MRI estimates of brain iron concentration in normal aging using quantitative susceptibility mapping

Abstract

Quantifying tissue iron concentration in vivo is instrumental for understanding the role of iron in physiology and in neurological diseases associated with abnormal iron distribution. Herein, we use recently-developed Quantitative Susceptibility Mapping (QSM) methodology to estimate the tissue magnetic susceptibility based on MRI signal phase. To investigate the effect of different regularization choices, we implement and compare ℓ1 and ℓ2 norm regularized QSM algorithms. These regularized approaches solve for the underlying magnetic susceptibility distribution, a sensitive measure of the tissue iron concentration, that gives rise to the observed signal phase. Regularized QSM methodology also involves a pre-processing step that removes, by dipole fitting, unwanted background phase effects due to bulk susceptibility variations between air and tissue and requires data acquisition only at a single field strength. For validation, performances of the two QSM methods were measured against published estimates of regional brain iron from postmortem and in vivo data. The in vivo comparison was based on data previously acquired using Field-Dependent Relaxation Rate Increase (FDRI), an estimate of MRI relaxivity enhancement due to increased main magnetic field strength, requiring data acquired at two different field strengths. The QSM analysis was based on susceptibility-weighted images acquired at 1.5 T, whereas FDRI analysis used Multi-Shot Echo-Planar Spin Echo images collected at 1.5 T and 3.0 T. Both datasets were collected in the same healthy young and elderly adults. The in vivo estimates of regional iron concentration comported well with published postmortem measurements; both QSM approaches yielded the same rank ordering of iron concentration by brain structure, with the lowest in white matter and the highest in globus pallidus. Further validation was provided by comparison of the in vivo measurements, ℓ1-regularized QSM versus FDRI and ℓ2-regularized QSM versus FDRI, which again yielded perfect rank ordering of iron by brain structure. The final means of validation was to assess how well each in vivo method detected known age-related differences in regional iron concentrations measured in the same young and elderly healthy adults. Both QSM methods and FDRI were consistent in identifying higher iron concentrations in striatal and brain stem ROIs (i.e., caudate nucleus, putamen, globus pallidus, red nucleus, and substantia nigra) in the older than in the young group. The two QSM methods appeared more sensitive in detecting age differences in brain stem structures as they revealed differences of much higher statistical significance between the young and elderly groups than did FDRI. However, QSM values are influenced by factors such as the myelin content, whereas FDRI is a more specific indicator of iron content. Hence, FDRI demonstrated higher specificity to iron yet yielded noisier data despite longer scan times and lower spatial resolution than QSM. The robustness, practicality, and demonstrated ability of predicting the change in iron deposition in adult aging suggest that regularized QSM algorithms using single-field-strength data are possible alternatives to tissue iron estimation requiring two field strengths.

Fig. 1

L-curve for ℓ₁-regularized QSM results for a young subject. X-axis: data consistency term ||δ – F⁻¹ DF χ||₂ in regularized reconstruction for varying values of the smoothing parameter λ. Y-axis: regularization term ||G χ||₁. Setting λ = 5·10⁻⁵ yielded an under-regularized susceptibility map with ringing artifacts (a), whereas using λ = 10⁻³ resulted an over-regularized reconstruction (c). For λ = 2·10⁻⁴, the operating point with the largest curvature on the L-curve was obtained (b). This setting was used for the reported ℓ₁-regularized results.

Fig. 2

L-curve for ℓ₂-regularized QSM results for a young subject. X-axis: data consistency term ||δ – F⁻¹ DF χ||₂ in regularized reconstruction for varying values of the smoothing parameter β. Y- axis: regularization term ||G χ||₂. Setting β = 3·10⁻³ yielded an under-regularized susceptibility map with ringing artifacts (a), whereas using β = 7·10⁻² resulted an over-regularized reconstruction (c). For β = 1.5·10⁻², the operating point with the largest curvature on the L-curve was obtained (b). This setting was used for the reported ℓ₂-regularized results.

Fig. 3

Young (left) and elderly (right) group averages for FDRI (a), ℓ₁-regularized QSM (b), and ℓ₂-regularized QSM (c). Greater iron concentration yields brighter QSM and FDRI images. Splenium reference ROIs are indicated with a white box on the axial QSM slices.

Fig. 4

X-axis: Mean ± SD iron concentration (mg/100 g fresh weight) determined postmortem in each ROI (Hallgren and Sourander, 1958). Y- axis: Mean ± SD ℓ₁-regularized QSM in ppm (left) and FDRI in s⁻¹/Tesla (right) indices in all 23 subjects (black squares); the gray circles indicate the mean of the young group, and the open circles indicate the mean of the elderly group.

Fig. 5

Correlation between FDRI and ℓ₁-regularized QSM results on the regions of interest. Results indicate strong relationship between the two methods (Rho = 0.976, p = 0.0098). Left: all 23 subjects; middle: young group; right: elderly group.

Fig. 6

Mean ± S.E.M. of average susceptibility in ppm computed by the two methods (ℓ₁-regularized QSM, top; ℓ₂-regularized QSM, bottom) for each ROI in the young and elderly groups.