MR physicistsAlthough magnetization transfer (MT) between macromolecules and “free” water has been demonstrated in fast MRI [1, 2], effects of MT are usually neglected in variable flip angle (VFA) T₁-mapping. To demonstrate the influence of MT on the estimated T₁, VFA experiments were performed at different pulse lengths (T_RF) using sinc and rect pulses. A simplified model for the influence of TRF on the estimated T₁ is suggested for low-power pulses.

Experiments were performed at 3 T (Siemens Magnetom Prisma) using a 20-channel head/neck receive coil on 4 healthy volunteers (26.3±5.1 y) giving informed written consent. VFA T₁-mapping with 1.25 mm isotropic resolution was executed on sagittal volumes with 5^○, 10^○ and 15^○ flip angles (α) at TR/TE = 11/4.92 ms (approximately 3×1.5 min). The pulse lengths T_RF of the non-selective pulse (i.e., rect or sinc of time-bandwidth-product 4) were 0.5, 1.0, 1.5 and 2.0 ms. T₁ maps were calculated from a linear representation of the simplified signal equation [3]:

$$S(\alpha) = Af\alpha \cdot\frac{TR/T_1}{TR/T_1 +(f\alpha)^2/2}\Leftrightarrow \frac{S(\alpha)}{\alpha}=Af-\frac{2f^2 T_1}{TR}\cdot\alpha S(\alpha) \qquad Eq. 1\hspace{3em}$$

where f is the flip angle bias factor, obtained from the B₁-mapping of the MRI unit (64 axial slices, 40 s). For comparison, inversion recovery (IR) T₁ estimates (T_1,IR) were obtained using TI = 250, 500, 1000, 2000, and 4000 ms in a single 5 mm slice through the splenium and caudate head, selected to represent white matter (WM) and gray matter (GM), respectively.The shortest rect and sinc pulses (T_RF = 0.5 ms) yielded T₁>T_1,IR, while a general trend of decreasing VFA T₁ estimates were observed for longer T_RF (i.e., decreasing pulse power) (Figures 1 and 2). To give equal T₁ estimates, sinc pulses needed to be longer than rect pulses. The T1 variability over TRF was 21 ± 5 % in WM and 15 ± 4 % in GM using rect pulses, and 19 ± 4 % in WM and 11 ± 3 % in GM using sinc pulses. For low-power rect pulses of 2 ms, a lower limit of the T₁ estimates was approached (Figure 2). This lower limit was approximately 14 % and 7 % lower than T_1,IR in WM and GM, respectively.

In this pilot study, the influence of excitation pulse length on T₁ in VFA experiments was investigated at 3 T. Substantial variations in T₁ were observed, which can be explained by inherent MT effects, i.e., if pulses are long (and thus of low power), macromolecules will be saturated less than water. Magnetization will then be transferred to the free water (i.e., “inverse MT”). The resulting increase in steady-state signal leads to shorter T₁ estimates. As an approximation, a single rect would impose a partial saturation of $$$1-cos(\alpha)\approx\alpha^2/2$$$ on water and $$$S\alpha^2/T_{RF}$$$ on macromolecules. Here, S represents the integrated absorption for a normalized pulse. These expressions are helpful to bring the closed-form solution of Ou and Gochberg [2] into the form of (Eq. 1), which then becomes similar to describing a traditional MT-pulse [4].

When $$$S\alpha^2/T_{RF}\approx \alpha^2/2$$$ for sufficiently short T_RF, no net MT takes place, and thus $$$T_1\approx T_{1,IR}$$$ assuming a homogenous B₁-field. Pulses with even shorter T_RF would predominantly saturate the macromolecules, as reported for balanced SSFP [1].

Because the partial saturations in both pools are proportional to α^2, the VFA estimate with MT-effects takes the form

$$T_{1,MT} = T_1\cdot(1-F(2 S/T_{RF}))\hspace{3em} Eq. 2$$

This relationship corresponded well with experimental data for low-power rect pulses, but not for sinc pulses, as the latter pulse shape show inherently higher power. The present results may help to explain the deviating T₁ values frequently reported in VFA studies on the brain.

Pulse length and shape impose substantial variations (11-21%) on VFA-based T₁ estimates, and these observations can be explained by inherent MT effects.