Callaghan, Paul T

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Principles of NuclearMagnetic ResonanceMicroscopyPaul T. CallaghanDepartment of Physics and BiophysicsMassey UniversityNew ZealandCLARENDON PRESS • OXFORDCONTENTS1 PRINCIPLES OF IMAGING	 11.1 Introduction	 11.2 Reciprocal space and Fourier transformation 	 21.2.1 Conjugate variables	 21.2.2 Cyclic frequency	 51.2.3 Convolution theorem	 81.2.4 Digital Fourier transformation 	 101.2.5 Real and imaginary parts of the transform 	 111.3 Fourier transformation and optical microscopy 	 121.4 Photon intensity tomography 	 151.5 The radio-frequency window 	 211.6 References	 232 INTRODUCTORY NUCLEAR MAGNETIC RESONANCE 	 252.1 Elementary quantum mechanics and nuclear magnetization 	 252.2 Resonant excitation and the rotating frame 	 332.3 The semi-classical description	 352.3.1 Excitation	 352.3.2 Relaxation	 382.3.3 Signal detection	 392.4 Other nuclear interactions 	 452.4.1 The visibility of fine details	 452.4.2 Magnetic field inhomogeneity	 452.4.3 Dipolar interactions	 472.4.4 Chemical shift	 492.4.5 Scalar coupling	 502.4.6 / >1: The quadrupole interaction 	 522.4.7 Multiple quantum coherence	 542.4.8 Bandwidth of the r.f. pulse 	 572.5 Relaxation and molecular motion	 572.5.1 Liquids	 582.5.2 Solids and slow motions 	 632.6 Introductory spin manipulation	 642.6.1 Signal averaging	 652.6.2 Phase cycling	 672.6.3 Inversion recovery	 682.6.4 Simple (Hahn) spin echo	 692.6.5 The Carr-Purcell-Meiboom-Gill echo train	 742.6.6 The stimulated echo	 752.6.7 Steady-sta.te free precession and driven equilibrium 	 772.6.8 Coherence transfer via J-couplings, dipolar interactions, andquadrupole interactions 	 79xiv	 CONTENTS2.6.9 The solid echo	 842.6.10 Multiple pulse line-narrowing and magic angle spinning	 852.7 References	 913 THE INFLUENCE OF MAGNETIC FIELD GRADIENTS 	 933.1 Spin density and k-space	 933.1.1 Conjugate spaces in reconstruction	 933.1.2 Efficiency	 973.2 Selective excitation 	 983.2.1 Soft and hard pulses	 983.2.2 Evolution of the magnetization during selective excitation	 1013.2.3 Alternative refocusing methods	 1133.2.4 Self-refocused pulses 	 1153.2.5 Spatially selective destruction and localized spectroscopy 	 1173.2.6 The DANTE pulse sequence	 1203.3 Reconstruction in two-dimensions 	 1213.3.1 Coordinate definition 	 1213.3.2 Two-dimensional Fourier imaging (FI) 	 1223.3.3 Two-dimensional projection reconstruction (PR)	 1243.3.4 Frequency and time domain relationships 	 1283.4 Alternative reconstruction methods 	 1293.4.1 Three-dimensional imaging 	 1293.4.2 Rotating frame imaging	1323.5 The use of echoes in imaging experiments	1333.5.1 The echo sampling scheme	1333.5.2 Multislicing and STEAM	 1383.5.3 Chemical shift selective imaging using stimulated echoes:CHESS	 1413.5.4 Echo summation	 1433.6 Rapid sampling of k-space	 1473.6.1 Low-angle excitation: FLASH imaging	1483.6.2 Steady-state free precession: FAST, CE-FAST, F I SP, andFADE	 1513.6.3 Echo planar imaging	 1523.7 Translational motion of the spins	 1573.7.1 The influence of diffusion in the presence of field gradients	1573.7.2 The pulsed magnetic field gradient: diffusion and velocity	1623.7.3 Reducing the influence of transverse relaxation	1663.7.4 Generalized treatment of diffusion and flow: TheBloch-Torrey equations	 1673.8 References	 1694 HIGH-RESOLUTION k-SPACE IMAGING	 1734.1 Sensitivity, motion, and resolution	 1734.2 The Signal-to-noise ratio in NM R	 1744.3 Frequency domain: discrete transformation in two dimensions	 179CONTENTS	 X V4.4 Influence of smoothing filters	 1854.5 T2-firnlied resolution	 1894.5.1 T2-optimal bandwidth	 1894.5.2 Multiple echo summation	 1944.5.3 Comparison of rapid acquisition methods 	 1974.6 Diffusion-limited resolution 	 2014.6.1 Diffusion-optimal bandwidth 	 2014.6.2 Multiple echo summation 	 2064.7 Susceptibility-limited resolution 	 2084.7.1 Susceptibility artefacts 	 2094.7.2 Distortionless imaging	 2164.7.3 Diffusive attenuation 	 2174.8 Comparison of Fourier imaging and projection reconstruction	 2244.9 Further resolution enhancement	 2254.10 References	 2265 k-SPACE MICROSCOPY IN BIOLOGY AND MATERIALSSCIENCE	 2275.1 Proton NM R in biological, synthetic, and mineral materials 	 2285.1.1 Water	 2295.1.2 Plant and animal tissue	 2335.1.3 Polymers	 2355.2 Proton density studies in the 'liquid' state 	 2365.2.1 Plant tissue images	 2375.2.2 Animal tissue images	 2445.2.3 Images in non-biological materials and in food products 	 2545.3 Contrast techniques in imaging 	 2675.3.1 T1 and T2 contrast	 2705.3.2 Chemical shift contrast	 2785.3.3 Multiple quantum filters	 2885.3.4 Signal suppression	 2905.3.5 Magnetization transfer via molecular exchange	 2965.4 Other nuclei	 2965.5 NM R imaging in the solid state 	 3065.5.1 The sensitivity problem	 3065.5.2 Dilute and low y spins 	 3075.5.3 Proton imaging in the solid state	 3085.5.4 Deuteron imaging and two-quantum coherence 	 3185.6 References	 3186 THE MEASUREMENT OF MOTION USING SPIN ECHOES 3286.1 Motional contrast and microstructure 	 3286.2 Introduction to translational dynamics 	 3306.2.1 The conditional probability function and self-diffusion	 3306.2.2 Velocity correlation, spectral density, and the seif-diffusiontensor	 334xvi	 CONTENTS6.2.3 The relationship between v,(0) vz (t) and PS	3356.3 PGSE: the scattering analogy and q-space 	 3366.3.1 The narrow-pulse approximation	 3386.3.2 Finite pulse widths, seif-diffusion, and flow	 3416.3.3 Anisotropic seif-diffusion	 3446.3.4 Comparison of the sensitivity resolution Limits in q-space andk-space imaging	 3506.4 General gradient modulation methods: the motional spectrum 	 3536.4.1 The effective gradient	 3536.4.2 The method of cumulants 	 3556.4.3 The spectrum of the gradient and the spectrum of themotion	 3576.4.4 Stationary and time-dependent random flow 	 362Appendix 6.1	 3676.6 References	 3687 STRUCTURAL IMAGING USING q-SPACE 	 3717.1 Restricted diffusion	 3717.2 Simple confining boundaries 	 3717.2.1 Rectangular boundaries 	 3717.2.2 Spherical boundaries 	 3737.3 The averaged propagator in the Jong time-scale limit	3757.3.1 Boxes and spheres 	 3757.3.2 Real space versus reciprocal space	 3807.3.3 Selection based an compartment size	 3827.4 Porous structures	 3837.4.1 Connected boxes in a regular lattice	3847.4.2 Partially connected structures: the connection matrix	3867.4.3 The finite time scale: diffusion in porous systems	3907.4.4 The irregular lattice and the pore glass	 3937.4.5 Structure determination	 3987.5 `Soft-bounded' systems	 4007.5.1 Diffusion near an attractive centre	 4007.5.2 Curvilinear diffusion	 4017.5.3 Diffusion in fractal geometries	 4047.5.4 Systems with multiple regions	 4057.6 Spin relaxation in microscopically inhomogeneous media	 4077.6.1 The two-phase model	 4087.6.2 Relaxation sinks and normal modes	 4087.6.3 PGSE experiment in a Brownstein-Tarr system	 4117.6.4 Susceptibility inhomogeneity	 4137.6.5 Signatures for relaxation	 4167.7 References	 417CONTENTS	 xvii8 SPATIALLY HETEROGENEOUS MOTION ANDDYNAMIC NMR MICROSCOPY	 4208.1 The influence of motion in imaging	 4208.1.1 Steady-state methods	 4228.1.2 Time-of-flight and spin `tagging'	 4238.1.3 Phase encoding	 4268.2 Periodic and slow motion 	 4348.2.1 Stroboscopic measurement	 4348.2.2 Echo planar imaging and snapshot FLASH imaging 	 4358.2.3 The magnetization grating	 4368.3 Dynamic NMR microscopy	 4388.3.1 Combined k-space and q-space imaging 	 4388.3.2 Digital computation of velocity and diffusion 	 4418.3.3 Applications in the study of diffusion and flow	 4438.3.4 More complex motion	 4498.4 Velocity-compensated dynamic imaging 	 4498.4.1 Even echoes: the double PGSE experiment 	 4498.4.2 The effect of velocity shear in the measurement of diffusion	 4508.5 Potential artefacts	 4528.5.1 Gradient-dependent phase shifts 	 4528.5.2 Influence of the slice selection gradient	 4528.5.3 Broadening and baseline artefacts in the digital FFT 	 4538.5.4 The influence of gradient non-uniformity 	 4548.5.5 Transverse diffusion	 4568.6 Applications of dynamic NMR microscopy 	 4568.7 References	 4579 ELEMENTS OF THE NMR MICROSCOPE	4619.1 The system	 4619.2 Gradient and r.f. coils 	 4639.2.1 Electromagnet and superconductive magnet geometry 	 4639.2.2 Current pulse shaping and active shielding 	 4709.3 Gradient coil design in solenoidal geometry	 4729.3.1 Fields due to currents an cylindrical surfaces	 4729.3.2 Single screening	 4739.3.3 Double screening and target fields	 4749.3.4 The Maxwell pair and saddle coil 	 4759.4 High-gradient PGSE	 4789.4.1 Echo instabilities	 4789.4.2 Removing phase instabilities by means of a read gradient 	 4799.5 References	 482INDEX	 483

Principles of nuclear magnetic resonance microscopy

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