Imaging neural architecture of the brain based on its multipole magnetic response
Graphical abstract
Highlights
► Magnetic response of the brain is described with multipole tensors ► Multipole tensor characterizes anisotropic magnetic response without any rotation ► Simulated axons are used to verify the properties of multipole tensors ► Fiber orientations of mouse brains are imaged with multipole tensors ► Fiber orientations of human brains are imaged in vivo
Introduction
Magnetic fields can penetrate deep into the body since they interact with biological molecules weakly as evidenced by the routine application of MRI in human bodies. Because of this weak interaction, MRI has traditionally relied on the amplitude of the nuclear magnetization from the very beginning to generate tissue contrast (Lauterbur, 1973). However, at high fields, interaction between magnetic field and the orbital electrons of biomolecules may introduce a measurable perturbation on the resonance frequency of surrounding water protons. This perturbation in turn reflects the molecular content and microstructure of the tissue. A notable example is the relative frequency shift between gray and white matter and between layers of the cortex which is thought to originate from variations of magnetic susceptibility (Duyn et al., 2007, Rauscher et al., 2005). Although frequency shift has provided a new image contrast for MRI, utilizing this contrast to infer neural architecture and brain structural connectivity remain challenging.
One potential way to fully utilize this frequency is to borrow techniques from NMR spectroscopy. Indeed, measuring frequency shift has been instrumental in NMR spectroscopy for probing molecular structure. While high-resolution NMR techniques provide a wealth of information (de Beer et al., 1994, Otting et al., 1990, Tolman et al., 1995, van Zijl et al., 1984), adapting those techniques to high-resolution imaging is not yet possible. The difficulty is partially due to low sensitivity, limited scan time and vastly more complex physiological conditions encountered in volumetric brain imaging. Because of these difficulties, frequency shift measured by MRI has been limited to the zero-th order information, i.e. the mean frequency of a whole voxel (Dixon, 1984, Glover and Schneider, 1991, Haacke et al., 1995, Rauscher et al., 2005, Weisskoff and Kiihne, 1992). Higher-order information such as susceptibility anisotropy of dipoles and quadrupoles, if resolved, would provide important information of sub-voxel tissue and cellular architecture. Similar to the important role that NMR has played in untangling molecular structure (Cavalli et al., 2007, Otting et al., 1990, Wishart et al., 1992), imaging higher-order frequency variation could provide a powerful tool for probing tissue microstructure such as brain connectivity noninvasively.
The backbone of brain connectivity is composed of bundled long projecting axons. Structurally, this connectivity backbone may be compared to the backbones of macromolecules. Ordered arrangement of atoms along the chain axis of macromolecules gives rise to an NMR measurable anisotropic susceptibility tensor. Similarly, on the tissue scale, the ordered arrangement of axon bundles also produces anisotropic frequency (He and Yablonskiy, 2009) and susceptibility (Lee et al., 2010, Li et al., 2012b, Liu, 2010). Although the mean susceptibility of a voxel can be measured with a gradient echo (de Rochefort et al., 2008, Li, 2001, Salomir et al., 2003), it does not measure the orientation dependence of the susceptibility (Li et al., 2011). To measure the anisotropy of magnetic susceptibility, the method of susceptibility tensor imaging (STI) has been used (Liu, 2010). A recent study also explored the capability of STI for tracking neuronal fibers in 3D in the mouse brain ex vivo (Liu et al., 2012). In large fiber bundles, the orientation determined by STI was found to be comparable to that by diffusion tensor imaging (DTI) of diffusion anisotropy (Basser et al., 1994, Basser et al., 2000, Moseley et al., 1990). However, this experimental procedure of STI requires rotating the object or the magnetic field. The requirement is clearly not convenient or even impractical for routine brain imaging on standard MRI scanners in vivo.
Here, we developed a method to measure higher-order frequency variations based on a single image acquisition without rotating the object or the magnet. This method utilized a multipole analysis of the MRI signal in a sub-voxel Fourier spectral space termed “p-space” for short. By sampling the p-space with pulsed field gradients or by shifted image reconstruction, we were able to measure a set of dipole and quadrupole susceptibility tensors. We illustrated the methodology in a simulation of aligned axons and demonstrated its use for 3D high-resolution imaging of mouse brains ex vivo at 9.4 Tesla and human brains in vivo at 3.0 Tesla. We anticipate that the p-space approach may provide a powerful method for studying tissue microstructure and brain connectivity in vivo and non-invasively.
Section snippets
The spectral space (p-space) of microscopic magnetic field
For a given imaging voxel containing heterogeneous structures, magnetic field within the voxel is also heterogeneous due to the interaction between tissue and external field. The total magnetization of the voxel is an integral of all spins within the voxel, each experiencing a slightly different local magnetic field. The phase angle of the resulting integral represents the amplitude of the mean field. The spatial heterogeneity, however, is lost during the ensemble averaging. If the field
Simulation of axon bundles
We first verified the validity of the approach using a simulated bundle of parallel axons that was situated in a cubic voxel (Fig. 2a). Without noise, both magnitude and frequency showed a quadratic relationship with p as illustrated for five representative orientations (Figs. 2b and c). The linear term was absent due to the symmetry of the phantom and the properties of Fourier transform which state that the Fourier transform of an even function is even. While the magnitudes were similar among
Discussion
At high fields, the weak interaction between magnetic fields and biological molecules is sufficiently strong to create a frequency shift in the Larmor frequency of nearby nuclear spins. Despite the paramount importance that frequency shift has attained in NMR, the utilization of frequency shift in MRI has been very limited. While measuring frequency shift and its anisotropy has enabled NMR to determine structures of large molecules, MRI has not been able to routinely utilize the vast
Acknowledgments
We thank G.A. Johnson for access to the 9.4T scanner at Duke Center for In Vivo Microscopy, Y. Qi, G. Cofer and R. Dibb for assistance in animal preparation and data acquisition. We thank A.W. Song and C. Petty of the Brain Imaging and Analysis Center for assistance with computing on the cluster.
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