To assess and numerically model the accuracy of quantitative susceptibility mapping (QSM) in a high susceptibility gadolinium balloon phantom study.

In continuous media, the connection between susceptibility and phase/field provides the basis for the continuous space dipole convolution model. In practice, data are acquired on discrete voxels and discrete space dipole convolution model is used in QSM. Thus imaging resolution and voxel sensitivity function (VSF)² affect QSM accuracy. In an 1D example, the complex signal $$$y_n$$$ at voxel $$$n$$$ in the lower resolution image is expressed by the higher resolution image $$$x_l$$$, i.e., $$$y_n = \sum_l x_l \cdot VSF(n,l)$$$. Even if the data acquired at high image resolution match the dipole convolution model, the lower resolution data may not.

This signal mixing effect of neighboring voxels at lower image resolution reduces the phase contrast, giving rise to underestimation in susceptibility values. Additionally, k-space filtering, commonly used to reduce Gibbs ringing, further modifies the VSF, leading to changes in the estimated susceptibility. Finally, the VSF mixing effect occurs on the complex signal, not just the signal phase such that the amount of underestimation also depends on the difference in signal magnitude between the different susceptibility regions.

A 1% agarose gel phantom containing four balloons filled with gadolinium solutions (Magnevist, Berlex Labrotories, Wayne, NJ) was constructed. It contains sources with susceptibility values of 0.4, 0.8, 1.6, and 3.2 ppm and was imaged at isotropic resolutions of 0.7, 0.8, 1.2 and 1.8 mm on a 3T scanner and a 1.5T scanner (GE healthcare, Waukesha, WI) using a multi-echo gradient echo sequence. With each imaging resolution, the numbers of slices were adjusted to cover the full sample height of 120mm. For all scans, FOV=180mm, FA=15° and BW=±62.5kHz. For 1.5T scans, the number of echo/minTE/ΔTE/TR=6/5ms/5ms/43ms for all resolutions. For 3T scans, the range in which the TEs were sampled was approximately halved in order to obtain the same phase accrual.

The same regularization parameter and the same edge map criteria were used for the morphology enabled dipole inversion (MEDI)³ L1 reconstruction for all data sets.

Numerical simulations were performed to understand the role of imaging resolution, magnitude contrast, sample orientation and k-space filtering. Simulations matching the 0.7mm resolution experimental setup was performed. All numerical multi-echo gradient echo data at lower resolutions were generated from k-space down-sampling the 0.7mm resolution simulation data. T2* decay and k-space Fermi filtering were also included. The down-sampled multi-echo data were then used as input for MEDI to compute the susceptibility values.

Systematic underestimation of the susceptibility values was observed to increase with decreasing imaging resolution, as seen in Figs. 1 and 2. The numerical simulation data including the T2* effect and k-space filtering were shown in Figs. 1 and 2. Good agreement was achieved between the experiments and numerical simulations.

Our data demonstrate that a systematic QSM underestimation exists in low resolution scans of high susceptibility sources. As shown in Fig. 1 and 2, the underestimation increases with decreased imaging resolution. 3T scans contains more underestimation than the 1.5T scans. In addition, the amount of underestimation is proportional to the susceptibility values: less underestimation is observed for balloons with lower susceptibility values. The lowest susceptibility value studied in this phantom was 0.4ppm, which is on the upper end of susceptibility values observed in healthy subjects. For this value, the lowest relative underestimation was observed (Figs 1 and 2).

Using numerical simulations, we demonstrated that the QSM underestimation originated from the signal formation in a voxel, which can be described by the VSF.

In our experiments, the 1.5T scans provided better accuracy than the 3T scans. This is due to the echo spacing and echo times being longer in the 1.5T scans, which was done to achieve similar phase accrual at the lower field strength. As a result, more significant magnitude decay was observed in the 1.5T scans, giving rise to less VSF mixing and less QSM underestimation.

This susceptibility underestimation is mostly pronounced in experiments with strong susceptibility difference, e.g., phantom studies or hemorrhage data. The amount of susceptibility underestimation depends on the susceptibility source geometry. A general relationship between the underestimation and resolution is thus not feasible.

We observed systematic underestimation in susceptibility value estimation in a high susceptibility phantom due to lowered imaging resolution. The underestimation originates from the signal mixing due to the VSF. To obtain accurate QSM estimates for high susceptibility values, high resolution imaging is needed.