In vivo quantitative susceptibility mapping (QSM) in Alzheimer's disease

Abstract

Background: This study explores the magnetostatic properties of the Alzheimer's disease brain using a recently proposed, magnetic resonance imaging, postprocessed contrast mechanism. Quantitative susceptibility mapping (QSM) has the potential to monitor in vivo iron levels by reconstructing magnetic susceptibility sources from field perturbations. However, with phase data acquired at a single head orientation, the technique relies on several theoretical approximations and requires fast-evolving regularisation strategies.

Methods: In this context, the present study describes a complete methodological framework for magnetic susceptibility measurements with a review of its theoretical foundations.

Findings and significance: The regional and whole-brain cross-sectional comparisons between Alzheimer's disease subjects and matched controls indicate that there may be significant magnetic susceptibility differences for deep brain nuclei--particularly the putamen--as well as for posterior grey and white matter regions. The methodology and findings described suggest that the QSM method is ready for larger-scale clinical studies.

Figure 1. QSM pre-processing.

Schematic depiction of the projection onto dipole fields (PDF) pipeline implementation. W: weighting matrix; : (measured) magnetic induction; : exobrain mask; : Fourier operator; D: magnetic dipole kernel; : dipole operator; : (estimated) exobrain dipole distribution; : (minimised) conjugate gradient residual matrix; : (estimated) background field; : (estimated) foreground field.

Figure 2. Regional QSM data extraction and reference selection.

(A) FIRST's automated regional data extraction from magnetic susceptibility maps after alignment to structural space. (B) QSM reference region (yellow) for a young subject (left), an elderly control (middle) and an AD patient (right). Note the avoidance of large QSM spatial gradients and the slight mask size adjustment according to ventricular size.

Figure 3. Differential performance of background field extraction methods.

(A) Low-frequency field removal using Hanning and PDF filtering. The effective dipole-fitting approach reduces edge artefacts while largely preserving local perturbations elsewhere. (B) PDF's conjugate gradient convergence pattern. All N = 21 experiments similarly approached the proposed tolerance limit.

Figure 4. QSM data fidelity and serial measurement robustness.

(A) Data consistency modulated by the choice of regularisation parameter. Data points represent data fidelity residuals for each reconstruction. λ = 10⁴ (not shown) led to the most incoherent solutions. The overall concave shape of the data, with a well-defined global minimum, points at optimally constrained reconstructions with λ≈1250. (B) Rigidly realigned magnetic susceptibility maps (1250) for a young control scanned in three sessions (time-points: t_0-2). Serial behaviour on a single subject was deemed highly robust.

Figure 5. - versus -norm QSM reconstructions.

The -norm approach yielded better-compartmentalised maps. The -norm method preserved more anatomical detail.

Figure 6. Regional QSM group results.

Permutation-based statistical comparisons between AD and control groups in eight regions of interest for six - and one -norm regularisation schemes. Each bar represents an absolute sum-of-ranks difference relative to that for P = 0.05 (if surviving such threshold); each solid horizontal line represents +2 (sum of ranks); and the discontinuous line marks the sum of ranks returning P = 0.005.

Figure 7. In-depth regional QSM data assessment.

(A) Median susceptibility values from the bilateral putamen for the AD and control groups plotted as a function of regularisation parameter, λ. Discontinuous lines represent linearly interconnected data points for each subject, whereas solid dots and error bars describe group means and standard deviations. -norm regularised values are stable across a large range of parameters; though strong dependency was found for λ<750. Upward trends from young to adult and from healthy to AD, almost complete separation between patients and controls, and narrow serial measurement dispersion were also clearly visible. (B) Histogram plots for regional data from 1250. (C) Median putamenal magnetic susceptibility values plotted against hippocampal volumes for all subjects in the study.

Figure 8. Whole-brain QSM group results.

Spatial distribution of thresholded (P_TFCE<0.05) magnetic susceptibility (1250) differences between AD and elderly control groups overlaid onto the MNI152 template.