MC BTS: simultaneously resolving magnetization transfer effect and relaxation for multiple components

TL;DR

MC BTS tackles the challenge of jointly quantifying magnetization transfer and multi-component relaxation in macromolecule-rich tissues while correcting for $B_1^+$ inhomogeneity. It extends BTS to a three-pool model and uses a multi-echo gradient-echo approach to derive an analytical signal equation, validated by Bloch simulations and Monte Carlo analyses. The method robustly estimates $T_1$ for all three pools, pool fractions, exchange rates, and $T_2^*$ across fast and slow water pools, demonstrated in vivo in brain and knee with plausible parameter maps. This framework enables richer tissue microstructure characterization and macromolecular content assessment with potential clinical relevance in demyelinating and degenerative diseases.

Abstract

We propose a signal acquisition and modeling framework for multi-component tissue quantification that encompasses transmit field inhomogeneity, multi-component relaxation and magnetization transfer (MT) effects. By applying off-resonance irradiation between excitation and acquisition within an RF-spoiled gradient-echo scheme, in combination with multiple echo-time acquisitions, both Bloch-Siegert shift and magnetization transfer effects are simultaneously induced while relaxation and spin exchange processes occur concurrently. Simulation results showed excellent agreement with the derived analytical signal equation across a wide range of flip angles and echo times. Monte Carlo analyses further validated that the three-pool parameter estimation pipeline performed robustly over various signal-to-noise ratio conditions. Multi-parameter fitting results from in vivo brain and knee studies yielded values consistent with previously reported literature. Collectively, these findings confirm that the proposed method can reliably characterize multi-component tissue parameters in macromolecule-rich environments while effectively compensating for $B_1^+$ inhomogeneity.

Figures (7)

• Figure 1: (a) Three-pool system composed of two “free” liquid proton pools, one fast-relaxing (F) and the other slow-relaxing (S), and a “restricted” macromolecule proton (R), where the magnetization exchange between these three pools is characterized by pseudo-first-order rates. (b) MC BTS acquisition scheme is composed of a magnetization transfer module (orange) and a spin exchange + decay module (green). When the BTS criteria are satisfied, in the magnetization transfer module, (c) transverse magnetization of the “free” liquid pools acquires a phase proportional to the peak magnitude of the BTS pulse. Concurrently, the “restricted” pool is partially saturated, which is reflected as a decrease in the observable transverse magnetization of the multicomponent “free” liquid pools ($\Delta M_\text{xy}^\text{F}$, $\Delta M_\text{xy}^\text{S}$). In the spin exchange + decay module, there is a constant exchange of spins between pools F and S while both pools undergo $T_2^*$ decay.
• Figure 2: Multiparametric estimation pipeline of MC BTS consists of 3 steps utilizing multi-echo acquisitions obtained with (BTS) and without (BL) off-resonance BTS pulse applied at multiple excitation angles. Step 1: Utilizing an additional BTS acquisition acquired at an excitation angle closest to the Ernst angle, any $\Delta B_0$ inhomogeneity and chemical shift originating phase is removed to extract Bloch-Siegert induced phase shift to derive a $B_1^+$ map and corresponding actual flip angle maps (FA$_\text{n}^\text{act}$). Step 2: The spatially varying actual FA maps, BTS and BL magnitude images acquired at the shortest identical echo time (TE$_4$ in this example) are used to fit the two-pool BTS signal model, generating $\rho$, $T_1^\text{S}$, $f_\text{R}$ and $k_\text{SR}$ maps. Step 3: Utilizing the estimated two-pool parameters as a prior, the multi-echo BTS and BL data obtained from multiple flip angles together with the actual FA maps are combined to estimate the three-pool parameters ($T_1^\text{F}$, $T_1^\text{S}$, $T_1^\text{R}$, $f_\text{F}$, $f_\text{S}$, $f_\text{R}$, $k_\text{FR}$, $k_\text{SR}$, $k_\text{SF}$, $T_2^\text{F*}$, $T_2^\text{S*}$) using the MC BTS signal model (Eqs. [\ref{['eq:20']}] and [\ref{['eq:22']}]).
• Figure 3: Simulation results overlaid with MC BTS signal model results for varying excitation flip angles are shown for the fast-relaxing pool (top row) and slow-relaxing pool (bottom row). For the fast-relaxing pool, simulation results (solid lines) of (a) longitudinal and transverse magnetization for (b) BL (light blue) and (c) BTS (yellow) show excellent agreement with the MC BTS signal model (circle and square markers). Further simulating across varying echo times shown by the dashed box in (b) and (c), where echo time increases going from top to down, excellent agreement between simulation and signal model is also observed, as can be seen in the figure inlets. The same applies for the slow-relaxing pool (d) – (f), where BL is color coded in navy and BTS in orange.
• Figure 4: MC BTS parameter estimation results from three sets of Monte Carlo simulations to validate the MC BTS parameter estimation pipeline, each generated using SNR of 25 (sky blue), 50 (light green) and 100 (light orange). $T_1$ (column 1), relative fraction (column 2) and exchange rate (column 3) of the fast-relaxing pool (top row), slow-relaxing pool (middle row) and restricted pool (bottom row), along with $T_2^*$ of the fast and slow-relaxing pools (column 4) agree well with their respective ground truth for all three sets, demonstrating our fitting procedure’s robustness over a wide range of SNR settings. Increasing SNR decreases its estimated variance due to decreased noise.
• Figure 5: Estimated $T_1$ (column 1), relative fraction (column 2) and exchange rate (column 3) of the fast-relaxing pool (top row), slow-relaxing pool (middle row) and restricted pool (bottom row), along with $T_2^*$ of the fast and slow-relaxing pools (column 4). The fast-relaxing pool shows relatively homogenous $T_1$ values across both the WM and GM regions. In contrast, the slow-relaxing pool exhibits higher $T_1$ values in GM compared to WM regions, as does the restricted pool but with lower contrast. In WM regions, there is an increased fraction of fast-relaxing and restricted pools compared to GM regions, reflecting the greater myelin content in these regions, whereas there is a decreased slow-relaxing pool fraction. This is accompanied by higher exchange rates from F to R, S to R and S to F in WM compared to GM. $T_2^*$ (column 4) of both the fast-relaxing and slow-relaxing pools displays lower values in WM compared to GM regions.