain tissue, we applied an indirect measurement approach based on transient MT effects after MP saturation with a brief, RF pulse (36). Using a range of specific RF frequencies allowed us to characterize MP spectral characteristics in human brain at 7 T in an efficient manner, while minimizing effects of CEST, tissue heating, and direct WP saturation.

Methods

MRI experiments were performed on eight human subjects (ages 20–49, average 30.6, 4 female), scanned under an IRB approval on a 7 T Siemens scanner using a 32-channel receive array. In order to study MT without CEST and direct MP saturation effects, we followed a recent approach based on monitoring the saturation of WP signal following a brief, 6–12 ms MP saturation pulse (3, 37). This saturation recovery (SR) approach resembles the selective inversion recovery (IR) approach (38, 39), but sacrifices some sensitivity to obtain an improved estimate of initial MP magnetization level, and render this level insensitive to B₁ variation (3, 37). Like the IR approach, it allows sensitive determination of the parameters describing the MT process, by accounting for the direct water saturation effects (3, 37–39), and minimization of CEST effects and tissue heating. First, experiments were performed to determine parameters describing MT kinetics, assuming a two-pool model of exchange between MP and WP (defined as Experiment I), and subsequently, MP spectral characteristics were investigated by studying the magnitude of the MT effects as a function of the frequency of narrowband MP saturation pulse (defined as Experiment II).

Two-pool model

Following an initial RF pulse that differentially saturates the WP and MP pools, the fractional saturations of the two pools, FS_WP and FS_MP, experience bi-exponential evolutions as follows (3, 37, 40):

$$F{S}_{\mathit{\text{WP}}}(t)=1-\frac{M_{\mathit{\text{WP}}}(t)}{M_{\mathit{\text{WP}}}(\infty )}=a_1{e}^{-{\lambda }_{1}t}+a_2{e}^{-{\lambda }_{2}t}$$ [1]

$$F{S}_{\mathit{\text{MP}}}(t)=1-\frac{M_{\mathit{\text{MP}}}(t)}{M_{\mathit{\text{MP}}}(\mathit{\infty })}=\frac{a_1(-{\lambda }_1+k_{\mathit{\text{WM}}}+R_{1,\mathit{\text{WP}}})}{k_{\mathit{\text{WM}}}}{e}^{-{\lambda }_{1}t}+\frac{a_2(-{\lambda }_2+k_{\mathit{\text{WM}}}+R_{1,\mathit{\text{WP}}})}{k_{\mathit{\text{WM}}}}{e}^{-{\lambda }_{2}t}$$ [2]

$$2{\lambda }_{1,2}=R_{1,\mathit{\text{WP}}}+R_{1,\mathit{\text{MP}}}+k_{\mathit{\text{MW}}}+k_{\mathit{\text{WM}}}\pm \sqrt{{(R_{1,\mathit{\text{MP}}}-R_{1,\mathit{\text{WP}}}+k_{\mathit{\text{MW}}}-k_{\mathit{\text{WM}}})}^2+4k_{\mathit{\text{MW}}}{k}_{\mathit{\text{WM}}}}$$ [3]

$$a_{1,2}=\pm \frac{F{S}_{\mathit{\text{WP}}}(0)(R_{1,\mathit{\text{WP}}}+k_{\mathit{\text{WM}}}-{\lambda }_{2,1})-F{S}_{\mathit{\text{MP}}}(0)k_{\mathit{\text{WM}}}}{{\lambda }_1-{\lambda }_2}$$ [4]

$$(1-f)k_{\mathit{\text{WM}}}=f{k}_{\mathit{\text{MW}}}$$ [5]

In these equations, M_WP and M_MP are the longitudinal magnetizations of the two pools, R_1,WP and R_1,MP are their relaxation rates, λ₁ and λ₂ are fast and slow rate constants of the saturation recovery, and a₁ and a₂ are the corresponding amplitudes. Parameters k_WM and k_MW represent the MT exchange rate constants relative to WP and MP pool sizes respectively.

Experiment I: Determination of MT parameters

To measure the parameters related to the two-pool exchange model, two types of preparation pulses, namely a WP IR pulse and a composite broadband MP SR pulse were used to saturate the two pools to different extents. After variable delay t, EPI image acquisition was performed to sample FS_WP(t). The use of two different preparation pulses facilitated fitting λ₁ and λ₂, and furthermore allowed extraction of k_MW, k_WM, f, and R_1,WP by assuming R_1,MP = 2 s⁻¹ and FS_MP(0) = 0.93 for the broadband SR experiment as determined previously (3). The inversion pulse was adiabatic, with a hyperbolic secant envelope, duration of 5.12 ms, energy of 0.51 (µT)²s, maximum B₁ (amplitude of the RF field) of 833 Hz (1 Hz equals 0.0235 µT) and β of 1400 s⁻¹ (41). The broadband SR pulse had a duration of 6 ms and consisted of a train of 16 hard pulses with angles 60°, −120°, 120°, −120°, ….120°, −60°, with a B₁ amplitude of 833 Hz (3).

Experiment II: Determination of MP spectral characteristics

To determine MP spectral characteristics, the broadband SR pulse was replaced by a frequency-specific SR pulse and applied at 12 different frequency offsets (F) with respect to the water resonance frequency, ranging from −16 kHz to 16 kHz (−16, −8, −4, −2, −1, −0.5, 0.5, 1, 2, 4, 8, 16 kHz). The order of scans for different values of F was randomized for each subject. The pulse had a duration of 12 ms, and a hyperbolic secant envelope for its amplitude, identical to that used for the inversion pulse described above, with a β of 600 s⁻¹ (41). The full width at half maximum (FWHM) of its power spectral density is 119 Hz. A relatively low B₁ amplitude of 200 Hz was used in order to avoid saturation and the non-linear relationship between FS_MP(0) and the integral of squared B₁ amplitude over the pulse duration for all values of F (42, 43). This simplified the derivation of the MP spectrum from the experimental data.

Image acquisition

For both IR and SR experiments, image data were acquired using single-shot EPI, sampling 5 slices consecutively after the preparation pulse; cycling the slice order over 5 repetitions thus resulted in acquisition of 5 delay times for each slice (44). Axial-oblique slices of 2 mm thickness were placed, with 3.4 mm inter-slice gap, parallel to AC-PC line and encompassed the central part of the corpus callosum. The delay times for the IR experiment were 6, 63, 144, 282 and 1200 ms (defined as the time from the center of the inversion pulse to the center of the EPI excitation pulse). The delay times for the broadband SR experiments were: 7, 127, 258, 401 and 559 ms and for the frequency-specific SR experiments were: 10, 130, 260, 402 and 559 ms. The IR and SR delay times were chosen to sample the signal recovery dynamics, within the constraint of the minimal slice repetition time (TR) set by the duration of the EPI readout. The image resolution was 144×108 with SENSE rate-2 acceleration, the field-of-view was 240×180 mm. The echo time (TE) was 24 ms, TRs were 6 and 3 s for IR and SR experiments respectively. In order to suppress signals from scalp lipids, the TE was increased by 0.49 ms on even numbered repetitions (3). A multi gradient echo (MGRE) sequence with TR of 0.2 s, TE of 2.5 ms, 7 echoes with echo spacing of 0.74 ms, the same resolution and field-of-view as the EPI scans and total scan time of 21.6 s, was scanned before all IR and SR experiments. This MGRE sequence served as reference to reconstruct the accelerated EPI scans and was also used to estimate the B₀ (amplitude of the static field) inhomogeneity. For IR experiments, six repeat measurements were performed, the first two of which omitted the inversion pulse and were used to provide a reference signal to estimate M_WP (∞) in Eq. [1], and allow conversion of the measured signals to FS_WP(t). Similarly, ten repetitions (including two serving as reference) and six repetitions (including one reference) were acquired for the broadband and frequency-specific SR experiments respectively.

Data Analysis

Pre-processing

Pre-processing included motion correction, signal polarity correction, averaging, and calculation of FS_WP(t). Prior to averaging repetitions, complex images were spatially registered to correct for motion. Only in-plane registration was performed, as the small number of slices did not support through-plane motion correction. Polarity correction was needed only for IR (magnitude) data, because of signal rectification during the complex-to-magnitude conversion. It was performed based on the phase difference between the IR images with the (un-inverted) reference image. The FS_WP(t) level expressed in Eq. [1] was determined by dividing each IR image by the corresponding reference image (i.e. data acquired without inversion pulse). Analogous analysis was performed for the SR data, however without performing the signal polarity adjustment. All processing was done in IDL (Exelsis Visual Information Solutions, Boulder, CO, USA).

Voxel-wise determination of MP saturation

To determine λ₁, λ₂, k_WM, k_MW, and R_1,WP, both the IR and the broadband SR data from Experiment I were analyzed on a voxel-wise basis. Defining FS_MP(0, F) as the FS_MP(0) created by a frequency-specific SR pulse applied at frequency F, FS_MP(0,F) can be then calculated based on analysis of the frequency-specific SR data in Experiment II. The following steps were involved:

1. Fit Eq. [1] to the IR and broadband SR data jointly, yielding one pair of decay rates (λ₁, λ₂) and two pairs of amplitudes (a₁, a₂) for each voxel.

2. Assuming R_1,MP=2 s⁻¹ and FS_MP(0) for the broadband SR experiment to be 0.93 as determined previously (3), calculate k_WM, k_MW, R_1,WP, using Eq. [3–4], based on the decay rates and amplitudes found under Step (a).

3. Fit Eq. [1] to the frequency-specific SR data, to find a pair of amplitudes (a₁(F), a₂(F)) for every voxel at each F, using decay rates (λ₁, λ₂) found under Step (a). Then calculate FS_MP(0,F) using these (a₁(F), a₂(F)) pairs, according to Eq. [2] by setting t=0 s, with all other parameters known from Steps (a) and (b), as shown in Eq. [6].

$$F{S}_{\mathit{\text{MP}}}(0,F)=\frac{a_1(F)(-{\lambda }_1+k_{\mathit{\text{WM}}}+R_{1,\mathit{\text{WP}}})}{k_{\mathit{\text{WM}}}}+\frac{a_2(F)(-{\lambda }_2+k_{\mathit{\text{WM}}}+R_{1,\mathit{\text{WP}}})}{k_{\mathit{\text{WM}}}}$$ [6]

Calculation of B₀ shift for frequency-specific SR scans

B₀ inhomogeneity and its drift over the course of the experiments can potentially change the effective F for each of the frequency-specific SR pulses. B₀ measurement with methods like WASSR (45) can be used to correct for these effects. Here, B₀ inhomogeneity for each scan was calculated voxel-wise as follows:

1. The phase of even echoes of the MGRE scan was fitted to a linear model to estimate spatial variations (inhomogeneity) in B₀.

2. The EPI (either IR or SR) scan following the MGRE was assumed to suffer from the same B₀ inhomogeneity as the MGRE scan.

3. The relative B₀ shift between successive EPI scans (temporal drift) was determined from their relative phase.

4. The absolute B₀ shift, ΔB₀, for a specific EPI scan was calculated by summing over all its previous relative B₀ shifts and the B₀ inhomogeneity of the first EPI scan, as determined in Step (c) and Step (b) respectively.

MP spectral characteristics in a WM region of interest

To infer MP spectral characteristics in WM in human brain, we performed region of interest (ROI) analysis. Since the total scan time for each subject took up to ~1.35 hours and only motion within the axial plane was corrected for by in-plane registration, care was taken to select the ROI well within WM. This was done from images of the MP fraction f thresholded at 0.2, and Gaussian smoothed over a kernel of 7 voxels. Fig. 1 shows an example of WM ROI’s on five slices for one of the 7 subjects studied.

FIG. 1.

Example of WM ROI selection. ROI location is shown superimposed on EPI scan (top row), together with corresponding f maps. Selection was based on thresholding f at 0.2, followed by Gaussian smoothing with a 7 voxel kernel.

The ROI averaged FS_MP(0,F) was calculated for each subject. Following previous work (14, 30), a SL lineshape (Eq. [7]) and Lorentzian (L) lineshape (Eq. [8]) were fit to this data.

$$g_{\mathit{\text{SL}}}((F-\mathrm{\Delta }{f}_0(F)-\mathrm{\Delta }{F}_{\mathit{\text{SL}}}),T_{2,\mathit{\text{SL}}},A_{\mathit{\text{SL}}})=A_{\mathit{\text{SL}}}\sqrt{\frac{2}{\pi }}{\int }_0^{\frac{\pi }{2}}\frac{T_{2,\mathit{\text{SL}}}}{|3{\mathit{\text{cos}}}^2\theta -1|}\mathit{\text{exp}}(-2{\left(\frac{2\pi (F-\mathrm{\Delta }{f}_0(F)-\mathrm{\Delta }{F}_{\mathit{\text{SL}}})T_{2,SL}}{3{\mathit{\text{cos}}}^2\theta -1}\right)}^2)\mathit{\text{sin}}\theta d\theta$$ [7]

$$g_L((F-\mathrm{\Delta }{f}_0(F)-\mathrm{\Delta }{F}_L),T_{2,L},A_L)=A_L\frac{T_{2,L}}{\pi (1+{(2\pi (F-\mathrm{\Delta }{f}_0(F)-\mathrm{\Delta }{F}_L)T_{2,L})}^2)}$$ [8]

In Eqs. [7] and [8], A is a scaling factor, F is the frequency of the applied frequency-specific SR pulse as mentioned above, and ΔF is the resonance frequency of MPs. Δf₀(F) is the WM ROI averaged frequency offset caused by the B₀ shift for a frequency-specific SR scan applied at frequency F, and is equal to γΔB₀/2π, with ΔB₀ determined above and γ being the gyromagnetic ratio. The averages and standard deviations were calculated for T₂ and ΔF over subjects for both lineshapes. Fitting using the sum of two Lorentzians to individual subject FS_MP(0,F) was also performed, using a common ΔF_L determined from the single Lorentzian fit for both Lorentzians, to account for the potential contribution of two MP pools with distinct spectral characteristics (31, 46–48). Finally, fitting SL, Lorentzian and sum of two Lorentzians to FS_MP(0,F) data combined from all subjects was also performed.

Potential effects of B₁ amplitude on the MP spectrum

The validity of our approach to infer the MP spectrum implicitly assumes a linear relationship between FS_MP(0,F) and the power of off resonance MT pulses, which holds true only when the B₁ amplitude is low enough to avoid substantial saturation (42, 43). To study the effect of B₁ amplitude of the frequency-specific SR pulse on the inferred MP spectrum, we fitted a Lorentzian lineshape to simulated FS_MP(0,F)’s using Bloch equation. First, FS_MP(0,F) for the MPs with a T_2,input of 65 µs is simulated, under the influence of frequency-specific hyperbolic secant SR pulse with a duration of 12 ms and a B₁ of 200 Hz (matching the preparation pulses used in the frequency-specific SR experiments), applied at several different frequency offsets, ranging from −16 kHz to 16 kHz. A Lorentzian fit yielded a T_2,output. Then, dependence of T_2,output on T_2,input and B₁ were studied by varying T_2,input while keeping B₁ fixed as 200 Hz, and varying B₁ while keeping T_2,input fixed as 65 µs, respectively. A Lorentzian rather than a SL lineshape was used in all these simulations, due to the lack of a rigorous way to simulate Bloch equations incorporating a SL lineshape, under influence of a shaped MT pulse (49).

Potential effects of assumptions for the values of R_1,MP and FS_MP(0)

A potential source for inaccuracies in the extracted parameters are incorrect assumptions for the values of R_1,MP and FS_MP(0). For the broadband SR experiment (Experiment I), R_1,MP=2.0 s⁻¹ and FS_MP(0)=0.93 were assumed, and these may not be entirely accurate. We investigated the effect of changes in these values on the MP T₂ determined in Experiment II, based on subject and ROI averaged values of decay rates (λ₁, λ₂) and amplitudes (a₁, a₂) for all IR and SR experiments, which were fitted without using any assumption. By varying R_1,MP from 1 to 3 s⁻¹ and FS_MP(0) from 0.8 to 1.0 respectively, and going through procedures described above, new T₂ values were found for both SL and Lorentzian lineshapes, and these were compared with the original values.

Quantification of the symmetry of the MP spectrum

The effect of CEST on our spectrum measurements is expected to be small because of the short, 12 ms duration of the RF pulses used for the SR experiment. To investigate the presence of any remaining CEST effect, we analyzed spectral symmetry with the notion that any asymmetries would point to a potential CEST contribution (28, 33, 42, 43). Symmetry was shown by inspecting the residuals after subtracting the fits from ROI averaged FS_MP(0,F) of all subject, done for all types of lineshapes, including SL, Lorentzian and sum of tow Lorentzians.

Results

Voxel-wise fitting of the 2-pool model (Eq. [1]) to the IR and broadband SR data allowed robust extraction of the model parameters. ROI averaged results are shown in Fig. 2 and Table 1. A single set of rate constants (λ₁ and λ₂) fitted both IR and SR data well, as judged from the close fit to the data apparent in Fig. 2. The ROI-averaged values for R_1,WP, f, and k_MW were similar to those found in a previous study based on IR and SR measurements at 7 T (37).

FIG. 2.

Two-pool model fitting (shown in lines) to subject and WM ROI averaged FS_WP(t) (shown in dots) of IR (a) and broadband SR (b) experiments, with the error bars representing the standard deviations over subjects.

Table 1.

Average (standard deviation) of the extracted two-pool model parameters in WM ROI’s over subjects from Experiment I, with R_{1, MP} assumed as 2.0 s⁻¹ uniform across the brain for all subjects, as determined previously by van Gelderen et al (3, 37); all rates are reported in s⁻¹; R² was adjusted for degrees of freedoms.

a1(IR)	a2(IR)	a1(SR)	a2(SR)	λ1	λ2	R1, WP	R1, MP	f	kWM	kMW	R2
0.216	1.75	−0.197	0.254	9.95	0.716	0.363	2.0	0.250	2.07	6.21	0.99996
(0.009)	(0.01)	(0.010)	(0.010)	(0.32)	(0.015)	(0.010)		(0.012)	(0.13)	(0.25)	(1 × 10−5)

With the voxel-wise fast (λ₁) and slow (λ₂) rate constants known, voxel-wise two-pool model fitting of FS_WP(t) to the frequency-specific SR data yielded maps of coefficients a₁(F) and a₂(F), as exemplified in Fig. 3 (top two rows). Next, using Eq. [6], voxel-wise values for a₁(F) and a₂(F) were used to calculate FS_MP(0,F), whose maps is shown as the bottom row of Fig. 3, and further ROI-averaged values for FS_MP(0,F) were determined for each subject. Before proceeding with fitting line shapes to these data, small adjustments to the data were made to correct for potential shifts in F due to instrument drift. These correction values Δf₀(F) were small relative to the spectral range.

FIG. 3.

Examples of maps of -a₁(F) (first row) and a₂(F) (second row), and FS_MP(0,F) (third row), for the frequency-specific SR data fit, at different frequency F (from left to right: −16, −8, −4, −2, −1, −0.5, 0.5, 1, 2, 4, 8, 16 kHz)

Table 2 summarizes the results of fitting a SL (Eq. [7]), Lorentzian (Eq. [8]), and sum of two Lorentzians to subject-wise ROI-averaged FS_MP(0,F). T_2,SL of 9.6±0.6 µs and ΔF_SL of −773±14 Hz (−2.58±0.05 ppm), and T_2,L of 65±2 µs and ΔF_L of −727±28 Hz (−2.42±0.09 ppm) were found for SL and Lorentzian fitting respectively. For the two-Lorentzian fit, a common ΔF_L of −727 Hz (−2.42 ppm) determined from the single Lorentzian fit was used. This fitting resulted in a 74±3% fraction of MPs with a T₂ of 23±5 µs, and a 26±3% fraction with a T₂ of 124±13 µs. Judging from the R² (adjusted for degrees of freedoms) values, the SL and sum of two Lorentzians had similar performance in the fitting, and both provided better fit than Lorentzian.

Table 2.

Results of T₂, ΔF and R² (adjusted for degrees of freedoms) for fitting of SL, Lorentzian and sum of two Lorentzians lineshapes to FS_MP(0,F) data, report in the form of subject average±(standard deviation over subjects); for sum of two Lorentzians fit, a common ΔF_L for both Lorentzians was assumed to be −727 Hz (−2.42 ppm), identical to that obtained from the single Lorentzian fit. The component with T₂ of 23±5µs, composes 74±3% of the total MPs, and the other component with T₂ of 124±13 µs composing the rest.

	SL	Lorentzian	Sum of 2 Lorentzians
T2 (µs)	9.6±0.6	65±2	23±5/124±13
ΔF (Hz)	−773±14	−727±28	−727
R2	0.982±0.005	0.939±0.013	0.989±0.003

SL and Lorentzian fits to ROI averaged FS_MP(0,F) data were also performed on all subjects jointly (but without averaging over subjects, since Δf₀(F) is different across subjects). This is shown in Fig. 4a, yielding T_2,SL of 9.5 µs and ΔF_SL of −781 Hz (−2.60 ppm) for the former, and T_2,L of 65 µs and ΔF_L of −726 Hz (−2.42 ppm) for the later. Fitting to the same data using sum of two Lorentzians, resulted in T_2,L ‘s of 23 µs (73%) and 122 µs (27%), as shown in Fig. 4b.

FIG. 4.

A SL lineshape (shown as the red dashed curve in a) and a Lorentzian lineshape (shown as the black solid curve in a) fitting to the WM ROI averaged FS_MP(0,F) of all subjects jointly (shown in blue dots); sum of two Lorentzians (shown as the curve in b) fits to the same data (shown in blue dots).

After subtraction of the fitted (symmetric) lineshapes from the spectral data, residual signal appears small for the SL fit (Fig. 5a), and the fit of two Lorentzians (Fig. 5c). The small residuals and the absence of any clear asymmetry in their distribution is consistent with expected suppression of CEST effects, and associated asymmetries, with the measurement approach followed here. However, deviation of the residuals from zero is obvious for the Lorentzian fit (Fig. 5b), confirming previous steady state MT studies (4–6, 19) where SL provided a fit superior over a Lorentzain lineshape.

FIG. 5.

Residuals for the SL fit (a), single Lorentzian fit (b), and sum of two Lorentzians fit (c) subtracted from the WM ROI averaged FS_MP(0,F) of all subjects (shown in dots), with data in range of 0 Hz<F<1500 Hz marked in red and −1500 Hz<F<0 Hz marked in blue.

Results of the simulations performed to investigate the influence of the B₁ amplitude on inferred T₂ are shown in Fig. 6. As expected, for an actual MP T₂ (T_2,input) of 65 µs, the inferred T₂ (T_2,output) drops precipitously with RF power (Fig. 6b). However, at the experimental B₁ amplitude of 200 Hz, this drop remains limited: the T_2,output of 60 µs underestimates T_2,input by 5 µs, i.e. less than 10%. According to Fig. 6b, variation of B₁ by 25 Hz results in an error in the estimation of T_2,output on the order of 1 µs, which suggest a low sensitivity to B₁ inhomogeneity. Similarly, at other values of T_2,input , and B₁ =200 Hz, the difference between T_2,input and T_2,output remains modest (Fig. 6c).

FIG. 6.

Simulations of influence of B₁ amplitude on inferred T₂: (a) Lorentzian fit (the curve) to simulated FS_MP(0,F) (the dots) of MP pool with T_2,input of 65 µs, using Bloch equation, under the influence of frequency-specific hyperbolic secant pulses with B₁ of 200 Hz, a common pulse duration of 12 ms, resulting in a T_2,output of 60 µs; (b) B₁ dependence of T_2,output by varying B₁ while keeping T_2,input fixed as 65 µs; (c) T_2,input dependence of T_2,output by varying T_2,input while keeping B₁ fixed as 200 Hz.

The extracted MP T₂ values proved robust against small changes in assumed values for R_1,MP and FS_MP(0). Changing R_1,MP from 1 to 3 s⁻¹ resulted in very little change in FS_MP(0,F). For the SL lineshape, T_2,SL changed from 9.4 to 9.3 µs, while for the Lorentzian, T_2,L changed from 65 to 64 µs. Changes of FS_MP(0) from 0.8 to 1.0 resulted in a similar T_2,SL in the range of 9.3–9.4 µs, and T_2,L remained at a constant value of 64 µs, although increasing FS_MP(0) of the broadband SR experiment results in increased FS_MP(0,F).

Discussion

In order to aid interpretation of MT contrast at high field, we investigated MP spectral characteristics in human brain WM at 7 T. For this purpose, we used a dedicated indirect measurement approach that minimized direct saturation of WPs, CEST effects, and tissue heating, problems often associated with the generation of MT contrast in-vivo. We found that at 7 T, the MP spectrum is well represented by a symmetric, SL lineshape with a time constant T_2,SL of 9.6±0.6 µs, and shifted by −2.58±0.5 ppm relative to the water resonance. As will be discussed in the following, these results are consistent with previous findings and mechanistic interpretations of MT from studies at lower field and point to dipolar coupling between methylene protons as a major determinant of the MP spectral characteristics. We anticipate that these values for the MP spectral characteristics will help design and quantification of future MT studies at 7T.

As has been found with previous indirect measurement of MP spectral characteristics at 1.5 T and 3 T, (4–6, 14) the 7 T data could be reliably fit with a SL lineshape. This is consistent with a dipolar coupling mechanism in semi-solids such as membrane proteins and lipids (14, 25, 29, 50). In addition, it was found that the 9.6 µs T_2,SL at 7 T was similar to the 9.2 µs – 13.1 µs range of values found in previous studies at lower fields between 0.5 T and 3 T (4–6, 28, 51). Like the SL lineshape, the field independence of the linewidth is suggestive of a dominant contribution of dipolar coupling, rather than width being determined by chemical shift differences between the ¹H species contributing to MT (26). Previous direct measurements of MP spectral characteristics on fixed human WM tissue samples have found 50– 65 µs for T_2,L (20, 23) at 7 T and 4.7 T. These values were based on Lorentzian lineshapes, and translate into T_2,SL values of 16–21 µs for SL lines of the same FWHM. These ex-vivo Lorentzian linewidths therefore are quite consistent with the in-vivo values, especially when considering the differences in measurement conditions.

Our MT study at 7 T found that the center of the MPs spectrum is shifted upfield relative to the resonance frequency of WPs by −2.58 ppm. This result agrees well with values of −2.34 ppm previously reported at 3 T (28), and the −2.55 ppm reported in WM of cat brain at 4.7 T (32). Combined, these studies show that the absolute spectral frequency shift is proportional to field strength, an observation consistent with a chemically shifted proton species contributing to MT. The value of the shift is somewhat smaller than the range of −3.2 to −3.9 ppm measured for methylene protons, the dominant proton species in myelin (24). While methylene protons are most abundant in WM (20), a not insignificant contribution to our MT signal may have come from, more downfield shifted proton species (e.g. in proteins and smaller molecules). These protons, while measured together with the methylene protons, may shift the combined spectral line downfield from the −3.2 to −3.9 ppm range.

To the extent that MT is caused by methylene protons in myelin lipids, their substantial orientational order may introduce a dependence of spectral linewidth on the direction of white matter fibers relative to the magnetic field. In fact, a recent study found that T_2,SL may vary between 12 and 15 µs, dependent on fiber orientation (29). Due to lack of information about fiber orientation, we could not confirm this dependence in our own data. Nevertheless, if confirmed, a fiber-orientation dependent MP T₂ would further underscore the importance of the dipolar coupling mechanism for the apparent MP T₂, and furthermore predict an orientation dependence of MT effects. Similarly, since the effect of an inversion RF pulse on MP magnetization depends on MP spectral characteristics (3), orientation dependence of MP T₂ may also render apparent T₁ (as measured from an IR experiment (3)) orientation dependent.

An advantage of the proposed method for the measurement of MP characteristic is the insensitivity to CEST effects, which can substantially contribute to so called “z-spectra” typically acquired to quantify MT effects (12, 28, 52), and thus confound interpretation. When generating MT contrast with seconds-long RF irradiation, MT from exchangeable protons can reduce the amplitude of the WP signal by as much of 2–4%, which is substantial when considering that typical asymmetry in z-spectra due to non-exchanging protons is only on the order of 1–2% (28). Although currently several approaches exist to distinguish CEST from other (non-exchange) MT effects (43, 52, 53), CEST effects were not explicitly excluded from z-spectrum asymmetry quantifications reported previously (28, 32). Nevertheless, it appears that the quantitative shifts characterizing this asymmetry are quite similar between the proposed and previous methods and amount to about −2.6 ppm.

A potential source for inaccurate quantification of MP spectral characteristics with the proposed method is the potential dependence on RF irradiation strength (B₁ amplitude). Preliminary experimental study of effects of B₁ on the spectrum measurement was performed on two subjects in a similar manner as described above. Experiment I was done in exactly the same way as described in Method for both subjects. In Experiment II, multiple B₁’s were used for the frequency-specific SR experiment, to quantify the B₁ dependence of ROI averaged FS_MP(0,F). In lack of a rigorous way to do the simulation based on a SL lineshape (49) as mentioned above, attempts were made to simulate these data using single Lorentzian and a combination of multiple Lorentzians respectively, however no close fit was found. This may reflect the intrinsic insufficiency of a Lorentzian lineshape to represent the underlying interaction between the immobile MPs. The situation may be further complicated by the existence of multiple MP species, each with a SL lineshape centered on a different resonance frequency (24). Thus, while our spectral measurements provide a measure of linewidth and chemical shift, both of which provide insights into the molecular source of MT in white matter, uncertainty remains about the precise lineshape.

Conclusions

A novel approach was introduced to study MPs spectral characteristics while minimizing effects of RF-related tissue heating, direct saturation of WPs and CEST effects. Applied to WM in human brain at 7 T, MPs were found to have a symmetric, SL lineshape with a T_2,SL of 9.6 µs and an resonance frequency ΔF_SL of −773 Hz (−2.58 ppm), consistent with previous results at low field, and consistent with a previously suggested major contribution of dipolarly-coupled lipid methylene protons. These results, as well as the proposed measurement approach, are expected to facilitate the use and interpretation of quantitative MT approaches at high field.