Copyright is owned by the Author of the thesis.  Permission is given for 
a copy to be downloaded by an individual for the purpose of research and 
private study only.  The thesis may not be reproduced elsewhere without 
the permission of the Author. 
 



Static and Dynamic Imaging 

using Magnetic Field Gradients 

A thesis presented in partial fulfilment of 
the requirements for the degree of 

Master of Science 
in Physics at 

Massey University 

by 

Yang Xia 

1988 



1 

Abstract 

The theory and techniques of NMR imaging are described together with a detailed 
description of the Filtered Back Projection (FBP) technique useJ in an existing NMR 
imaging system. 

The existing 'static' NMR imaging system has been modified to be capable of 
performing 'dynamic' NMR imaging experiments, as well as better 'static' NMR 
imaging experiments. 

The potential of NMR microscopy in the imaging of both the static spin distribution 
P(ro) and the dynamic spin correlation function P(r01r,t) has been investigated. Both 
homogeneous and inhomogeneous systems have been studied. Detailed theoretical 
a~1alysis and experimental considerations of dynamic imaging experiments have been 
given. 

A transverse resolution of 15 µm for a 1 mm slice thickness is obtained from a static 
imaging experiment of a phantom using the modified system. The rabbit trachea 
imaging experiment has revealed the asymmettical collapse of tracheas under negative 
pressures, a collapse which had previously been considered as symmetrical process. 

The Poiseuille flow experiment has involved the first simultaneous measurement of 
flow and diffusion at the microscopic level. Maps of two dimensional distribution 
functions of flow and diffusion are given by this experiment, highlighting this totally 
non-invasive dynamic imaging technique. 

As an example of dynamic imaging, the wheat grain experiment has displayed the flow 
and diffusion maps within a single wheat grain in vivo. 



11 

Acknowledgments 

First, I would like to thank my parents for their constant encouragement from the early 
years of my education by creating an environment conducive to study and thinking. 

I wish to express my sincere gratitude to my supervisor, Professor Paul Callaghan, for 
providing continuing theoretical and technical guidance and careful instruction, for his 
great enthusiasm and patience while this manuscript has been written. 

I would also like sincerely to thank the following people who have contributed to this 
work: 

Dr Craig Eccles, now doing post-doctoral research at ETH, Switzerland, for his 
invaluable advice and great help during his time at Massey University. 

The mechanical workshop staff for manufacturing parts of the gradient power supply. 

The electronic workshop staff for providing technical assistance on a number of 
occasions. 

Dr Rod Lambert of Physics and Biophysics Department and Dr Roger Pack of 
Physiology and Anatomy Department for their advice in the rabbit trachea experiment. 

Dr Colin Jenner of the Waite Research Institute, Adelaide for his advice in the wheat 
grain experiment. 

Dr Ian Brooking of the Plant Physiology Division of the DSIR for supplying the wheat 
samples used in the in vivo experiment. 

Dr John Skipworth of Botany and Zoology Department for identifying the plant used in 
the static imaging experiment. 

The academic, technical and clerical staff of Physics and Biophysics Department for 
their kindness and help. 

Fellow post graduate students, Peter Daivis, James Conway, Peter Saunders and Mark 
Huirua for their friendship and support. 

Massey University for providing financial support in the form of a Graduate 
Assistantship. 

Finally I would like to express my deep appreciation of the unfailing encouragement 
and support given to me by my wife, Ping. 



111 

Contents 

Abstract ..... .... .... . ..... . .. ... .. ... ...... . ..... . ....... . . ... ....................... . .... 1 

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v111 
List of Symbols . .. .. ... . .. ... . .. . . . ....... . ...... . ..... . .. . . . ..... .. ... . .... . ... .. . .. . ... ix 

Chapter 1 
1.1 
1.2 

Introduction . . . .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 
Introduction . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 
Organisation of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 

Chapter 2 Theory of NMR Imaging . . .. .. . .. . . .. . .. . .. . . . . . . . . . . . . . . . . . . . . . 3 
2.1 NMR Theory . . . . . . . . . . . . .. . . . . . . .. . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . . 3 

2.1.1 Nuclear Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
2.1.2 Macroscopic Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
2.1.3 Relaxation Processes .. .. . . .. .. . . .. . .. .. .. .. .. . . . . . . . . . . .. . .. . .. .. 9 
2.1.4 Bloch Equation . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 13 
2.1.5 The Signal to Noise Ratio . .. . .. . .. . . . .. .. . . . .. . .. . .. . ... .. ... . ... 16 

2.2 Static NMR Imaging Theory . . .. . . . . . . . . . . . . . . . . .. . .. . .. . . . . .. . ... . 18 
2.2.1 The Field Gradient . . .. . .. . .. . .. . . . . . . . . . . . . . .. . ... . . .... .. .... .. .. 18 
2.2.2 Selective Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ... . . . .. . . . ... . 19 
2.2.3 Filtered Back Projection Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 24 
2.2.4 NMR Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . .. . .. . .. . . 29 
2.2.5 SIN and Resclution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . . . . .. . 29 

2.3 Dynamic NMR Imaging Theory .. . . . ..... . ...................... . . 31 
2.3.1 Pulse Gradient Spin Echo Technique ......................... .. 31 
2.3 .2 Stejskal Equation ... . . .. .. . ........... ... . . . .... . . . ........... . .. .. 33 
2.3.3 Combined PGSE-Imaging Experiment . . . . ................ .. ... 34 
2.3.4 Interpreting the Velocity and Diffusion Digits . ................ 38 
2.3.5 Uncertainty of Velocity and Diffusion Data ................... 41 

Chapter 3 NMR Imaging System and Its Development .. . . .. .... .. . 48 
3 .1 NMR Imaging System .. ... .. ... .. ... . .. .. ... . .............. : . . . . . . . 48 

3.1.1 Static Magnetic Field Unit ... . . . . . . . .. . . . . .. .. . .. . .. . .. .. ... ..... 50 
3.1.2 Field Gradients Unit .. .. ..... .... .. . .. . .... . ........... . ... . .... .. 51 
3.1.3 RF Pulse Field Unit . . . . . . . . . . . . .. .. . . ... . . . ... .. . .. . . . .. . . ... . . . . 51 
3.1.4 Experimental Controller . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . . . .. 52 
3. 1.5 Pulse Programmer Unit . . .. . .. . .. . .. . .. . . . . . . . . . . . . . .. . .. . .. . .. . . 52 
3.1.6 RF Coil and Its Tuning Circuit . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . 52 
3 .1. 7 Receiver Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 
3.1.8 Image Processing and Display Unit . . . . . . . . . . . .. ... . .. . . .. . . . .. 53 

3.2 Small RF Coil (<j) 2.1 mm) and Its Tuning Circuit ... . ... ....... 55 
3.2.1 Design and Constructions ...... .. . ....... .. . .... . ...... . .. . ...... 55 
3.2.2 CalibrationoftheRFCoil . . . . ......... .. . .. ... . ..... . .. . . .. ..... 58 
3.2.3 System Performance .... . .. ... .... . . .. ...... . .. .. . .. ............. . 62 

3.3 Y Gradient Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 
3.3.1 Effects of Ripple on Gradients . . . . . . . . . . . . .. . .. . .. . .. . . . . . . . .. . . 63 
3.3 .2 KEPCO Power Supply and Its Ripple .. .. . . . . . .. . . . . . . . .. . .. . . 63 
3. 3. 3 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 
3. 3. 4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

3.4 Y Gradient Coil . ..... .. .............. . . .... .. ..... . .... ... ... .. . ... . . 70 



IV 

3.4.1 Some Considerations ................................ . ............ 70 
3.4.2 Calculations of the Gradient . . . . . . . . . . . .. . .. . .. . . . . .. . .. . .. . . .. .. 71 
3.4.3 Construction and Performance .. ... .. .. .. .... .. .. .. .. .. .... ... .. 74 

3.5 Software Development for Dynamic Imaging Experiments .... 81 
3.5.1 General Considerations for Dynamic Experiments .. . .. ... . .. 81 
3.5.2 Programs for Disk Read/Write .. . .. . ... .. .... .. ... .... .. .... .. .. 82 
3.5.3 Programs for Searching Peak and Calculating FWHM .. .... 86 
3. 5 .4 Program for Imaging Experiments and Reconstruction . . . . . . 89 
3.5.5 Modifications to TI 980A Programs ............................ 90 
3.5.6 Program for Dynamic Image Analysis .. .. .... .. .... .. .. ...... . 90 

Chapter 4 Static Imaging Experiments ................................... . 95 
4.1 Experimental Considerations for Static Imaging.................. . 95 
4.2 Three-Tube Phantom Image ...... ................................. 98 
4.3 Plant Stem Image . .. .. .. .. ... .. .. ..... .. .... .. .... .. . .. ...... .... .. .. 100 
4.4 Rabbit Trachea Images . . . . .. . .. . .. . .. . . . . .. . .. .. . . . . ... . .. . ... .. ... 102 

4.4.1 Experimental Arrangement .. .. .... .. .... ... .. .... .. . .. ... ... ..... 102 
4.4.2 Results and Discussions .... .. ... .... ... .. .... ...... ...... .. ..... 105 

4.5 T 1 Contrast Imaging .. .. .. . .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 114 

Chapter S Dynamic Imaging Experiments ............................... 117 
5 .1 Experimental Considerations for Dynamic Imaging . . . . . . . . . . . . 117 
5.2 Poiseuille Flow Images . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . .. . .. . . . . 118 

5.2.1 Experimental Arrangement . .... .. ... .... .. .... .. .... .. .... .. ..... 118 
5.2.2 Results and Images ... .... .. .... .. . .. .. .. .. .... .. ...... ......... .. 122 
5.2.3 Discussions and Conclusions ... .. .. .. .... ........ ...... .... ... . 122 

5. 3 Wheat Grain Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 
5. 3 .1 Experimental Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 
5.3.2 Results and Images .. . .... .. . .. .... .. .... ...... .. .... .. .... .. ..... 133 
5. 3. 3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 

Chapter 6 Summary and future work .. .... .. .... ... .. . .. ...... .... .. .... .. 140 

Appendix A Software for Flow and Diffusion Experiments ........ . 141 
A.1 DREAD.ASM .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . ... .. . .. . .. . . .... . .. . . 141 
A.2 DWRITE.ASM ...................................................... 144 
A.3 VD.ASM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 
A.4 Description of NMR.LIB .. .. ... .. .. .. .. . .. . .. ... .... .. .... ...... .. 152 
A.5 FLOW.FOR . . .. . .. . .. . . . . .. . .. . .. . . . . .. . .. . . . . ... . . . .. . .. . .. . .. . .. . . 162 
A.6 TI 980A Software Modifications .. .. . .... .. .... .. .... .. .... ... ... . 168 
A.7 FLOWD.FOR ........ ... .. ....... ... ............................. ... 175 

Appendix B Software for Simulating the Gy Field Gradient Uniformity 
....................................... ... .... .. .......................... . 188 

B.1 Program to Calculate Gy (Z-X Plane) .. .. .. .. .. .... .. . .. .... .. ... 188 
B.2 Program to Calculate Gx (Z-X Plane) .. .. ...... . .. .... .. .... .. ... 190 
B.3 Program to Calculate Gz (Z-X Plane) ... .. ....... ................. 192 

Appendix C Publications 194 

Bibliography . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . .. . . . . .. . . . . . . . . . . . . . .. . .. . . . . .. . . . . .. . .. 195 



Figure 2.1 
Figure 2.2 

Figure 2.3 
Figure 2.4 
Figure 2.5 

Figure 2.6 

Figure 2.7 
Figure 2.8 
Figure 2.9 
Figure 2.10 
Figure 2.11 
Figure 2.12 
Figure 2.13 
Figure 2.14 

Figure 2.15 

Figure 2.16 
Figure 2.17 
Figure 2.18 
Figure 2.19 
Figure 2.20 
Figure 2.21 
Figure 2.22 
Figure 2.23 
Figure 2.24 
Figure 2.25 
Figure 2.26 

Figure 2.27 
Figure 2.28 
Figure 2.29 
Figure 2.30 
Figure 2.31 
Figure 2.32 
Figure 2.33 
Figure 2.34 
Figure 2.35 
Figure 2.36 
Figure 2.37 

Figure 3.1 
Figure 3.2 
Figure 3.3 
Figure 3.4 

Figure 3.5 
Figure 3.6 
Figure 3.7 
Figure 3.8 
Figure 3.9 

V 

List of Figures 

A Spin j = 1/2 System . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
A Semiclassical Description of the Macroscopic Magnetization 
Vector ... ......... ..... ......... ..... .......... ... ............. . ...... . 6 

A Rotating Frame (y > 0) .. . . . . .. . . . .. . . . . . . . . . . . . . . . .. .. . . . . .. . . . . . 7 
Motion of Magnetization in the Laboratory Frame . . . . . . . . . . . . . . 8 
Motion of Magnetization in the Rotating Frame . . . . . . . . . . . . . . . . . 9 

90°1x• - 'C - 180°1y• Pulse Sequence and Spin Echo .. . .. . .. . . . . .. 11 

90°lx• - 'C - 180°lx• Pulse Sequence and Spin Echo . .. . .. . .. . . . . . 12 
Motion of Mx(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 
Motion of My(t) ..... ......... ... ... ... ......... ....... .. . ...... .. ... 14 
Motion ofMz(t) . ...... ....... .. ... . .. . .. . ... .. ............. ... .. . ... . 14 
Time and Frequency Domain Signals in NMR .................. 14 
The Transverse Magnetization Vector in Two Frames ......... . 15 
The Effect of Field Gradient in NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 
Magnetic Field Gradients (along the axes) . . . . .. . .. . .. . .. . . . . . . . . 19 

Transverse Magnetization at Time 2-c as a Function of 
Position due to Selective Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 
Pulse Sequences for Selective Excitation . ... . . . .. . .. . . . . .. . . . . ... 21 
The Larmor Frequency is a Function of the Position . . . . . . . . . . . 22 
The Rotating Frames and the Magnetization . . . . . . . . . . . . . . . . . . . . . 22 
The Transverse Component of M in Two Rotating Frames . . . 23 
Filtered Back Projection Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 26 
Time Domain Signal and k Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 
The Interpolation Process in FBP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 
Data Processing Sequence of FBP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 
Spin Echo and Field Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 
Pulse Gradient Spin Echo Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 
Fluid Velocity and Diffusion Measurement using 
the POSE Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 
Data Processing Sequence for Dynamic Imaging . . . . . . . . . . . . . . . 37 
Convolution in Dynamic Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 
Discrete Time and Frequency Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 
Possible Error of FWHM due to the Software . . . . . . . . . . . . . . . . . . 41 
Experimental Data and its Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 
Decomposition of FT Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 
Simulating the Effect of Ao being Halved . . . . . . . . . . . . . . . . . . . . . . . . 44 
Simulating the Effect of Finite Base Line . . . . . . . . . . . . . . . . . . . . . . . . 45 
Effect of Zero-filling in Dynamic Imaging . . . . . . . . . . . . . . . . . . . . . . . 45 
Simulating the Effect of Zero-filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 
Oscillation due to Data Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 

Block Diagram of an NMR Imaging System . . . . . . . . . . . . . . . . . . . . 48 
Massey NMR Imaging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 
The Coordinates of the NMR Imaging System . . . . . . . . . . . . . . . . . . 50 
Structure of the Probe (without the side pcbs) . . . . . . . . . . . . . . . . . . . 50 

<j> 2.1 mm RF Coil Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 
RF Tank Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 
RF Coils ....... . ... .............. ..... . ................ . .... ....... .. . 57 
System RF Response Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 
Tip Angle as a Function of DAC Level . . .. .. .. .. .. .. .. .. .. .. . . .. . 60 



Figure 3.10 
Figure 3.11 

Figure 3.12 

Figure 3.13 

Figure 3.14 
Figure 3.15 

Figure 3.16 
Figure 3.17 
Figure 3.18 
Fig1,1re 3.19 
Figure 3.20 
Figure 3.21 

Figure 3.22 

Figure 3.23 
Figure 3.24 
Figure 3.25 
Figure 3.26 
Figure 3.27 
Figure 3.28 
Figure 3.29 
Figure 3.30 
Figure 3.31 

Figure 3.32 
Figure 3.33 
Figure 3.34 

Figure 4.1 
Figure 4.2 
Figure 4.3 
Figure 4.4 
Figure 4.5 
Figure 4.6 
Figure 4.7 
Figure 4.8 
Figure 4.9 
Figure 4.10 
Figure 4.11 
Figure 4.12 
Figure 4.13 
Figure 4.14 

Figure 4.15 
Figure 4.16 

Figure 5.1 

VI 

Circuit Diagrams of Duplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 
Simplified Schematic Diagram of KEPCO ATE 75-15M 
Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 
Main Chassis Assembly and Component Locations of 
KEPCO ATE 75-15M Power Supply ............................ 65 
The Internal Layout of the Reconstructed KEPCO 
Power Supply .. .. .. . ... . ..... ........ .. .. ....... .. . . ... . .... .. . . .. .. 66 
The Reconstructed KEPCO Power Supply . . . . . . . . . . . . . . . . . . . . . . 67 
Output Waveforms of the Reconstructed KEPCO 
Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 
Dimension of the Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 
Planar Coil Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 
Magnetic Field Strength .. . . . . . . . . . . . . . . . .. . . . . . . . .. . . . . . . . . . . .. . . . . 72 
Schematic Percentage Variations in Gy Gradient ................ 76 
Percentage Variations in Gy Gradient . . . .. .. . . .. . . . . . . . . .. . . . . .. . 77 
Percentage Variations in Gx Gradient due to Gx 
Orthogonal Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 
Percentage Variations in Gz Gradient due to Gz 
Orthogonal Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 
New Gy Coil and the Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 
Flow Chart for Dynamic Imaging Experiments . . . . . . . . . . . . . . . . . 81 
Floppy Disk Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 
Flow Chart for Disk Reading Program . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 
Flow Chart for Disk Writing Program . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 
Information Position on File Directory . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 
Methods for Searching Peak and Calculating FWHM . . . . . . . . . . 87 
Effect of Finite Base Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 
Flow Chart for the Program Searching Peak and 
Calculating FW1IM ................................................. 88 
Memory Map for Dynamic Imaging Experiments . . . . . . . . . . . . . . . 89 
Memory Map for Dynamic Image Analyses . . . . . . . . . . . . . . . . . . . . . 90 
Flow Chart for the Program Analyzing Dynamic Image Data 
(a) General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 
(b) Menu Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 
(c) Mode Loop and Function Loop(i) .............. ...... ... ..... 93 
(d) Parameter Adjustment Loop and Function Loop(ii) . . . . . . . . 94 

Pulse Sequence for Static Imaging Experiments . . . . . . . . . . . . . . . . 95 
Three-Tube Phantom ............................................... 98 
Microscopic NMR Image of the Three-Tube Phantom . . . . . . . . . 99 
NMR Image of a Plant Stem (Cyperus Eragrostis) ......... .... 101 
Sample Holder Assembly for Rabbit Trachea Experiment . . . . . 103 
Sample Assembly in Rabbit Trachea Experiment . . . . . . . . . . . . . . . 104 
Experimental Set Up for Rabbit Trachea Experiment . . . . . . . . . . . 105 
NMR Spectra in Rabbit Trachea Experiment . . . . . . . . . . . . . . . . . . . . 106 
T 1 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 
T2 Measurement ..................................................... 107 
Interpretations of the Rabbit Trachea Image . . . . . . . . . . . .. . . . . . . . . 110 
Images from the Deflation Sequence of Trachea #2 . . . . . . . . . . . . 111 
Images obtained from Tracheas #5 and #6 . . . ...... ..... .. .. .. .. . 112 
Images from Trachea #8 showing 
the Collapsing Process in Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 
Pulse Sequence for T 1 Contrast Imaging Experiment . . . . . . . . . . 114 
Proton Signals through a Line of T 1 Contrast Images . . . . . . . . . . 116 

Pulse Sequence for the Poiseuille Flow Imaging . . . . . . . . . . . . . . . 118 



Figure 5.2 
Figure 5.3 
Figure 5.4 
Figure 5.5 
Figure 5.6 
Figure 5.7 
Figure 5.8 
Figure 5.9 
Figure 5.10 
Figure 5.11 
Figure 5.12 

Figure 5.13 
Figure 5.14 
Figure 5.15 
Figure 5.16 
Figure 5.17 
Figure 5.18 

Figure A.I 

V 11 

Sample System for Poiseuille Flow Experiment . . . . . . . . . . . . . . . . 119 
Fluid Flow in a Pipe .... . . .. ... .. ..... .. .... . ...... . .. . .... . ... . .... 120 
Calibration of the Poiseuille Flow System . . . . . . . . . . .. . ... . .. . . . . 121 
Data Images of the Poiseuille Flow Experiment . . . . . . . .. . . . . . . . . 123 
Velocity and Diffusion Images of Poiseuille Flow . . . . . . . . . . . . . . 124 
Stacked Plots of the Poiseuille Flow Image . . . . . . . . . . . . . . . . . . . . . 125 
Velocity Profiles of the Poiseuille Distribution . . . . . . . . . . . . . . . . . . 126 
Noise Effect in Diffusion Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 
Schematic Diagram of a Wheat Ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 
Experimental Preparation for Wheat Grain Imaging .. . . ... ..... 131 
Experimental Arrangement for the Wheat Grain Imaging . . . . . . 132 
a) A Wheat Grain Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 
b) Sample and NMR Imaging System .................. . .. . ... ... 132 
Transection of a Wheat Grain .. ....... ........... .. . .. ..... ....... 133 
Pulse Sequence for the Wheat Grain Imaging . . . . . . . . . . . . . . . . . . . 134 
Velocity and Diffusion Maps of a Wheat Grain ... . .. ..... ... .. . 135 
Central Regions of the Wheat Grain Velocity Images .. ..... .. . 136 
Central Regions of the Wheat Grain Diffusion Images . . . . . . . . . 137 
Stacked Plots of the Wheat Grain Images .. .... .............. . .. . 138 

Flow Chart for the TI 980A Modifications 168 



Table 3.1 
Table 3.2 
Table 3.3 
Table 3.4 
Table 3.5 
Table 3.6 
Table 3.7 
Table 3.8 

Table 4.1 
Table 4.2 

Table 5.1 
Table 5.2 

Vlll 

List of Tables 

Characteristics of RF Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 
RF Pulse Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 
System Performance . .. . .. . .. . . . . .. . .. . .. . . . . .. . .. . .. . . . . .. . .. ... . .. . . 62 
The Ripple Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 
Comparison of the Ripple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 
Performance of the Gradient Power Supplies . . . . . . . . . . . . . . . . . . . . . . 68 
Calculations of the Unit Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 
Characteristics of the Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 

Imaging Parameters for Static Imaging Experiments . . . . . . . . . . . . . . 97 
Relaxation Times of Rabbit Trachea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 

Imaging Parameters for Dynamic Imaging Experiments . . . . . . . . . . 117 
Velocity Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 127 



a 

amj 
A 
A 
A 
Beff 
B 
Bo 
Bo 
B1 
B 1 (t) 
D 
D 
De 
E(mj) 
f 
F 
F{ } 
Fs{ } 
Fe{ } 
g 
g 
gm 
G 
G 
h(t) 
Hr 
HR 
H(f) 
:J{ 

:J{1(t) 

1 

I 
Im[ ] 
J 
J 
k 
k 
kB 
K 
1 
L 
mj 
M 
Mo 
Mj_ 
n 
nD 
n1 

IX 

List of Symbols 

RF coil radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 
Complex admixture amplitudes of a spin system . . . . . . . . . . . . . . . . . . . . . . 3 
An operator representing an observable quantity . . . . . . . . . . . . . . . . . . . . . . . 5 
Signal amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 
Cross sectional area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 
Effective field in the rotating frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 
Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 
Amplitude of the main magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
Main magnetic field, directed along the z axis . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
Amplitude of the transverse rf field B1(t) . ...... ..... ............. .... 7 
RF field (in the transverse plane) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 
Self-diffusion coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 
Self-diffusion tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 
Extra broadening due to velocity spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 
Energy eigenvalues of a spin system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
Spectrometer frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 
Noise figure of the spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
Fourier transform of the function in { } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 
sin transform of the function in { } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 
cos transform of the function in { } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 
Amplitude of PGSE gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 
PGSE gradient in dynamic imaging . . .. . . . . .. . . . . . . . .. . .. . .. . .. . .. . .. . .. 32 
Maximum gradient employed in dynamic imaging . . . . . . . . . . . . . . . . . . . . . 40 
Amplitude of field gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 
Field gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 
Fourier transform of frequency domain function H(f) . . . . . . . . . . . . . . . . 38 
Imaginary part of the discrete function H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 
Real part of the discrete function H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 
Fourier transform of time domain function h(t) . . . . . . . . . . . . . . . . . . . . . . . . 38 
Hamiltonian operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
Perturbation tem1 in Hamiltonian operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

(-1) 1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
Function selected in dynamic imaging analysis program . . . . . . . . . . . . . . 91 
Imaginary part of a complex function in [ ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 
Spin quantum number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
Spin angular momentum operator ......................... ............. . . 3 
Frequency domain (digital) variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 
Static reciprocal space vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 
Boltzmann constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 
Numerical factor in the calculation of SIN . . . . . . . . . . . .. . . . . .. . . . . .. . .. . . 16 
Length of the pipe in Poiseuille sample system . . . . . . . . . . . . . . . . . . . . . . . . 119 
Length of the conductor . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
Azimuthal quantum numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
Macroscopic magnetization vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 
Magnitude of Min the equilibrium state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 
Transverse component of M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 
Time domain (digital) variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 
Maximum number of data images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 
A constant in the 'tube law' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 



X 

N Number of spins per unit volume ...................................... .. 5 
N Total number of digits in time domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 
Nh Numberofhydrogennucleiperunitvolume ........................... 16 
NP Number of projections . . .. . . . .. . . .. . . . . . . .. . . .. . . .. . . .. . . .. . . . . . . ... . ... . . 29 
Nace Number of accumulations per projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 
p Perimeter of the conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
P Transmural pressure difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 
P1 Constant asymptotic pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 109 
P s Self-correlation function of the nuclear spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 

P* Filtered profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 
Q Quality factor of the coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
Q Volume amount of fluid ................................................... 120 
q Dyt:~mic reciprocal space vector . . . . .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. . . .. 34 
r Pos1t1on vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 
R Attenuation factor . . .. . . . . . . .. . . .. . .. . . .. . . . . . . .. . . . . . . .. . . .. . . . . . . .. . .. . . .. 33 
R Radius of the pipe in dynamic imaging experiment . . . . . . . . . . . . . . . . . .. . 120 
Re[ ] Real part of a complex function in [ ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 
S Fluid displacement vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 33 
S(t) FID signal . .. .. .. . .. . . .. . . .. . .. . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . .. . . .. 24 
S* Complex conjugate of S ... ... . .... ... . ... . ... . . ... ... .. ....... ... ..... ... 25 
tp Duration of the pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 
trep Repetition time of in experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 
T Absolute temperature of a spin system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 
T Time domain sampling interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 
T Sampling time in imaging experiments ................................. . 96 
Tc Probe temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 
Ts Sample temperature . . ...... ... . .... ... ... . . .. .. ... ... ... . . .. .. ... . ... ...... 16 
T 1 Spin-lattice relaxation time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 
T2 Spin-spin relaxation time . . .. . . .. . . .. . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . 10 

T 2 * Transverse relaxation time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 
Tr( ) Trace of the operator in ( ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
Uit) Evolution operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

Rotation operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
Velocity of fluid flow ..................................................... 33 
Volume of the coil ... ........ ... . ... . ....... ... . . .... ... . ... . ..... ... .. . ... 16 
Sample volume ............................................................ . 16 
Weight of the fluid . . .. . . .. . . . . . . .. . . .. . . .. . .. . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . 120 

ex. A variable in discrete Fourier transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 

y Gyromagnetic ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

o Duration of the PGSE pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 

11 Fraction of the coil volume occupied by the sample . . . . . . . . . . . . . . . . . . . 16 

11 Dynamic viscosity of the fluid . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .. . 120 

0 Rotation angle of the magnetization vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

A Wave length .. . .. .. ...... .. . . .. . .... .. . . .. ... . . .. . . .. . . .. . .. . . .. . . .. ..... .. . 61 

µO Permeability of free space . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 16 

µ Magnetic moment vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

v Kinematic viscosity of the fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 

~ Complex FID signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 



p 

p 

PI 

PR 
PT 
p(r) 
(J 

<J(n) 

'C 

(I) 

(I) 0 

C01 

COeff 

13. 

<l> 
lj mj> 

I\Jf> 

<A> 

la -12 
ffiJ 

Af 
Ah 
AV 
6X 

AZ 
AE 
AP 
A<j> 

v7Bo 
VP 

h 

Xl 

Density operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

Density of the fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 
Imaginary part of nuclear spin density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 

Real part of nuclear spin density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 

Resistivity of the conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

Nuclear spin density . .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . 24 

RF coil proximity factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

Noise function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 

Short time interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

Larmor precession frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

Larmor precession frequency due to Bo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

Larmor precession frequency due to B 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

Precession frequency in the rotating frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

Separation of the PGSE pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 

Projection angle in imaging experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 
Basis eigenket set of a spin system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

General quantum state of a spin j system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

Ensemble average of the observable quantity A . . . . . . . . . . . . . . . . . . . . . . . . 4 

Normalized population in the eigenstate lj mj> . . . . . . . . . . . . . . . . . . . . . . . . . 5 

Bandwidth of the receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. . . .. . 16 
Height difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 
Velocity spread between the adjacent pixels . . . . . .. . . . . . . . . . . . .. . . . . . . . . 47 
Transverse resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 
Slice thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 
Energy difference between the two adjacent states . . . . . . . . . . . . . . . . .. . . 7 
Pressure difference along the length of the pipe . . . . . . . . . . . . . . . . . . . . . . . 119 
Step angle in imaging experiment ....................................... . 25 

Magnetic field gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

Pressure gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 

Planck's constant divided by 2rc ···································· 3 



1 

Chapter 1 Introduction 

1. 1 Introduction 

Nuclear Magnetic Resonance (NMR) Imaging is a non-invasive technique which gives 
the spatial distribution of the NMR signal intensity or other NMR parameters in a 
heterogeneous sample. The firs t experimental demonstration of the feasibility of 
macroscopic NMR imaging was given by Lauterbur in 1972 (1,2). 

In conventional NMR it is usual to place the sample, which is homogeneous and small, 
in a very uniform magnetic field, so that the resonant frequency depends upon the 
external field modified slightly by the local environment. NMR spectra obtained in this 
way yield details of the local molecular environment. 

By contrast, NMR Imaging concerns a sample which is heterogeneous, and usually not 
small. Furthermore, the sample is placed in a deliberately non-uniform magnetic field, 
which enables the hetero-structure of the sample to be derived and displayed. 

Many different techniques have been described for NMR Imaging(3,4,5). Among these 
the Projection Reconstruction technique, originally from X-ray Tomography, is the 
most sensitive one(6)_ 

The proton (1 H) is the most commonly used nucleus when doing imaging experiments, 
Hydrogen being the most abundant element in the living systems. lH is isotopically 
almost 100% abundant, and has the highest magnetic moment among stable nuclei, thus 
yielding optimum sensitivity. l9p and 3lp nuclei are next in sensitivity and have some 
practical interest. Other nuclei are, in practice, difficult to image. 

Traditionally NMR imaging reveals some stationary distribution functions of a nuclear 
spin system, for example, the spin density distribution. Such imaging is termed 
'static' NMR imaging in this thesis. 

By incorporating the Pulse-Gradient-Spin-Echo (PGSE) technique, the NMR imaging 
can describe time-dependent functions . This technique is termed 'dynamic' NMR 
imaging. Simultaneous imaging of flow and diffusion at the microscopic level can be 
performed using this new technique, which has been demonstrated by some imaging 
experiments in this work. 



2 

1.2 Organisation of the Thesis 

This thesis is divided into 6 chapters. 

Chapter 2 provides a description of NMR and NMR imaging. One of the most 
commonly used imaging techniques, Filtered Back Projection (FBP), is 
described in detail. The theory of dynamic imaging is discussed extensively in this 
chapter. · 

In Chapter 3 a brief description of an existing static NMR microscopic imaging system 
is given first, followed by some developments and modifications to this system which 
form part of the present work. These have improved this system and enabled the 
performance of the flow and diffusion imaging experiments. 

The static imaging experimental results are presented in Chapter 4, while the dynamic 
results are in Chapter 5. 

A brief summary and some comments about possible future work are given in Chapter 
6. 

Appendix A gives the complete software listings for the flow and diffusion imaging 
experiments. Appendix B gives the software listings for the simulating the uniformity 
of Gy field gradient.