MRI estimates of brain iron concentration in normal aging using quantitative susceptibility mapping
Highlights
► QSM finds increased iron deposition in striatal and brain stem structures with age. ► QSM results are strongly correlated with postmortem studies and the FDRI method. ► QSM requires data at a single MR field strength, while FDRI requires two. ► QSM has high resolution enabling detection of iron in small brain structures.
Graphical abstract
Introduction
Excessive iron deposition in subcortical and brain stem nuclei occurs in a variety of degenerative neurological and psychiatric disorders, including Alzheimer's disease, Huntington's chorea, multiple sclerosis, and Parkinson's disease (Hallgren and Sourander, 1960). Further, postmortem (Hallgren and Sourander, 1958) and in vivo (Bartzokis et al., 2007b, Haacke et al., 2007, Pfefferbaum et al., 2009, Pfefferbaum et al., 2010, Raz et al., 2007) studies have revealed that deep gray matter brain structures accumulate iron at different rates throughout adult aging. Structures that exhibit iron accrual support components of cognitive and motor functioning (Bartzokis et al., 2010, Raz et al., 2007, Sullivan et al., 2009). To the extent that excessive iron presence may attenuate neuronal function or disrupt connectivity, quantification and location of iron deposition may help explain age- and disease-related motor slowing and other selective cognitive decline.
Several MRI methods have been proposed for in vivo iron mapping and quantification. Bartzokis et al. (1993) capitalized on the enhanced transverse relaxivity (R2) due to iron with increasing main field strength for the Field-Dependent Relaxation Rate Increase (FDRI) method. FDRI relies on the use of R2-weighted imaging at two different field strengths and attributes the relaxation enhancement at higher field to iron, which may be a specific measure of tissue iron stores (Bartzokis et al., 1993).
Whereas FDRI relies on the modulation of signal intensity in MRI to infer iron concentration, MRI signal phase has also been proposed as a source signal for iron mapping, both by direct evaluation of phase images (Haacke et al., 2004, Haacke et al., 2005a) and by reconstruction of magnetic susceptibility images that derive from the phase data (Haacke et al., 2005a, Haacke et al., 2007). Local iron concentration is strongly correlated with the magnetic susceptibility values (Duyn et al., 2007, Liu et al., 2010c, Schweser et al., 2011b); therefore, quantification of this paramagnetic property presents a sensitive estimate of iron concentration, although possibly complicated by more uncommon factors, such as pathological manganese deposition (Hazell and Butterworth, 1999). Phase mapping yields high-resolution, high-SNR data that demonstrate correlation with iron (Haacke et al., 2007), but as an estimate of the underlying magnetic susceptibility, it suffers from non-local effects and spatial modulation artifacts due to the non-trivial mapping from susceptibility to phase (de Rochefort et al., 2010). To overcome these limitations, we made use of regularized Quantitative Susceptibility Mapping (QSM) algorithms that robustly estimate the magnetic susceptibility χ of tissues based on gradient-echo signal phase. The magnetic susceptibility χ maps to the observed phase shift in MRI via a well-understood transformation, but the inverse problem, i.e., estimation of χ from phase, is ill posed due to zeros on a conical surface in the Fourier space of the forward transform; hence, χ inversion benefits from additional regularization. Recently, elegant regularization methods were proposed for deriving susceptibility inversion. In the work by de Rochefort et al. (2010), smooth regions in the susceptibility map are promoted to match those of the MR magnitude image by introducing a weighted ℓ2 norm penalty on the spatial gradients of χ. Likewise, Liu et al. (2010a) regularized the inversion by minimizing the ℓ1 norm of gradients of χ, again weighted with a mask derived from the image magnitude. Kressler et al. (2010) experimented using ℓ1 and ℓ2 norm regularizations directly on the susceptibility values, rather than posing the minimization on the gradient coefficients. Another method to stabilize the susceptibility reconstruction problem is to acquire data at multiple orientations and invert them simultaneously without regularization. This approach was introduced by Liu et al. (2009) and also investigated by others such as Wharton and Bowtell, 2010, Schweser et al., 2011b.
In this work, we investigate two different regularization schemes for susceptibility inversion; using ℓ1-regularized QSM that parallels the approach of Liu et al. (2010a) and ℓ2-regularized QSM which was introduced by de Rochefort et al. (2010). Given that magnetic susceptibility is a property of the underlying tissue, in ℓ1-regularized QSM we make the assumption that it is approximately constant within regions of the same tissue type or within an anatomical structure. Based on this premise, the ℓ1-norm-penalized QSM algorithm regularizes the inversion by requiring the estimated χ to be sparse in the image gradient domain. On the other hand, placing an ℓ2 norm penalty on the spatial gradients of χ does not promote sparsity, but results in a large number of small gradient coefficients and thus incurs a smooth susceptibility reconstruction. In addition to regularized susceptibility inversion, our approach incorporates a robust background phase removal technique based on effective dipole fitting (Liu et al., 2010b), which addresses the challenging problem of removing phase variations in the data that arise primarily from bulk susceptibility variations between air and tissue rather than the more subtle changes of χ within the brain. Dipole fitting contains no parameters that need tuning and preserves the phase variations caused by internal susceptibility effects more faithfully than high-pass filtering, as employed in susceptibility-weighted imaging (SWI) (Haacke et al., 2004, Haacke et al., 2005a). All susceptibility mapping methods require data acquired at only one field strength, thereby overcoming certain limitations of the FDRI approach, including long scan times and the need for spatial registration of image data acquired with different scanners at different field strengths.
Here, we describe the ℓ1 and ℓ2 norm regularized QSM methods and apply them to SWI data previously acquired in groups of younger and elderly, healthy adults (Pfefferbaum et al., 2009). To validate the iron measures, we compared the results of QSM methods with values published in a postmortem study (Hallgren and Sourander, 1958). As further validation, we compared QSM results with those based on FDRI collected in the same adults (Pfefferbaum et al., 2009) to test the hypothesis that the iron deposition in striatal and brain stem nuclei, but not white matter or thalamic tissue, would be greater in older than younger adults.
Section snippets
Susceptibility and MR signal phase
The normalized magnetic field shift δ measured in a gradient-echo sequence is related to the MR image phase φ via δ = − φ/(B0 ·γ· TE), where B0 is the main magnetic field strength, γ is the gyromagnetic ratio, and TE is the echo time. It follows from Maxwell's magnetostatic equations that the relationship between the underlying susceptibility distribution χ and the observed field shift δ is given by (de Rochefort et al., 2010, Marques and Bowtell, 2005, Salomir et al., 2003)
Correlations of FDRI and QSM values with postmortem iron concentrations
Fig. 4 presents the mean ± SD iron concentration determined postmortem in each ROI (Hallgren and Sourander, 1958) on the x-axis and the mean ± SD FDRI values in s-1/T and ℓ1-regularized QSM values in ppm for young plus elderly subjects on the y-axes. The correlations between ℓ1-regularized QSM and postmortem (Rho = 0.881, p = 0.0198), between ℓ2-regularized QSM and postmortem (Rho = 0.881, p = 0.0198), and between FDRI and postmortem iron indices (Rho = 0.952, p = 0.0117) were high.
Correlations between in vivo QSM and FDRI iron concentration metrics
To investigate the
Discussion
This study presented regularized QSM methods with two different choices of regularization, namely ℓ1 and ℓ2 norm penalties, for quantifying susceptibility-weighted imaging data, and established their ability to measure iron concentration in regional striatal and brain stem nuclei of young and elderly adults. The in vivo estimates of regional iron concentration comported well with published postmortem measurements (Hallgren and Sourander, 1958), with both approaches yielding the same rank
Conclusion
Herein are presented two regularized Quantitative Susceptibility Mapping algorithms, employing ℓ1 and ℓ2 norm regularization, which successfully remove background phase effects via dipole fitting and solve for the tissue susceptibility distribution via convex optimization. The performance of these algorithms was favorable when compared with other published in vivo and postmortem estimates of regional tissue iron concentrations. Because the accumulation of iron in the brain can have untoward
Conflict of interest statement
Drs. Bilgic, Pfefferbaum, Rohlfing, Sullivan have no conflicts of interest with this work, either financial or otherwise.
Author Adalsteinsson receives research support from Siemens Healthcare and the Siemens-MIT Alliance.
Acknowledgments
National Institutes of Health, Grant numbers NIH R01 , , , , ; National Science Foundation (NSF), Grant number 0643836; Siemens Healthcare; Siemens-MIT Alliance; MIT-CIMIT Medical Engineering Fellowship.
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