Jingu Lee^{1}, Taehyun Hwang^{1}, Yoonho Nam^{2}, Se-Hong Oh^{3}, and Jongho Lee^{4}

We proposed a new QSM algorithm that
automatically sets CSF as a susceptibility reference. The algorithm utilizes susceptibility
effects on R_{2}’ as a regularization term. The proposed algorithm does
not require either segmentation of CSF or a well-refined brain mask and,
therefore, can be used reliably.

**Purpose**

**Methods**

**[QSM _{auto_ref}: Automatically referenced QSM]**
A susceptibility source in the magnetic field
creates field perturbation that increases reversible transverse magnetization
relaxation rate (R

In
order to designate susceptibility reference regions as voxels with zero R_{2}’,
QSM_{auto_ref} utilizes the following model:
$$argim_{\chi_{pos},\chi_{neg}}|(R_2^{\:'}+i2{\pi}f)-D_m*(|\chi_{pos}+|\chi_{neg}|)-i2{\pi}D_p*(\chi_{pos}+\chi_{neg})|+{\lambda}g(\chi_{pos},\:\chi_{neg})\:\:\:\:[Eq. 2] $$
where f
is frequency shift, D_{p} is a field perturbation
kernel, g(χ) is a regularization term^{5}, and λ
is a regularization factor. The algorithm with no regularization and that with
regularization were tested.

**[Numerical simulation]** A geometric phantom was deveoped to validate the proposed
QSM algorithm. Total seven different cylinders were included in one large
cylinder with different compositions of susceptibility values (values: -0.05:0.03:0.13,
and 0 ppm; location: center, bottom, counter-clockwise, and large cylinder) and
R_{2}’ (values: 9:1:15, and 0 Hz; the same location as susceptibitlies). Frequency shift maps
were generated following the dipole field convolution model^{6}. In
order to confirm the automatic convergence of the reference, five different
initial susceptibility values were tested (Fig. 2b).

**[In-vivo
experiment]**
Five
healthy volunteers were scanned at 3T MRI.

To estimate R_{2}* and
frequency shift, 3D multi-echo
GRE data were acquired with the following parameters: voxel size=1×1×2mm^{3}, TR=64ms, TE=2.9 to 25.9ms with echo
spacing of 4.6ms, flip angle=22°, and acquisition time=7:02min.
For R_{2}* mapping, the multi-echo magnitude data were fitted to a
mono-exponential decay function.

For
R_{2} estimation, 2D multi-echo
SE data were acquired with the following parameters: voxel size=1×1mm^{2}, slice thickness=2mm, #slices=36,
TR=4800ms, TE=20 to 120ms, and acquisition time=7:09min. R_{2}
values were fitted from the multi-echo data with stimulated echo and
slice-profile corrected mono-exponential fitting^{7}.

Negative
values of R_{2}’ was set to zero enforcing physical mechanism. For an ROI analysis, six regions (see Fig. 4) were
manually selected.

**Results**

In numerical simulation, the area with
R_{2}’ = 0 is indicated by red arrow in Fig. 2a. When five different
initial susceptibility values were tested, all of the reconstructed susceptibility
values in the R_{2}’ = 0 region automatically converged to zero as the
algorithm iterated (Fig. 2b). An example is visualized in Fig. 2c, revealing
the automatic convergence of the susceptibility map from an initial point to
the final results while enforcing the susceptibility reference to the region
with R_{2}’ = 0 (Fig. 2c).

In the brain, the CSF region has
nearly zero R_{2}’ (red arrow in Fig. 3i). Therefore, the results from QSM_{auto_ref}
show uniformly zero susceptibilities in the CSF region (red arrows in Fig. 3c, d)
while those from the conventional QSM reveal brighter and non-uniform contrasts
(red arrows in Fig. 3a, b). QSM results, streaking artifacts become severe when regularization is not used (Fig. 3e, f). On the other hand, the new algorithm helps to prevent streaking
artifacts. In the sagittal view of the conventional QSM results, streaking
artifacts become severe when regularization is not used (Fig. 3e, f). On the
other hand, there are no clear streaking artifacts in the non-regularized
results of the proposed method (Fig. 3f, h).

For further analysis, ROI averaged
susceptibility values were reported (Fig. 4). In the CSF region, QSM_{auto_ref}
shows nearly zero susceptibility while the conventional QSM has positive
susceptibility. This may result in the higher susceptibility values in deep
gray matter (CN, Put, and GP) from the conventional QSM than those from the
proposed algorithm.

**Conclusion and Discussion**

[1] Liu, Z., Spincemaille, P., Yao, Y., Zhang, Y., & Wang, Y. (2017). MEDI+0: Morphology enabled dipole inversion with automatic uniform cerebrospinal fluid zero reference for quantitative susceptibility mapping. Magnetic Resonance in Medicine.

[2] Bilgic, B., Pfefferbaum, A., Rohlfing, T., Sullivan, E. V., & Adalsteinsson, E. (2012). MRI estimates of brain iron concentration in normal aging using quantitative susceptibility mapping. Neuroimage, 59(3), 2625-2635.

[3] Langkammer, C., Schweser, F., Krebs, N., Deistung, A., Goessler, W., Scheurer, E., ... & Ropele, S. (2012). Quantitative susceptibility mapping (QSM) as a means to measure brain iron? A post mortem validation study. Neuroimage, 62(3), 1593-1599.

[4] Sedlacik, J., Boelmans, K., Löbel, U., Holst, B., Siemonsen, S., & Fiehler, J. (2014). Reversible, irreversible and effective transverse relaxation rates in normal aging brain at 3T. Neuroimage, 84, 1032-1041.

[5] Liu, T., Liu, J., De Rochefort, L., Spincemaille, P., Khalidov, I., Ledoux, J. R., & Wang, Y. (2011). Morphology enabled dipole inversion (MEDI) from a single‐angle acquisition: comparison with COSMOS in human brain imaging. Magnetic resonance in medicine, 66(3), 777-783.

[6] Salomir, R., de Senneville, B. D., & Moonen, C. T. (2003). A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility. Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering, 19(1), 26-34.

[7] McPhee, K. C., & Wilman, A. H. (2017). Transverse relaxation and flip angle mapping: evaluation of simultaneous and independent methods using multiple spin echoes. Magnetic resonance in medicine, 77(5), 2057-2065.