Improved Magnetic Resonance Fingerprinting for Relaxation Measurement in the Presence of Semisolid Magnetization Transfer

Abstract

Purpose:

To characterize and minimize the magnetization transfer (MT) effect in magnetic resonance fingerprinting (MRF) relaxation measurements with a 2-pool (2P) MT model of multiple tissue types.

Methods:

Semisolid MT effect in MRF was modeled using 2P Bloch-McConnell equations. The combinations of MT parameters of multiple tissues (white (WM) and gray matter (GM)) were used to build the MRF dictionary. Both 1-pool (1P) and 2P models were simulated to characterize the dependence on MT. Relaxations measured using MRF with spin-echo saturation-recovery (SR) or inversion-recovery (IR) preparations were compared with conventional SR-prepared T₁ and multiple spin-echo T₂ measurements. The simulations results were validated with phantoms and brain tissue samples.

Results:

The MRF signal was different from the 1P and 2P models. 1P MRF produced significantly (p<0.05) underestimated T₁ in WM (20-30%) and GM (7-10%), while 2P MRF measured consistent T₁ and T₂ in both WM and GM with conventional measurements (pairwise test p>0.1; correlated p<0.05). Simulations showed that SR-prepared MRF measuring T₁ had much less errors against the variation of the macromolecular fraction. Compared to IR preparation, SR-prepared MRF produced higher relaxation correlations (R>0.9) with conventional measurements in both WM and GM across samples, suggesting that SR-prepared MRF was less sensitive to the compositive effect of multiple MT parameters variations.

Conclusions:

2P MRF using a combination of MT parameters for multiple tissue types can measure consistent relaxations with conventional methods. With the 2P models, SR-prepared MRF would provide an option for robust relaxation measurement under heterogeneous MT.

1. Introduction

Magnetic resonance fingerprinting (MRF) is an emerging MRI approach for fast and simultaneous T₁ and T₂ measurements (1). The relaxation MRF approach varies the flip angle (FA) and repetition time (TR) to generate a signal evolution pattern unique to a set of relaxation parameters. The measurement is then compared against a simulated dictionary to determine the best matching relaxation rates. MRF has been extended to a host of applications, including perfusion (2), exchange rate (3), chemical exchange saturation transfer measurements (4,5), and simultaneous imaging of multiple MRI contrast agents (6). It is worth mentioning that modeling biological tissue often involves more than one spin pools (i.e., the bulk tissue water, semisolid macromolecules and/or dilute mobile proteins and peptides) (7). The measured bulk water relaxation rates depend not only on their intrinsic values but also on the properties of the exchangeable pools (8,9). While the relaxation time is an essential magnetic resonance parameter to distinguish characteristics of tissue compartments (i.e., WM/GM, normal/abnormal tissue) across subjects, it is important to access their reliable values (10). Consequently, it is necessary to take into account the concomitant saturation effects such as semisolid macromolecular magnetization transfer (MT) for an accurate quantification of relaxation maps (9,11–16).

It has been shown that the MT effect in non-balanced steady-state free precession MRI (SSFP) can be modeled by numerical fitting (16), and can be attenuated with longer repetition time (TR) or reduced radio-frequency (RF) power (17). Recently, a modified phase graph framework was proposed for modeling MT, in which a stable relaxation measurement was obtained with a controlled saturation magnetization transfer (14,15). It was also shown that the confounding MT effect in MRF relaxation measurement can be mitigated by changing the pulse duration during successive signal excitations (18).

The work here aimed to develop a MRF approach to minimize the MT effect for simplified relaxation measurement by numerical simulations, phantoms and brain tissue experiments. The 2P Bloch-McConnell equations were used to describe the MT effect in MRF measurement (19–21). Considering MT parameter variations by tissue types (8,9,22), the 2P MRF dictionary was built with combined MT parameters from both WM and GM, instead of from only a single tissue type. In addition, the effect of magnetization-preparation in MRF was analyzed. In previous relaxation measurements with MRF, an inversion pulse was usually applied before a train of fast imaging with variable flip angles and repetition time delays (1,23–26). With IR preparation, the recovery signal is susceptible to MT and the measured T₁ depends on the inversion time (9,27), while the SR-prepared acquisition produces more accurate measurements than the IR-prepared repetitive acquisition (13). In this work, to further minimize the MT effect for MT parameters variations, relaxation measurements with IR and SR preparations were compared with numerical simulation, pixel-wise analysis, and inter-subject statistics in brain tissues.

2. Theory

The MRF signal of bulk tissue water in the presence of MT was described using 2P Bloch-McConnell equations as (19–21)

$${\text{dM(t)/dt=A(ω}}_{\text{1}}\text{(t))}·\text{M(t)}$$ (1)

where M(t) = [M_xf(t) M_xm(t) M_yf(t) M_ym(t) M_zf(t) M_zm(t) 1], in which M_xf(t), M_xm(t), M_yf(t), and M_ym(t) are the transverse magnetizations for free water and macromolecular protons, respectively, and M_zf(t) and M_zm(t) being their longitudinal magnetizations. With the 2P model, not only are the intrinsic characteristics but also the MT parameters for free water and macromolecular protons are taken account into the evolution matrix A (as in Eq. [1]) in which the magnetizations of both pools evolve with time (t). The evolution matrix A is:

$${\text{A(ω}}_{\text{1}}\text{(t))=}\left(\begin{array}{ccccccc}{\text{−1/T}}_{\text{2f}}{\text{−k}}_{\text{fm}}& {\text{k}}_{\text{fm}}& \text{Δω}& \text{0}& \text{0}& \text{0}& \text{0}\\ {\text{k}}_{\text{fm}}& {\text{−1/T}}_{\text{2m}}{\text{−k}}_{\text{mf}}& \text{0}& \text{Δω}& \text{0}& \text{0}& \text{0}\\ \text{−Δω}& \text{0}& {\text{−1/T}}_{\text{2f}}{\text{−k}}_{\text{fm}}& {\text{k}}_{\text{fm}}& {\text{ω}}_{\text{1}}\text{t}& \text{0}& \text{0}\\ \text{0}& \text{−Δω}& {\text{k}}_{\text{fm}}& {\text{−1/T}}_{\text{2f}}{\text{−k}}_{\text{fm}}& \text{0}& {\text{ω}}_{\text{1}}\text{t}& \text{0}\\ \text{0}& \text{0}& {\text{−ω}}_{\text{1}}\text{t}& \text{0}& {\text{−1/T}}_{\text{1f}}{\text{−k}}_{\text{fm}}& {\text{k}}_{\text{fm}}& {\text{M}}_{\text{0f}}\text{/T1f}\\ \text{0}& \text{0}& \text{0}& {\text{−ω}}_{\text{1}}\text{t}& {\text{k}}_{\text{fm}}& {\text{−R}}_{\text{1m}}{\text{−k}}_{\text{fm}}& {\text{M}}_{\text{0m}}{\text{/T}}_{\text{1m}}\\ \text{0}& \text{0}& \text{0}& \text{0}& \text{0}& \text{0}& \text{0}\end{array}\right)$$ (2)

where Δω is the frequency difference between the RF irradiation and free bulk water and the macromolecular proton pools, ω₁(t) is the RF irradiation amplitude at time t, M_0m and M_0f are their equilibrium spins of macromolecular proton and free water with exchange rate R, the total equilibrium spins M₀ = M_0m + M_0f, and k_mf (k_mf = R·M_0f) and k_fm (k_fm = k_mf ·M_0m/M_0f) are forward MT exchange rates from the macromolecular to free water and vice versa, respectively (28,29). In addition, T_1f/1m and T_2f/2m are spin-lattice and spin-spin relaxation rates for free bulk water (f) or macromolecule (m) pools, respectively.

The magnetization for the f frame in MRF acquisition (the number f of the MRF images; f ≥ 1) is M_f = A_TE · A_exc · (M_s · A_r · A_exc)^f−1 · A_d · M_s · A_p · M₀, and is modulated by evolution matrices. In the MRF sequence, considering that the shaped RF pulses used in magnetization-preparation and excitation have varying amplitudes in segments, the effect for the magnetization modulation was calculated segmentally for the shaped RF pulses. First, with the magnetization-preparation RF pulse (saturation or inversion RF pulse with N_p segments and duration τ_p), the magnetization is modulated by ${\text{A}}_{\text{p}}\text{=}{\prod }_{\text{n=1}}^{{\text{N}}_{\text{p}}}{\text{exp[A(ω}}_{\text{1}}{\text{((N}}_{\text{p}}\text{−n+1)}\cdot \frac{{\tau }_{\text{p}}}{{\text{N}}_{\text{p}}}))\cdot \frac{{\tau }_{\text{p}}}{{\text{N}}_{\text{p}}}\text{]}$ and M_s (M_s = [0 0 0 0 0 0 0; 0 0 0 0 0 0 0; 0 0 0 0 0 0 0; 0 0 0 0 0 0 0; 0 0 0 0 1 0 0; 0 0 0 0 0 1 0; 0 0 0 0 0 0 0]), which is a spoiler matrix for transverse magnetization suppression. Next, there is a preparation delay (τ_d) and the magnetization is further modulated by A_d = exp[A(0)·τ_d]. Finally, after the excitation RF pulse with duration τ_e and N_e segments and the echo time (TE) respectively, the magnetization is modulated by ${\text{A}}_{\text{exc}}\text{=}{\prod }_{\text{n=1}}^{{\text{N}}_{\text{e}}}{\text{exp[A(ω}}_{\text{1}}{\text{((N}}_{\text{e}}\text{−n+1)}\cdot \frac{{\tau }_{\text{e}}}{{\text{N}}_{\text{e}}}))\cdot \frac{{\tau }_{\text{e}}}{{\text{N}}_{\text{e}}}\text{]}$ and A_TE = exp[A(0) ·TE]. Considering the successive excitations with an interval TR, the following M_f is calculated by repeatedly multiplying the evolution matrix A_exc and A_r (A_r = exp[A(0)·(TR− τ_e)]) for magnetization-recovery after excitation RF pulse and M_s.

3. Methods

3.1. MRF Simulation

The MRF sequence was implemented with fast imaging with steady-state precession (FISP) with either a SR or IR preparation module, using a Gaussian shaped pulse duration τ_p = 1 ms, segments N_p = 256, and an inversion/saturation preparation delay time τ_d = 5.5 ms. The magnetization-preparation module was followed by 600 consecutive readout frames (f) with randomized TR ranging from 10 to 12 ms and flip angles (FA) containing a pattern of FA(f)=sin(f·π/100)·FA_m, where FA_m was randomly varied from 5º to 90º (24). The signal was excited using a sinc7 shaped pulse, with a duration τ_e = 2 ms, and segments N_e = 256 (24). TE stayed constant at 2.5 ms. To build the MRF dictionary, T_1f was varied from 100 to 2000 ms with 10 ms intervals, and 2000 to 6000 ms with 500 ms intervals; T_2f was varied from 10 to 150 ms with 2 ms intervals, and 150 to 300 ms with 5 ms intervals. For the macromolecular pool, it was assumed that T_1m was 0.5 s and T_2m was 10 μs (9,22). For WM tissue simulation, T_1f was 2.5 s and T_2f was 50 ms (9,30). For WM and GM, the macromolecular exchange rate R was 23 s⁻¹ and 40 s⁻¹, and M_0m was 30% and 7%, respectively (8,9). In addition, a 1P model without MT was evaluated and compared with the 2P model with IR (1P-IR-MRF) and SR (1P-SR-MRF). For each 2P model, a single MRF dictionary that contained the two kinds of MT parameters for both WM and GM was built, and T₁ and T₂ for free water (i.e., T_1f and T_2f) were determined by obtaining the maximum inner product of the acquired signal and the signal from the single dictionary. The normalized root mean square error (NRMSE) of the signal between 1P and 2P models was calculated. In order to assess the potential relaxation measurement errors with the MT parameters variations, the relative measurement errors for T₁ and T₂ were calculated by using a variable MT parameter (M_0m from 15% to 40%; T_1m from 0.4 s to 0.6 s; T_2m from 5 μs to 20 μs; R from 20 s⁻¹ to 40 s⁻¹) while keeping the rest of MT parameters constant.

3.2. MRI Experiment and Data Analysis

To demonstrate the difference of MRF signal evolution with or without MT, one spherical phantom was filled with CuSO₄ solution (CuSO₄·5H₂O, 1g/L) and the other one was filled with 2% agar gel to measure their respective MRF signal evolutions and relaxations (28,29,31). The animal experiments were in compliance with the Institutional Animal Care and Use Committees (IACUC) of Emory University. Fixed macaque monkey brains without any history of neurological disease or brain injury were used. These animals were euthanized for the purpose of research due to the IACUC endpoint by pentobarbital overdose and their brains were immediately intracardially perfused with saline followed by 10% buffered formalin. MRI scans were performed by using a Bruker Biospec 7.0 Tesla MRI scanner (Bruker Biospin Corporation, Billerica MA) with a 7 cm inner-diameter quadrature volume coil for uniform signal excitation. The SR or IR prepared FISP MRF sequences were implemented with the following parameters respectively: TE = 2.5 ms, magnetization-preparation module and 600 frames of varying TR and FA identical to the simulation, matrix size = 128 × 128, isotropic spatial resolution = 0.47 × 0.47 mm², and scan time = 15/25 min for SR MRF/IR MRF. In addition, routine MRI measured T₁ and T₂. T₁ was measured by a saturation-recovery prepared spin-echo sequence with TR varying from 394 ms to 5000 ms in 20 intervals (i.e., TR = 394, 448, 504, 564, 628, 696, 769, 848, 934, 1027, 1131, 1246, 1376, 1526, 1702, 1916, 2188, 2564, 3173, 5000 ms), and T₂ was measured by a multiple spin-echo sequence with TE varying from 10 ms to 200 ms with 20 echoes at 10 ms intervals. NRMSE between the simulated and experimental signal was calculated. Correlation and pairwise comparison between relaxation measurements from the routine and MRF methods were evaluated with p < 0.05 as the significant threshold.

4. Results

Figure 1 shows the MRF signal evolution trajectories using 1P and 2P models and the potential measurement errors for MT parameters variations. As shown in Fig. 1a, the signal evolution trajectories simulated with 1P model deviated substantially from those of the 2P models, particularly in the initial period (i.e., the first 100 frames). Notably, the SR MRF produced fewer differences between the 1P and 2P MT models than that of the IR MRF, with NRMSE values of 6.1% and 12.0% for SR and IR preparations respectively. Fig. 1b shows the susceptibility of the relaxation time measurement as a function of MT parameters. The M_0m variation produced around −10% to −60% T₁ errors with 1P models, and produced much less T₁ errors (20%) with 2P-SR-MRF than with 2P-IR-MRF. With 1P models, the T₁ error was around −50% with variations of T_1m, T_2m, or R. With 2P models, the T₁ error was −30-40% when T_1m was varied from 0.4 s to 0.6 s, but when T_2m was varied from 5 μs to 20 μs or when R was varied from 20 s⁻¹ to 40 s⁻¹, the errors were less than 20%. Compared to the T₁ errors, the T₂ errors were much smaller. 1P IR model produced comparable T₂ relative errors to 2P models, while 1P SR model produced more errors than 2P models. With the 2P models, the T₂ relative errors were less than 12% when M_0m was varied from 0.15 to 0.4, was minimal (<4%) with T_1m and T_2m variations, and was less than 16% when R was varied from 20 s⁻¹ to 40 s⁻¹.

Figure 1.

Simulation results. (a) Simulated MRF signal evolution with 1P (blue color) and 2P (red color) MT models. The signal evolution was also compared with IR prepared MRF (IR-MRF, left) and SR prepared MRF (SR-MRF, right) methods. (b) Numerical simulations for the potential T₁ (left) and T₂ (right) relaxation measurement errors with MT parameters variations. The relaxation errors were compared with 1P (blue color) and 2P (red color) models, IR (solid line) and SR (dash line) preparations.

Figure 2 showed the differences between the measured and simulated 1P MRF signals, which were quantified by NRMSE between the two. The two signals matched well for CuSO₄ solution in which it is believed to have minimal semisolid MT effect (31), while deviated a lot from each other for the 2% agar gel. For 2% agar gel, the 2P model was simulated with R = 176 s⁻¹, M_0m = 0.005, T_1m/T_2m = 1 s/10 μs (28). Statistics were done for the two phantoms with the same volume size. With IR and SR, NRMSE for CuSO₄ solution was 2.3% and 2.1%, while the 2% agar gel was 3.3% and 3.2% with 1P model, and 2.7% and 2.6% with 2P model, respectively. For the CuSO₄ solution, T₁/T₂ was 290±2 ms/185±1 ms and 295±5/180±1 ms with 1P IR and 1P SR models respectively, in which the relative T₁/T₂ errors were within 2% of the values measured with conventional methods (T₁/T₂ = 293±4 ms/182±1 ms). For the 2% agar gel, T₁/T₂ was 1980±5 ms/58±1 ms and 1990±5 ms/56±1 ms with 1P IR and 1P SR models respectively, in which the T₁/T₂ values were 10% less than the values measured with conventional methods (T₁/T₂ = 2210±8 ms/57±1 ms).

Figure 2.

1P/2P simulated (blue color) and the measured MRF signal evolutions (red color) from a CuSO₄ (CuSO₄·5H₂O, 1g/L) solution (top) and a 2% agar gel phantoms (bottom). The measured results were compared with IR (1P-IR-MRF, left) and SR (1P-SR-MRF, right) preparations. With conventional relaxation measurement methods, T₁/T₂ = 293±4 ms/182±1 ms for the CuSO₄ solution, and T₁/T₂ = 2210±8 ms/57±1 ms for the 2% agar gel phantom.

The simulated MRF signal evolutions were compared with the measured ones that were averaged from WM (areas = 111 mm²) or GM (areas = 54 mm²) in a monkey brain (Fig. 3a). As shown in Fig.3b, the measured WM/GM signal was more consistent with its simulated 2P signal (with IR, NRMSE = 2.6%/2.8% in WM/GM, respectively; with SR, NRMSE = 2.3%/2.4% in WM/GM, respectively) than the simulated 1P signal (with IR, NRMSE = 3.7%/3.2% in WM/GM, respectively; with SR, NRMSE = 2.8%/2.9% in WM/GM, respectively). Additionally, the measured signal was closer to the simulated one with 2P-SR-MRF than that with 2P-IR-MRF (e.g., NRMSE = 2.6%/2.3% in WM with IR/SR, respectively). Pixel-wise statistics in Table 1 and the relaxation maps in Fig. 4 showed similar findings. Although the measured relaxations were significantly correlated with those with conventional measurements, T₁ with 1P models was significantly shorter than those with conventional measurements, and additionally the T₁ standard deviations measured with 2P-SR-MRF were much smaller than those with 2P-IR-MRF (Table 1). As shown in Fig. 4, although the T₁ maps with 2P-IR-MRF/2P-SR-MRF were much more similar to the conventional measurement than those with 1P-IR-MRF/1P-SR-MRF, the 2P-SR-MRF also produced smoother T₁ transitions in the borders between WM and GM than those with 2P-IR-MRF. The differences in T₂ measurements from conventional to 2P MRF (2P-IR-MRF or 2P-SR-MRF) methods were not as obvious as those in T₁ measurements, however, T₂ in WM with 1P-SR-MRF was slightly shorter than the conventional measurement (Table 2 and Fig. 4). The relaxation measurements across animals showed that there were no significant differences between the T₁ values, nor were there any between the T₂ values when measured with 2P MRF and conventional methods in either WM or GM (p>0.05). Additionally, the relaxation correlations with 2P MRF and conventional methods for T₁ or T₂ were significant in both WM and GM (p<0.05, as seen in Table 2 and Fig. 5).

Figure 3.

Experimental results from a representative monkey brain. (a) WM (blue color) and GM (red color) for ROI-based and pixel-wise analysis overlaid on a T₂-weighted image (TE=80 ms). (b) Comparison of the simulated (dash line; blue color: 1P; red color: 2P) and the measured (solid black line) signal evolutions. The signal evolutions were compared with WM (top) and GM (bottom), and with IR MRF (left) and SR MRF (right).

Table 1.

Pixel-wise relaxation statistics (Mean±SD, ms) for WM and GM from an ex-vivo brain (Fig. 3a) and comparisons with conventional and MRF methods.

		Conventional	1P-IR-MRF	P.W. P	Corr. P	1P-SR-MRF	P.W. P	Corr. P	2P-IR-MRF	P.W. P	Corr. P	2P-SR-MRF	P.W. P	Corr. P
WM	T1	640±12	445±15	<0.01	<0.01	496±13	<0.01	<0.01	620±27	0.17	<0.01	660±18	0.18	<0.01
	T2	33±1	33±2	0.20	<0.01	31±1	0.06	<0.01	33±2	0.15	<0.01	32±1	0.23	<0.01
GM	T1	690±20	590±47	<0.01	<0.01	615±42	0.02	<0.01	697±30	0.11	<0.01	704±18	0.22	<0.01
	T2	46±4	46±3	0.40	<0.01	45±3	0.16	<0.01	47±4	0.23	<0.01	47±4	0.35	<0.01

P.W.: pair-wise; Corr.: Correlation; SD: standard deviation

Figure 4.

Comparison of T₁ and T₂ maps with conventional T₁/T₂ mapping, 1P-IR-MRF, 1P-SR-MRF, 2P-IR-MRF and 2P-SR-MRF methods, and relaxation map differences between 2P-IR-MRF and 2P-SR-MRF methods (i.e., Map_(2P-IR-MRF) - Map_(2P-SR-MRF)). It is noted that there was a radio-frequency zipper artifact in the T₁ maps with MRF methods.

Table 2.

Relaxation statistics (Mean±SD, ms) for ex-vivo WM and GM across samples (n=6) and comparisons with conventional and MRF methods.

		Conventional	1P-IR-MRF	P.W. P	Corr. P	1P-SR-MRF	P.W. P	Corr. P	2P-IR-MRF	P.W. P	Corr. P	2P-SR-MRF	P.W. P	Corr. P
WM	T1	643±46	451±27	<0.001	0.011	508±33	<0.001	<0.01	648±44	0.49	<0.01	652±47	0.14	<0.001
	T2	32±2	33±2	0.375	<0.01	31±2	<0.01	<0.01	32±2	0.18	0.01	33±2	0.47	<0.01
GM	T1	683±44	618±48	<0.01	0.017	638±36	<0.01	0.014	691±43	0.45	0.047	679±46	0.67	0.013
	T2	43±2	43±2	0.516	<0.01	42±2	0.052	0.018	43±3	0.47	<0.01	43±2	0.24	<0.01

P.W.: pair-wise; Corr.: Correlation; SD: standard deviation

Figure 5.

Correlations of T₁ (a, b) or T₂ (c, d) values from six monkey brains with conventional T₁/T₂ mapping and IR MRF (a, c) / SR MRF (b, d) methods. The hollow (∘) and solid (•) circles with standard error bars represent the values in WM and GM respectively, and the blue/dark blue and red/dark red colors represent the 1P and 2P models respectively.

5. Discussion

Biological tissues are complex and they include multiple spin pools. For example, up to 30% fraction of proteins and lipids in myelin exhibit large invisible portion of hydrogen protons (32). Therefore, MT needs to be considered since it may affect MRF signal evolution. Previously, a modified Bloch-McConnell model was used to analyze MT in chemical exchange (3). In this work, the Bloch-McConnell model was applied to analyzing the MT between bulk free water and semisolid macromolecule protons (19–21), and the results showed that there were non-negligible biases when using 1P and 2P models (Fig. 1a). After the magnetization-preparation, the simulated 2P model signal almost immediately deviated from but then merged with the 1-pool model signal afterwards. These findings coincided with the simulated results through the use of an extended phase graph framework and super-Lorentzian shapes in modeling semisolids (15), which suggests that the initial disagreement is likely due to MT perturbation but mitigates with longer evolution period as both the macromolecular and bulk water pools achieve an equilibrium. The biases from using 1P and 2P models were also validated by relaxation measurements in phantoms with minimal (CuSO₄ solution) and potential MT effect (2% agar gel) (28,29,31), showing that the measured signal and relaxations of CuSO₄ solution were closer to those with conventional measurements. As shown in Fig. 4 and Tables 1-2, 1P MRF produced significantly shorter T₁ measurements in WM (−30%) and GM (−10%). The differences in the measured T₁ errors between WM and GM are explainable, since the MT effect differs much between WM and GM with significant macromolecular fraction contrast (8,22). With 2P MRF, the measured relaxations were consistent with those with conventional methods. The measured ex-vivo T₁ was 50-60% shorter than that measured in in-vivo macaque monkey (T₁ = 1.5 s/1.8 s in WM/GM, respectively) or human brains (T₁ = 1.4 s/1.7 s in WM/GM, respectively) at the same 7 Tesla (22,30,33), which agrees with the previous report that T₁ in human brain specimens could decrease 50% of the initial value during progressive 10% formalin fixation (34).

MT parameters vary by tissue types (8). For example, the macromolecular fraction can vary from 9-13% in GM and 15-30% in WM, while the exchange rate can vary from 23-30 s⁻¹ in WM and 33-40 s⁻¹ in GM (8,9,22). The MT parameters in tissue also differ from normal subjects to those patients with diseases, such as Alzheimer disease (35), systemic brain inflammation (36), and multiple sclerosis lesions (37,38). It is difficult to build a universal MRF dictionary with varied MT parameters, even for the same tissue type. Therefore, it is helpful to develop a MRF method that is less sensitive to the confounding MT parameters for reliable relaxation measurements. To consider the significant MT parameters differences between tissue types, the MRF dictionary was built with MT parameters of both WM and GM. Furthermore, the relaxation measurement errors with the 2P model were evaluated with MT parameters variations. By simulations, while the errors induced by the variations of the MT parameters (T_1m, T_2m, R) were comparable with IR/SR preparations and the IR preparation produced slightly less measurement errors than those with the SR preparation when the variations were within certain regimes, the T₁ measurement accuracy with 2P-SR-MRF is much less sensitive to macromolecular fraction variation than that with 2P-IR-MRF (Fig. 1b). The simulated results were validated by the experiments through showing that the standard deviation of the measured T₁ with SR was much less than that with IR, and the SR-prepared MRF produced higher relaxation correlations (R>0.9) with conventional measurements across samples. These results confirmed the simulated error assessments (Fig. 1b) and the observation that the acquired MRF signal evolution with 2P-SR-MRF was closer to the simulated one than that with 2P-IR-MRF (Fig. 3b). This is likely attributed to the smaller magnetization difference between the free water and macromolecular proton signal recovering from saturation than inversion, resulting in free water signal evolution to be insensitive to MT effect with SR preparation. Based on this special experiment described here, the results suggest that 2P-SR-MRF would be less sensitive to the compositive effect of multiple MT parameters variations. Compared to T₁, the T₂ measurement accuracy was found to be less sensitive to MT parameters variations. In semisolid macromolecules, T₂ is much shorter than T₁, which causes the transverse magnetization for semisolid macromolecules to disappear rapidly and to be less prone to saturation transfer effect.

In this work, MRF measurements were compared with the conventional relaxation measurements in which the MT effect may exist (15). With IR preparation, the measured T₁ heavily depended on the magnetization recovery time for MT effect between the two pools (9). It was also shown that SR preparation produced more accurate measurements than IR preparation in short repetitive acquisitions (13). For this reason, it makes more sense that conventional T₁ measurement with SR preparation was chosen for comparison with the MRF measurements in which the 2P model was also used to minimize the MT effect. Here, the T₁ measurements with the conventional method were consistent with those with 2P-SR-MRF. Furthermore, although T₁ in WM measured with 2P-SR-MRF insignificantly differed from that measured with the conventional method, the mean values were longer, which agrees with the previous finding that the MT model measured longer relaxation times than those without MT (9,22,30,39).

In this work, MRF signal was acquired with traditional k-space sampling. While more k-space samplings after signal excitation can further reduce the scanning time, TR would be longer for the lengthened k-space sampling window (25,40). The transient steady-state free precession (SSFP) signal in MRF is sensitive to MT effect, especially with short TR (16), and MRF signal is usually acquired with TR as short as possible for significant acquisition time reduction (25). As a result, the MT effect would vary with MRF parameters. In this experiment, the 1P model in WM had 20-30% T₁ underestimation. A recent publication showed that while comparing to that with conventional method, T₁ in WM measured in the same brains was 10% underestimated with MRF in which TR was from 15 to 55 ms longer than that (from 10 to 12 ms) in our experiment (26). As compared to the previous in-vivo studies (26,40), another possible explanation for the increased sensitivity to MT effect in WM in this ex-vivo experiment would be from the potential increase of the fractional water binding with myelin and thus the MT due to the delamination and formation of vacuoles in the myelin sheath in the brain tissue fixed with formalin (41). Though there would be adjustable options for attenuating the MT effect (16,17), a 2P model here was used to directly address the MT effect and the proposed framework can be combined with partial or single-shot k-space sampling techniques for further acquisition time reduction.

An ex-vivo experiment was used here to assess the 2P MT model in MRF. In the macromolecular pool, T₂ was approximately 10 μs and the fraction was around 10% in the postmortem WM immersed in 10% buffered formalin which was used similarly in this experiment (38,42). Although the measured MT parameters may depend on methods, it is still worth noting that the ex-vivo MT parameters may deviate from those in in-vivo situations. Nevertheless, there were consistency between the results by simulations and experiments, suggesting that the potential measurement derivation induced by such MT parameter variations was within the individual derivation across brain samples, and that the proposed framework would be helpful in designing in-vivo experiments in the future.

6. Conclusions

In summary, the feasibility of using a 2P model based on MT parameters of multiple tissue types to probe the MT effect in MRF was demonstrated by simulations and experiments. The results showed that the measured T₁ was more sensitive to MT parameters variations than the measured T_2. Furthermore, 2P-SR-MRF could provide an option for mitigating the heterogeneous MT effect in brain tissue to access reliable relaxations with controlled MT effect.