q-Space: What is it?
Qiuyun Fan1

1Massachusetts General Hospital, Charlestown, MA, United States

Synopsis

Diffusion MRI can provide useful information on microstructures that are much smaller than the imaging voxel sizes. This presentation will start from the original idea by Callaghan and Cory and Garroway showing that the diffusion NMR signal is the Fourier transformation of the displacement probability function, followed by examples of MRI experiments to infer microstructural properties of biological tissues. The basic concepts of q-space and propagator based methods will be discussed.

Introduction

The Brownian motion of water molecules in the presence of magnetic resonance gradient yields a spread of phase in the spin transverse magnetization. The sensitivity of spin echoes to self-diffusion has been demonstrated by Hahn [1, 2] and by Carr and Purcell [3] in the classic experiments in the 1950’s. The de-phasing due to self-diffusion causes MR signal dropouts, which can provide useful information about heterogeneous structures. In neuronal tissues, the self-diffusion of water molecules is interrupted by barriers such as cell membranes and myelin etc., and thus demonstrates non-Gaussian characteristics. Callaghan showed that the spin displacement probability distribution function is the Fourier transformation of diffusion MR signal in q-space [4-6]. This relationship can be used to infer microstructural information such as axon diameter in white matter, which is of a much smaller length scale than imaging voxels [7]. It has become the origin of the many modern microstructural diffusion imaging methods.

Target Audience

Students and researchers interested in the basic principles of q-space diffusion MRI methods and their applications in studying biological tissues.

Summary

This presentation will start from the original idea by Callaghan [4] and Cory and Garroway [7] showing that the diffusion MR signal is the Fourier transformation of the displacement probability density function. The idea of k-space and q-space are very analogous, where the k-space relates the MR signal to the spatial information, and q-space relates to the displacement information [6]. Early NMR experiments have shown the diffraction pattern of the signal in media with uniform pore sizes [5] and how the pore size could be inferred from the pattern of diffraction peaks.

For biological tissues, based on the q-space theory, imaging techniques using single Pulsed Gradient Spin Echo (PGSE) experiments to gain microstructural information were introduced, including the most popular AxCaliber and CHARMED methods [8-10]. In this presentation, the challenges in q-space measurements on human scanners, along with recent studies on the human connectome scanner will be discussed. Double-PGSE is a more recent extension of single PGSE for diffusion compartment mapping [11], which will also be briefly explained. In addition, the basic concepts of Oscillating Gradient Spine Echo (OGSE) technique and some of the experimental results will be reviewed [12], in comparison with the PGSE experiments.

Some of the q-space and propagator based imaging techniques will be discussed in this presentation, including Diffusion Spectrum Imaging (DSI), Q-Ball Imaging (QBI), Mean Apparent Propagator (MAP)-MRI, etc. [13-15]. Their alternative model-based methods [16-18] that are frequently used to resolve complex white matter structures will also be briefly introduced, with discussions on advantages and limitations.

Acknowledgements

No acknowledgement found.

References

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Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)