Unbiased signal equation for quantitative magnetization transfer mapping in balanced steady-state free precession MRI

Abstract

Purpose: Quantitative magnetization transfer (qMT) imaging can be used to quantify the proportion of protons in a voxel attached to macromolecules. Here, we show that the original qMT balanced steady-state free precession (bSSFP) model is biased due to over-simplistic assumptions made in its derivation.

Theory and methods: We present an improved model for qMT bSSFP, which incorporates finite radiofrequency (RF) pulse effects as well as simultaneous exchange and relaxation. Furthermore, a correction relating to finite RF pulse effects for sinc-shaped excitations is derived. The new model is compared to the original one in numerical simulations of the Bloch-McConnell equations and in previously acquired in vivo data.

Results: Our numerical simulations show that the original signal equation is significantly biased in typical brain tissue structures (by 7%-20%), whereas the new signal equation outperforms the original one with minimal bias (<1%). It is further shown that the bias of the original model strongly affects the acquired qMT parameters in human brain structures, with differences in the clinically relevant parameter of pool-size-ratio of up to 31%. Particularly high biases of the original signal equation are expected in an MS lesion within diseased brain tissue (due to a low T2/T1-ratio), demanding a more accurate model for clinical applications.

Conclusion: The improved model for qMT bSSFP is recommended for accurate qMT parameter mapping in healthy and diseased brain tissue structures.

Keywords: balanced SSFP; magnetization transfer; quantitative imaging.

FIGURE 1

Original (red) and refined (blue) qMT bSSFP signal equation, next to the numerically simulated data (black dots), in a standard acquisition scheme of varied flip angles (left) and pulse durations (right). The plot used the parameters in Table 1 and constant values are $\alpha ={35}^{\circ }$ and $T_{\mathit{RF}}=0.3\mathrm{ms}$

FIGURE 2

QMT parameter maps of a healthy brain, as analyzed by the original (top row) and the refined (bottom row) model. In addition, the residual sum of squares (RSS) of the fit and $T_{1f}$ maps are displayed. The qMT parameters, fitted for each voxel, are as follows: pool‐size‐ratio F, exchange rate $k_{\mathit{mf}}$ and relaxation time of the free pool $T_{2f}$. Red squares mark ROIs

FIGURE 3

Illustration of hard pulse equivalent for Gaussian and sinc pulse shapes. The RF pulse (left) and the corresponding transverse magnetization trajectory (right) are plotted for both pulse shapes and their hard pulse equivalent. Both pulse shapes are plotted for $\alpha ={40}^{\circ }$, $T_{\mathit{RF}}=1\mathrm{ms}$. To allow for a clear distinction, $TBW=2$ for sinc pulse and $TBW=2.6$ for the Gaussian pulse