q-Space: What is it?
Flavio Dell'Acqua1

1Neuroimaging, King's College London, London, United Kingdom

Synopsis

In this lecture the concepts behind q-space and q-space imaging will be reviewed. Starting from an historical overview on the major advances, the development of the q-space formalism and the concept of the diffusion propagator will be described and used to explain the origin of diffraction peaks and their possible application to infer pore sizes and other microstructural features. Q-space and Propagator based imaging techniques will then be introduced highlighting advantages and limitations of these techniques. Finally, the use of diffusion time as an new contrast to probe microstructure at different length scales will be discussed.

HIGHLIGHTS

• Diffusion MRI can be used to non-invasively probe living biological tissues at the micron-scale and extract unique information about their microstructural organisation.

• The q-space formalism directly links the spin displacement probability distribution function with the Fourier transform of the diffusion MR signal. Model “free” descriptions of the underlying diffusion propagator for complex biological systems are possible.

• Over the years several methods have been developed but hardware and time constraints have limited direct and widespread clinical applications. Q-space and similar imaging techniques are mainly limited by the many diffusion weightings or multiple diffusion times required.

• The advent of new MR technologies and new diffusion imaging methods has the potential today not only to revitalise q-space methods but also to reshape the whole field of diffusion imaging. Very complex diffusion experiments are about to enter the realm of real clinical applications. Exciting times are ahead!

TARGET AUDIENCE

This lecture is aimed at all students and researchers working or starting to work in the field of Diffusion NMR/MRI and that are interested to learn more about the underlying principles of Diffusion MR and their potential applications to study biological tissues.

SUMMARY

The effects of diffusion on the final NMR signal have been described since the original 1950 Hann paper on the discovery of “spin-echoes” [1]. Today diffusion has become one of the major MR contrasts used to study the microstructural organisation of several systems from minerals to living biological tissues.

In this lecture the concepts behind q-space and q-space imaging will be reviewed [2],[3]. Starting from an historical overview on the major advances, the development of the q-space formalism and the concept of the diffusion propagator will be described and used to explain the origin of diffraction peaks and their possible application to infer pore sizes and other microstructural features [4],[5]. Here, results from traditional single pulsed gradient spin echo (single-PGSE) experiments will also be presented and compared with more recent double-PGSE approaches [6].

Q-space and Propagator based imaging techniques (QSI, DSI, 3D-SHORE, MAP-MRI, etc. [7],[8],[9]) will then be introduced highlighting advantages and limitations of these techniques and their derived metrics. A brief comparison will also be shown with alternative model-based approaches (multi-tensor, spherical deconvolution and multi-compartmental models [10],[11]).

Finally, the use of diffusion time as an effective contrast to probe microstructure at different length scales will be discussed [12][13]. It will be shown also how, over the years, diffusion time has become an increasingly important dimension in some of the most advanced diffusion experiments (e.g. Axon caliber mapping techniques [14][15] and Oscillating Gradients [16]).

To conclude the lecture, the practical applicability of these techniques will be discussed. In particular, focusing on the limiting constraints that have until now prevented a large adoption of these techniques. With the advent of new ultra-fast acquisition technologies like multiband and new custom built “microstructure” MR scanners, exciting opportunities await new generations of researchers.

Acknowledgements

No acknowledgement found.

References

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[2] Callaghan, P. T., Eccles C. D., and Xia Y, 1988, “NMR microscopy of dynamic displacements: k-space and q-space imaging, J Phys. E: Sci Instrum, 21, 820–822

[3] Callaghan, P. T., A. Coy, D. MacGowan, K. J. Packer, and F. O. Zelaya, 1991, “Diffraction-like effects in NMR diffusion stud- ies of fluids in porous solids,” Nature , London 351, 467–469.

[4] Callaghan, P. T. (1995). Pulsed-gradient spin-echo NMR for planar, cylindrical, and spherical pores under conditions of wall relaxation. Journal of Magnetic Resonance, Series A, 113(1), 53–59.

[5] Bar-Shir, A., Avram, L., Ozarslan, E., Basser, P. J., & Cohen, Y. (2008). The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations. Journal of Magnetic Resonance 194(2), 230–236.

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[8] Wedeen, V. J., Hagmann, P., Tseng, W.-Y. I., Reese, T. G., & Weisskoff, R. M. (2005). Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magnetic Resonance in Medicine, 54(6), 1377–1386.

[9] Ozarslan, E., Koay, C. G., Shepherd, T. M., Komlosh, M. E., Irfanoglu, M. O., Pierpaoli, C., & Basser, P. J. (2013). Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure., 78, 16–32.

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[11] Panagiotaki, E., Schneider, T., Siow, B., Hall, M. G., Lythgoe, M. F., & Alexander, D. C. (2012). Compartment models of the diffusion MR signal in brain white matter: a taxonomy and comparison., Neuroimage, 59(3), 2241–2254.

[12] van Gelderen P, DesPres D, van Zijl PC, Moonen CT. Evaluation of restricted diffusion in cylinders. Phosphocreatine in rabbit leg muscle. J Magn Reson B 1994;103(3):255–260.

[13] D. S. Grebenkov, NMR Survey of Reflected Brownian Motion, Rev. Mod. Phys. 79 1077–1137 (2007).

[14] Assaf, Y., Blumenfeld-Katzir, T., Yovel, Y., & Basser, P. J. (2008). AxCaliber: a method for measuring axon diameter distribution from diffusion MRI. Magnetic Resonance in Medicine 59(6), 1347–1354.

[15] Alexander, D. C., Hubbard, P. L., Hall, M. G., Moore, E. A., Ptito, M., Parker, G. J. M., & Dyrby, T. B. (2010). Orientationally invariant indices of axon diameter and density from diffusion MRI. NeuroImage, 52(4), 1374–1389.

[16] Gore, J. C., Xu, J., Colvin, D. C., Yankeelov, T. E., Parsons, E. C., & Does, M. D. (2010). Characterization of tissue structure at varying length scales using temporal diffusion spectroscopy. NMR in Biomedicine, 23(7), 745–756.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)