  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 radio-frequency (RF) pulse effects as well as simultaneous
exchange and relaxation. Further, a correction 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.
