Susceptibility: Principles & Methods
Manisha Aggarwal1
1Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, Baltimore, MD, United States

Synopsis

This lecture will cover the concepts and principles of magnetic susceptibility as a contrast mechanism in MRI. We will discuss the principles of magnetic susceptibility and its sources in biological tissues. MRI acquisition sequences and methods for generating susceptibility-based contrasts including susceptibility-weighted imaging, quantitative susceptibility mapping, and susceptibility tensor imaging will be discussed. We will explore some recent applications of magnetic susceptibility in MRI for probing various aspects of tissue composition as well as white matter microstructure in the brain.

Target audience

Scientists, researchers, and clinicians interested in the principles and applications of MRI methods for probing tissue microstructure based on magnetic susceptibility.

Outcomes/Objectives

- To understand the principles of magnetic susceptibility and its sources in biological tissues
- To understand the concepts of MRI methods for susceptibility mapping
- To explore applications of susceptibility contrast in MRI for probing tissue microstructure

What is magnetic susceptibility?

Magnetic susceptibility (χ) is the physical property of a material that characterizes its tendency to magnetize when placed in an externally applied magnetic field. When placed in the static magnetic field of an MRI scanner with field intensity H, a material gains a magnetization M (defined as the dipole moment per unit volume) proportional to its magnetic susceptibility, i.e., M = χH.1,2 For materials with χ > 0 (paramagnetic), the magnetic moments align parallel to the external magnetic field B0, while for materials with χ < 0 (diamagnetic), the moments align anti-parallel to B0. Note that χ is a dimensionless quantity and has no physical units. The magnetic susceptibility of most constituents of biological tissues is close to that of water (-9.04 parts-per-million or ppm), and typically varies across gray and white matter of the healthy human brain in the range of about -9.2 to -8.8 ppm.3,4 The magnetic susceptibility of biological tissues depends on their molecular composition (e.g., iron, calcium, lipid or myelin content) as well as their microstructural organization, for example, the arrangement of myelin lipid bilayers in white matter.5 Magnetization induced in tissues with local susceptibility variations results in a perturbation of the homogeneous static magnetic field, which affects the MR signal evolution.

Magnetic susceptibility: Effects on the NMR signal

Gradient-recalled echo (GRE) is the most frequently used pulse sequence to probe magnetic susceptibility effects in MRI. Multiple-echo sequences can be used to acquire data with short echo times (TEs) for detection of strong susceptibility effects and long TEs for weak susceptibilities. GRE magnitude (T2*-weighted) and phase images are both differentially affected by susceptibility-induced field perturbations. In the simplest case, susceptibility-weighted imaging (SWI) combines magnitude and phase information to qualitatively display the magnetic field variations6. However, the GRE signal phase is non-local, i.e., the phase value depends not only on local tissue properties but also on the surrounding susceptibility distribution. The field perturbation caused by a known distribution of isotropic susceptibility can be considered as a convolution of the susceptibility distribution with the unit dipole kernel. Quantitative susceptibility mapping (QSM) aims to solve this inverse problem to estimate the underlying magnetic susceptibility distribution2,4,7,8, and can overcome some limitations of SWI related to the non-local nature of the GRE signal phase and its dependence on tissue geometry9,10.

Additionally, both GRE signal phase and magnitude have been shown to exhibit dependence on the orientation of white matter and muscle fibers with respect to the main magnetic field11. Mechanisms proposed to explain this orientation dependence include the anisotropy of magnetic susceptibility12,13 and structural tissue anisotropy14. This dependence has been used for mapping white matter orientation in the brain with susceptibility tensor imaging (STI)13,15. The effects of microstructure can also manifest as non-linear evolution of the GRE signal phase with TE as observed in white matter fibers16-18. Frequency difference mapping, which measures the deviation from phase linearity between short- and long-TE regimes, can be used to probe the effects of local tissue microstructure and white matter orientation on the GRE signal phase in a manner independent of non-local phase effects16,19.

Susceptibility as a probe of tissue composition and microstructure

The main sources of magnetic susceptibility variations in brain tissue include iron, calcium, lipid and myelin content20. Variations in tissue susceptibility assessed with MRI can allow probing changes in brain tissue composition in both health and disease. For instance, QSM has been widely used to assess iron content in deep gray matter nuclei and its changes with aging21. Validation with mass spectrometry showed that susceptibility measured by QSM is linearly correlated with iron concentration in deep brain nuclei22. QSM has also been used to distinguish diamagnetic and paramagnetic brain lesions, allowing differentiating between calcifications and hemorrhages or iron deposits in neurological disorders23,24. The magnetic susceptibility of white matter has been shown to become increasingly diamagnetic with brain development, followed by continuing decrease in diamagnetism with aging25, reflecting underlying changes in myelination and age-related demyelination. Recent advances in QSM and microstructure modeling techniques are likely to lead to many promising new applications for characterization of brain tissue.

Acknowledgements

National Institutes of Health (NIH) grant R01AG057991

References

1. Schenck, J.F., The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med Phys, 1996. 23(6): p. 815-50.

2. Wang, Y. and T. Liu, Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker. Magn Reson Med, 2015. 73(1): p. 82-101.

3. Duyn, J.H. and J. Schenck, Contributions to magnetic susceptibility of brain tissue. NMR in biomedicine, 2017. 30(4): p. 10.1002/nbm.3546.

4. Haacke, E.M., S. Liu, S. Buch, W. Zheng, D. Wu, and Y. Ye, Quantitative susceptibility mapping: current status and future directions. Magn Reson Imaging, 2015. 33(1): p. 1-25.

5. He, X. and D.A. Yablonskiy, Biophysical mechanisms of phase contrast in gradient echo MRI. Proceedings of the National Academy of Sciences, 2009. 106(32): p. 13558-13563.

6. Haacke, E.M., Y. Xu, Y.C. Cheng, and J.R. Reichenbach, Susceptibility weighted imaging (SWI). Magn Reson Med, 2004. 52(3): p. 612-8.

7. Liu, C., H. Wei, N.J. Gong, M. Cronin, R. Dibb, and K. Decker, Quantitative Susceptibility Mapping: Contrast Mechanisms and Clinical Applications. Tomography, 2015. 1(1): p. 3-17.

8. Langkammer, C., F. Schweser, K. Shmueli, C. Kames, X. Li, L. Guo, C. Milovic, J. Kim, H. Wei, K. Bredies, S. Buch, Y. Guo, Z. Liu, J. Meineke, A. Rauscher, J.P. Marques, and B. Bilgic, Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge. Magnetic Resonance in Medicine, 2018. 79(3): p. 1661-1673.

9. Shmueli, K., J.A. de Zwart, P. van Gelderen, T.-Q. Li, S.J. Dodd, and J.H. Duyn, Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data. Magnetic Resonance in Medicine, 2009. 62(6): p. 1510-1522.

10. Liu, C., W. Li, K.A. Tong, K.W. Yeom, and S. Kuzminski, Susceptibility-weighted imaging and quantitative susceptibility mapping in the brain. J Magn Reson Imaging, 2015. 42(1): p. 23-41.

11. Lee, J., Y. Nam, J.Y. Choi, E.Y. Kim, S.-H. Oh, and D.-H. Kim, Mechanisms of T2* anisotropy and gradient echo myelin water imaging. NMR in Biomedicine, 2017. 30(4): p. e3513.

12. Lee, J., K. Shmueli, M. Fukunaga, P. van Gelderen, H. Merkle, A.C. Silva, and J.H. Duyn, Sensitivity of MRI resonance frequency to the orientation of brain tissue microstructure. Proc Natl Acad Sci U S A, 2010. 107(11): p. 5130-5.

13. Liu, C., Susceptibility tensor imaging. Magn Reson Med, 2010. 63(6): p. 1471-7.

14. Yablonskiy, D.A. and A.L. Sukstanskii, Generalized Lorentzian Tensor Approach (GLTA) as a biophysical background for quantitative susceptibility mapping. Magn Reson Med, 2015. 73(2): p. 757-64.

15. Li, W., C. Liu, T.Q. Duong, P.C. van Zijl, and X. Li, Susceptibility tensor imaging (STI) of the brain. NMR Biomed, 2017. 30(4).

16. Wharton, S. and R. Bowtell, Fiber orientation-dependent white matter contrast in gradient echo MRI. Proc Natl Acad Sci U S A, 2012. 109(45): p. 18559-64.

17. Schweser, F., A. Deistung, D. Güllmar, M. Atterbury, B. Lehr, K. Sommer, and J. Reichenbach. Non-linear evolution of GRE phase as a means to investigate tissue microstructure. in Proceedings of the 19th Meeting of the International Society for Magnetic Resonance in Medicine. 2011.

18. Aggarwal, M., Y. Kageyama, X. Li, and P.C. van Zijl, B0 -orientation dependent magnetic susceptibility-induced white matter contrast in the human brainstem at 11.7T. Magn Reson Med, 2016. 75(6): p. 2455-63.

19. Tendler, B.C. and R. Bowtell, Frequency difference mapping applied to the corpus callosum at 7T. Magn Reson Med, 2019. 81(5): p. 3017-3031.

20. Duyn, J.H., Studying brain microstructure with magnetic susceptibility contrast at high-field. Neuroimage, 2018. 168: p. 152-161.

21. Bilgic, B., A. Pfefferbaum, T. Rohlfing, E.V. Sullivan, and E. Adalsteinsson, MRI estimates of brain iron concentration in normal aging using quantitative susceptibility mapping. Neuroimage, 2012. 59(3): p. 2625-35.

22. Langkammer, C., N. Krebs, W. Goessler, E. Scheurer, F. Ebner, K. Yen, F. Fazekas, and S. Ropele, Quantitative MR imaging of brain iron: a postmortem validation study. Radiology, 2010. 257(2): p. 455-62.

23. Schweser, F., A. Deistung, B.W. Lehr, and J.R. Reichenbach, Differentiation between diamagnetic and paramagnetic cerebral lesions based on magnetic susceptibility mapping. Medical Physics, 2010. 37(10): p. 5165-5178.

24. Aggarwal, M., X. Li, O. Gröhn, and A. Sierra, Nuclei-specific deposits of iron and calcium in the rat thalamus after status epilepticus revealed with quantitative susceptibility mapping (QSM). J Magn Reson Imaging, 2018. 47(2): p. 554-564.

25. Li, W., B. Wu, A. Batrachenko, V. Bancroft-Wu, R.A. Morey, V. Shashi, C. Langkammer, M.D. De Bellis, S. Ropele, A.W. Song, and C. Liu, Differential developmental trajectories of magnetic susceptibility in human brain gray and white matter over the lifespan. Hum Brain Mapp, 2014. 35(6): p. 2698-713.

Proc. Intl. Soc. Mag. Reson. Med. 30 (2022)