Julian Pfister^{1}, Felix A. Breuer^{1}, Peter M. Jakob^{2}, and Martin Blaimer^{1}

An
inversion recovery bSSFP measurement allows to generate a spectrum of the
apparent relaxation time T_{1}* and hence to identify multiple
components in a voxel. However, it is not possible to extract unambiguous T_{1}
and T_{2} information for each individual component. Here, we
demonstrate that this limitation can be overcome by an additional bSSFP
measurement without inversion pulse. Additive and subtractive combinations of
the measured signal courses provide enough information for assigning
unambiguous T_{1}, T_{2} and proton density values to each
component. In that way, 2D T_{1}-T_{2} correlation spectra can
be generated voxel-wise in a very time-efficient manner.

Assuming
a single tissue component, quantitative T_{1}, T_{2} and PD
values can be simultaneously obtained from an IR bSSFP measurement, when the
initial signal after inversion (S_{0}), the steady-state signal (S_{stst})
and T_{1}* are determined. Additionally, multiple components can be
identified by analyzing the IR bSSFP signal course using the inverse Laplace
transform. However, the spectral amplitudes of the resulting T_{1}*
spectrum depend on the sum of S_{0} and S_{stst} and hence it
is not possible to extract T_{1} and T_{2} information for an
individual T_{1}* peak. To overcome this limitation, two bSSFP
measurements can be performed,
one with an inversion pulse and one without an inversion pulse prior to the bSSFP
readout.^{5} Both signals approach the same steady-state but from a
different initial signal. The added signals depend only on S_{stst} and
T_{1}*:

$$S_{add}(t)=2·S_{stst}·(1-exp(\frac{-t}{T_1^*})) $$

The subtracted signals depend only on S_{0} and T_{1}*:

$$S_{sub}(t)=2·S_0·exp(\frac{-t}{T_1^*}) $$

T_{1}* spectra can
be generated from S_{add}(t) and S_{sub}(t) as shown in Fig. 1.
The areas under the peaks of the resulting T_{1}* spectra represent S_{0}
and S_{stst} respectively and are used to calculate T_{1}, T_{2}
and PD for each peak. The result can then be plotted in a 2D correlation
spectrum (Fig. 2).

Phantom measurements were performed on a 3T MRI system
to validate the principle of this technique. The phantom contained four
different components - pure water, water with contrast agent, and sunflower oil
with two specific chemical substances. 2048 echoes were acquired without phase
encoding (TR = 4.6 ms, excitation angle = 60°). Spatially resolved reference
measurements for T_{1} and T_{2} were performed using an
inversion recovery spin-echo based sequence with different inversion times for
T_{1} estimation and multiple spin-echo experiments with varying echo
times for the calculation of T_{2}.

In vivo experiments with 2048 radial projections were performed
with a projection increment of 38.98° (TR = 5.0 ms, excitation angle = 40°).
This tiny golden angle reduces eddy currents and provides sufficient k-space
information for a narrow sliding window reconstruction with a high temporal
fidelity.^{6}
In total 408 images per measurement were reconstructed using the T_{1}*
shuffling method.^{4,7 }

T_{1}* spectra were generated by applying the
inverse Laplace transform on the added as well as the subtracted signals and T_{1},
T_{2} and PD were calculated for each appearing peak.

The
phantom experiment shows an excellent agreement with the reference
measurements. Fig. 3 illustrates the spectra from the subtracted and added
signals as well as the resulting T_{1}/T_{2} correlation
spectrum. In vivo results are shown in Fig. 4 and highlight the added and
subtracted spectra from three exemplary voxels obtained by the inverse Laplace
transform. The resulting T_{1}/T_{2} pairs in the correlated
spectra indicate e.g. myelin (T_{1}* ≈ 100 ms), white matter (T_{1}*
≈ 400 ms), gray matter (T_{1}* ≈ 550 ms) and the cerebrospinal
fluid (CSF) (T_{1}* ≈ 3300 ms) in the expected brain areas.

Deviations from literature T_{1} and T_{2} values may occur
due to B0 inhomogeneities and inaccurate flip angle information. Furthermore, deviations
from the ideal radial trajectory may alter the steady-state signal and hence
lead to a mismatch between the positions of the individual peaks of the
combined T_{1}* spectra.

1. Schmitt P. et al.: Inversion
Recovery TrueFISP: Quantification of T_{1},
T_{2}, and Spin Density. MRM 2004;
51:661–667.

2. Ehses P. et al.: IR TrueFISP With a Golden-Ratio-Based Radial
Readout: Fast Quantification of T_{1}, T_{2}, and Proton Density. MRM 2013; 69:71-81.

3. Hargreaves B.A. and Nishimura D.G.: Relaxometry using Transient Steady-State Free Precession Imaging. Proc. ISMRM 2003.

4. Pfister J. et al.: Simultaneous T1/T2 measurements in combination with PCA-SENSE reconstruction (T1* shuffling) and multicomponent analysis. Proc. ISMRM 2017.

5. Pfister J. et al.: Fast spatially-resolved multi-component T1 and T2 parameter mapping. Proc. ESMRMB 2017.

6. Wundrak S. et al.: A Small Surrogate for the Golden Angle in Time-Resolved Radial MRI Based on Generalized Fibonacci Sequences. IEEE Transactions on Medical Imaging 2015; 34:1262-1269.

7. Tamir J.I. et al.: T_{2} Shuffling: Sharp,
Multicontrast, Volumetric Fast Spin-Echo Imaging. MRM 2017; 77:180-195.

Scheme
1: Signal courses of two bSSFP measurements
(without and with inversion pulse), their additive and subtractive combination
and the subsequent T_{1}* spectra obtained by the inverse Laplace transform (ILT).

Scheme
2: Calculation of T_{1}, T_{2} and
PD for each peak in the T_{1}* spectra and the correspoding representation in a 2D correlation spectrum.
The diagonal line indicates T_{1}=T_{2} and peaks are
expected in the area below this line where T_{1}>T_{2}.

Resulting
T_{1}* spectra for the added and the subtracted signals of the phantom
measurements (top). 2D correlation spectrum of measured and reference T_{1}/T_{2}
value pairs in comparison to the reference values (bottom). Peaks #1 and #2
originate from the sunflower oil, peak #3 represents water and contrast agent
and peak #4 is from pure water. The standard deviations of the measured
values in the error bars originate from 32 pseudo-replicas.

Resulting
T_{1}* spectra for the added and the subtracted signals of three
exemplary voxel-elements from an in vivo measurement. The associated 2D T_{1}/T_{2}
correlation spectra are shown in the right column.