The Basics: Dynamics of Water & Other Molecules in Biological Tissue
Olivier M. Girard1,2
1Aix Marseille Univ, CNRS, CRMBM, Marseille, France, 2APHM, Hôpital Universitaire Timone, CEMEREM, Marseille, France

Synopsis

Keywords: Contrast mechanisms: CEST & MT, Contrast mechanisms: Relaxometry, Contrast mechanisms: Microstructure

Biological tissues are dynamically heterogeneous spin systems containing a large variety of proton-carrying molecules, evolving in different magnetic environments, and exchanging magnetization over the time course of an MRI experiment. The MRI signal is typically measured from free water, but it carries the signature of the interactions the water protons have evolved through. Hence “free water” relaxation globally reflects on multiple contributions of different types of protons, including water protons in different magnetic environments and other exchanging non water protons. This lecture aims at building intuition on the basic principles of relaxation and magnetization transfer effects occurring in biological tissues.

Biological tissues are dynamically heterogeneous spin systems that contain a large variety of proton-carrying molecules including free water, cellular membranes, solute proteins, metabolites, and others. The protons of these molecules evolve in different magnetic environments, and they may exchange magnetization over the time course of a typical MRI experiment, through chemical exchange processes (i.e. physical exchange of a proton from one molecule to the other) or by through-space dipolar interaction (i.e. exchange of spin polarization). The MRI signal is typically detected from free water, but it carries the signature of the molecular environment the water protons have evolved through and exchanged with. In general, the various magnetization pathways throughout the microscopic environment involve multiple mechanisms, such as for instance intra-molecular spin diffusion (dipolar mediated transfer) followed by chemical exchange to free water, and diffusion of the water molecules in the intra/extra cellular space.

From this general picture, it appears that “free water” relaxation globally reflects on the multiple contributions of different types of protons, including water protons in different magnetic environments and other (fast-) exchanging non water protons. This relatively simple concept explains why MRI is so versatile in providing soft tissue contrast and why is has become particularly useful to distinguish various physio-pathological processes in the clinics. It also underlines that magnetization transfer effects (in their broad meaning) are important driving mechanisms of relaxation in biological tissues.

The usual formalism to describe the magnetization dynamics over the time course of an MRI experiment consists in integrating the Bloch equations. In a typical MRI experiment the magnetization will undergo multiple RF excitations (usually associated with a flip angle) and relaxation periods (usually described by a single set of T1 and T2 relaxation constants). Actually, according to the Bloch equations, longitudinal magnetization follows an exponential recovery model with a T1 relaxation constant, and the transverse magnetization follows an exponential decay with a T2 relaxation constant.

Whereas the Bloch equations are very useful representations of the MRI signal and are valid for free water protons experiencing isotropic rotations (isolated ½ spin systems), they cannot describe accurately the magnetization dynamics of motion-restricted macromolecules for which the secular part of the dipolar interaction does not average to zero (coupled spin systems). These molecules have a non-null residual dipolar coupling and are characterized by a broad spectrum that can span several kHz, leading to fast loss of transverse magnetization (or coherences) in a few 10-100s of µs. The Provotorov theory of RF saturation, originally developed for solids, may be applied to motionaly-restricted macromolecules to describe their magnetization dynamics, hence providing a useful formalism complementing the Bloch equations. Of note, lineshape models differ for motionaly-restricted macromolecules as compared to isotropic liquids (free water, solute molecules).

This lecture aims at building intuition on some basic principles of relaxation and exchange processes occurring in biological tissues to better understand how the water signal may inform on underlying contrast mechanisms.


Outline:
1. Biological tissues as dynamically heterogeneous spin systems
2. A brief introduction to molecular motions and their effects on NMR properties
3. Fast and slow exchange regimes
4. Liquid state vs. (semi-)solid state MRI signal modelling

Acknowledgements

I thank my colleagues, collaborators, and all the other researchers with whom I have had highly stimulating and helpful scientific discussions about molecular dynamics, NMR, relaxation, MT or ihMT.

This work was performed by a laboratory member of France Life Imaging network (grant ANR-11-INBS-0006). This work was partly supported by the French National Research Agency ANR [ANR‐22‐CE17‐0060].

References

Useful Journal References:

1. Vinogradov E. A brisk walk through the fields of relaxation, saturation, and exchange: From solid state NMR to in-vivo imaging. J Magn Reson Open. 2023;16-17:100130. doi:10.1016/j.jmro.2023.100130

2. Calucci L, Forte C. Proton longitudinal relaxation coupling in dynamically heterogeneous soft systems. Prog Nucl Magn Reson Spectrosc. 2009;55(4):296-323. doi:10.1016/j.pnmrs.2009.06.003

3. van Zijl PCM, Lam WW, Xu J, Knutsson L, Stanisz GJ. Magnetization Transfer Contrast and Chemical Exchange Saturation Transfer MRI. Features and analysis of the field-dependent saturation spectrum. NeuroImage. 2018;168:222-241. doi:10.1016/j.neuroimage.2017.04.045

4. Henkelman RM, Huang X, Xiang QS, Stanisz GJ, Swanson SD, Bronskill MJ. Quantitative interpretatioof magnetization transfer. Magn Reson Med. 1993;29(6):759-766.

5. Alsop DC, Ercan E, Girard OM, et al. Inhomogeneous magnetization transfer imaging: Concepts and directions for further development. NMR Biomed. August 2022:e4808. doi:10.1002/nbm.4808

6. Donahue KM, Weisskoff RM, Burstein D. Water diffusion and exchange as they influence contrast enhancement. J Magn Reson Imaging JMRI. 1997;7(1):102-110. doi:10.1002/jmri.1880070114

7. Bloembergen N, Purcell EM, Pound RV. Relaxation Effects in Nuclear Magnetic Resonance Absorption. Phys Rev. 1948;73(7):679-712. doi:10.1103/PhysRev.73.679

8. Solomon I. Relaxation Processes in a System of Two Spins. Phys Rev. 1955;99(2):559-565. doi:10.1103/PhysRev.99.559

9. McConnell HM. Reaction Rates by Nuclear Magnetic Resonance. J Chem Phys. 1958;28(3):430-431. doi:10.1063/1.1744152

10. Novikov DS, Kiselev VG, Jespersen SN. On modeling. Magn Reson Med. 2018;79(6):3172-3193. doi:10.1002/mrm.27101

11. Rioux JA, Levesque IR, Rutt BK. Biexponential longitudinal relaxation in white matter: Characterization and impact on T1 mapping with IR-FSE and MP2RAGE. Magn Reson Med. 2016;75(6):2265-2277. doi:10.1002/mrm.25729

12. Does MD. Inferring brain tissue composition and microstructure via MR relaxometry. NeuroImage. 2018;182:136-148. doi:10.1016/j.neuroimage.2017.12.087

13. Gochberg DF, Gore JC. Quantitative magnetization transfer imaging via selective inversion recovery with short repetition times. Magn Reson Med. 2007;57(2):437-441. doi:10.1002/mrm.21143

14. Manning AP, MacKay AL, Michal CA. Understanding aqueous and non-aqueous proton T1 relaxation in brain. J Magn Reson San Diego Calif 1997. 2021;323:106909. doi:10.1016/j.jmr.2020.106909

15. Wolff SD, Balaban RS. Magnetization transfer contrast (MTC) and tissue water proton relaxation in vivo. Magn Reson Med. 1989;10(1):135-144.

16. Edzes HT, Samulski ET. The measurement of cross-relaxation effects in the proton NMR spin-lattice relaxation of water in biological systems: Hydrated collagen and muscle. J Magn Reson 1969. 1978;31(2):207-229. doi:10.1016/0022-2364(78)90185-3

17. Morrison C, Stanisz G, Henkelman RM. Modeling magnetization transfer for biological-like systems using a semi-solid pool with a super-Lorentzian lineshape and dipolar reservoir. J Magn Reson B. 1995;108(2):103-113.

18. Wennerström H. Proton nuclear magnetic resonance lineshapes in lamellar liquid crystals. Chem Phys Lett. 1973;18(1):41-44. doi:10.1016/0009-2614(73)80333-1

19. Bloom M, Burnell EE, Roeder SBW, Valic MI. Nuclear magnetic resonance line shapes in lyotropic liquid crystals and related systems. J Chem Phys. 1977;66:3012

20. Malyarenko DI, Zimmermann EM, Adler J, Swanson SD. Magnetization transfer in lamellar liquid crystals. Magn Reson Med. 2014;72(5):1427-1434. doi:10.1002/mrm.25034

21. Varma G, Girard OM, Prevost VH, Grant AK, Duhamel G, Alsop DC. Interpretation of magnetization transfer from inhomogeneously broadened lines (ihMT) in tissues as a dipolar order effect within motion restricted molecules. J Magn Reson. 2015;260:67-76. doi:10.1016/j.jmr.2015.08.024

22. Manning AP, Chang KL, MacKay AL, Michal CA. The physical mechanism of “inhomogeneous” magnetization transfer MRI. J Magn Reson. 2017;274:125-136. doi:10.1016/j.jmr.2016.11.013

23. Swanson SD, Malyarenko DI, Fabiilli ML, Welsh RC, Nielsen JF, Srinivasan A. Molecular, dynamic, and structural origin of inhomogeneous magnetization transfer in lipid membranes. Magn Reson Med. 2017;77(3):1318-1328. doi:10.1002/mrm.26210

Useful textbooks:

1. Levitt MH. Spin Dynamics: Basics of Nuclear Magnetic Resonance, 2nd Edition. Wiley. 2008

2. Keeler J. Understanding NMR Spectroscopy, 2nd Edition. Wiley. 2010

3. Kowalewski J. and Maler L. Nuclear Spin Relaxation in Liquids: Theory, Experiments, and Applications. Taylor & Francis, 2006

4. Slichter CP. Principles of Magnetic Resonance. 3rd Edition. Springer. 1990

5. Goldman M. Spin Temperature and Nuclear Magnetic Resonance in Solids. Oxford University Press. 1970.

Related material may be found in lectures from previous years:

1. Girard OM. ihMT Principles & Applications. ISMRM 2020. Weekend Educational Session. Signal Enhancement: The Power & the Glory. https://www.ismrm.org/20/program_files/WE18.htm

2. Girard OM. Magnetization Transfer (for brain microstructure). ISMRM 2021. Weekend Educational Session. Brain Microstructure. https://www.ismrm.org/21/program-files/WE-32.htm

3. Girard OM. MT and ihMT: basic principles and applications (and how they relate to relaxation). ISMRM 2023. Weekday Course. Relaxation: Principles & Acquisition/Reconstruction Strategies. https://www.ismrm.org/23/program-files/Th-02.htm


Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)