Principles of Nuclear Magnetic Resonance Microscopy

Transcription

1 Principles of Nuclear Magnetic Resonance Microscopy Paul T. Callaghan Department of Physics and Biophysics Massey University New Zealand CLARENDON PRESS OXFORD

2 CONTENTS 1 PRINCIPLES OF IMAGING Introduction Reciprocal space and Fourier transformation Conjugate variables Cyclic frequency Convolution theorem Digital Fourier transformation Real and imaginary parts of the transform Fourier transformation and optical microscopy Photon intensity tomography The radio-frequency window References 23 2 INTRODUCTORY NUCLEAR MAGNETIC RESONANCE Elementary quantum mechanics and nuclear magnetization Resonant excitation and the rotating frame The semi-classical description Excitation Relaxation Signal detection Other nuclear interactions The visibility of fine details Magnetic field inhomogeneity Dipolar interactions Chemical shift Scalar coupling / >1: The quadrupole interaction Multiple quantum coherence Bandwidth of the r.f. pulse Relaxation and molecular motion Liquids Solids and slow motions Introductory spin manipulation Signal averaging Phase cycling Inversion recovery Simple (Hahn) spin echo The Carr-Purcell-Meiboom-Gill echo train The stimulated echo Steady-sta.te free precession and driven equilibrium Coherence transfer via J-couplings, dipolar interactions, and quadrupole interactions 79

3 xiv CONTENTS The solid echo Multiple pulse line-narrowing and magic angle spinning References 91 3 THE INFLUENCE OF MAGNETIC FIELD GRADIENTS Spin density and k-space Conjugate spaces in reconstruction Efficiency Selective excitation Soft and hard pulses Evolution of the magnetization during selective excitation Alternative refocusing methods Self-refocused pulses Spatially selective destruction and localized spectroscopy The DANTE pulse sequence Reconstruction in two-dimensions Coordinate definition Two-dimensional Fourier imaging (FI) Two-dimensional projection reconstruction (PR) Frequency and time domain relationships Alternative reconstruction methods Three-dimensional imaging Rotating frame imaging The use of echoes in imaging experiments The echo sampling scheme Multislicing and STEAM Chemical shift selective imaging using stimulated echoes: CHESS Echo summation Rapid sampling of k-space Low-angle excitation: FLASH imaging Steady-state free precession: FAST, CE-FAST, F I SP, and FADE Echo planar imaging Translational motion of the spins The influence of diffusion in the presence of field gradients The pulsed magnetic field gradient: diffusion and velocity Reducing the influence of transverse relaxation Generalized treatment of diffusion and flow: The Bloch-Torrey equations References HIGH-RESOLUTION k-space IMAGING Sensitivity, motion, and resolution The Signal-to-noise ratio in NM R Frequency domain: discrete transformation in two dimensions 179

4 CONTENTS X V 4.4 Influence of smoothing filters T2-firnlied resolution T2-optimal bandwidth Multiple echo summation Comparison of rapid acquisition methods Diffusion-limited resolution Diffusion-optimal bandwidth Multiple echo summation Susceptibility-limited resolution Susceptibility artefacts Distortionless imaging Diffusive attenuation Comparison of Fourier imaging and projection reconstruction Further resolution enhancement References k-space MICROSCOPY IN BIOLOGY AND MATERIALS SCIENCE Proton NM R in biological, synthetic, and mineral materials Water Plant and animal tissue Polymers Proton density studies in the 'liquid' state Plant tissue images Animal tissue images Images in non-biological materials and in food products Contrast techniques in imaging T1 and T2 contrast Chemical shift contrast Multiple quantum filters Signal suppression Magnetization transfer via molecular exchange Other nuclei NM R imaging in the solid state The sensitivity problem Dilute and low y spins Proton imaging in the solid state Deuteron imaging and two-quantum coherence References THE MEASUREMENT OF MOTION USING SPIN ECHOES Motional contrast and microstructure Introduction to translational dynamics The conditional probability function and self-diffusion Velocity correlation, spectral density, and the seif-diffusion tensor 334

5 xvi CONTENTS The relationship between v,(0) vz (t) and PS PGSE: the scattering analogy and q-space The narrow-pulse approximation Finite pulse widths, seif-diffusion, and flow Anisotropic seif-diffusion Comparison of the sensitivity resolution Limits in q-space and k-space imaging General gradient modulation methods: the motional spectrum The effective gradient The method of cumulants The spectrum of the gradient and the spectrum of the motion Stationary and time-dependent random flow 362 Appendix References STRUCTURAL IMAGING USING q-space Restricted diffusion Simple confining boundaries Rectangular boundaries Spherical boundaries The averaged propagator in the Jong time-scale limit Boxes and spheres Real space versus reciprocal space Selection based an compartment size Porous structures Connected boxes in a regular lattice Partially connected structures: the connection matrix The finite time scale: diffusion in porous systems The irregular lattice and the pore glass Structure determination `Soft-bounded' systems Diffusion near an attractive centre Curvilinear diffusion Diffusion in fractal geometries Systems with multiple regions Spin relaxation in microscopically inhomogeneous media The two-phase model Relaxation sinks and normal modes PGSE experiment in a Brownstein-Tarr system Susceptibility inhomogeneity Signatures for relaxation References 417

6 CONTENTS xvii 8 SPATIALLY HETEROGENEOUS MOTION AND DYNAMIC NMR MICROSCOPY The influence of motion in imaging Steady-state methods Time-of-flight and spin `tagging' Phase encoding Periodic and slow motion Stroboscopic measurement Echo planar imaging and snapshot FLASH imaging The magnetization grating Dynamic NMR microscopy Combined k-space and q-space imaging Digital computation of velocity and diffusion Applications in the study of diffusion and flow More complex motion Velocity-compensated dynamic imaging Even echoes: the double PGSE experiment The effect of velocity shear in the measurement of diffusion Potential artefacts Gradient-dependent phase shifts Influence of the slice selection gradient Broadening and baseline artefacts in the digital FFT The influence of gradient non-uniformity Transverse diffusion Applications of dynamic NMR microscopy References ELEMENTS OF THE NMR MICROSCOPE The system Gradient and r.f. coils Electromagnet and superconductive magnet geometry Current pulse shaping and active shielding Gradient coil design in solenoidal geometry Fields due to currents an cylindrical surfaces Single screening Double screening and target fields The Maxwell pair and saddle coil High-gradient PGSE Echo instabilities Removing phase instabilities by means of a read gradient References 482 INDEX 483