Fast macromolecular proton fraction mapping from a single off-resonance magnetization transfer measurement

Abstract

A new method was developed for fast quantitative mapping of the macromolecular proton fraction defined within the two-pool model of magnetization transfer. The method utilizes a single image with off-resonance saturation, a reference image for data normalization, and T(1), B(0), and B(1) maps with the total acquisition time ~10 min for whole-brain imaging. Macromolecular proton fraction maps are reconstructed by iterative solution of the matrix pulsed magnetization transfer equation with constrained values of other model parameters. Theoretical error model describing the variance due to noise and the bias due to deviations of constrained parameters from their actual values was formulated based on error propagation rules. The method was validated by comparison with the conventional multiparameter multipoint fit of the pulsed magnetization transfer model based on data from two healthy subjects and two multiple sclerosis patients. It was demonstrated theoretically and experimentally that accuracy of the method depends on the offset frequency and flip angle of the saturation pulse, and optimal ranges of these parameters are 4-7 kHz and 600°-900°, respectively. At optimal sampling conditions, the single-point method enables <10% relative macromolecular proton fraction errors. Comparison with the multiparameter fitting method revealed very good agreement with no significant bias and limits of agreement around ± 0.7%.

Fig. 1

Sensitivity analysis of pulsed Z-spectra in WM (a-c), GM (d-f), and an MS lesion (g-i). Source experimental data (points on plots a,d,g) were measured in ROIs corresponding to frontal WM (a) and the head of caudate nucleus (d) from images of a healthy subject and a lesion (g) from images of an MS patient. Four-parameter fit of the pulsed MT model (lines on plots a,d,g) resulted in the following parameter sets: f=14.8%, k=3.5 s⁻¹, (R=20.1 s⁻¹), T₂^B=9.7 μs, and T₂^F=21.0 ms for WM; f=6.5%, k=1.9 s⁻¹, (R=27.3 s⁻¹), T₂^B=9.3 μs, and T₂^F=27.1 ms for GM; and f=9.1%, k=1.8 s⁻¹, (R=18.0 s⁻¹), T₂^B=10.6 μs, and T₂^F=49.8 ms for the MS lesion. Complementary R₁ for these measurements were 1.172, 0.745, and 0.763 s⁻¹ in WM, GM, and the MS lesion, respectively. For the above model parameters, relative sensitivities to the parameters f (black), R (red), T₂^B (green), and T₂^F (blue) are plotted as functions of Δ at FA_MT=600° (b,e,h) and of FA_MT at Δ=4 kHz (c,f,i). Other sequence parameters used in simulations correspond to experimental ones detailed in the Materials and Methods section.

Fig. 2

Examples of the two-pool model parameter maps and their combinations obtained from an MS patient including the primary parameters reconstructed by the four-parameter fit: f (a), k (b), T₂^F (d), and T₂^B (f); the parameter combinations R (c) and R₁T₂^F (e); the MPF (f) maps reconstructed by the single-point method for Δ=4 kHz and FA_MT=600° (g), Δ=1 kHz and FA_MT=980° (i), and Δ=12 kHz and FA_MT=600° (k); and the MPF difference (Δf) maps calculated by subtracting single-point maps (g,i,k) from the reference map (a) for Δ=4 kHz and FA_MT=600° (h), Δ=1 kHz and FA_MT=980° (j), and Δ=12 kHz and FA_MT=600° (l). Arrow indicates an MS lesion. Grayscale window range corresponds to parameter ranges as follows: 0-22% for all MPF maps (a,g,i,k), −11%-+11% for all MPF difference maps (h,j,l), 0-6 s⁻¹ for k map (b), 0-45 s⁻¹ for R map (c), 0-50 ms for T₂^F map (d), 0-0.05 for R₁T₂^F map (e), and 7.8-13.3 μs for T₂^B map (f). All maps are presented in linear scale with window centers corresponding to the middle of parameter ranges.

Fig. 3

Example T₂^B maps obtained from an MS patient. Several anatomic structures are marked by arrows to illustrate anatomical variability of this parameter in WM. The longest T₂^B values (~11-12 μs) are associated with the through-plane fiber tract direction as seen for the corona radiata (CR), posterior limb of the internal capsule (PL), and the cerebral peduncle (CP), which mainly contain fibers of the corticospinal tract. The shortest T₂^B values (~8-9 μs) are related to compact tracts with fibers primarily parallel to the imaging plane, such as the corpus callosum (CC) and anterior commissure (AC). Slightly shorter T₂^B (~9-9.5 μs) are also observed in GM and an MS lesion (L).

Fig. 4

Histograms of the two-pool model parameters in the brain averaged for control subjects (black lines) and MS patients (gray lines). a-c: Histograms of the parameters R (a), R₁T₂^F (b), and T₂^B (c) constrained during single-point MPF reconstruction. d: Comparison between MPF histograms calculated from MPF maps reconstructed by the four-parameter fit (solid lines) and by the single-point method for Δ=4 kHz and FA_MT=600° (dashed lines). The histograms were normalized to the total number of voxels and computed with the following bin sizes: 0.75 s⁻¹ for R (a), 0.00075 for R₁T₂^F (b), 0.1 μs for T₂^B (c), and 0.25% for MPF (d).

Fig. 5

Analysis of errors in single-point MPF mapping based on the error model given by Eqs. [9]-[12]. a: Total absolute percentage error δ_f=σ_f/f simulated as a function of saturation parameters Δ and FA_MT for SNR_ref=150. The grayscale-coded levels (from darker to lighter) correspond to δ_f intervals of 8-8.5%, 8.5-10%, 10-20%, 20-40%, 40-80%, and >80%. b: Comparison between the experimental mean absolute percentage error per voxel (Eq. [13]) averaged across all subjects (points with error bars indicating ±SD) and the simulated total absolute percentage error for SNR_ref=170 approximately corresponding to that in experimental images (lines). c: Effect of SNR_ref on the total absolute percentage error simulated as a function of Δ at FA_MT=600°. SNR_ref values are specified against each curve on the plot. d: Effect of noise (Eq. [11]) and bias (Eq. [12]) terms on the absolute percentage error for WM (black lines) and GM (gray lines) simulated as a function of Δ at FA_MT=600°. Solid lines represent the total error for SNR_ref=170. The contribution of bias (long-dashed lines) was calculated by setting noise terms σ_i,j,k=0 (Eq. [11]). The contributions of noise for SNR_ref=170 (short-dashed lines) and SNR_ref=50 (dotted lines) were calculated by setting bias terms β_i,j,k=0 (Eq. [12]). Simulations for plots (a-c) were carried out for approximate average-brain values of f=9% and R₁=0.9 s⁻¹. In plot (d), tissue parameters were: f=13.5%, R₁=1.11 s⁻¹ for WM and f=6.5%, R₁=0.72 s⁻¹ for GM. Experimental R, T₂^B, and R₁T₂^F histograms (Fig. 4) averaged across all subject were used to construct the joint distribution of these parameters. For this purpose, the coefficients h_i,j,k in Eq. [9] were calculated as the products of R, T₂^B, and R₁T₂^F histogram frequencies across all possible combinations taken in 90% central ranges (above 5^th and below 95^th percentiles) followed by renormalization of the resulting joint distribution. The fixed parameters R=19.0 s⁻¹, R₁T₂^F=0.022, and T₂^B=9.7 μs determined from experimental data were used to calculate deviations ΔR_i, $\Delta T_{2j}^{\mathrm{F}}$, and $\Delta T_{2k}^{\mathrm{B}}$ in Eq. [12]. The pulse sequence parameters used in simulations correspond to experimental ones detailed in the Materials and Methods section.

Fig. 6

Statistical comparison between the pooled ROI data measured from MPF maps reconstructed by the four-parameter fit (f_ref) and by the single-point method for Δ=4 kHz and FA_MT=600° (f_{4 kHz/600°}). The measurements for WM regions, GM regions, and MS lesions are identified by black dots, gray dots, and crosses, respectively. a: Correlation between the two measurements. The diagonal line corresponds to the line of unity. b Bland-Altman plot (the difference vs. mean of two measurements). The solid line corresponds to the mean difference, and the dashed lines represent the limits of agreement.

Fig. 7

Representative MPF maps obtained from an MS patient and reconstructed by the single-point method for Δ=4 kHz and FA_MT=600°. Each second cross-section is shown after exclusion of four superior and inferior slices from the volume totally comprising 48 reconstructed slices with 2.5 mm thickness.