Sensitivity of literature T1 mapping methods to the underlying magnetization transfer parameters

TL;DR

The paper analyzes how MT parameters shape the observed $T_1$ in $T_1$ mapping by simulating $T_1^ ext{o}$ across 25 published protocols at 3T and computing derivatives with respect to six MT parameters, including $m_0^ ext{s}$, $T_1^ ext{f}$, $T_2^ ext{f}$, $T_ ext{x}$, $T_1^ ext{s}$, and $T_2^ ext{s}$. A linear mixed-effects framework, aided by AIC-based model selection and Nakagawa/Shapley decompositions, quantifies how much of the derivative variability is explained by MT parameters, ROI, sequence type, and individual sequences. Results show strong sensitivity to $m_0^ ext{s}$, $T_1^ ext{f}$, $T_1^ ext{s}$, and $T_ ext{x}$ across sequences, with $R^2_ ext{full}$ typically between $0.90$ and $0.99$, while $T_2^ ext{f}$ and $T_2^ ext{s}$ are less influential. The findings highlight that MT-related variability can bias $T_1$ estimates in a sequence- and parameter-specific manner, and offer a framework to predict and potentially mitigate these effects in protocol design and interpretation.

Abstract

Purpose: Magnetization transfer (MT) has been identified as the principal source of $T_1$ variability in the MRI literature. This study assesses the sensitivity of established $T_1$ mapping techniques to variations in the underlying MT parameters. Methods: For each $T_1$-mapping method, the observed $T_1$ was simulated as a function of the underlying MT parameters $p_i^\text{MT}$, corresponding to different brain regions of interest (ROIs) at 3T. As measures of sensitivity, the derivatives $\partial T_1^\text{observed} / \partial p_i^\text{MT}$ were computed and analyzed with a linear mixed-effects model as a function of $p_i^\text{MT}$, ROI, pulse sequence type (e.g., inversion recovery, variable flip angle), and the individual sequences. Results: The analyzed $T_1$-mapping sequences have a considerable sensitivity to changes in the semi-solid spin pool size $m_0^\text{s}$, $T_1^\text{f}$ of the free, $T_1^\text{s}$ of the semi-solid spin pool, and the (inverse) exchange rate $T_\text{x}$. All derivatives vary considerably with the underlying MT parameters and between pulse sequences. In general, the derivatives cannot be determined by the sequence type, but rather depend on the implementation details of the sequence. One notable exception is that variable-flip-angle methods are, in general, more sensitive to the exchange rate than inversion-recovery methods. Conclusion: Variations in the observed $T_1$ can be caused by several underlying MT parameters, and the sensitivity to each parameter depends on both the underlying MT parameters and the sequence.

Figures (2)

• Figure 1: Absolute value of the observed $T_1^\text{o}$'s derivative with respect to the 6 MT parameters. I calculated the derivatives for 9 brain regions of interest (ROIs) and for 25 pulse sequences, grouped into different sequence types (cf. legend). Here, WM denotes white matter, CC the corpus callosum, and GM gray matter. The derivatives $\partial T_1^\text{o} / \partial p_i^\text{MT}$ are normalized by $p_i^\text{MT}$, averaged over all ROIs, to allow for a comparison between the parameters.
• Figure 2: Validation of the mixed effects model, where "simulated" denotes the simulated derivatives, and "predicted" denotes the output of the mixed model. The sequence type is here color-coded, while the maker shape identifies the region of interest. Here, WM denotes white matter, CC the corpus callosum, and GM gray matter. The dotted line represents the perfect fit. For convenience, the $R^2_\text{full}$ is denoted in the bottom right of each plot, repeating the values shown in Tab. \ref{['tab:R2_full']}. For an interactive version of this plot, where the sequence type and ROI can be toggled for display, refer to the link in the data availability statement.