Quantitative susceptibility mapping of human brain reflects spatial variation in tissue composition

Abstract

Image phase from gradient echo MRI provides a unique contrast that reflects brain tissue composition variations, such as iron and myelin distribution. Phase imaging is emerging as a powerful tool for the investigation of functional brain anatomy and disease diagnosis. However, the quantitative value of phase is compromised by its nonlocal and orientation dependent properties. There is an increasing need for reliable quantification of magnetic susceptibility, the intrinsic property of tissue. In this study, we developed a novel and accurate susceptibility mapping method that is also phase-wrap insensitive. The proposed susceptibility mapping method utilized two complementary equations: (1) the Fourier relationship of phase and magnetic susceptibility; and (2) the first-order partial derivative of the first equation in the spatial frequency domain. In numerical simulation, this method reconstructed the susceptibility map almost free of streaking artifact. Further, the iterative implementation of this method allowed for high quality reconstruction of susceptibility maps of human brain in vivo. The reconstructed susceptibility map provided excellent contrast of iron-rich deep nuclei and white matter bundles from surrounding tissues. Further, it also revealed anisotropic magnetic susceptibility in brain white matter. Hence, the proposed susceptibility mapping method may provide a powerful tool for the study of brain physiology and pathophysiology. Further elucidation of anisotropic magnetic susceptibility in vivo may allow us to gain more insight into the white matter micro-architectures.

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 − 3k_z² = 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.