Quantitative susceptibility mapping of human brain reflects spatial variation in tissue composition
Research Highlights
► Phase wrap insensitive removal of background phase ► High quality reconstruction of magnetic susceptibility map of human brain ► Susceptibility map shows excellent delineation of iron-rich deep nuclei ► Susceptibility map exhibits good contrast between gray and white matter ► Susceptibility of white matter is dependent on its underlying microstructure
Introduction
The phase information present in MRI images are typically discarded except in a limited number of cases such as the measuring of flow in angiography, enhancing image contrast in susceptibility weighted images and temperature mapping (Gatehouse et al., 2005, Haacke et al., 2009, Haacke et al., 2004, Mittal et al., 2009, Ishihara et al., 1995). Traditionally, in the vast majority of MRI acquisitions, phase images are typically noisy and lack of tissue contrast, hence have limited diagnostic utility. With improved phase processing, Rauscher et al. (2005) demonstrated that phase images could show excellent contrast and reveal anatomic structures, such as the deep nuclei and white matter structures, which are not visible on the corresponding magnitude images at 1.5 T. The emerging ultra-high field (7T and higher) MRI have started to reveal more interesting contrast in the phase images with improved signal-to-noise ratio (SNR). Using gradient-echo MRI at 7T, Duyn et al. (2007) showed that phase contrast was associated with major fiber bundles within white matter, while the contrast within gray matter exhibited characteristic layered structure. More recently, they demonstrated that the layered phase variations in cerebral cortex were highly correlated with ion distribution (Fukunaga et al., 2010). Despite these advances, one intrinsic limitation of signal phase is that phase contrast is non-local, orientation dependent, and thus not easily reproducible. Therefore, it is of great interest to determine the intrinsic property of the tissue, i.e. the magnetic susceptibility, from the measured signal phase.
The quantification of susceptibility from phase images is a well-known ill-posed problem, since the Fourier transform of susceptibility, denoted as χ(k), cannot be accurately determined in regions near the conical surfaces defined by k2 − 3kz2 = 0 (de Rochefort et al., 2010). A variety of approaches have been proposed to address this issue. For example, threshold method has been used to avoid division by zero and approximate the χ(k) values at the two conical surfaces (Shmueli et al., 2009). This method is straightforward to implement; the accuracy, however, is rather limited. Residual artifacts and noise amplification in the reconstructed susceptibility maps may hamper the visualization of subtle tissue structures, especially at ultra-high resolution. A more effective but less efficient way to address the issue is to increase the number of sampling orientations by rotating the object in the scanner (Liu et al., 2009, Wharton et al., 2010). The multiplied scan time is unfortunately unfavorable, especially when the acquisition of high resolution 3D images is already lengthy. Further, recent studies showed that susceptibility of white matter is orientation dependent (Lee et al., 2010, Liu, 2010). Thus, the multiple orientation method may not be accurate for susceptibility mapping of white matter. In this regard, single-orientation susceptibility mapping method is desirable, especially for assessment of susceptibility anisotropy of white matter. Numerical optimization relying on nonlinear regularization has shown an excellent capability in suppressing the streaking artifacts (de Rochefort et al., 2010, Kressler et al., 2010). Typically, regularized optimization requires a careful choice of the regularization parameters. One common concern is the introduction of excessive external constraints that may cause degradation of intrinsic tissue susceptibility contrast. Although the aforementioned methods are different in many aspects, they share one common feature: additional data or constraints are introduced to compensate the uncertainty in χ(k) at the conical surfaces. In this regard, it would be more desirable if the true solution at conical surfaces of χ(k) can be determined from the same dataset and included in the process of susceptibility reconstruction.
In the current study, we developed a novel susceptibility mapping method insensitive to phase wrapping that, in principle, provides the exact solution of the underlying susceptibility distribution given a 3D volume of measured phase images. The objective of the proposed approach is to generate two equations that complement each other so that the zero-coefficient surface can be completely eliminated. The first equation is described through a Fourier transform (FT) relationship; the second equation is generated by taking a first-order partial differentiation of the first equation with respect to spatial frequency coordinates. In numerical simulations, the proposed method offers a direct inversion, which results in a near exact solution. We further demonstrate that combining the two equations allows high quality reconstruction of susceptibility maps of human brain in vivo. The resulting maps allowed quantitative assessment of the susceptibility contrast at various anatomical structures (e.g. the iron-rich deep brain nuclei and white matter bundles) and the dependence of susceptibility on the white matter microstructures.
Section snippets
Fourier relationship between phase and magnetic susceptibility
Given a susceptibility distribution, χ(r), and the applied magnetic field, H0, the resonance frequency offset, Δf(r), can be determined using the following equation (Koch et al., 2006, Marques and Bowtell, 2005, Salomir et al., 2003):where k is the spatial frequency vector, k =(kx2 + ky2 + kz2)1/2, D2(k) =(1/3 − kz2/k2). Δf(r) can be determined from the phase offset divided by the time of echo (TE). The non-local property of phase data, and its orientation dependence is
Numerical simulations
A 3D 128 × 128 × 128 Shepp–Logan phantom was generated to evaluate the accuracy of these susceptibility mapping methods. The phantom was composed of multiple ellipsoids placed in a homogenous background with zero susceptibility. The susceptibility values for the ellipsoids were 0, 0.2, 0.3 and 1 ppm, respectively. To minimize Gibbs ringing, the phantom was further zero padded to 256 × 256 × 256 for accurate simulation of the corresponding resonance frequency map. Both the direct method and the threshold
Susceptibility mapping of the numerical phantom
The phase image simulated using the Shepp–Logan Phantom shows the bipolar patterns around the phantom in the X–Z (and Y–Z, not shown) plane (Fig. 1A). Such bipolar pattern is not present in the X–Y plane, which is perpendicular to the main magnetic field that is along the Z-axis (Fig. 1B). The spectrum of the susceptibility, χ(k), was calculated from the simulated phase images using two methods: the threshold method and the direct method. The threshold method yielded discontinuous χ(k) at the
Discussion
In this study, we have developed a novel method for susceptibility reconstruction from single-orientation 3D phase data. The proposed method is based on two complementary equations. The first equation is the well-known Fourier relationship between phase and susceptibility; the second equation is constructed as the first-order derivative of the first equation evaluated on and near the conical surfaces defined by D2(k) < ε, where the inversion of the first equation fails. In principle, the
Conclusion
In conclusion, we developed a novel susceptibility mapping method with phase wrap insensitive background phase removal using single-orientation 3D phase images. The validity and accuracy of this method is demonstrated using the numerical phantom. This method allows high quality reconstruction of susceptibility map of human brain in vivo. The reconstructed susceptibility maps highlight regions rich in iron content, providing clear visualization and intrinsic quantification of, for example, the
Acknowledgment
We are grateful to Arnaud Guidon and Alexandru Avram for the help with brain analysis software. The study is supported by the National Institutes of Health (NIH) through grant R00EB007182 to C. L.
References (36)
- et al.
MR diffusion tensor spectroscopy and imaging
Biophys. J.
(1994) Study of brain anatomy with high-field MRI: recent progress
Magn. Reson. Imaging
(2010)- et al.
Imaging iron stores in the brain using magnetic resonance imaging
Magn. Reson. Imaging
(2005) - et al.
Dlpolar magnetic field effects in NMR spectra of liquids
Chem. Phys. Lett.
(1982) - et al.
Alignment effects on high-resolution NMR-spectra, induced by the magnetic-field
Chem. Phys.
(1978) - et al.
Whole-brain susceptibility mapping at high field: a comparison of multiple- and single-orientation methods
Neuroimage
(2010) - et al.
Susceptibility contrast in high field MRI of human brain as a function of tissue iron content
Neuroimage
(2009) - et al.
User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability
Neuroimage
(2006) - et al.
Role of iron and ferritin in MR imaging of the brain - a study in primates at different field strengths
Radiology
(1990) - et al.
Quantitative susceptibility map reconstruction from MR phase data using Bayesian regularization: validation and application to brain imaging
Magn. Reson. Med.
(2010)
High-field MRI of brain cortical substructure based on signal phase
Proc. Natl Acad. Sci. USA
Layer-specific variation of iron content in cerebral cortex as a source of MRI contrast
Proc. Natl Acad. Sci. USA
Applications of phase-contrast flow and velocity imaging in cardiovascular MRI
Eur. Radiol.
Filtered deconvolution of a simulated and an in vivo phase model of the human brain
J. Magn. Reson. Imaging
Susceptibility-weighted imaging: technical aspects and clinical applications, part 1
Am. J. Neuroradiol.
Susceptibility weighted imaging (SWI)
Magn. Reson. Med.
Biophysical mechanisms of phase contrast in gradient echo MRI
Proc. Natl Acad. Sci. USA
A precise and fast temperature mapping using water proton chemical-shift
Magn. Reson. Med.
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