Paramagnetic & Diamagnetic Susceptibility in Tissue
Ferdinand Schweser1,2

1Buffalo Neuroimaging Analysis Center, Department of Neurology at the Jacobs School of Medicine and Biomedical Sciences, University at Buffalo, The State University of New York, Buffalo, NY, United States, 2Center for Biomedical Imaging, Clinical and Translational Science Institute, University at Buffalo, The State University of New York, Buffalo, NY, United States

### Synopsis

This class will discuss the chemistry and physics of magnetic susceptibility, explaining why some substances affect tissue susceptibility substantially when they are present in very low concentrations whereas other substances need to be present in high concentrations to alter the tissue’s susceptibility measurably. We will discuss the how and why of the differential effects of magnetic susceptibility on gradient-echo magnitude and phase image contrast. An overview of the clinical potential of Quantitative Susceptibility Mapping (QSM) will be provided by discussing the different tissue properties that have been related to magnetic susceptibility in the more recent past.

### Target Audience

Scientists and clinicians interested in quantifying clinically relevant tissue properties, such as iron, calcium and myelin content, based on magnetic susceptibility.

### Objectives

As a result of attending this class, participants should be able to explain what magnetic susceptibility is, what substances dominate tissue susceptibility, and what pathological processes can affect tissue susceptibility.

The class will equip participants with a sufficiently broad understanding of tissue susceptibility to anticipate biomedical applications of Quantitative Susceptibility Mapping (QSM), discussed in more detail later in this course.

### What is magnetic susceptibility?

MRI and magnetic susceptibility share an intimate relationship.1 The magnetic susceptibility, typically expressed by the Greek symbol $\chi$, is the physical property that characterizes a material’s tendency to magnetize when it is exposed to an externally applied magnetic field, such as the strong static field in an MRI scanner. Being a dimensionless quantity, the magnetic susceptibility is a pure number without any physical unit. Biomaterials typically have very low magnetic susceptibility values on orders of magnitude between 10-6 to 10-5, which are referred to as paramagnetic and diamagnetic if $\chi>0$ and $\chi<0$, respectively.1 The magnetic susceptibility of biological tissues is close to that of water -9.04 · 10-6, or -9.04 parts-per-million (ppm), and often varies between different tissue types only on the order of parts-per-billion (ppb; $\Delta \chi \approx 10^{-9}$). This explains why the MRI literature often reports susceptibility differences in “ppb” or “ppm”.

The magnetic susceptibility of biological tissues depends on their molecular composition as well as the microstructural organization down to the molecular level,1,2 often referred to as magnetic tissue architecture. In the human brain, tissue susceptibility is primarily determined by the concentration of heme- and non-heme iron, myelination, fiber orientation, and calcium.

This class will discuss the chemistry and physics of magnetic susceptibility, explaining why some substances affect tissue susceptibility substantially when they are present in very low concentrations whereas other substances need to be present in high concentrations to alter the tissue’s susceptibility measurably.

### How does magnetic susceptibility affect the MRI signal?

Magnetic susceptibility affects the homogeneity of the strong static magnetic field in the MRI scanner.3 Simply put, a magnetized material or tissue is itself a magnet. Magnets are associated with their own magnetic field. The intrinsic magnetic field associated with tissue magnetization, and, hence, magnetic susceptibility, is the so-called demagnetization field.4 Hence, if a tissue is placed in the homogeneous static magnetic field of an MRI scanner, the homogeneity is disturbed, rendering the total resulting magnetic field in the scanner inhomogeneous. The effect this inhomogeneity has on the MR images depends on the particular pulse sequence employed and on the spatial distribution of the magnetic susceptibility.

Gradient-recalled echo (GRE)5 with long echo times,6 often referred to as T2*-weighted (T2*w) imaging, is the most widely employed pulse sequence for studying tissue susceptibility. Here, one has to distinguish between the magnitude GRE images, which are typically reconstructed by default by the MRI scanner by default, and the phase GRE images, which are often not automatically reconstructed by the scanners.3 The GRE magnitude images are particularly sensitive to magnetic field inhomogeneities caused by variations in magnetic susceptibility on sub-voxel length scales (microscopic), whereas they are less sensitive to magnetic field variations on a voxel length scale (macroscopic). On the other hand, GRE phase images are particularly sensitive to magnetic field inhomogeneities on the voxel-scale.

The class will discuss the how and why of the differential effects of magnetic susceptibility on GRE magnitude and phase image contrast.

### Why care about tissue magnetic susceptibility?

The assessment of variations in tissue susceptibility with MRI has been a subject of research for the past three decades.7 Until recently, the primary focus of these efforts laid on the visualization of iron-containing tissues and fluids. T2*w magnitude imaging is widely used clinically to diagnose and monitor iron-overload diseases. The paramagnetism of deoxy-heme allows visualizing microbleeds and venous malformations using a commercially available hybrid magnitude-and-phase technique called Susceptibility Weighted Imaging (SWI).8-10 The difference in magnetic susceptibility between oxygenated and deoxygenated blood, the BOLD effect,11-13 is the ultimate basis of functional MRI (fMRI).

The past ten years have been characterized by impressive progress in the physics-based analytical processing of the GRE signal.3,14-18 The introduction of Quantitative Susceptibility Mapping (QSM) enabled the quantitative measurement of tissue magnetic susceptibility, rather than a purely qualitative analysis of the visual appearance on phase and magnitude images.2,15,16,19-23 The availability of QSM has shed light on the susceptibility contributions of non-iron components, including myelin, calcium, fat, bone, and cartilage, which created a very active new research field that led to many promising new clinical applications of magnetic susceptibility.19,21,23-25

The class will provide an overview of the clinical potential of QSM by discussing the different tissue properties that have been related to magnetic susceptibility in the more recent past.

### Acknowledgements

No acknowledgement found.

### References

[1] Schenck JF, The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med Phys, 23(6):815–50

[2] Duyn JH. MR susceptibility imaging.” J Magn Reson, 229:198–207, 2013.

[3] Schweser F et al. Foundations of MRI phase imaging and processing for Quantitative Susceptibility Mapping (QSM). Z Med Phys, 26(1):6–34, 2016.

[4] Li LZ and Leigh JS, Quantifying arbitrary magnetic susceptibility distributions with MR. Magn Reson Med, 51(5):1077–1082, 2004.

[5] Haase A et al. FLASH imaging: rapid NMR imaging using low flip-angle pulses.” J Magn Reson, 67:258–266, 1986.

[6] Reichenbach JR et al. Theory and application of static field inhomogeneity effects in gradient-echo imaging. J Magn Reson Imaging, 7(2):266–279, 1997.

[7] Young IR et al. Clinical magnetic susceptibility mapping of the brain. J Comput Assist Tomogr, 11(1):2–6, 1987.

[8] Reichenbach JR and Haacke EM. High resolution BOLD venographic imaging: a window into brain function. NMR Biomed, 14(7-8):453–467, 2001.

[9] Reichenbach JR et al. High-resolution MR venography at 3.0 Tesla. J Comp Assist Tomogr, 24(6):949–957, 2000.

[10] Reichenbach JR et al. Small vessels in the human brain: MR-venography with deoxyhemoglobin as an intrinsic contrast agent. Radiology, 204(1):272–277, 1997.

[11] Ogawa S et al. Brain magnetic resonance imaging with contrast dependent on blood oxygenation. Proc Natl Acad Sci U S A, 87:9868–9872, 1990.

[12] Ogawa S and Lee TM. Magnetic Resonance Imaging of Blood Vessels at High Fields: In Vivo and in Vitro Measurements and Image Simulation. Magn Reson Med, 16:9–18, 1990.

[13] Ogawa S et al. Oxygenation-sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields. Magn Reson Med, 14(1):68–78, 1990.

[14] Chung J and Ruthotto L. Computational methods for image reconstruction. NMR in Biomedicine, 30(4), 2017.

[15] Wang Y and Liu T. Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker,” Magn Reson Med, 73(1):82–101, 2015.

[16] Haacke EM et al. Quantitative susceptibility mapping: current status and future directions. Magn Reson Imaging, 33(1):1–25, 2015.

[17] Robinson SD et al. An illustrated comparison of processing methods for MR phase imaging and QSM: combining array coil signals and phase unwrapping. NMR Biomed, 30(4):e3601, 2017.

[18] Schweser F et al. An illustrated comparison of processing methods for phase MRI and QSM: removal of background field contributions from sources outside the region of interest. NMR Biomed, 30(4):e3604, 2017.

[19] Liu C et al. Quantitative Susceptibility Mapping: Contrast Mechanisms and Clinical Applications. Tomography, 1(1):3–17, 2015.

[20] Liu C et al. Susceptibility-weighted imaging and quantitative susceptibility mapping in the brain. J Magn Reson Imaging, 42(1):23–41, 2015.

[21] Reichenbach JR et al. Quantitative Susceptibility Mapping: Concepts and Applications. Clin Neuroradiol, 25(S2):225–230, 2015.

[22] Reichenbach JR. The future of susceptibility contrast for assessment of anatomy and function. NeuroImage, 62(2):1311–5, 2012.

[23] Deistung et al. Overview of quantitative susceptibility mapping. NMR Biomed, 30(4):e3569, 2017.

[24] Eskreis-Winkler S et al. The clinical utility of QSM: disease diagnosis, medical management, and surgical planning. NMR Biomed, 30(4):e3668, 2017.

[25] Wang Y et al. Clinical quantitative susceptibility mapping (QSM): Biometal imaging and its emerging roles in patient care. J Magn Reson Imaging, 46(4):951–971, 2017.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)