Quantitative susceptibility mapping (QSM) is a recent phase-based MRI technique that yields unprecedented anatomical contrast^1,2 and is currently regarded the most sensitive technique to study tissue iron in vivo^3,4.

Despite increasing exploration of QSM in humans and the method's potential to study tissue iron pre-clinically, few studies have yet applied QSM to rodents in vivo at ultra-high magnetic field strength^5,6. Most pre-clinical work involving QSM thus far relies on post mortem tissue, often perfused with a T₁-shortening agent⁷.

We presume that one of the reasons for the low number of applications in vivo is the relatively poor visual quality of susceptibility maps obtained with currently available algorithms, including streaking artifacts and inhomogeneities.

In the present work we hypothesized that the low quality of pre-clinical QSM compared to human QSM is due to the combination of a similar level of non-susceptibility phase contributions (e.g. macromolecular proton exchange effects⁸) with much lower susceptibility variations. Here, we propose a new type of QSM algorithm that accounts for non-susceptibility phase effects and thus enables pre-clinical QSM: QUAntitative Susceptibility And Residual mapping (QUASAR).

Assume that the MRI phase φ consists of two components, a susceptibility-related component φ_s=d*χ (χ is the underlying susceptibility distribution, d is the unit dipole response and * denotes the convolution operation) and a non-susceptibility component φ_ns. In this case, susceptibility mapping can be understood as solving the highly under-determined problem φ=d*χ+φ_ns for φ_ns and χ. The under-determination is illustrated by the trivial solution with χ=0 and φ = φ_ns (φ_ns can also be understood as the residual of the problem). Additional constraints are needed to obtain a physically meaningful solution.

To avoid the direct incorporation of (potentially incorrect) a priori information into the susceptibility map, we propose to impose constraints only on the (unknown) φ_ns. In the present work, we forced φ_ns to obtain the same values throughout the ventricles (cerebrospinal fluid; CSF), which is justified by the homogeneous nature of CSF.

Algorithm: Least-squares with QR decomposition (LSQR; tolerance 10^-5) was used to solve the following optimization problem: min_χ,φns ||φ-d*χ-λ·φ_ns||² with φ_ns=const. throughout the ventricles. The regularization parameter λ defines a trade-off between attribution of phase to susceptibility and non-susceptibility phase, respectively. For λ=0 the conventional LSQR solution is obtained. We incorporated QUASAR into our HEIDI-QSM algorithm⁹ and defined the φ_ns-constraint via R₂*<10/s.

Animals: We demonstrated the algorithm in an SJL/J mouse (8 weeks of age). The experiment was approved by our Institutional Animal Care & Use Committee (IACUC).

Data acquisition and reconstruction: Experiments were performed on a 9.4 Tesla Bruker BioSpec 94/20 USR equipped with a two-element transmit-receive ¹H cryogenically cooled MRI coil. The protocol involved a 3D multi-echo gradient-echo sequence (TR/TE₁/ΔTE=90ms/2.38ms/4.4ms, 9 monopolar echoes, FA=18°, 80μm isotropic resolution, TA=27min). Phase images were obtained by scalar phase matching¹⁰, best path unwrapping¹¹, multi-echo combination¹², and V-SHARP^4,13. R2* was calculated with the Power-method¹⁴ using logarithmic calculus.

Effect of λ: We performed an L-curve optimization of λ (steps of 0.01 between 0 and 0.1, and 0.05 between 0.1 and 0.5).

Figure 1 shows the L-curve optimization, which yielded λ=0.2 as the optimal parameter.

Figure 2 illustrates results obtained with different λ-values. Conventional HEIDI (λ=0; left) was not able to correctly reconstruct the frontal horn of the lateral ventricles (cf. arrows in Fig. 4), which was resolved with QUASAR even when λ was chosen too low. However, in this case the residual phase resembled exactly the constraint (right-hand side in Fig. 2). Too high a value of λ yielded a pale susceptibility contrast with dipole-like patterns around the ventricles, indicating incomplete inversion. The optimal λ-value yielded a map with meaningful anatomical contrast and reduced inhomogeneity in both the susceptibility and the residual maps.

Figure 3 directly compares QUASAR with HEIDI, illustrating the inaccurate reconstruction of the frontal horn of the lateral ventricles. Interestingly, the phase residuals (right) were almost identical between the two methods.

Figure 4 shows the (input) SHARP phase, R₂* map, QUASAR, and HEIDI. The side-by-side comparison illustrates that QUASAR yielded a more reasonable anatomical contrast.

The present work introduced QUASAR, a novel susceptibility mapping approach that yields improved susceptibility maps and decouples non-susceptibility phase contributions, potentially providing valuable information on macromolecular tissue composition including myelin integrity.

It is interesting to note that the absence of ventricular phase contrast (arrows in Fig. 4) was also previously reported in humans by Duyn et al.¹⁵ and He and Yablonskiy¹⁶. Hence, our study provides further support for a significant contribution of non-susceptibility effects to MRI phase in the brain.