Rui Pedro A. G. Teixeira^{1,2}, Anthony N. Price^{1,2}, Ana A. Baburamani^{1}, Shaihan J. Malik^{1}, and Joseph V. Hajnal^{1,2}

Variable Flip Angle (VFA) relaxometry methods have recently been shown to be sensitive to magnetization transfer (MT) induced bias. Common description of this effect relies on a two-pool model (restricted macromolecular pool & visible free water pool). Current practice to restrict influence of MT consists in stretching of RF pulse durations in order to minimize/counter-balance the effect of macromolecular exchange for different flip angle measurements. This work proposes to minimize the estimation bias by using constant saturation MT pulses that simultaneously excite the free-water pool and saturate the restricted-pool creating constant RF-saturation conditions independently of the flip angle (FA) applied.

Tissue T_{1} and T_{2} are known to be
dependent on measurement technique, with T_{1} in particular influenced by MT and
the RF conditions employed^{1,2}. For a two pool system, the observed
T_{1} depends on the saturation state of the background pool, which is modified by
the RF (B_{1}^{+}) pulses in the sequences applied in
measurement. This effect can be quantified using [Eq.1]^{6} and the
time structure of the measurement sequence$$<W>=\frac{\pi}{T_{RF}}\int_0^{T_{RF}}\omega_1^2(t)dt G(\Delta)=\frac{\pi}{T_{RF}}P_{RF}G(\Delta)[Eq.1]$$where T_{RF} is the
duration of the pulse, $$$\omega_1(t)=2\pi\gamma\int_0^{T_{RF}}\omega_1^{ref}(t)dt$$$is the instantaneous rotation rate caused by
the pulse, $$$G(\Delta)$$$ models the absorption line-shape of the
magnetization pool and P_{RF} is the integral of $$$\omega_1^2(t)$$$. In
steady-state Variable Flip Angle (VFA) methods^{4} a range of flip
angles are deployed, creating variable saturation of the background pool within
the measurement. Unless this is taken into account, the measured relaxation
properties vary with the measurement parameters^{2,5}. With this in mind, we've explored VFA T_{1}
and T_{2} measurement using pulses that keep <W> constant to see if consistent
saturation and hence MT conditions allow stable relaxation time measurements.

Figure 1 summarizes how apparent T_{1} (from DESPOT1) alters for Agarose as the P_{RF} of the CSMT pulse is increased.

Figure 3 shows T_{1} (top) and T_{2} (bottom) maps in an exemplar axial slice using all measured data for both block pulse (left) and CSMT pulse (right).

Figures 4 show histograms of T_{1} and T_{2} values from white matter for subsets 1-6 for the block and CSMT pulse, which stabilises the T_{1} values and results in higher T_{2} values, more consistent with spin echo measurements at 3T^{4}.

1. Bieri O. and Scheffler K. On the origin of apparent low tissue signals in balanced SSFP. Magn Reson Med. 2006; 56(5): 1067-74.

2. Yosef Al-Abasse and Gunther Helms. Influence of pulse length and shape on variable flip angle T1 mapping of the human brain. Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

3. Graham SJ, Henkelman RM. Understanding pulsed magnetization transfer. J Magn Reson Imaging 1997;7:903–912.

4. Deoni SCL, Rutt BK, Peters TM. Rapid combined T1 and T2 map- ping with gradient recalled acquisition in the steady-state. Magn Reson Med 2003; 46:515–526

5. Gloor, M, et al. Nonbalanced SSFP-based quantitative magnetization transfer imaging. Magn Reson Med 2010; 64:149–156

6. L. Yarnykh, Vasily. Actual Flip-Angle Imaging in the Pulsed Steady State: A Method for Rapid Three-Dimensional Mapping of the Transmitted Radiofrequency Field. Magn Reson Med 2007; 57:192–200

7. A. G. Teixeira Rui Pedro, J. Malik Shaihan, V. Hajnal Joseph. Joint System Relaxometry (JSR) and Crámer-Rao Lower Bound optimisation of sequence parameters: a framework for increasing precision of DESPOT T1 and T2 Estimation. Under review

8. J. Stanisz, et al. T1,T2 Relaxation and Magnetization Transfer in Tissue at 3T. Magn Reson Med. 2005; 54:507–512;

9. Crooijmans, HJA et al. Finite RF pulse correction on DESPOT2; Magn Reson Med. 2011; 65:858–862;

Figure 1 - Time
representation of the proposed CSMT pulse for different (top). Frequency representation of the
rotation induced due to the CSMT for each (bottom).
Note off-resonance rotation has no meaning due to the inherently short T_{2} of
the restricted-pool of magnetization (~14µs)

Table 1 - Summary
of flip angle subsets explored in oder to inspect stability of relaxometry
estimation. Highlighted FA correspond to each measurement used at its
corresponding subset.

Figure 2 - (Left)
Apparent mean DESPOT T_{1} as a function of CSMT pulse Energy. (Right) Exemplar
DESPOT1 T_{1}map of the 3-layer Phantom at
increasing concentration of Agarose from top to bottom.

Figure 3 - Comparison
between JSR T_{1} and T_{2} maps using Block Pulse and CSMT to generate excitation.
For each case, all available FA were used to estimate the relaxometry
parameters. Deep grey matter shows improved estimation
when using the CSMT compared to the standard Block Pulse. T_{2} relaxation times
are more consistent with reported spin-echo measurements^{4}

Figure 4 - T_{1}(left)
and T_{2}(right) distributions in WM for all subjects for Block Pulse and CSMT
pulse for all the subsets summarised in Table 1. Use of constant saturation
aligns the T_{1} histograms (removes systematic bias in measurement) however there
is still a range of different standard deviations – this is to be expected
since the different flip angle sets will yield estimates with different
precision.