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The role of magnetic field gradients in nuclear magnetic resonance Luck, Stanley David 1986

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THE  ROLE OF MAGNETIC F I E L D GRADIENTS IN NUCLEAR MAGNETIC RESONANCE  by STANLEY DAVID LUCK  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE  FACULTY OF GRADUATE STUDIES Department  We a c c e p t to  THE  this  of  Chemistry  thesis  the r e q u i r e d  as  conforming  standard  UNIVERSITY OF BRITISH COLUMBIA November  ©  17, 1986  Stanley David  Luck,  1986  In  presenting  requirements  this for  an  B r i t i s h  Columbia,  freely  available  that  permission  scholarly  I  agree for  understood  that gain  his copying  shall  the  reference  may  by  p a r t i a l  degree  that  extensive  purposes or  in  advanced  for  Department  financial  thesis  not  be or  be  and  of  Date:  November  17,  1986  study.  I  this  granted  by  the  allowed  Columbia  of  further  Head  of It  thesis my  of it  agree  thesis  this  without  the  make  representatives.  publication  of  University  s h a l l  of  Chemistry  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook Place Vancouver, Canada V 6 T 1W5  The  copying  permission.  Department  the  Library  her or  at  fulfilment  for my is for  written  ABSTRACT A c o i l s  high (31  c o i l  and  and  for  c o i l s  by  the  induced  these  f i e l d echo  at  c o e f f i c i e n t  of  gradient  each  in  a c r y l o n i t r i l e and  t r i p l e  gradient In l i v i n g  spin  of  characterize  forearm.  water  signal  to  Comparison two  pulse part  were  that  echo  was  relatively that of  different  of  the echo  of  from  for  experiments  and  Tanner,  the  magnetic  measurements  the  known  gradients linewidths  diffusion  of  at  short  diffusion the  The  diffusion  c o e f f i c i e n t  the  using  a  decay  of  modified  of  surface  the  the  Stejskal  set  determine  effective  single,  pulsed  of double  f i e l d  sequence. of  this  of  thesis,  The  water  spectra  long  f i r s t  spin  attributed  and  d i f f u s i v i t y  of  suggest  i i  examples  involved  human  in-vivo,  extracellular  water water, that  (20-30 from  the  to in  forearm  relaxation  of  the  measurements  l i p i d ,  from to  three  echo  spin-spin  i n t r a c e l l u l a r  times  larger  to  gradient  motion  Spin  with  from  studied.  pulsed  the  human  compared  echoes  second  application  of  measured  echo  systems  used  In  gradient  translational  constructed  variation  experiments was  a  magnitudes  of  with  of  and  determined  slow  experiment.  quantum  the  because  water  was  The  interfered  these  was  method  and  modified  imaging,  spectra.  gradient  sample For  were  was  measurement  diameter)  gradient  currents  the  times.  cm  c o i l s  of  pulsed  eddy  the  measurements.  lineshapes  using  for  microscopic  (15  diffusion  produced  NMR p r o b e  mm d i a m e t e r )  d i f f u s i o n gradient  resolution  gave  water time  (0.8  s)  ms).  experiments  major  a  part  of  at the  motion  of  randomized The  bulk  the  aqueous  upward  diffusion briefly showed The  the  two  spin  cone  features  the  smallest  than  caps  molecular the  that  upon  the  the  chemical  colf  of  med'i t erranea as  well  the  estimated was  D  0.  by  be  feature  i i i  with  caps  T  of  these  structure  0.1 in  1  T  #  obtained  comparison to  the head  of  obtained  was  A l l  radial  found  distinguishable  2  of  mature  as  2  in  pupae  Proton  orientation,  were  D G—contrasting caps  axi ana.  of  pupae.  images  sequence  in  distribution  the  shift  d i r e c t i o n ,  v e r t i c a l  of  dimensional  the  d i f f u s i o n .  d i s t r i b u t i o n ,  Barbara  downward,  and  directionally  involved  moth  resembling was  to  anteroposterior  showed  echo  submerging  of  the  contrasting.  resolution  views  or  due  proton  Acetabularia  alga  normal  the  depended  F i n a l l y , marine  rather  along  maps  fluid  pointing  the  of  Douglas-fir  distribution  was  application  mapping  one-dimension, of  flow  second  resolved  in-vivo,  water,  with mm,  the  the  using 2  and by  images of  the  caps.  microscopic  determined  image.  as  Table I.  II.  of  Contents  INTRODUCTION 1 .  OVERVIEW  2.  HISTORICAL  SURVEY:  DIFFUSION  3.  HISTORICAL  SURVEY:  IMAGING  10  4.  ORGANIZATION  THESIS  13  MAGNETIC A.  OF  OF  THE  GRADIENTS  NUCLEAR  1 .  GENERAL  2.  LINESHAPE: SHAPE  IN  AND  FLOW  8  NMR  MAGNETIC  14  RESONANCE  17 17  RELATION  TO  GRADIENT  AND  SAMPLE 30  3.  TWO-DIMENSIONAL  4.  IMAGE  5.  SPATIAL  6.  SPIN ECHO: PULSED-FIELD FOR D I F F U S I O N  8.  NMR  IMAGING  38  CONTRAST  45  RESOLUTION  IN  NMR  MEASUREMENT OF SPIN ECHOES  DIFFUSION  SPIN  EFFECT  ECHO:  THE  IMAGING  GRADIENT  48 TECHNIQUE 51  BY  MULTIPLE  QUANTUM 59  OF  RANDOMIZED  FLOW  EXPERIMENTAL 1.  2.  3. C.  . .1  FIELD  THEORY  7.  B.  1  64  APPARATUS FOR D I F F U S I O N MICROSCOPIC IMAGING APPARATUS S P I N ECHO  MEASUREMENT  NMR  AND 64  FOR S U R F A C E C O I L , MEASUREMENTS  PARAMETERS FOR  RESULTS  62  PULSED  GRADIENT  EXPERIMENTS  76 79  AND  DISCUSSION  81  1.  GRADIENT  MAGNITUDES  81  2.  EFFECT  OF  RECEIVER  3.  EFFECT  OF  RADIOFREQUENCY  4.  STATIC  GRADIENT  DEAD  TIME  DIFFUSION  iv  85  INHOMOGENEITY  88  MEASUREMENT  92  5.  PULSED  6.  DIFFUSION  7.  IMAGING WATER  III.  DIFFUSION  AND  DIFFUSION  MEASUREMENTS  ACRYLONITRILE  GLASS  BY  CAPILLARIES  MQ  ECHOES  B.  DIFFUSION  IN  ACETONE  104  110 115 115  LIQUIDS  1.  EXPERIMENTAL  2.  RESULTS  IN-VIVO  95  CONTAINING  MEASUREMENT  INTRODUCTION  AND  PROTON  116 118  DISCUSSION SPECTROSCOPY  118 OF  HUMAN  FOREARM  ..123  1.  INTRODUCTION  1 23  2.  EXPERIMENTAL  131  3.  RESULTS  NMR  AND  DISCUSSION  131  IMAGING  143  A.  INTRODUCTION  B.  Barbara  C.  OF  OF  A.  C.  IV.  GRADIENT  143  colfaxi  144  ana  1 .  INTRODUCTION  144  2.  EXPERIMENTAL  145  3.  RESULTS  AND  Acetabularia  DISCUSSION  146  156  mediterranea  1.  INTRODUCTION  156  2.  EXPERIMENTAL  158  3.  RESULTS  AND  DISCUSSION  159  CONCLUSIONS SUGGESTIONS 1.  2.  168 FOR  FUTURE  WORK  I N - V I V O PULSED MEASUREMENTS  169 GRADIENT  SPIN  ECHO 169  IMAGING  170  v  GLOSSARY  OF  BIBLIOGRAPHY  TERMS  LIST Table  2.1  Magnitudes y  Table  2.2  and  z  of  Magnitudes  of  gradients  produced  by  x,  Diffusion single,  72 gradients  analysis,  c a l i b r a t i o n 2.3  the  TABLES  c o i l s .  lineshape  Table  OF  by  determined  linewidths  d i f f u s i o n  c o e f f i c i e n t  double  and  of  by  and  measurement.  84  a c r y l o n i t r i l e  t r i p l e  quantum  from  spin  echoes. Table  3.1  109  Diffusion anomers  c o e f f i c i e n t s  of  D-glucose  Table  3.2  Cross-sectional  Table  3.3  Chemical spin-spin 1ipid  Table  3.4  /n-vi  Normal  s h i f t s ,  of  and  areas  of  the  and  120  blood  130  times  vessels.  c o e f f i c i e n t s for  water  and  and 136  vo.  tissue  0  methylglycoside.  d i f f u s i o n  relaxation  a  water  humans.  content  in  adult 140  vii  LIST F i g .  2.1  The  projected  c y l i n d r i c a l Fig.  2.2  General  OF  spin  FIGURES  d i s t r i b u t i o n  for  a  object.  scheme  35  for  a  two  dimensional  NMR  experiment. F i g .  2.3  Timing  diagram  imaging Fig.  2.4  The  F i g .  2.5  Pulse  39 for  a  two  dimensional  NMR  experiment.  effect  of  a  sequence  chemical  shift  41  180° p u l s e . for  the  42  one-dimensional,  resolved  mapping  of  spin  d i s t r i b u t i o n . F i g .  2.6  The  F i g .  2.7  Pulse  inversion-recovery sequence  diffusion F i g .  2.8  45  Pulse  for  2.9  The  sequence  pulse  selective  the  sequence.  pulsed  f i e l d  47  gradient  experiment. for  two-dimensional F i g .  pulse  55  d i f f u s i o n  contrasted  imaging.  sequence  for  detection  58  the  of  preparation  multiple  and  quantum  spin  echoes. F i g .  2.10  Position point  F i g .  2.11  for  current  element  dl  and  P.  the  Golay 2.12  vectors  67  Cross-sectional and  Fig.  61  view  of  configurations  the of  sample  the  chamber  Maxwell  and  c o i l s .  69  Circuit  diagrams  f i l t e r s  and  control  unit.  for  the  schematic  high  diagram  frequency of  the  gradient 73  viii  Fig.  2.13  Graph DAC  of  amplifier  Cross-sectional  Fig.  2.15  Spectra  and  position  f i e l d Spin  for  Fig.  2.17  Normal  50 2.18  of  us  2.21  pulse  vs  the  in  a  pulsed 82  in  the  presence  of  of  rf  measured  Spin  echo  the  2.22  Pulsed  Fig.  2.23  Decay  using f i e l d of  the  diffusion NMR  dwell  echo  times  across  the  of  distribution  maps the  90 of  saddle-shaped 91  spectra 151  the  for  mTm"  1  NMR  gradient echo  experiment  in  with  echo a  of  the  93 of  method.  94  spectra.  96  pulsed  the  with  coefficient  gradient spin  tube  applied.  diffusion  static  spin  sample.  c o i l .  and  of  the  the  high  gradient resolution  probe.  Decay  of  dimensional  f i e l d  75  the  one  of  gradient  Determination  with  spin  d i s t r i b u t i o n  from  of  and  88  for  the  f i e l d  spectra  us.  100  One-dimensional  Fig.  2.24  and  78  86  sequence  water  Fig.  c o i l .  frequency  echo  acquired  spectra  gradients Fig.  surface  c o i l s  spin  transmitter-receiver 2.20  the  Larmor  shim  signal  and  Pulse  the  Fig.  of  experiment.  radiofrequency 2.19  of  of  the  gradient  mapping  Fig.  function  y-gradient.  gradient  Fig.  the  gradient echo  view  graphs  attenuation  a  a  75  2.14  2.16  as  input.  Fig.  Fig.  output  97 spin  echo  IX  in  a  pulsed  gradient  diffusion  experiment  with  the  surface  c o i l  apparatus. Fig.  2.25  Spin  echo  99 FID  diffusion  signals  experiment  from  a  using  pulsed  the  gradient  surface  c o i l  apparatus. Fig.  2.26  Decay  of  101  the  experiments for F i g .  2.27  the  Graphs of  a  2.28  The  of  the  the Fig.  2.29  2.30  2.31  2.32  and  2.33  Fig.  3.1  gradient  c o i l  apparatus 102  the  for  the  ethanol,  d i f f u s i o n 4:1  (v/v),  apparatus.  amplitude  quantum  104  of  spin  the  echoes  single, with  time.  decay  of  and  106 the  spin  t r i p l e  echoes  quantum  for  coherences  a c r y l o n i t r i l e .  Schematic an  AMX  spin  and  Pulsed  images  in  plot 1.0  energy  levels 108  of  glass  c a p i l l a r y  water.  contianing  gradient  D-glucose  the  111  two-dimensional  acetone  Stacked  showing  system.  containing  Normal  107  diagram  Two-dimensional  and  and  c o i l  t r i p l e  double  surface  water  in  single,  pulsed  amplitude  surface  c a p i l l a r i e s Fig.  of  preparation  tubes Fig.  the  in  gradients.  signal  and  for Fig.  z  Spectra  of Fig.  and  variation  double  echo  using  mixture  using Fig.  x  spin  images  water  diffusion  and  of acetone.  spectra  for  113  water  c a p i l l a r i e s .  of M  pulsed in  gradient  water.  114 spectra  for 119  Fig.  3.2  Stacked  plot  of  Dextran-T10, Fig.  3.3  The  4.3  variation  glucose  pulsed %(w/v)  of  with  gradient  the  in  D  2  spectra  0 .  diffusion  concentration  for 122  c o e f f i c i e n t  in  of  aqueous  solution. Fig.  3.4  Cross-sectional the  3.5  In-vivo  Fig.  3.6  Hahn  Fig.  3.8  through  the  middle  of 126  proton  echo  spectra 3.7  view  forearm.  Fig.  Fig.  123  spectra  and pulsed  of  Decay  of  l i p i d  from  Decay  of  l i p i d  from  human  the  human  gradient  forearm.  spin  132  echo  forearm.  proton  Hahn  proton  in-vivo  134  signals  in-vivo,  the  of  echo  signals pulsed  for  water  and  spectra.  for  water  gradient  135 and  spin  echo  spectra. Fig.  4.1  Normal  138  proton  spectra  of  Barbara  colfaxi  ana  pupae. Fig.  4.2  Proton  147 spectra  function  Fig.  4.3  of  and graphs  recovery  signals  from  Barbara  colfaxiana.  Proton  signals  of  peak  for  and  spectra  as  a  l i p i d of  148 and graphs  echo  from  height  water  inversion-recovery  spectra  function  time  of  time  Hahn  echo  for  of  peak  water  spectra  height  and of  as  a  l i p i d Barbara  149  colfaxiana. Fig.  4.4  Normal  proton  spectrum  Fig.  4.5  Proton  d i s t r i b u t i o n  of  maps  xi  haemolymph. for  a  live,  151 Barbara  colfaxiana Fig.  4.6  Proton  pupa.  152  distribution  colfaxiana  pupa  removal  from  a  maps  several  spectra  of  Barbara  Fig.  4.8  Proton  spectra  of  mature  Fig.  4.10 A  a  pupae.  Acetabularia  echo  spectra  mediterranea and a  for  caps.  mediterranea  cap.  Fig.  Fig.  163  4 . 1 1 Images caps 4.12 A  of mature  with  T,  4.13 A  Acetabularia  and T  normal  mediterranea image  mediterranea  of  mediterranea  contrast.  2  diffusion-contrasted  Acetabularia Fig.  161  deuterium-contrasted  Acetabularia  mature  155  160  Acetabularia  of  colfaxiana  and Hahn  photomicrograph  image  after  caps.  Inversion-recovery mature  after  154  Proton  4.9  Barbara  cone.  4.7  Fig.  a  weeks  Fig.  mediterranea  for  an  cap.  image  164 of  an  cap.  165  Acetabularia 166  xii  ACKNOWLEDGEMENTS It  is  a  stimulating are  given  e f f o r t s Robert  to  thesis for  their  in  Talagala  works,  and  shared  in  special  the  in  with  many  not  to  have  his  instruction numerous  to  of  and  sorrows  my  wife,  preparing  the  how  other of  Ada,  this  I  the  thesis.  xiii  NMR  to for  and  wish of  to  Dr. his  Cedric  thank  imaging  imaging  members  her  and  and  samples,  graduate  for  thanks  these  art  b i o l o g i c a l  about  a l l  in  and  Matter  which  possible.  ideas  f r u i t i o n ,  Emil  without  been  whose to  and  Special  discussions  Markus,  work  discussions  joys  come  interesting  H a l l .  without  have  Tom  many  Laurie  interesting  and  not  Dr.  Harrison  would  running  f i n a l l y  thanks  assistance  for  for  acknowledge  beautiful  would  Rajanayagam  assistance S.  Lionel  comments,  experiments V.  Dr.  Snider  for  to  discussions  this  c r i t i c a l Neale  pleasure  of  the  school.  invaluable  really lab  who  F i n a l l y ,  I.  1.  OVERVIEW In  the  resonance  developing  (NMR)  applications  (rf)  excitation  (1-4). the  The  gradients the  are  are  echoes.  and  of  In  of  NMR  convenient  means  associated  with  translational  for the  the  diffusion  and  transform  NMR  c o i l s  diffusion of  a  used  in  a  of  and  magnets  a  wide  to  for  set  measurements. compared  part  of  high  mm d i a m e t e r )  larger  the  bulk  in  the  flow  the  in  location  gradients kinds  they  is  f i e l d  spatial  various  spins  roles  excitation  pulsed  of  key  of  offer  time  and  rf  spin a  dependence  including  (5-9),  and  for  multidimensional  Fourier  thesis  the  (10).  f i r s t  (31  of  play  magnetic  because  observation  motion  phase-encoding  modification  produce  important  s o - c a l l e d  The  whereas  which  radiofrequency  gradients  characterize  to  magnetic  spectroscopy  biology,  NMR m e t h o d s ,  are  nuclear  radiofrequency  signals  combined  echoes  and f i e l d  the  to  for  l o c a l i z e d  magnetic  pulsed  often  Spin  and  medicine  applied  spins.  pulses  in  importance  generation  technologies  imaging  have  of  INTRODUCTION  resolution for  the  microscopic  of  gradient  bore  magnet  The  those  allows  this  the  smaller b u i l t  probe  imaging,  for  (15  and  of  the of  1  with of  gradient  translational  the  construction  cm d i a m e t e r )  surface  size  generation  NMR  measurement  c o i l s  into  describes  these  c o i l  larger  be  diffusion  gradient  respective  to  c o i l s  superconducting  gradients  with  2  shorter by  rise  these  times.  c o i l s  lineshapes obtained  were  of  with  the  values  absolute 2.23  x  10"  gradient  2  at  1  with  tracer The  diffusion  involves  gradient  the  for  inhomogeneously  on  multicomponent  the  gradient  pulsed  which  gradient  intervals spectra,  different static subject sample passing  gradient to  are  the  the  compared through  of  the  method,  to the  the  give  a  is  2.19  a  From an  water, static  in x  good  10"  determining  such  m s"  9  2  1  as  would  is  the  the  at  gradient  of  then  in  of  and  be  l i p i d . and  (12),  in  timed  to  Unlike method  magnetic  switching By  Consequently,  c o e f f i c i e n t s  gradient  c o i l s .  in  resolution  sample.  the  rise  measurements  Tanner  high  f i e l d  gives  found  possible  the  pulsed  for  magnetic  specially  diffusion  response time  and  Stejskal  applied  It  a  diffusion  prohibiting  water  of  of  experiment  l i n e s ,  components  slower  of  to  of  in  value  for  measurement  determine  chemical  obtained  the  spectra  apparatus,  coefficient  application  method  implemented.  simultaneously  resolution  This  containing  pulses  allowing was  the  systems  systems  spin  value  broadened  b i o l o g i c a l  NMR  d i s t r i b u t i o n .  method  duration  to  are  and  (11).  gradient  c o e f f i c i e n t s  linewidths  the  was  literature  produced  applied  high  °C,  the  gradients  gradient  diffusion  23  the  These  experiment.  the  static  of  the  the  diffusion  agreement from  using  for  m s"  9  appropriate  of  from  spectra.  projection  and  value  magnitudes  determined  gradient  one-dimensional these  The  of  making  f i e l d  the  of  the  the is at  the  current  measurements  3  for  increasing  gradient  pulses,  means  for  f i e l d  at  spin  sample.  f i e l d  the  magnet,  was  large  the  It  delays  the  after  measurements technique.  could  c o e f f i c i e n t s dilution)  and  6.24  1  literature 6.3  x  10"  to  from  the  s "  1  a  2  s  _  to  the  of  the  applied  For  the  the  spin  accuracy  and  10"  pulsed  the  1  in  with  the  be  0  long  diffusion  pulsed  the 1  or  s u f f i c i e n t l y  gradient the  pulsed  diffusion  m s" 2  4.3  (at  1  % W/V  agreement  (117,118)  0  the  infinite  in  D 0), 2  with  the  and  gradient  diffusion  single,  higher  double  order  spin  echo  coefficient and  triple  coherences  are  of  method  was  a c r y l o n i t r i l e  quantum more  echoes.  sensitive  gradient.  surface  eddy  gradient  x  were  of  respectively.  (102)  1  MW 9 0 0 0 ,  these  6.75  modified  decay  expected  and  may  apparatus,  determine  (T-10,  magnetic  supplies,  the  10~  simple  superconducting  accurate  x  a  response  magnet  resolution  of  interactions  the  using  6.70  the  slow  using  pulses,  to  of  but  the  by  obtained  provided  power  of  that  high  of  the  from  bore  used  ,  determine  As  c o i l s ,  m  1  Also, used  2  of  their  D-glucose,  values 1  and  dextran m  1  the was  of  f i e l d  found  application  times  investigated  the  be  the  measurements  cause  gradient  Using  10"  in  after  s e t t l i n g  The  c o i l s  was  method  the  not  metal  responsible.  x  echo  static  shim  surrounding  gradient  intervals  determining the  magnetic either  time  c o i l  current  echo  apparatus  effects  measurements  precision.  Using  with  were could  echo  more be  times  the  larger  severe  and  performed of  220  gradient  ms,  pulsed  with  less  4  diffusion ethanol values  c o e f f i c i e n t s  gave  values  determined  In  imaging  for- a  which  using  the formation  been  previously  and  Wade  diffusion  it  NMR i s  effects  considerable  of  from  The  question  therefore:  on  a  clear  when  examples  work,  each  water  studying  by  echo  a model  that  serves  which  to  has  Hrovat times  system  as of  accurate  from  diffusion  of  of  one  l i v i n g  chemical  forearm. solution  between  f i e l d  bulk  known  i s  distribution can  behaviour  the second  quite  chemical part  of  gradient  systems. this  work  NMR a t  see? systems kind  kinds  l i p i d s ,  there  systems  inanimate  different  different  and of  separation  does  a  Such  physicochemical  with  of  (1-4),  without  the spatial  in-vivo.  one looks  t h e human  simple  in  in  with  and giving  of  with  technique  systems  addressed  what  Three  region  gradient  be o b t a i n e d  the properties  systems,  of  Using  the  apparatus.  measurements  non-invasive  substances  complexities  basic  10 % o f  strategy  experiments  on b i o l o g i c a l  different  both  a  interest  movements  method  diffusion  a  and  experiments.  Because  this  the echo;  could  water  only  imaging  was d e m o n s t r a t e d  c o e f f i c i e n t s  contrasting  l i v i n g  for  the  be performed.  and acetone  is  of  of  resolution  7 ms c o u l d  water  exhibit  the high  imaging  as  and  within  (13). T h u s  short  serious  agreed  experiments,  s t a b i l i z e used  4:1 mixture  of  h a s been If  such  have of  of  f i e l d  studied  studied  in  Motion, a  measurements expect  in  gradient  information.  one would flow  been  to  the solution  small were  made  achieve and  a  5 molecular kinds  of  random paths  liquids  on  blood back in  the  are  compared  to  small  which  somewhat  streaming.  is  in  Does  processes  that  there  very  l i p i d .  forearm aqueous  for  attributed  Consequently,  measured L i p i d s ,  for on  expected  water  the  from  experiment,  protons  other  hand,  molecular  and  it  is  is  had  the  for  flow  direction  mainly  water  probably  in  what  Under  spectra  of  showed  flow. than  time-scale of  the  direction  blood  faster  type  the  i n t r a c e l l u l a r  randomized  the  was  because  and  times  answer  l i p i d s  decayed  resulting  100  the  measurements,  most  clear  and  cytoplasmic  d i f f u s i o n .  of  diffusion  not  poolings  here,  flow  move  small are  measure  diffusion  water  bulk  NMR  nor  true  extracellular the  scale  the  and  flow  diffusion?  from  and  not  examples  as  reported  accurate  times to  gradient  material  i n t r a c e l l u l a r  relaxation  2  well  many  numerous  spatial Two  be  are  i n t r a c e l l u l a r l y ,  study  contribution  to  signals  true  which a  can  that  flow-rate  molecular  signal T  and  (as  or  required  short  on  f i e l d  conditions due  randomize  veins)  in  observed.  c a p i l l a r i e s  for  much  direction  there  flows  but  in-vivo  human  neither  bulk  scale,  sample  can  larger  the  in  total  however,  undergo  molecular  the  eddies  For  which  randomized  flow  these  In-vivo,  d i f f u s i o n .  motion  of  the  is  involved. The  other  two  two-dimensional is are  a  function two  of  biological  NMR m e t h o d s . two  independent  applications In  variables. time  this, In  intervals  the  the  both signal  f i r s t  under  the  use intensity  instance, control  of  these the  6 experimenter. converted data one  into  Fourier  two  constitutes of  them  direction, into one  By  is and  position can  of  two  or  In  the  second  converted  into  the  either  example  each  an  its  Chemical  Barbara  haemolymph, the  blood  simple  of  of  the  lymphatic of  indicating  a  shift  used  in  to  pupae  of  or  f i r s t  the  case,  distribution of  a  organism.  of  in-vivo  one  NMR.  distinguish  .the  along  Douglas  f l u i d  for  pupae  shift  the  l i p i d  aqueous  the  on  fixed  two-dimensional  and  system  some  describes of  insect  turning  In  of  ultimately,  chemical  f l u i d  The  array  two-dimensional  thesis  was  aqueous  serves  the  a  application  colfaxiana.  and  a  dimension  obtain  be  But  along  d i r e c t i o n .  This  direction  which  position  one  can  resulting  spectrum.  into  along  imaging  the  the  they  information  can  shape.  experiment  changes  one  shift of  a  orthogonal  kind  anteroposterior Moth,  other  case,  of  and  dimensional  substances  projection  distributions  two  simultaneous  more  of  frequencies  a  in  obtain  transformation,  the  is  the Fir  Cone  the  purposes  higher  of  animals.  upside-down  both  The  produced  distribution  of  the  haemolymph. The  very  large  medi t erranea, produces  a  object  for  powers  of  at  the  discoid study the  s i n g l e - c e l l e d culmination  reproductive  with  optical  a  good  of  cap  It the  in  size  from  0.3  near  center.  This  is  mm n e a r a  very  l i f e  which  magnifying  is  glass  has rim  suitable  Acetabular'!  alga  its  microscope.  tapering the  marine  cycle, a  very or  tens  object  suitable  the  features to  a  lowest  radially of  for  microns imaging  7 i n two s p a t i a l d i m e n s i o n s t o d e t e r m i n e t h e s p a t i a l r e s o l u t i o n a c t u a l l y a c h i e v e d i n t h e i m a g e . The s i z e o f i t s features challenges the present  state-of-the-art  spatial  i s no t o m o g r a p h y ,  resolution.  selection,  Since there  or s e c t i o n i n g  o p t i c a l photographs  involved,  NMR i m a g e s a n d o r d i n a r y  makes v i s i b l e  95 % o f s u c h an o r g a n i s m w h i c h i s w a t e r , and photography  remarkable that  the outer  while  sees the other  the  roughly  optical  5%. I t  i s perhaps  t h e NMR image a n d t h e p h o t o g r a p h have a n y  resemblance whatever of  slice  c a n be c o m p a r e d i n d e t a i l .  P r o t o n NMR i m a g i n g , h o w e v e r ,  observation  l i m i t s of  t o each o t h e r ,  margin of t h e o b j e c t .  w e a l t h of p r e c i s e l y  beyond g i v i n g In f a c t ,  they  t h e shape show a  c o r r e s p o n d i n g d e t a i l s down t o 0 . 1 mm  d i m e n s i o n s . An o b j e c t  s u c h a s t h e Acetabularia  c a p , which  wet t h r o u g h o u t ,  provides  a good t e s t  different  of water  i n t h e s a m p l e , i n t h e NMR i m a g i n g ,  types  by r e l a x a t i o n  times, diffusion rates,  w i t h D 0 . The c o n t r a s t s w h i c h e x i s t 2  living  (2)  field-gradient  A greater  water  are another  exchange  property  of  i n most s i m p l e  systems.  What d o e s one s e e in-vivo?  (1)  contrasting  or r a t e s of  s y s t e m s w h i c h h a v e no c l o s e a n a l o g u e  chemical  proton  o f means o f  is  variety  than the chemist  Some r a t h e r  physiological  The c u r r e n t  visibilities,  NMR, seem t o b e : of d i r e c t i o n a l l y - r a n d o m i z e d  f l o w s of  envisages.  generalized  i n d i c a t i o n s of  i n t e r a c t i o n s of w a t e r ,  a l o n g one d i m e n s i o n ; a n d a c l e a r  differing  spatially  resolved  s e p a r a t i o n of aqueous and  in  8  l i p i d (3)  phases.  Spatial  good  magnifying  uniformly  2.  features  f u l l  HISTORICAL The  flow  induction Purcell  glass, of  of  soon by  (15).  molecular  The  by  spin  signals in  an  echo by  produced  NMR was  the  of  spins spins, the  in  Larmor  frequency motion  Shortly  a  which  leads  to  to  a  to  Following  a  groups of  (16).  which  with  seems  a  almost  only  by  is  the  the  Bloch  NMR  to  directly  arose  Carr  in  of  that  two the  also  by  alternate  method  in  the Motion  containing the  of  of  (17)  .  the  the  using  of of  spins  spin  applied  (18),  the  Brownian  c o e f f i c i e n t al  the  variation  of  phase  of  variation  random  intensity  et  pulses  but  molecules  McCall  rf  relaxation  magnet.  diffusion  more  spin  the  Purcell  discovery  the  of  the  the  of  spins  the  E.M.  secondary  decay  the  in  and  measure  are  of  the  bulk  nuclear  the  or  presence  and  the by  echoes  of  (14)  from  in  uncertainty  of  F.  The  an  and  of  spins.  obtained  decrease  liquids  accompanied  is  an  in  spin-spin  f i e l d of  of  suggestion  FLOW  Spin  diffusion  determine  developed  observations  observations  found  f i e l d  thereafter,  gradients  motion  Hahn  precisely  frequency  eventually  Tanner  not  AND  application  inhomogeneous  such  object  an  molecules  the  translational  more  in  f i r s t  echoes  by  governed  or  of  experiment.  inevitably  of  capability  motion  Hahn  the  research  translational E.  even  scale  DIFFUSION  after  the  the  water.  SURVEY:  study  began  on  echo.  static of  water.  Stejskal pulsed  and  f i e l d  and  9 gradients multiple pulses  (PFGs) gradient  (20)  have  techniques  using  used  to  measure  general  theory  reviewed of  by  A l l  of  the  these  of  of  in  with  from  the  shape  echo  signal  magnitudes,  water  of  a  in  geometry  But  c a l i b r a t i o n  to  the  study  by  from  the  using  to  tracer  allow  used  a  in  for  theoretical  function  the  (25),  of  position  (26,27),  (FID)  or  and  spin  experimental  values of  of the  diffusion  diffusion  echo  measurement  decay  of  the  dimensions  of  for  c a l c u l a t i o n  include  as  (24).  means  variation  shape  the  Tanner  some  induction  accurate  The  application  small  because  obtaining  from  of  (21,22).  was  without  frequency  free  especially  obtained  been  been  NMR  magnitudes  sample  the  the  have  by  require  from  echoes  diffusion  reviewed  have  resonant  (17,28).  d i f f i c u l t i e s  spin-echo,  which  c o i l  the  gradient  recently  crystals  of  magnitude  gradient  measurements f i e l d  was  gradient  calculations.from  the  whilst  More  spin  l i q u i d  techniques  Methods  (MQ)  measurement  (23)  involving  alternating  described.  in  c o e f f i c i e n t  determination  and  multiquantum diffusion  the  modifications  (19)  been  diffusion  diffusion  amplitude.  also  Reeves  determining the  pulses  of  restricted  Further  (12).  data  gradient FID  or  c o e f f i c i e n t is  s t i l l  of  preferred  (29, 30) . Motion nature,  due  have  Translational whereas  flow  to  bulk  different  flow  effects  diffusion affects  and  its  causes phase  Brownian  upon the  motion,  by  their  the  spin  dynamics.  spin  echo  to  (5-9).  The  f i r s t  decay experiments  10  with  flowing  liquids  The  experiments  the  steady  of  the  involved  state  measurements  of  V.  and  blood R.L.  flight  in  mice  using  J.R.  Singer  a  Suryan  in  of  variation  flow-rate  Bowman  of  by  time,  in-vivo  flow  time  of  with  relaxation  two-magnet, t a i l s  reported  measurements  signal  s p i n - l a t t i c e  Kudravcev  were  (32)  the  for  T,.  The  were in  and  similar  of  f i r s t by  forearm  by  (31).  determination  performed  human  technique  technique  the  1950  J.R. to  using  a  Singer  that  (33)  of  Suryan. Later, properties  of  distribution fingers.  Spin of  many  et  parts  described  in  Stepisnik  (38)  measurement  3.  The  study water,  in  of  the  the  with  also  water  in  measure  reviews is  by now  the  rat  t a i l s to  (35).  observing signal,  developed  a r t e r i a l  body  in  real-time  van  As  and  (36).  Schaafsma  in  human  the  By  been  p u l s a t i l e  interest  and  steady-state  have  the  velocity  applied  plants of  exploited  the  in  been  arrangements  human  (34)  determine  amplitude  combining  by  blood  flow  As (37)  and  flow  imaging.  SURVEY:  f i r s t  Grover  blood-flow  have  to  there  concept  was the  al.  the  HISTORICAL  sample  in  T.  to  for  flowing  experimental  B a t t o c l e t t i in  echoes  variation  various  echoes  function  measurement the  spin  and  that  IMAGING NMR  data  discussed  by  NMR  response  from  the  presence  of  can  reflect  Gabillard  glass  (39)  objects,  gradients.  The  the  shape  who f i l l e d  f u l l  of  went  on  the to  with  realization  of  11  the  mapping  three  of  large  of  arrays In  of  of  a  obtained  Later,  by  another et  al.  signal,  a  strategy  was  vary  as  a  using  who  with  for  had  the  used cause  function  varying  the of  how  the  map  time two  This  proved  to  be  versatile  application  in  spectroscopic  d i f f r a c t i o n variations was  made  (44,45), Fourier  to  the At  same  investigating  the  NMR  techniques  methods using  transformation  between  time,  have  of  Fourier NMR  The  spin  system  time  has  has  scanning  to  be  much  show  with  applied  applied by  the  to  many  while  some  through  methods  found  maps  and  led  and  would  spectrum.  structures  process,  proven  image  by  the  where  spins  work  transient  the  response  and  Mansfield  periodic  for  the  transformations  experiments  imaging  of  scheme  a  algorithm.  multidimensional  Further  (43).  develop  a  two  of  in  and  independent  Fourier  couplings the  method of  very  scanned  distribution.  more  of  the  method,  time  evolution  or  with  properties  spatial  dimension  for  the handling  developed  measured  one  gradients  of  direction  the  yield  a  was  was  each  (10,42).  required for  wave  reconstruction  corresponding  f i e l d s  wait  dealing  spectrum  imaging  to  to  work  The  of  to  capability  intervals.  correlations  spins  continuous  showed  applied  be  a  The  (40).  method  to  with  projection  (41)  could  imaging  published  gradient  transformation,  to  NMR  of  data.  imaging,  of  distribution  computers  c a p i l l a r i e s  presence  Kumar  and  1973 L a u t e r b u r  dimensional  was  spatial  dimensions,  development  set  a  of  very  an  NMR  effort  object  detection versatile  and and  12  are  The by  (1-4).  favored range  several to  of  work  high  application  factors  signal the  of  noise has  abundance  which  affect  ratio  and  dealt  with  of  mobile  (1-4).  Images  d e t a i l  equals  or  techniques involves that  of  scanning  show  structure  density.  radiation nuclear  water  structure. than  one A  perform  fat,  The  and  for  Furthermore,  the  properties Thus  internal  in  of  of  the  NMR  imaging  structure  and  response and  so  of  on  varies  a  means  arises by  distribution the  2-3  is  of  emitted  tissue  s l i g h t l y  chemical  provides chemical  measured  is  The  degrees  the  NMR m e t h o d  noninvasively  radiation  depict  thicknesses  the  the  spins  images  which  detected.  then  maps  largely  such  s l i c e  advantage  imaging  images  is  and  the  show  (CAT)  the  is  of  other  d i f f e r i n g  absorbed  NMR  the  scans  most  high body  Tomography  that  date,  have  of  include  because  human  unabsorbed  signal  f i r s t  measurements  opaque.  important.  is  the  CAT  r e f l e c t s  the  resolution  primary these  which  Proton  millimeter  are  the  that  In  also  that  Assisted  object  NMR  of  surpasses  To  systems  which  determined These  resolution.  parts  X-rays.  the  In  spins.  and  of  is  quality.  b i o l o g i c a l  even  with  imaging  image  s p a t i a l  Computer  through  electron  the  as  passes  scans  from  such  NMR  protons  s e n s i t i v i t y that  of  less  mm.  the  a b i l i t y  objects  to  which  depending  upon  environment  is  for  composition  studying of  objects.  13  4.  ORGANIZATION The  OF  remainder  parts.  In  of  effect  of  based  upon  the  method  a  and  diffusion both  resolved  f i e l d  gradients  the  studied.  forearm  and  NMR  III  imaging  b i o l o g i c a l  are  probe  deals  motion and  by  the  IV  motion and  systems:  Acetabularia  and  also  with  the  NMR.  to  diffusion  the  pulsed  map  pupae  for  imaging  modification for  of  imaging  c o i l  model  systems  and  of  proton  demonstrate  of  for  fat  the  range  chemical  glucose  gradient  and  method  in-vivo  dextran  is in  shift  used  to  human  tissue). application  proton of  A  determining  surface  applications  water  for  c o i l s  on  account  reviewed.  The  measurement  F i r s t  taking  methods  for  three  described.  the  the  is  gradient  be  into  NMR  lineshapes  measurements  w i l l  of  of  described.  connective  to  organized  apparatus  and  describes  methods  of  with  possible  Secondly,  is  l i n e a r i t y ,  measurement,  (muscle  Chapter  of  analysis  measurements,  characterize  caps  magnetic  measurement  quantitation  NMR  theory  instruments  translational  was  basic  measurements  Chapter  of  the  II,  resolution  diffusion  using  thesis  magnitudes  diffusion  high  of  THESIS the  chapter  gradient and  THE  two-dimensional  distribution  Barbara  mediterranea.  of  col faxi ana  in  two  and  mature  II. In  this  diffusion results begins  for  by  the  a  and  imaging  by  NMR,  w i l l  described.  of  of  a  the  used  section  spectra  with  replaced  by  NMR  two  the  NMR  gradient for  relative  are  then  features  discussion  section  spectrum,  and  related  in  is  and  to  the  small can  l i n e a r i t y .  two-dimensional with  one  described. or  A . 1 .  broadened  relationship  obtaining  intensities  between  in  magnitude  coordinates  shift  The  linewidth  This  for  experimental  directly  natural  linewidth.  spatial  resolution  the  methods  chemical  affect  spatial  provided  determine  A . 3 ,  the is  apparatus  and  theory  that  NMR  the  NMR  gradient,  overall  to  be  standard  application  be  which  and  shown  to  IN  principles  is  distribution  GRADIENTS  the  systems  review  A . 2 ,  FIELD  it  compared  In  model  with  section  then  chapter,  measurement  In  spin  MAGNETIC  coordinate  The  factors  contrast,  NMR  and  images  are  the also  discussed. In f i e l d  sections  gradients  diffusion  and  description  of  Stejskal  echo  pulse  introduced, before  and  systems, absence  the  of  flow  of  Bloch  of  wherein  gradients,  spins  equations, A . 4 ,  echo  and  signal  due  flow  The  by  the  the  discussion  gradient (12)  to  spin  is  applied  equally  multi-component is  resolution  14  and  Tanner  For  magnetic  discussed.  pulsed  are  of  motion  follows  the  pulses  180° pulse.  high  is  diffusion  Stejskal  spin  application  translational  of  gradient  the  the  the  section  sequence  the  A . 5 ,  effects  In  after  and  studying  the  (5).  since of  for  bulk  of  modification  A.4  measured spectra  in  can  the be  15  obtained  and  for  chemical  each In  section  obtained  by  averaging shown  the  A . 5 ,  a  the  the  spin  echo  possible  distinguish flow  b i o l o g i c a l  system.  diffusion and  the  spin  designs  constructed  magnets.  The  to  built  allows  the  times.  To  windings  used  measurements  suitable  those  decays  for  into  maximize were  only  working  the  magnetic  c o i l s  were  For  were  imaging, which  was  the  on  a  PVC  for  over  the  mounted  with  former  Gradient  standard  c o i l s  compared  on  surface which  that  sample  a  were high  c o i l s ,  was  then  magnets  shorter the  However,  c o i l s  B.1)  superconducting  with  so  for  gradient  using of  is  (section  samples,  enough  gradient  then  used  described.  bore  placed.  large  f i e l d  measurements  wound  are  it  superconducting  area  is  living  pulsed  gradients  approximately  of  probe.  larger  It  and  a  gradient  respective  variation  NMR  these  then  Thus  imaging  c o i l ,  c y l i n d r i c a l  of  time.  apparatus  systems,  c o i l s  former  the  for  of  and  is  v e l o c i t i e s .  in  B.2)  the  Perspex  occur  (section both  flow  diffusion  surface  of  microscopic  determined  effective  echo  for  the  the  an  true  may  of  microscopic  diameters  For  be  motion  and  size  generation  the  section,  the  smaller  with  with  which  experimental  apparatus  were  can  randomized  uniform  between  of  measurements  echo  c o i l s  both  of  distribution  increases  randomized  the  for  Gaussian  that  In  effect  solving  d i f f u s i v i t y to  c o e f f i c i e n t s  s h i f t .  f i r s t  over  that  diffusion  rise current  the the  was  linear.  wound  on  a  resolution the  gradient  placed  in  16  the  bore  of  including  the  data  equalization In  the  section, from rf  magnet.  of  the  f i r s t  lineshapes  part  time  were  with  lineshapes  c a p i l l a r y obtained  and  agree  quite with  water,  the  c o e f f i c i e n t  the  are  magnitudes  effects  the  gradient  that  of  were  with  gradient  the  described.  ensuring  obtained expected across  magnitude  determination  of  using  the  the  receiver  applied  absolute water  and  discussion  spectra  well  methods  gradient  After  the  the  and  of  that  NMR  imaging  results  gradient  particular,  the  r  apodization  for  described.  minimized,  allowing  diffusion  the  uniform  containing  view  determination be  that  B.3  procedures, of  of  the  is  dead  f i e l d  w i l l  distribution  In  section  acquisition  C . 1 - C . 4 ,  lineshape.  In  of  a  was  the  static  gradient  technique. The using C.5.  determination  the  pulsed  (B.2).  rephasing  were  apparatus  Eddy  current  of  the  echo  amplitude,  were  minimized  were by  pulse  the  echo  double quantum  and  and  varying  gradient  diffusion  time.  measurement  was  with  the  of  both  both  a  C.6,  echoes  performed  is  of  the  These  the  the effects  gradient  measurement  from  described.  using  of  and  parameters  the  a c r y l o n i t r i l e  high  apparatus  dephasing  systems.  duration  water  section  reduction  experimental  section  of  modified  c o i l  unequal in  in  the  surface  causing  on  coefficient  described  resulting  In  quantum  is  the  magnitude,  coefficient  t r i p l e  and  observed  the  the  performed  e f f e c t s ,  spins  diffusion  method  (B.1)  including and  the  gradient  Measurements  resolution  of  of  single, The  standard  single pulsed  17  gradient  method.  measurements was  used In  proton  In  fields Bloch  the  system  quantum  echo  sequence  echoes.  imaging  containing  the  chemical  frame  radiofrequency  the of  Bloch  the  spin  that  the  lines  is  of  the  water  and  introduced  magnetic  equations  combined  application  Lorentzian  effects system.  of  a  adopted  l i q u i d s ,  spectrum  90° p u l s e ,  corresponding  on to  external  For  frequency  f i e l d s  are  of  for  to  of  the the  consists  spins  of  with  s h i f t s .  GENERAL atomic  momentum,  Ifi,  collinear  with  called 0  of  predict  after  Many  B ,  of  The  relaxation  of  spin  RESONANCE  rotating  (46,47).  equations  different  1.  effect  description  series  t r i p l e  quantum  described.  review,  and  t r i p l e  gradient  c a p i l l a r i e s  this  the  and  dimensional  MAGNETIC  response, a  two  NUCLEAR  spin a  in  and  OF  describing  give  pulsed  the  C.l,  be  double  double  distribution  THEORY  the  select  w i l l  the  modified  section  acetone  A.  to  a  For  the  and  a  it.  have  dipolar The  gyromagnetic  different  b r i e f l y ,  nuclei  with  different  values  quantized  along  of the  magnetic  ratio. of  respect the  non-zero  constant  orientations  spin,  a  In the  to  the  quantum  f i e l d  and  of  spin  angular  moment,  =  yfil,  proportionality, a  static  nuclear f i e l d  number,  correspond  y,  magnetic spin  are I  = to  or  is  f i e l d ,  more  described  by  m,  spin  of  the  different  18 magnetic  energies,  The  E^.  interaction  energies  are  given  by  the  hamiltonian  = -y-hB i . 0  The  latter  along  the At  spins  expression  holds  z - d i r e c t i o n ,  equilibrium,  along  the  magnetization, distribution  B  a  =  of  ,  the  f i e l d  and  of  is  the  alignment  f i e l d  described of  the  gives  by  a  *fi ^— me  ^  m  f i e l d ,  the  angular  energy  absorbed,  terms  system  of  a  s t a t i s t i c a l  defined  so  such  spins), that  net  k  T  ^_  a  of  static  technique an  is  applied  levels  in  for  o s c i l l a t i n g  f i e l d ,  Resonance the  kT  in  the  the  magnetic  form  condition  radiation order  measuring  that  must  of where  match  energy  be  AE.  a  (the  the  of  For  systems is  to  between =  is  application  radiation.  -ftw  a  [2-2]  resonance  frequency  i . e . ,  to  p  Im = -IeXfimB /  the  differences  rise  nuclear  i  perpendicular  radiofrequency  the  Q J L J  magnetic by  of  levels  o /  B  0  magnetism  l i e  T  *  the  to  Maxwell-Boltzmann  energy  v  Nuclear  chosen  0  populations  N  is  B z.  preferential  direction M  if  [2-1]  2  as  this,  ensemble  involves  for  any  a of  the  convenient quantum density  observable  Q,  description  in  mechanical operator  the  p  which  expression  for  19  the  expectation  value  is  given  (48,49)  by  E-3  <Q> = Tr(Qp). The  density  operator  (i)  Trp  (ii)  p  must  (iii)  p  is  p  must  satisfy  the  three  conditions:  = 1 be  Hermitian  and  The the  diagonal  finding of  physical  the  the  elements system  in  of  the  p  the  of  these  constitute  the  corresponding  equals  corresponding  equilibrium,  definite.  interpretation  p r o b a b i l i t i e s  operators At  positive  to  density  unity, any  and  physical  operator  conditions  p r o b a b i l i t i e s  pure  state.  expectation  the  The  are  form  where  Z The  In  equilibrium  the  high  = Tr(e  magnetization  temperature  is  VkT,  given  approximation,  by  /kT  <<  that of sum  values  observable  takes  is  1,  and  of  real.  20  expanding  the  magnet i z a t  The is  exponential  directly  picture  which  gives  Curie's  law  for  the  the  f i e l d  ion  equilibrium  The  terms  magnetization  proportional  time is  evolution  given  may  also  by  be  to of  the  the the  von  written  is  aligned  with  magnitude  of  system  Neumann  in  the  the  f i e l d .  Schrodinger  equation  as  [2-9]  dt "Hh^e using For  the  spin  notation X 1/2,  the  for  density  [W,  ],  a  operator  superoperator.  can  be  expressed  as  p4o-p-<n where are y  P  the  is  the  Pauli  components  expressions  polarization spin  of  the  and  matrices.  vector The  polarization  (48)  [2  and  time are  the  components  evolution then  given  of by  the the  of x  .  10]  £ and  21  dt  3  d?  [2-11]  Q  dt which  has  the  solution  Rj = Py cos (0  cJ i 0  [212]  Fx =Rj,osin u) t 0  for  the  i n i t i a l  equation  [2.12]  diagram  as  This  1  result  value,  P  can  represented  be  y  is  d i r e c t l y a  B,  M x  B  equal  to  momentum.  Since  M =  angular moment  is  .  analogous  where  torque  P  The in  described  magnetic  by  the  to  moment  the  7fil  rate  the  M.  BLOOM,  a  given  by  precession  Lectures,  UBC,  that  of  the  c l a s s i c a l  M experiences of  change  motion  of  dl dt  ft  the  in of  a  f i e l d its  magnetic  equation  J f = *M*B. 1  motion  follows  description a  of  Q  1981.  . [2-13]  22  If  now a n o s c i l l a t i n g  f i e l d  with  frequency  u)  is  2  applied,  B =2B.cos<^t x  [2-1 A]  r  to  describe  coordinate frequency sum  of  the motion system  -w.  is  rotating  useful  around  The o s c i l l a t i n g  two c o u n t e r  becomes  i t  rotating  to  the  f i e l d  transform  to  z-direction  at  may b e w r i t t e n  components  and the  a  as the  hamiltonian  2  [2-151 i i(w-u)t -i(cj*cj)t i(cj.+u)t -i(cj-u)t \ = - f i < j I - ^cj,[[e Mcj.lle e ]I +[e +e 0  where  CJ, =  7 B , . If  u  r  z  2  z  +  2  2  +  = u  then  W =-f>o) I -^(j,(I IJ ••^cj (e" " I e R  In rapidly  0  the  z  ++  rotating  o s c i l l a t i n g  I  frame terms  2,  approximation, is  small  t  ++  the  2,6)t  effect  2  Note:  $  i s  the  rotation  2  of  the  giving  !H = - f ^ - f ^ , i . R  [2-16]  U.  [2-17]  x  generator  for  operators.  23  Now,  applying  the  same  transformation  to  the  density  operator  -i«4t the  time  derivative  is  dp(t)  .  dp  -\o$ t z  = I-l".-u)4-u,jl lp(t) <  = -<•>.*-iff (>(tK  [2-19]  R  The  effective  direction  of  f i e l d  in  J ^ ^ a n d  the  rotating  causes  a  frame  is  precession  in  with  the frequency  0)^=1 (a-of* of]* At  resonance,  u>  0  = w  and  6 J  Then  the  application  polarization  along  [2.20]  of  the  [2-21]  eff4ff=°.^the  B,  z-axis  f i e l d to  for  rotate  a  time  through  t'  causes  an  angle  a  24  =  co,t'  and  around  is  said  indicates absence the  to  the  of  In Larmor  direction  of  radiofrequency occurs  sample,  a°  pulse;  X  the  a  the  applied  radiation,  at  there  frequencies f u l f i l l e d  However,  in  applied  that  i.e. Thus  the  u, in  y - a x i s .  transverse  and for  pulsed  » a  magnetization  is  B,  the  frequency  l i k e l y  the  subscript f i e l d .  In  the  precession  u>'  NMR  of  the  ~ w)  0  which  inducing  transformation  o  r  a  1  i n i t i a l l y  action  components  f  in  = CJ  0  -  1  w  o  around  u> i n  the  of of a  the  [2.21]  is  n  voltage of  this  in time  a  the  not  be  z  at  f i e l d to  c o i l domain  radiation  is  approximately  sample.  90° pulse  magnetization  w i l l  of  simultaneously. rf  along  static  d i s t r i b u t i o n  intense  i a  a  condition  Eq.  experiment,  is  be  spins  s u f f i c i e n t l y  relationship (CJ  to  resonance  a l l  typical  The  z - d i r e c t i o n , Fourier  an  frame. a  exactly  true,  x-axis:  constitute  z-direction  rotating  the  the  rotates  equilibrium causes  precess which  is  signal  to  the around  the  measured. yields  the  25  frequency  spectrum  of  the  response  (50)  S M =J f(t)e  [2-22]  dt.  -to With  a  phase  projections the  xy  of  plane  U n t i l system which  sensitive  randomly Various  can  now  has the  the  rotating  be  only  been  detector,  (51).  the  of  may  action  f i e l d  of  changes  when  used.  These  changes  are  rapid  molecular  fluctuating rotational  from  molecule  one  Mechanisms coupling,  required  for  relaxation given  of  here.  a  individual  of  molecules  migrations to  for  and  large  of  the  undergo are of  the  motions  or  spins.  random  generate  atoms  by  require  existence  and  even,  the  samples  molecules, and  a l l  by  the  These  in  include  relative because  groups  of  of atoms  another. relaxation  include  relaxation,  scalar  quantum  processes  but  amplitude which  on  therefore  by  axis  mechanisms  gaseous)  about  relaxation.  quadrupole  spin-rotation  (or  for  motion  exchange,  l i q u i d  of  several  magnetism  any  f i e l d s  experienced  samples,  tumbling  chemical  be  these  f i e l d s  translational  to  external are  about  along  equilibrium  brought  motions  inside  to  nuclear  substantial  character,  There  return  fluctuating properties  magnetization  obtained  discussed.  system  information  coupling  mechanical  are  not  dipole-dipole  chemical  shift  (46,47).  The  description  needed  and  too  anisotropy, calculations  of  bulky  spin to  be  a  26  From of  phenomenological  simple  equations  quantitative of  the  provide  description,  magnetic  external  that  arguments,  most  s u f f i c i e n t  properties  magnetic  in  f i e l d s  of  Bloch  These  (52).  cases  for  ensembles  proposed  the of  a  a  correct  purpose  nuclei  consist  of  set  here,  in the  following  dM  L2-23]  dT where T,  i ' , j ' , k '  and  times  T  are  2  of  of  the  relaxation  interactions The motion  of  to  the  the  f i e l d ,  to  between of  l a t t i c e .  the  various  decay  is  molecules in  terms  latter  degrees  b(t),  be  involves  the  equilibrium  components  of  Transverse of  the  a r i s i n g  from  surroundings.  upon  d e t a i l s  spins  expressed  of  and  for  as  GCr) = <b.(t)-b (t* r)>  a  the  these  functions  G(r),  with the  the  the  L  relaxation  freedom.  correlation  function,  frame,  consists  f i e l d s  with  containing  of  of  local  correlation could  thermal  dependent  of  rotating  transverse  The  and  the  relaxation  dephasing  spins  of  towards  rotational  due  and  Longitudinal  the  and  described  example, local  rate  vectors  longitudinal  involves  magnetization  unit  magnetization  energy  translational  often  the  the  respectively.  return loss  are  (53).  are For  fluctuating  27  where  the  second of  angular  equality  G(t).  The  brackets  is  an  imply  often  correlation  an  made  time  ensemble  assumption  average as  to  characterizes  T  and the  the  the  form  time  c scale  of  the  fluctuations.  Nuclear  relaxation  correlation by  Fourier  spectral  functions  rates  of  the  transformation.  density  fluctuations.  or  For  power  the  This  the  general  G(T)  given  dipole-dipole forms  of  the  gives  spectrum,  2  the  local  J(CJ) ,  to of  this  time interations  the  s o - c a l l e d  the has  the  form  ?'  [2-25]  interactions  relaxation  (Ti)"d = /3 ^  to  rise  above  ,  2  magnetic  related  fluctuating  J ( « ) = <b,>  For  are  between  rates  like  are  [j(u ) 4j(2o) )]  2  0  +  0  and  [2-26] ( T  where  J(CJ)  form  given  ^  7 <b >  =  2  dipolar result and  }  = 2 /  3 A^[3/ j(0)*5/ j(u )*j(2^ )] 2  a  in  equation  is  'reduced'  a  coupling from  indicate  quanta.  2 d  is  2  spins  a  of  strength.  quantum that  spectral  [2.25]  measure  2  the The  can  be  which  frequencies  only  the  and  mean-squared 0,  description be  for  J(co)/2<b^>,  appropriate  mechanical  energy  density  would  o  o  u> of  exchanged  a n d 2CJ  0  the in  0  spins  discrete  28  Neglecting  the  effect  of  B,  the  Bloch  equations  give  M =M (1-e~ .) z  t/T  0  M =M  The  signal  referred form  of  obtained  to a  as  a  after  free  damped  [2.27]  e '2  the  application  induction  o s c i l l a t i n g  decay  of  a  (FID),  function  of  90° pulse  and  takes  The  frequency  spectrum,  transformation, imaginary  is  the  (dispersion)  t/T  yj0  [2-28]  e  obtained sum o f  after  real  the  time  M = M e" 2cosco t. y  is  Fourier  (absorption)  and  components  2 S M = - ° (  2 - 3 - ;  2  The  counter  rotating  component  has  linewidth  at  tumbling of  1 0 "  1  2  the half  form  to  10"  1  of  maximum  molecules 1  s  with  leads  a  0  (46,47).  were  neglected  Lorentzian  of  2/T . 2  In  to  motional  l i q u i d s ,  and the  spectra  with the  and  that  of  real  a rapid  correlation  averaging  interactions, The  2  function  reorientational  and quadrupole  anisotropies  1 + (6J-(J )T  2  components  of  dipole-dipole shift  1*[u-ujT  [2-29]  h)  * —  times  the  chemical  are  obtained  29  consist order  of  of  f i e l d  narrow  a  hertz  l i n e s . and  are  structure  magnetic  shielding  indirect  coupling  electrons. f i e l d  at  the  The  the  of  one  nucleus  w i l l  a  is  The nuclear  the  which  spin  the  B .  t y p i c a l l y  largely  by  of  the  magnetic  iocai  of  a  the  described  l o c a l  *> ( 1  the  of by  f i e l d other. the the  Vj - J f J  protons.  While  spectra,  they  discussed  any  is  usually  these are  with  another  the  via  the  produces  and  magnetic  the  and  electrons  proportional  via  experience  spectra  constant  electrons  from  in  a  opposition  f i e l d  at  the  of  effects  not  further.  t2-30]  < 5 )  s h i f t .  s p l i t t i n g s  is  = E  coupling  orientation  and  is  arises  by  chemical  to  by  o r b i t a l  The  0  given  indirect  nuclei  the  c h a r a c t e r i s t i c  The  are  spectra  nucleus  of  f i e l d ,  be  these  the  of  B  upon  determined  in  motion  applied  nucleus  where  linewidths  inhomogeneity. Further  to  The  of  which This  lines  •  w i l l  causes  varies  in  one  depending  interaction high  expression  the  concern  electrons  causes  resolution  (54)  T.  [231]  order be here  of  several  observed and  w i l l  in  hertz some  not  be  for  30  2.  LINESHAPE: While  has  often  RELATION  the  effect  been  TO of  GRADIENT  AND  SAMPLE  SHAPE  inhomogeneity  of  magnetic  p a r t i c u l a r l y  in  terms  discussed,  f i e l d s  of  a  * shortened  transverse  evaluation in NMR  the  of  the  frequency  lineshape  presence  of  Following spectrum  relaxation  effect domain  for  a  of  linear  has  c y l i n d r i c a l  magnetic  f i e l d  the  analysis  of  shown  to  be  the  with  for  l i q u i d s .  When  natural  the  overall  Lorentzian and  the  lineshape  frequency  d i s t r i b u t i o n v a l i d  when  small.  between  at  the  spins same  frequency  magnitude  of  linewidth  or,  relationship  the for  of at  between  magnetic  different and  position  gradient a  the  can  would be  c y l i n d r i c a l lineshape  small  a  by  the  f i e l d  be  spin  by  function  spin also  only  gradient the  sample  from  The  the  inverting  the  d i s t r i b u t i o n  function. The composite  NMR of  signal the  in  the  frequency  contributions  from  domain, the  S(a>),  various  to  the  unique.  determined  and  compared  delta  is  of  function  correspondence  not  sample,  spin  by  parts  the  the  frequency  the  relation  the  discussed.  applied,  given  The  frequency  and  is  gradient  then  in  lineshape  approximated is  lineshapes,  the of  e x p l i c i t  section,  be  al.(41),  linewidth  d i r e c t l y .  variation  Otherwise,  resonate  be  on  this  w i l l  Lorentzian  the  spectrum  function  the  a  with can  et  no  measured  convolution  function  linewidth  In  object  Kumar  (55),  2  gradients  gradient  d i s t r i b u t i o n  the  T  appeared.  a  is  time,  is  volume  a  is may  31  elements  where  of  c(r)  the  is  distribution volume axis  change  a  of  the  x  the  and  be  S(r,a>)  single  the  axis.  coordinates is  can  expressed  is  in  the  nuclear  spin  the  signal  gradient  NMR  applied  form  from  a  the  x  along  by  represents  component,  In  For  given  onto  and  three-dimensional  function  is  c(x)  density  D(CJ),  the  element.  S(CJ)  where  sample  sum  projection The  and of  of  the  signal,  NMR  neglect  of  S(CJ),  the  absorption,  nuclear  A(CJ),  spin  after  a  counter-rotating and  dispersion,  components  liquids,  contribution magnetic  the  absorption  due  f i e l d  to  spins  gradient,  signal at  G  ,  is  Lorentzian  position  x',  is  by  given  in  and  a  the  linear  A(x,w) =  M /T e  where  M  0  is  the  equilibrium  2  magnetization  and  T  2  is  the  32  spin-spin  relaxation  time.  For  frequency  was  equal  to  /,  ^  with  D  p r i n c i p a l  M =  with  a  symmetry,  axis,  absorption  V  chosen  and  c(x)  signal  is  can  a  zero.  constant,  be  at  and  the  an  f i e l d  obtained  Larmor  object  of  gradient  the  length,  along  exactly  x  2  [2-36]  2  half-height  VXV^'T For  NMR  imaging,  the  spatial  gradient. then given  the by  the  natural  resolution  If  we  let  magnitude the  /  be  of  the  the  similar  expression of  of  cylinder  with  the A  (56).  solution  p r i n c i p a l  imposes  with  smallest  gradient  a  a  limit  particular  resolvable  which  on  is  element,  required  is  expression  inhomogeneity Bottomley  [2-37]  linewidth  attainable  G  A  its  normalized  - tan"G T (-l/  2  linewidth  For  linear  ^( ~V,(i/ -%) tan  convenience  Eq.  also  magnetic  [2.33]  the  axis.  that  common  [2-38]  >W, incorporates  the  f i e l d  has  been  situation,  for  which  has  gradient  not  been  applied  obtained,  effect  given the is  perpendicular  of  by a n a l y t i c a l  that to  of its  a  33  To of  extend  gradient  Eq.  [2.33]  the  analysis  nonlinearity, by  of  spin-spin  is  small  we  considering relaxation  compared  to  and  incorporate  simplify  systems  to  that  to  the of  for  the  the  effects  integration  which  linewidth  the  the  (as  gradient;  in  in  contribution Eq.  [2.38])  i . e . , Y G  /  >>  a  weak  X  2/T . 2  For  gradient the  a  sample  of  1 mTnr , 1  contribution  A(x',w),  In  a  to  x  contained  can  linear  be  to  T  2  the  replaced  f i e l d  in  a  5 mm NMR  should  be  signal  from  by  gradient,  a  greater  delta  with  spins  tube than at  in 15  ms.  Now  position  x',  function:  u> d i r e c t l y  proportional  A(w)= A(G x) x  = c(x). The  absorption  lineshape  d i r e c t l y  measures  the  spin  d i s t r i b u t i o n . For  a  c y l i n d r i c a l  object  of  radius  r,  with  a  linear  34  gradient spin  applied  perpendicular  d i s t r i b u t i o n  function  can  to  its  be  expressed  c(x)=-^ (r-x )  corresponding  signal Eq.  is  obtained  [2.41]  analogy  expression  which  with  Eq.  by  taking  gives  the  [2.37],  for  the  the  Fourier  Bessel  the  as  axis,  the  (Fig.  2.1)  -rsxsr.  J  The  p r i n c i p a l  FID  or  time  domain  transform  function  linewidth  Q./J]  at  J,(G  of  rt)  half  height  vv(4*3rtfrT Before NMR  proceeding  lineshapes  distribution nuclear  are  of  the  responses.  positions observed  in  also  the  s i g n a l .  further  it  affected  is by  radiofrequency Identical  sample The  do  not  resultant  is  12-42] worthwhile  the  used  spins  contribute spectrum  to  note  inhomogeneity  f i e l d  nuclear  By  (17).  at  to  e l i c i t  the the  different  equally  can  of  that  be  to  the  represented  as  A(u)=Jf(x')c(x') when  T  2  e f f e c t s  radiofrequency discussion and  is  f(x')  omitted.  are f i e l d is  S(G X-CJ) X  neglected  and  distribution assumed  to  be  12-43]  dx  where  f(x')  function. constant  is In  a  the  across  reduced following the  sample  35  Fig.  2.1  The  number  of  spins  in  a  thin  s l i c e ,  dx,  through  a  1 /2 cylinder where  r  is is  proportional the  radius.  to  y  =  2(r  2  -  x ) 2  '  /irr  2  36  To to  describe  introduce  a  the  effect  frequency  of  chemical  offset,  w  f  .  shift  Equation  it  is  useful  [2.39]  then  becomes  Al^Mp)*  When  the  frequency  frequency,  u,  we  0  [2-AA]  jc(x') 6 ( < V 6 x ' - ( " ^ ) ) d x ' . x  offset,  ,  +  is  equal  to  the  Larmor  obtain  [2-45]  A(u) w ) =C(x). +  The  spectrum  position  of  s t i l l the  line  frequency  and  different  Larmor  overlapping particular In given  measures is  chemical  set  each  of  general,  the  spin  shifted s h i f t .  frequencies,  lines  0  giving  distribution  depending  In  a  sample  but  upon  the  with  spins  the  result  would  the  d i s t r i b u t i o n  the  Larmor  be  a  of  a  having set  of  spins. the  frequency,  CJ, o f  spins  at  position  x  is  by  (J = Q + G x x  0  = 0  where  the  series. terms in  the  magnetic  In in  ..GWx-?a!«Al^?x'-...  a  Eq.  object  f i e l d  nonlinear [2.46], may  gradient  gradient,  i d e n t i c a l  resonate  at  is  expressed  caused spins  the  at  same  by  the  [2-46] as  a  Taylor  higher  different frequency.  order  positions The  net  37  absorption  signal  can  then  be  represented  as  n A^M=I!  c(x.) 1=1  such  OJ=  that  G  X  sample  are  i  >  In  a  square-profile  1.  However  1  usually this  Thus  x..  we  relaxation  shown  that  when  negligible  small,  the  distribution domain.  inhomogeneity  of  the  In  the  the  the  d i s t r i b u t i o n .  be  allows  given the  by  function  of of  variation determined  to  of  from  i s  independent  gradients  the  where of  x  inverted. are  of  NMR and  the  A  can  gradient  the  In  applied  then  effect  This  the  the  then  the  NMR  imaging  along  three  into  of  the  of  f i e l d ,  the  projection  lineshape of  of  would  intensity  spins  Larmor  sample  along  and  can  cannot  relation  of  a  a  the  be  in  experiments  as  be  distribution  axes  the  frequency  prepared  procedure spin  mapping  coordinates  of be  from  the  the  domain  measurement  graph  reduced  because  by  the  of  for  0  spin-spin  of  x  s p a t i a l  =  spectrum  of  the  the  the  n o n l i n e a r i t i e s .  effects  tube  across  slope.  the  given  over  c(x^)  the  radiofrequency  a  gradient.  the  is  displacement  displacement  situations  be  of  of  one-dimensional  [2.41]  the  the  to  cannot  Eq.  the  that  nonlinearity  from  absence  For  c a l c u l a t i o n  corresponding direction  reflect  so  the  signal  applied  should  then  NMR  nonlinearities  reflect  the  function  spectrum spin  and  [2.47]  i + 1  appearance not  is  frequency  the  x  small  w i l l  gradient spin  NMR,  object  have  are  in  s u f f i c i e n t l y  situation  <  x.  applied function  Eq.  where  spherical  [2.40]  38  object,  analysis  function  of  x,  determination magnetic  3.  the z  of  the  displacement  used which  in,this  be  between  features  imaging  w i l l  be  called  measurements give  an  divided  detection  In  the  imaging  relative the  a  and  periods  (Fig.  the  is  in  transformation  of  the  frequency  spectrum,  influence  of  or  both,  of  " the  transformation  described.  2  )  S(w,  ,CJ ) . 2  by  the  signal  next  S(t  1  f  co  acquired again  2  t,,  ).  The w i l l  signal yield  contrast  two  is  period,  the  time  ( 2 >  /•  the  and  phase,  the  Fourier  corresponding  cause  the  intervals  and  under  be  NMR  requires  evolution  to  in  sections.  time  evolution  give  factors  Following  detection  w i l l  sequence  experiments  hamiltonian  the  resolution  (10).  such  of  The  the  independent  for  the  or  the  preparation,  during  w i l l  c o i l s .  pulse  spectroscopy  S ( t , , t  During  governed  a  the  three  a  H evolution  and  properties  spatial  two  sequence for  2.2).  for  be  NMR  of  signals,  pulse  object  intensities  discussed  function of  as  the  the  following,  w i l l  image  briefly  as  of  allow  further  two-dimensional  the  into  for  in  array  convention,  excitation,  the  and  frequency  IMAGING  studied.  work  yield  distribution  NMR  the  determine  So  coordinates  gradient  varying can  w i l l  and  f i e l d  magnetism  spectra  y  TWO-DIMENSIONAL By  to  of  modulated  associated  the  and  amplitude Fourier  spectrum,  39  PREPARATORY EVOLUTION DETECTION PERIOD PERIOD PERIOD t  Fig.  2.2  The g e n e r a l experiment  scheme wherein  f o r a two t h e time  into  two independent  time  evolution  rr  a n d rh  time  i s governed during  periods respectively.  dimensional  axis  i s partitioned  intervals  t , and t  2  . The  by t h e h a m i l t o n i a n s  the e v o l u t i o n and d e t e c t i o n  40  The was in  pulse  used Fig  in  this  2.3.  aligned  sequence work  Starting  along  the  using  for  magnetic  two  from  z - a x i s ,  f i e l d  dimensional  gradients  imaging  equilibrium  with  a  rotates  90° pulse  the  is  that shown  magnetization the  X  magnetization  to  magnetization  w ill  rise an  to  an  the  precess  observable  inhomogeneous  application different  y - d i r e c t i o n .  of  the  Larmor  such  by  a a  T,  pulse  shown  in  the  Fig  y-direction -2(u T  phase  T  increase. +  A l l 2r  r,  then  of  the  =  2T  +  observable time,  2T,  2.4,  The At  at  2d.  i  The  =  are  +  0  In  the  caused  spins  by  w i l l  giving presence  of  the precess  with  for to  CJ T 0  the  with  a  a  +  d.  a)  of  the  w i l l  be  to  spins  around  decrease causes  of  a>  0  the  until  y-gradient  p h a s e 4>^ time  is  applied.  y-direction  spins  produces  referred  as  a  time.  spin The  echo spin  (16) echo  the  by  the  the  echo  followed  along  of  the  the  frequency  and  [2-49]  precession  re-aligned  d  180° pulse  refocussing  c a l l e d  duration  the  phase  CJ^ w h e n  to  [2-48]  y.).  G  rotation  subsequent  frequency  signal is  the  f i r s t  spins  T(B  prior  180° causes  w^d).  +  0  to  by  the  z-direction 21).  that  applied  0  As  as  p.  the  frequencies  y-gradient delay  the  (see  y-gradient,  wj =  For  around  signal  f i e l d ,  Subsequently  at another  and is  the  measured  4 OA  Fig.  2.3  Timing  diagram  for  a  experiment.  Starting  application  of  formation of  fixed  of  time  delay  delay +  T t . 2  T  T,  T  repeated 128  equal  echo is  duration  after  is the  the  at  =  T  of  +  T  y-gradient  and  switched the  the G a  d.  a  the pulse  on  on  for  that  again  a t,  experiment is  varied,  negative  After  a  further  detection  180° such  from  A  induce  duration  switched  that  the  immediately  a d  is  magnitude  increments  2T.  for  imaging  pulses  applied  that  indicates  as  equilibrium  90£ pulse  x-gradient  work  dimensional  180° rf  y-gradient  the  immediately g r i l l  spin  such  the  for  The  a  the  at  90° and  magnitude  following  two  at  period, time  t,  <  The  T. is  usually  value.  in  ^2,  TT. ACQUISITION I  A  quilibrium  spin echo  T 0  T  I  T  2Z T  I  1  >  42  Fig.  2.4  Precession pulse arrows  for  diagram the  pulse  indicate  indicated  the  magnetization  showing  sequence  the  to  following the  effect  of  F i g .  2.3.  in  direction  motion back  the  of  the The  precession.  the  180°  As  180° brings  y-direction  at  time  the 2T.  43  as  a  function  dimension obtained in  the  of by  the  interval  gradient  observation  experiment.  T,  a  x-gradient  pulse  is  application  of  the  spins  gained  the  to  by  of  vary  the  2  ,  forming  G  for  for  a  along  spins  the  is  duration The  various  causes  v  one  dimension  180°pulse.  repeated  The  is  t  second  .  that  time  The  following  procedure  G  frequency  the  applying  acquisition  phase  of  spin  values  the  t  t,  r  echo of  the  Larmor  x-direction.  during  1  from  G  The causes  X  the  refocussing  hence  G  is  x  amplitude  of  the  referred  of  the  spins  to  echo  as  at  the  quickly  time phase  2r  to  be  incomplete,  encoding  decreases  as  G  pulse.  The  becomes  x  larger. The  resulting  two-dimensional  array  of  measurement  data of  constitutes  the  time  a  response  S(G  ,t  2  )  X  with  # If  now  k,  =  with  7G  0)  =-X(B G x)I 0+  the  vector  t i  and k  x  respect  signal  to  2  k  x  k  of  =  7G  and # = -? ( B G y)I .  z  0+  reciprocal y  gives  t  2  then  the  space  the  spatial  is  Fourier  y  [2-50]  z  defined  such  that  transformation  distribution  of  t h e NMR  (57)  [251] A  t h i r d  component  dimensional  for  version  of  k  would the  be  required  experiment.  In  for  the  general,  three the  44  signal  S(r)  function  is  c(r)  Lorentzian A  a  convolution  with  for  to  resolved during  lineshape  the  allows  values  (Fig.  of  as  2.5).  period The  G^.  S(k  ,t )  A  S(z,w) along  the  intensity  two  of  NMR  signal  for  as  a  distribution  4.  IMAGE  response  due  to  is  which  of  =  is  one  chemical  spins the  chemical pulse  data  7G_t  in  is  set  and  are absence  shift is  applied  measured may  the  for  be  corresponding  z  a  as  the  signal  two-dimensional  spectrum  axis  frequency  and  dimensional a  Larmor  spectrum  function  shift  and  of  shows one  w i l l  be  the  spatial referred  to  map.  obtained  from  give  rise  change  different  to  structure  experimental the  the  the  differences  internal  to  each  dimensions,  NMR  spins,  which  CONTRAST image  spatial  on  The  the  the  k  gives  z-coordinate  coordinate,  An  (41)  z-gradient  resulting  other.  proton  distribution  detection  z  transformations with  the  and  with  2  in  measurement  z Fourier  spin  function  during  the  evolution  represented  the  procedure  freely  spectra  the  various  of  evolve  gradient  a  of  l i q u i d s .  variation  allowed of  a  in  the  the  relative in  and  which  sample.  such  as  image.  usually the in  the  the  echo  For  of  reflect  of  the  the the  the  time  contrast the  two  intensity  relaxation  varying  or  in  intensity  generally By  intensities the  of  Variations  density  patterns of  displaying,  distribution  sample.  parameters  features  by  pulse  it  is  possible  between sequences  45  Acquisition  180,  90,  t. T  0  Fig.  2.5  Pulse  X  sequence  mapping  of  the  for  the  spin  The  echo  of  and  a  during  the  shift  d i s t r i b u t i o n  z - d i r e c t i o n . gradients  chemical  is  acquired  z-gradient  evolution  period,  along in  pulse t,.  resolved the  the is  absence  applied  46  shown sets  in of  Figs.  2.3  spins  and  with  2.5,  the  spin-spin  relative  intensity  relaxation  times,  T  for  two  and  0  z, a T,  h  ,  is  given  by  -(1/T 0  w  where  ( A ^ A ^ o  larger  than  increased It  T  by  is  2  is  the  i n i t i a l  ^ ,  the  relative  making  also  the  differences  in  achieved  by  applying  consists  of  a  spins  are  to  s p i n - l a t t i c e an  to  evolve  (Fig.  equilibrium  magnetization  according  2.6).  delay, to  the  the  time  contrast  The  by  freely,  the  eq  is  may  be  applied  -Z  magnetization  equilibrium  inversion-recovery  for  the  spectroscopic  relaxation  such  in  that  contrasted  is  a  be  a  a  can  sequence  delay  to  This  in  system  rotates  direction returns  to be  which  which  the  at the  and  to  during  the  equilibrium  F i g .  image.  The  2.3  times may  t / T  [2-53]  ')  value,  the  s p i n - l a t t i c e as  2  expression  the  Following  T  according  times.  180° pulse  to  can  a  features  relaxation  2  M  A /A^  If  longer.  M (t)=Me,(1-2e'  where  intensity.  intensity  followed  equilibrium  subsequent  [2-52]  e  inversion-recovery  l 8 0 ° - p u l s e  allowed  -1fU2?  relative  echo  possible  2 4  or be  relative  an  sequence,  a  determination imaging  applied  to  intensities  pulse give of  a  9 0 ° - p u l s e of sequence T,  signals  from  47  180°  x  ~1  d,  B z  Z  11 •*y  1804  14  2.6  (A)  Inversion-recovery  the  delay,  the  spectroscopic  imaging may  be  (B) on  recovery  inversion  equilibrium  Fig.  *y  The a  d , ,  pulse  a  90°-pulse  sequence to  give  effect  of  an  system,  sequence.  may  determination  applied  spin  pulse  be  applied  of that  T,  such  as  a  contrasted  T,  in  inversion-recovery  i n i t i a l l y  at  Following  or  for an  F i g .  2.3  image. sequence  equilibrium.  48  spins be  with  given  s p i n - l a t t i c e  by  the  relaxation  < f  M , 2  contrast  components  w i l l  is  SPATIAL As  for  the  be  t  completely  discussed mapping  Larmor  spin-spin  Also,  in  of  of  the such  relaxation, limit  translational  an  uncertainty  to  be  the  imaging  the  spin  Factors  further,  IN  magnetic  frequency  positions.  vary  of  in  process  methods  and  ,a  T  w i l l  1,b'  when  removed  =  T  1,a  the by  [2-54]  or  signal  In  b  IMAGING  two  previous  distributions  spins  to  vary  magnetic cause  spatial  diffusion position  ultimately  upon  the  l i m i t i n g  Larmor  methods  the  to  the their  frequency  of  these  motion)  spins the  NMR  inhomogeneity,  resolution  of  condition  cause  according  (Brownian  the  [2-55]  which  f i e l d  the  of  2.  rely  gradients  one  the  sections,  f i e l d  as  from  satisfying  NMR  which  the  the  (1).  (1-2e  a  highest  RESOLUTION  application  1  -t/Ta )M^b (1-2e  t  5.  T  expression  Mz.q, _ M ,  The  times  and  and to  methods.  contributes is  resolution  thought of  NMR  49  For by  the  an  unwanted  linewidth  resolution,  /,  at  can  dispersion half-height,  be  l  combined  spin-spin l i m i t i n g  effects  resolution  1  /  /2'  from  fc  ^  l i f t i n g  e  the  characterized spatial  expression  4  .  r  yo/2/T(Hz/cm) ' magnetic  and can  frequencies  W (Hz)  -  of  relaxation  w  estimated  .  The  of  f i e l d  inhomogenity,  translational be  estimated  t 2 5 6 ]  diffusion  from  the  on  the  expression  ^ = • 7^/2DF  (1)  [2-57]  * where  G  f i e l d  inhomogeneity,  the be  x  indicates  position applied  that  of  the  along  spatial  the  effective  t  is  spin  the  the and  x-gradient  measurement the  resolution  may  be  The  to  time,  gradient  x - d i r e c t i o n .  due  is  x  by  indicates  considered  expression  improved  magnetic  to  suggests  increasing  the  * gradient also  and  implies  homogeneity A  and  of  given  for  the  short  For  measurement  imaging  magnetic  source  s h i f t s .  apparent is  using  that,  further  chemical an  by  of  of  larger  f i e l d  must  frequency  spins  displacement,  with Ax,  times. objects be  between  the  G  x  term  the  higher.  variation  chemical  The  is  from  shifts  a,  spins  is  and  o, 2  observed  by  AX:'V' °B  [2-58]  50  For  a  (4.8  f i e l d PPM)  and  gradients imaging  of  In  spatial  -  100  spins  be  chemical  the  imaging spatial  shift  structure  of  Other to  and  the  a  experimental derived  an  imaging  time  2  large  optimum  and  whereas is  the  of  the  mm  for  shift  distinction  chemical  In  about  chemical  possible spins  would  the  to  at  give  each  the  (58). affect  the  receiver  repetition  to  for  information  distribution  expression,  Thus,  the  is  ratio,  0.2  minimized.  image  water  gradients.  it  composite  for  mm a n d  chemical  experiments  which  needed  is  experiments,  spins  object  factors noise  using  determined of  PPM)  respectively.  1  by  is  displacement  suppress  NMR  shifts  distribution  determine  to  resolution  can  (1.2  mTnr  necessary  resolved  signal  and  chemical  composition  the apparent  protons  between  high  between  shift  10  is  differences  T,  l i p i d  of  it  6.3  rate. under  resolution  c o i l  dimension,  Mansfield optimum  resolve  a  are  and  and  Morris  conditions,  volume  the  element,  the (1)  have  for  the  (Ax) , 3  as  follows  where  S/N  radius, this and  is  and  the f  the  expression, Callaghan  (59)  desired  signal  spectrometer for  an  to  frequency  imaging  estimated  noise,  the  time  of  " a "  the  c o i l  in  megahertz.  1000  seconds  attainable  resolution  From Eccles for  51  small-scale but At  or  suggested a  microscopic that  frequency  of  270  optimal  resolution  include  line  SPIN  or  ECHO:  an  inhomogeneous  MHz  in  this  19  along  the  y - a x i s .  Spins  at  precess  at  used Mm.  of  from  x-axis  in  a  different  and  by  the  disappearance  magnetization.  The  application  of the  w i l l  change  the  motion  w i l l  result  in  one  neglects  A l l  of  the  effects  sign a  giving  effect  of  Brownian  Larmor  frequency  of  rise  correspondingly.  As  a  and  the  uncertainty sharp  of  which  d i s t r i b u t i o n ,  of  result,  w i l l  Gaussian  in  the  wi l l  phase  signal  the  w i l l  dephase transverse  and  along  the  at  or  and  to  is  to  The  cause  the  vary  be  predicted  only  distribution  if  y  echo.  of  time.  2T,  d i f f u s i o n .  the  spin  the  subsequent  time  along  molecules spins  is pulse  to  sample  180° pulse  with  90°  magnetization  positions  increase  there  A  the  can  DIFFUSION  an  prevails.  aligned  the  magnetic  that  relaxation  associated  spins  a  be  value.  not  FOR in  so  rephasing  another  motion the  phase  w i l l  Mm,  predicted  does  spins  the  a  spin-spin  to  of  the  complete  magnetization  direction  of  of  12  variation.  liquid  positions  frequencies  the  TECHNIQUE  the  be  anisotropic  narrowing  rotates  to  reasonable  work,  identical  f i e l d ,  MHz  estimation  GRADIENT  motional  y-axis  more  chemical-shift  FIELD  different  This  effects  ensemble  and  applied  accompanied  a  magnetic  tumbling  600  be  from  PULSED  Consider  rapid  is  at  urn w o u l d  broadening  s u s c e p t i b i l i t y  6.  30  imaging  So of  the  molecules  with  instead phases  some of is  a  52  obtained The  causing  amplitude  effects  of  The random  an  of  averaging  the  signal  walk  of or  (17)  is  also  be  has  been  discussed  attenuated.  lessened  by  the  by  adding  a  diffusion  term  in to  terms the  of  Bloch  (12,50)  Y  x  signal  w i l l  diffusion  HM mM M  the  relaxation.  effect  equation  For  and  and  M  - U  X§  the  y  MM - ~ . v.D.VM.  MT + MT  following  dM ^ = dt  is  3  [2-60]  K  obtained  M SB M - - * V-D.VM, T - * " +  2  2  y  2  [2-61]  dNL M ^ = -XB M,--^ V.D.VM . dt T - * r  z  Combining expression  the  expressions  for  the  complex  +  x  y  y  2  for  M  and  x  to  magnetization,  give m =  an +  i  M  y  f  w  e  obtain  lni dt  Transforming transverse  to  [2-621  =- i c j m - ^ V.D-Vm-iyG.rm. l ~ ~ 0  +  2  the  rotating  relaxation,  S  5  frame  and  allowing  for  the  set  - K + \ ) t  m-.Ve  2  .  [263]  53  Then  taking  the  derivative  dm _  with  respect  to  -(i^  0  time  +1/  Tjt  [2-64]  ff-(i«jf /Tjy 1  dt " dt and  by  comparison  with  Eq.  dt For  D  and  depending  G  expression  for  \p a n d  [2.62]  obtain  = v-D.vr-rG.rr.  only  on  hence  time,  for  a  m can  [2-65]  formal be  solution  obtained  to  the  (12)  J F.g.Fdt'-Afl-Dj F d / A r f D f ( t - r ) +  m = nrv e  [2-66]  o  with  £ =0 for o<t<r r =1 The  quantity  the  p r i n c i p a l  0  is  which (12),  and  Tanner  occur  any  time  and  the  independent  echo  Stejskal at  applied  Gdt  and f = 0 r i .  t>r,  for m/m  E= J  or  not  gradient.  occurs the at  at  spatial t  =  formation  a l l  Any  of  2r.  depending  coordinates As  of  the upon  inequivalence  [2-67]  of  discussed echo  for by  may  the  sample  the  time  54  evolution pulse  w i l l In  Fig.  induced cause  the  2.7,  spin  pulsed  echo  gradients  echo  to  gradient pulses  before  shifted  or  modification magnitude  and  the  after  (12).  For  isotropic,  decay  of  the  180°  experiment,  duration  and  the  the  attenuated.  of  G,  after  before  sequence  d i f f u s i o n ,  be  of  applied  pulse  independent given  are  A,  the  the  gradient  separation a  by  the  echo  6,  and  180° pulse  of  time  amplitude  is  by  - 2 r -*VDS(A- S/3) 2  m(2r)=m e  T  e  Thus  a  determination  obtained  by  gradient  pulse,  method is  when  b i o l o g i c a l  molecules barriers For by  w i l l to  longer the  w i l l  6,  measures  useful  and  varying  of  D,  the  G,6  or  A.  is  the  that  occurred  is  (24,61).  travel Thus  the  boundaries  and  the  diffusion  intervals,  determined For  the  of  and  the  effective  size  time,  found  w i l l  not  w i l l  be  molecule  the  the  A  in  This  porous  media  the encounter unrestricted. be  limited  c o e f f i c i e n t  over  a  restrictions  range can  (24). static  gradient  experiment  6,  be  PFG  (12).  w i l l  diffusion  can  the  A,  times,  measurements of  of  during  short  diffusion  performing the  far  c o e f f i c i e n t ,  the  as  Over  very  motion  By  bounded  [2-68]  duration  motion  the  reduced.  the  than  times,  be  When  less  tissue  motion.  diffusion  much  diffusion  not  .  * e  A and  T  are  be  of  55  77/2  / T  i  Fig.  2.7  Pulse  sequence  translational Gradient applied echo  2T  T  0  for  pulse  measurement  diffusion  pulses before  the  of and  using  duration after  sequence.  SPIN ECHO  the  of  pulsed  6 and  gradients.  separation  180° pulse  of  a  A  are  Hahn  56  equal,  so  the  decay  is  given  by  m(2r) = m„e The  decay  the  rf  is  independent  pulses  experiment  provided For  (62).  experimental), expressions The scalar to  spin  the  gradient  make  has  resolution. diffusion  This  reproducibility subject gradient that  as  of  the  increases. signal,  due  the  or  order  of  to  bandwidth  the  by  c o i l  (see  these  the  time  same  effect  of  gradient shift  determination as  accuracy  The  and have  more  detection  been  static  experimental NMR  of  aqueous  the  a  Compared  (64).  microemulsions.  the  This  spin-spin  and  the  the  fixed.  chemical  such  of  advantageous  2A,  and  measurements  measure  the  thus  pulsed  giving  increased,  the  by  analysis  (13,29,65).  from  of  of  the  surface  duration  echo  mixtures  diffusion  is  the  simultaneous  affect  suffers  is  J-coupling  solutions  gradient In  for  lengths  during  given  It  the  to  the  papers  be  a  modulated  simplifying  which  several  using  (54,63).  advantage  of  method  be  keeping  allows  vary  and  inhomogeneity.  measurements  micellar factors  not  then  magnitude  c o e f f i c i e n t s  solutions,  rf also  effects  the  amplitudes  do  w i l l  coupling  gradient  technique  The  may  constant,  static  [2-69]  3  the  these  the  whilst  the  e  experiments  gradient  pulse  relaxation to  echo  -22f6Dr  2  of  decay  despite  spin-spin  vary  would  the  T  3  2  .2  -2T  the  f i e l d  limitation  linewidth  rapidly system  also  decaying w i l l  have  to  57  be  increased  which  w i l l  power  output  keep The  the  generation  if  the  are  and  amplitude  means  of  for  eddy  where  z-gradient of  the  in  applied  normal  intensities the  and for  a  D  given  D,  A  =  2r.  Since  the  eddy  evidence  that  and  of  used a  (65).  pulse  in  for  imaging  further  the the  diffusion spins.  In  images,  spins for  pick-up  experiments,  contrasted set  power  is  given  spins  with  the by  is D  -* G 8  with  to  the  of  shown  cause  intensities  and a  stable  imaging  is  containing  diffusion  relative  c o e f f i c i e n t s  to  in  achieved  are  proportional  molecules  d i f f i c u l t y  the  to  linewidth.  movement  sequence  are  the  in  the  increased  the  imaging  gradients  procedure  compensation  be  NMR  applied  pulse  signal  and  1% c a n  pulses  change  diffusion  a  be  requiring  sample  y  the  and  of  to  than  a  linewidth,  experimental  and  comparing  [2.68]  pulses  x  the  of  greater  currents,  are  have  encounters  contrasting  Such  w i l l  provided  pulses  (66-68).  c o e f f i c i e n t s  has  response,  increasing  elimination  acccuracies  gradient  attenuation  Eq.  B,  gradient  clean  diffusion  in  With  of  minimized,  2.8,  noise.  transmitter  Callaghan  sequence  transient  technique  effects  further  the  its  gradient  and  For  Fig.  of  more  f i e l d  pulsed  currents.  improve  admit  rf  supplies  to  y-gradient  (A-S/3)(D,-D ) 2  is  applied  in  a  similar  58  go;  180  1  0  2T  Time Fig.  2.8  Pulse The  sequence  spin  echo  y-gradient is  repeated  encoding  cause  is  d i f f u s i o n  acquired  starting for  at  time  pulses  diffusion  pulses  also  of  contrasted  in  incremental  x-gradient  z-gradient to  for  the  presence  2 r - d . values of  The of  duration  duration  contrasting.  imaging.  6,  of  the  experiment phase 6. are  Fixed applied  59  fashion,  7.  a  normal  MEASUREMENT Multiple  OF  has  of  been  resonances  in  the  applied  gradients d i f f u s i o n a l  We  describe  was of  used  to  work  was  cycling  of  of  measuring  the  In  double  measured  the  operators  coherences,  observed a  I  (77).  convenient  is  I x =  to ,  a  quantum  NMR  I  ±1.  y Zero  y  and  ,  2 I  However, means  for  in the  pulses has  absence  (75,76)  only  and  described and  phase for  been  the of  to  this  the  used  for  (74). free  rf  radiation,  described single  by  quantum  coherences by  combinations  cannot  two-dimensional observing  While  molecules where  method  diffusion  using  polarization,  quantum  pulsed The  (21,22).  echoes,  the  using  anisotropic  excitation  of  coherences.  echoes.  method,  correspond  are  z  the  experiments  of  I  spin  to  measurement  quantum  crystals  spin  the  diffusion  fluorinated  measured  >  of  Multiple  s e n s i t i v i t y  allow  single  similar  of  and  AM  by  coupled  out  (69).  increased  liquid  quantun  pulsed  AM  x  in  components  correponding  than  ECHOES  between  f i l t e r i n g  spectra  measuring  diffusion  decay  the  operators  for  in  SPIN  allowing  coherences  would  radiofrequency  normal  induction  and  completed  the  an  multiple  molecules  detection  show  contrasted.  QUANTUM  by  useful  measurement  select  being  order  be  motion  the  diffusion  MULTIPLE  overlapping  also  previously  oriented  to  (70-73)  slower  BY  higher  complex  coherences  gradients  already  spectroscopy,  shown  quantum  now  is  DIFFUSION  quantum  manipulations spins,  image  be  the  d i r e c t l y  NMR m e t h o d s  multiple  of  quantum  provide  60  transitions. The  pulse  pulse  sequence  90  T/2  -  X  to  -  prepare  allowed and  at  180  a l l  to t  sequence,  -  X  orders  evolve  =  t,  T/2  +  -  of  a  in  90  T/2  -  X  F i g .  -  coherence  freely  2T,  shown  during  180  uses  -  x  period  pulse  is  the  T/2  The  (7 8).  the  90° mixing  2.9,  -  rf  90  coherences  2T  <  t  <  t,  are +  2T  applied  A  to  transform  single  the  quantum  magnetization  coherences. from  achieved  by  multiple  quantum  signal  which  coherence  (71,79).  measuring  diffusion before  evolution  period.  the  with  spins  proportional magnitude. the only may  sign  p a r t i a l have  to  The  of  a  a  spatially order  phase.  rephasing during  and  delay  followed  by  during  n  is  due  t,  as  an  is  modified  applying  only  to  n  quantum  gradient during  the  dependent  phase  which  coherence along  second the  n,  and  the  time to  to  gradient  time.  of  label  is gradient  y-axis  positions  intervening  for pulses  serves  because  the  identical  pulse  the  is  period.  sequence  applied  the  of  gradient  of  Then  observable  coherences  180° pulse  f i r s t  180° pulse  changed  during  further  after  of  mixing  obtained  pulse  by  The  the  the  the  into  detection  pulse  period  evolved The  and  orders  gradient  in  coherences  Selective  evolution  echo  magnetization  equally,  a  periods  spin  MQ  different  applying  gradient-delay The  unobservable  changes  pulse the  The  causes  spins  spin  echo  61  TT/2,  MQC PREPARATION  A  2T  7T  7T/2, l y  B  3T <  —  s  8  + mixing period  2.9  Pulse  sequence  detection pulse the of  MQC  +  Eq.  After  pulses  double pulse  before  in  preparation  coherence.  (A),  the  multiple  sequence  gradient  7r  of  for  and  (B)  with  quantum [2.71]  period the  applied  (ir/2)^  mixing  and  t r i p l e  are  is  selective  echoes.  prepare  applied  gradient  spin  and  to  are  after,  measurement.  preparation  The  during  a l l  orders  pulse,  to  produce  single  (C)  quantum  echoes.  pulses  applied  of for  duration diffusion  6,  A  62  w i l l  decay  according  evolution,  by  to  Eq.  replacing  KITT\  G  by  '  A  [2.68]  2  T  /  nG,  T  A(2r)=At,e  8.  SPIN  ECHO:  Flow  w i l l  out  of  the  gradient,  to  the  vary  THE  EFFECT  diminish  region  with  of  also  cause  their  to  for  -**nG D/(A-*/3)  2  OF  spin  the  quantum  2  RANDOMIZED  c o i l  n  give  ' e  the  the  modified  echo  and  [2-72]  FLOW signal  w i l l ,  Larmor  .  in  by  the  frequency  moving presence  of  the  0  spins  t  [2-73]  = c J * G . r ( O M G . [ ydt 0+  = «j'+ o  v  may  the term  CJ '  is  0  depend  phase o> ' 0  the upon  that is  is  i n i t i a l  gained  completely consequently,  from  i n i t i a l  the  Larmor  the  Bloch  equations  - ;  by  is (5)  frequency, time.  the  removed only  0  o  and  positions  frequency  t Tvdt -  Larmor  position  experiment their  of  v e l o c i t i e s  *j(t) = w +*G.r(t)  where  spins  spins at  the is  As  due  to  the  2T  in  a  time  displacement  by  the  an  velocity  discussed  measured.  described  and  The  e a r l i e r , constant  spin of  echo  the  spins  variation  additional  term  of in  63  The  f  echo  indicates  the  experiment,  magnetization  contribution  the  expression  due for  to  flow.  the  For  a  spin  complex  becomes  {-iJ[Hir)-2Jhl} [275]  m(T) = m(0)e f  where  T  was  defined  previously  H (t)=  and  S-Gdt',  h=H(r)  [276] S(t)= J y d t ' , s = S(r). For flow  a  with  pulsed  gradient  velocity  o s c i l l a t o r y  v ,  experiment  the  0  amplitude  (  weighted  v e l o c i t i e s  of  steady,  the  echo  uniform shows  behaviour  m|2T) = e -  The  with  average  for  a  i j e v  -  r S  Gaussian  .  [277]  distribution  of  is CO  1  1  m(2T) =  e  f  J2 TT <V*> v where is  <v>  zero,  echo  w i l l  is for  the  decay  ^(v-<v>f  e  -i,6vT«  d  v  [  2  7  8  ]  00  average  motion  2 < v  which  according  velocity. is  If  random  the in  average  orientation  velocity then  the  to  m(2r = )f  e  4<v  ' ' >!r  eVs  '  [2-79]  64  with  an  apparent  and  [2.79]  d i f f u s i v i t y ,  by  comparison  of  Eqs.  [2.69]  D^ = 3<v >r/4. 2  The  combined  single  system,  c o e f f i c i e n t  The  A.  the  would  diffusion  give  apparent  observation  rise  and  to  a  random  net  flow,  for  a  diffusion  diffusion  coefficient  would  increase  time.  EXPERIMENTAL The  aspects  following of  magnet  and  on  c o i l s  APPARATUS  a  discussion  c o i l  f i r s t ,  then  measurements gradient  is  gradient  implemented,  1.  of  of  observed  with  effects  for  design  surface  the  1.9  FOR  and  microscopic  for  are  of  T  c o i l ,  DIFFUSION  in  requirements,  modifications  which  imaging  the  pulsed  magnet.  summarized  the  using  gradient  Specifications Table  MEASUREMENT  6.3  spin of  were  echo  the  2.1.  AND  MICROSCOPIC  IMAGING Measurements contained (see  in  chapter  of  5 mm NMR IV)  and  diffusion tubes on  and  imaging  including  Acetabularia  for  samples  Barbara medi t erranea  colfaxiana (see  T  65  chapter 54  IV)  were  mm b o r e  with  programmer.  the  for  these  lock  and  the  y  such  sample.  the  The  objects  length.  of  the  c o i l  and  in  the  shape  s i m p l i f i e s the  probe  for  G^  which  and same  the in  of  G^,  of  an  of  an  f i e l d  T,  pulse  was  not with  already  gradients  of  necessary  1 mTm"  to  1  construct  gradients  measurements  the 1  in  of  can  NMR  be  Maxwell were  size  which  and  up  to  higher  probe and Such c o i l s for  to  of  that  allow  imaging  approximately produces  for  for  G  distortions  to  the  x,  can  be  have  and  conform  inserted Golay  (56,80). y  and  This  include z  1 cm  superconducting  preferred.  c o i l s  of  measurements,  c y l i n d r i c a l l y  samples  a  the  configurations  but  are  wires  produces  were  diffusion  Several  of  region  c o i l s  gradient  wound  used  the  achieved  with  way.  current  gradient  the  be  arrangement  over  l i t e r a t u r e ,  usual  designs  6.3  interfere  was  larger  e l e c t r i c  minimum.  the  and  was  diffusion  construction  the  it  magnet  generate  interferes  described  the  gradients  produce  range  a  c o i l s  the  to  for  at  magnets  since  consists  kept  293B  spectrometer  100 m T m "  might  and  the  which  a  Oxford  of  the  magnetic  about  by  on  imaging.  Nonlinearity  image be  in  passage  which  in  should  c o i l s  made  based  1180 c o m p u t e r  directions,  c r i t e r i a  of  magnet  While  accurate  varying  gradients  these  for  spectrometer  channel  c o i l s  z  of  gradient  linearly  with  shim  resolution  that  been  lock  and  required  A  a  Nicolet  vice-versa.  system  spatial  a  experiments  with x,  another are  The  in  supplied  with  superconducting  Instruments,  used  made  z  into  c o i l s  Presumably shim  c o i l s .  66 One  other  design  inductance  10  quadrupole  c o i l  windings these  is  for The  which  times  that  current  Biot-Savart  that  gradients  of  a  the  is  d i f f i c u l t  more  is  distribution to  an the  of  construct  magnet.  B,  passing  with  Maxwell  However it  f i e l d ,  law  uniform  than  superconducting  magnetic  e l e c t r i c  less  (81,82).  such  a  gives  produced  through  a  at  a  wire  point  is  P  given  by  an  by  the  (83)  }X l  r  B(r )  djx(r 2  0  £ t  )  [282]  z  where for  I  is  the  (Fig.  point  2.10).  closed  loop  induction of  the  the  P  and  The in  due  The  the  magnitude  the  two  and  r  or  is  are  2  current  integral  to  element  over  current more  induction  the  every flows.  current  produced  position  d l  by  respectively  element The  loops the  vectors  dl  of  the  magnetic is  the  vector  individual  separately. magnetic  inhomogeneous. produced  r,  the  which  magnetic  elements  loop,  current,  by  a  A  f i e l d simple  single  direction is  produced  given  i l l u s t r a t i o n  current of  by  B  loop.  p a r a l l e l  by 2  any  c o i l  of  this  Along to  the  the axis  is is  the  axis and  f i e l d  of its  the  sum  67  Fig.  2.10  The  coordinates  produces  a  position  vectors  of  magnetic r,  the  current  f i e l d and  r  at 2  element  point  P,  dl with  respectively.  which  68  In  general,  rank  the  gradient  of  a  magnetic  f i e l d ,  B,  is  a  second  tensor,  =VB  H,  =Z j r ' J  [2-84]  U=x,y,z  ij but  in  the  presence  components  with  s i g n i f i c a n t l y  Thus  for  G  z  to  f i e l d ,  is  a  much  p a r a l l e l  and  the  gradient,  B  of  good  along  given  to  larger the  f i e l d  main  axis  of  only  0  f i e l d  approximation  the  B ,  those  contribute  (I)  the  current  loop,  the  by 2  (z + r ) which  is  required depends  to  of  the  Maxwell wire  w i l l  generate  even  order  of  the  is  zero  shown  not  in  the  However  undistorted  inhomogeneities 1  c o i l  consists  opposing  derivatives  F i g .  'Originally  an  connected  opposing at  constant.  produce  upon  The loops  also  loops c o i l  so  a  image  of of  uniform  the two  and  gradient the  current  passing  magnetic  f i e l d s .  By  is  the  f i e l d s  chosen  center  (84).  so  The  the  circular through  symmetry,  cancel.  that  f i e l d s .  of  that  of  resolution  applied sets  The third  resulting  is  them  the  separation derivative  geometry  is  2.11(B).  referred  to  as  anti  or  opposed  Helmholtz  c o i l .  68A  Fig.  2.11  (A)  Cross-sectional  chamber  of  aluminium c o i l  the can  four  slots  v e r t i c a l  at  are  are  with  Only  the  ,the  The  angles  to  sample  outer  slots  concentric  shown.  right  the  with  former each  for  the the  also  other  has for  the  windings.  (B)  &  (C)  the  windings  and  the  The  x-gradient  rotated  which  former  through  probe  removed.  windings  Perspex  NMR  view  The  positions for  the  y-gradient  through  and  z-gradient  (Golay)  c o i l 9 0 ° .  the  is  the  c o i l same  directions (Maxwell)  of c o i l  respectively. as  in  (C)  but  B  C  i«-2r—H  i<— 2 r—>i  Perspex gradient coil glass rf coil sample tube  i—•—i  1 cm  ON  70  The the  Golay  magnetic  c o i l  f i e l d  design in  is  terms  based  of  upon  the  spherical  expansion  harmonics  of  (85)  where  oo 77  =-I Z r" P™( cose) [A* cos m0 • B ^ s i n m / ] .  5  n-o  7?-/  In  the  along  presence z,  expressed  [2-87]  the  z  in  of  a  strong  component  terms  of  magnetic  and  the  its  f i e l d  B  derivatives  spherical  chosen  0  may  to  be  expansion  B =- e | | ^ | f .  [2-88]  2  The vary  f i r s t with  few x,  constructed sphere  along  terms y,  by  where  positive  and  and  this x  2  - y  locus  the  of  expansion  conductors a  vanished,  values  configurations  of  of  the  the  viewed  from  flat  pole  faces  for  electromagnet.  producing  x  y  described  by  Hoult  Numerical the  Golay  c o i l  gradients and  of  keeping  a  the  gradients  of A  which  c o i l s  surface  spherical  center  Richards  evaluation produces  for  such  the  current  projected,  and  the  those  of  a  of  the  These  flow the  were  harmonic  track  function.  then  an  on  particular  function  negative  include  Originally  (84).  2  positioning  the  function  geometrical  z  of  l i e  loci  were  sphere,  modified  to  version  superconducting  for  magnet  is  (80). Biot-Savart which  are  law  shows  linear  to  that within  71  -5%  over  a  The in  F i g .  should  region  2.11(B) be  be  wound  on  aluminium  5  mm.  outer gauge,  of tube  as  in  37  Grooves, surface  the  copper  2.11(A)).  I n i t i a l l y ,  three  c o i l s  another  20  turns  for  magnitudes given  in  discussed (Fig.  z  of  was the  Table in  the  2.12(A))  inductive  with  reduce  problems  ( d i g i t a l  to  the  set  with  for  the  gradients and  on  both  c o i l s with  analog  the  The  of rf  served  feedback.  converter)  for  to  the  and  by  each  replaced  x  into  these by  for  the  y,  the  and The  are to  be  f i l t e r s  minimized  the  27  c o i l s  methods  interface from  the  c o i l s  Resistors  the  connected  impedance with  a  the  work.  frequency  increase  of  and  the  by  thickness  used  for of  c o i l  for  wall  were  an  glass  gradient  turns  High  usual  inside  machined  each  input  the  outer  mm a n d  majority  An  a l l  simplify  l o c a l i z a t i o n  c o i l .  to  were  insulation  determined  leads  with  34  12  section.  of  removed  produced  were  results  coupling  series  used  2.1,  thermal  turns  c o i l s gradients  to  fitted  diameter.  used  elements  the  the  (56).  2.11(A)).  physical  8  of  necessary  3 mm w i d e ,  wire  current  gradients  device,  was  radius  which  consisted  diameter  (Fig.  but  work  and  c o i l of  on  z  (Fig.  operation  provided  and was  provides  3 mm d e e p  insulated  it  shown  outer  the  linearity y  mm o u t e r  temperature of  x,  this  is  location  resolution  normally  cylinder  for  a  surfaces  former,  high of  the  optimal  c o i l s  slots  a  for  that  used  where  define  same  to  which  variable  so  the  probe  components  Perspex  0.5a  (C)  When  shapes The  &  wound  achieved.  Dewar,  £  specifications  is  these  r  and  DAC  computer  in  and  72  Coils for 270 A.  B.  Number Gradient Magnitudes { mTm" A"') of turns 1  X Y  8 8  Z  8  X Y Z  12 12 20  Resistance Inductance (n) (yUH)  38-9 382 —  48-3 50-4 655  Radius of coils Gauge of wire C. X.Y shims —  1-1 1-1 0-6  35 32 12  1-8 1-6  60 62  1-0  43  1-1 1-1 0-5  360 370 110  1-6 cm 27  1-1 mTm'  1  D. Coils for 80 X Y Z  10 10 15  1-82 1-82 1 85  Radius of coils Gauge of wire  Table  2.1  8 cm 12  Specifications  and  gradient  gradient  for  the  c o i l s  resolution  probe  shim  c o i l s  of  (C) ,  and  (D)  .  for  the the  in  modified  (A)  high  magnitudes  and  (B),  resolution  surface  c o i l  of  high the  x  and  magnet  apparatus  in in  y  73  0  3fl  x,y  2 A  z  coil  5^tH  0 5^H  -^nnr—i  100 p F  _n_  B  inv/non inv  100 p F  on/off manual control  OUT  DAC O  Fig.  2.12  (A)  Circuit  f i l t e r s  diagram  placed  on  for  each  the lead  high of  frequency  the  gradient  c o i l s . (B)  Schematic  unit.  diagram  of  the  gradient  control  74  control the  lines  from  generation  of  the  variable  pulses  (Fig.  2.12(B)).  TECRON  7560,  supplied  constant  voltage  provided  currents  susceptible  to  up  feedback  it  safely.  Measurement  times  was  with were  found  the 60  of  c o i l s  MS f o r  2.13).  Correspondingly,  shaped a  l i n e a r i t y  1 ms.  of  NMR  length  Further experiments.  of  into  the  50  mTm" . 1  made  ms  with  aluminium Slots,  to  11.5  currents  were  the  resistors showed  % of than  in  rise  gradient 99  %  (Fig.  applied  using  mm i n  longer  a  for  a  saddle  diameter,  for seen  pulses  of and  with  decay in  away the  moderate most  in  the 5  cm  The  were No  magnet times  f i e l d s  in  and  long,  there.  the in  by  probe  gradients  often  applied.  NMR  induced  currents  effects  variations  were  gradient  eddy  such  actual  currents  mm w i d e  should  observed  effects  2  in  covering  minimize  eliminate  much  These  experiments  to  eddy  ms, 50  the  covering  produced  measured  c o i l ,  was  cut  to  were  eddy  the  electronic  were  from  f i r s t  magnet.  5-10  pulses  The  of  While  better  observed  wall  i t s e l f .  was  the  were  be  98  were  the  up  output  of  in  controls  oscilloscope,  achievement  working  in  across  and  amplifiers  could  complications  in  for  an  A  and  M-600  29 M S .  pulses  was  15  gradient  gradient  attempt  to  signals  (AMCRON  the  gains  allowed  control  gain  However,  voltage  transmitter-receiver  180° pulse  about  high  the  The  of  at  using  pulse.  minimum  A.  the  TTL  variable  20  up  programmer  INTERNATIONAL)  with  that  pulse  amplifiers  CROWN  and to  293B  amplitude  Audio by  mode  testing  series  Nicolet  spin  source  of  lasting of echo of  75  < CL  o  0  2  4  6  8  Input (a.u.)  Fig.  2.13  Graph  of  amplifier  input  (arbitrary  output units).  (A)  as  a  function  of  DAC  76  these shim  2.  variations c o i l s  or  APPARATUS  is  the  unknown.  main  FOR  Interactions  f i e l d  SURFACE  may  COIL,  be  the  PULSED  with  either  the  cause.  GRADIENT  SPIN  ECHO  MEASUREMENTS Pulsed (see  chapter  Oxford  III)  NT-300  magnet  inadequate  for  rise-times,  of  gradient  gradients wound  around  diameter pegs the  with  with  were  The  The  amplifiers operated gradients the  in  Z  spherical  c o i l  constant  bulb  2  and  by  be  PVC  using was was  were  to  current  B.2) mode.  gradient  of  linewidths  (4  cm  for  diameter)  and  The  grooves, the  except The  spectra  f i l l e d  y  another  higher  c o i l s in  were  outer  locations  3  of  same  the  were  8.3  mm d e e p  of  the  cm  for  and  Tecrons of  were the  determined  taken  9  audio  magnitudes  c o i l s  by  Hence  radius  using  long  provide  inches  provided  of  overcome  6.5  (section  the  but  former,  in  modified  directions  x  wound  bore  of  e f f e c t s .  effective  cm  c o i l s  The  an  a  forearm  gradient  p a r t i a l l y  thickness.  30  with  times.  wall  human  T,  because  constructed  rise  a  z  measurements  was  inch  before  measurement  y  eddy-current  on  produced  x,  large  current  as  for  - 1  on  1.9  b u i l t - i n  only  shorter  0.25  The  a  magnet  could  determined  c o i l s .  mm w i d e .  console.  c o i l s  pegs  using  superconducting  diffusion  and  measurements  performed  10 m T m  which  pre-emphasis, set  NMR  gave  spin-echo  were  Instruments  Nicolet the  gradient  with  by  a  with  2  [2-89]  77  water  (Table NMR  surface Teflon  2.1).  signals c o i l  tape  produced  only the  the  a  surface the  depends  of  c o i l  f l i p  B  is  their in  1  using  a  27  loops  of  of  and  to  the  center  the  The  exact  the  signal  is  of f l i p  assumed  is  xy  in  plane  magnitude  provided (Fig.  insertion It  was  of  found  aluminium  c o i l ,  where  the  region was  support  2.14).  percent  angle  that  c o i l  few  with  The beaker produce  the  magnet  of  water,  spectra  is  of  depend is  the  is  matching  of  the  caused to  and  surface  wrap  minimize c o i l  Perspex  the  palm the  of  spins  to  For  NMR,  c o i l .  Along  decreases  of  1.5r  from  (86,87).  radius  region  the  from  pulse  from  of  f i e l d  , xy  the  a  The  plate  which  also  tuning  to  capacitors  was  rest  such  on  and  that  the  plate.  capacitors  coupling  except  It  roughly  c o i l .  c o i l  which  length.  the  plate  inductive system,  rf  important.  c o i l  upon  diameter a  the  distance the  with  and  B.  detected  for  the  a  and  on  arm  to  r  mounted  transmitter-receiver i t s e l f ,  of  necessary  f o i l  w i l l  signal  Placement the  at  distribution  obtained  hemispherical surface  a  wire  contribution  position  the  diameter  the  inhomogeneous  1  monotonically  mm  copper  distribution  angle  l , xy c o i l , the  the  two  The  upon  component  axis  of  insulation.  by  signal  measured  consisting  correspondingly the  were  for  of the  with  the c o i l  sample. was  shimmed  using with  an  using  optimal  linewidths  of  the  surface  pulse about  c o i l  length 14  Hz.  of  and 1 0 M S  a to  TOP VIEW  It surface coil  SIDE VIEW Perspex  capacitor  Styrofoam support  1 cm Fig.  2.14  Schematic  diagram  of  surface  c o i l  probe.  OO  79  3.  PARAMETERS A l l  c y c l i n g  to  and  was  for  that  imaging with  A l l  NMR  here  to  of  pulse  was  a  for  an  and  data  the  before  time  point  to  FID,  was  k  e~^^, is  -y  at  to  echo  time  In coincide  period. and  signal  r a t i o . the  apodized  refers  to  with  transformation  given  180°  directions  the  chosen  where  echo  the  obtained.  Apodization  noise  spin  d i f f u s i o n  corrected  experiments  and  and  In  a c q u i s i t i o n  Fourier  exponential  y  be  NMR  a l l  phase  measurement,  the  could  domain  signal  In  i n i t i a t e d  baseline  time  d i f f u s i o n  decaying N  echo  were  the  function  improve  90°  the  was  transformation.  m u l t i p l i c a t i o n weighting  of  signals  Fourier  along  spectra  the  quadrative  c o r r e c t i o n .  d i f f u s i o n  a c q u i s i t i o n  experiments,  with  imperfections.  sensitive  middle  before  pulse  data  the  and  alternately  for  phase  performed  baseline  imaging  applied  compensate  EXPERIMENTS  were  automatic  experiments, so  NMR  experiments  experiments, pulse  FOR  For  a and  is  used  normal  weighting integer  the  j  function =  0  to  N-1  by  7T * line broadening 2 « s w e e p width The  l i n e  and  surface  weighting for  an  N  broadening c o i l  transformation. power  spectrum  0.3  spectra  function point  was  FID  of was  After was  the  Hz  3  respectively. form  applied the  and  sin(7r  c a l c u l a t e d  to  for In  high  NMR  j/N),  resolution  imaging,  where  N-1  Fourier  transformation,  the  produce  the  each  j  =0  a to  before  second  Hz  Fourier  image.  80  The is  f i e l d  given  by  of  the  view  (FV)  r e l a t i o n  in  a  dimension  of  the  NMR  image  the  entire  3  sweep width (Hz) y gradient magnitude (Hz/cm)'  FV =  2TT The  sweep  spectrum an  width of  same  the  pulse  in  condition  be  frequencies  undistorted  the  must  image  each  of  the  sequence dk,  =  dk  be  in  in  enough  the  spatial 2.3,  7t,dG  =  components In  so  that  which  imaging, for  8  could  as  the  used  were  increasing  with  by  16  peak  Straight determination  3  of  this 7G  Sweepwidth  of  dt  in  view the  the  where  k,  and  2  that  must  be  image.  in  reciprocal  available  samples,  k  For  are  2  the  either  stacked  is  each  from  time  maximum  period  as  space.  dwell  detection  levels,  the  and  used  line  of  in  k  diffusion  III  were  of  of  order  results  x-coordinate,  relaxation  (chapters  heights  f i e l d  in  dark  14 M S  gradient 210  mTm" . 1  plots  for to  was  a  of  proton  fixed  light  y  or  for  s i g n a l .  integration of  the  color  proton  measurements samples  in  Also,  y  smallest  versus  Measurements were  vector  displayed  amplitude  images  the  mm d i a m e t e r  be  Images signal  of  the  encompass  dimensions  x the  to  sample.  obtained,  F i g .  or  2  large  f i t s  to  high  appropriate times, IV)  and  because  spin-spin  the  from  of  data  T,  and  T  overlap  from  see  s i g n a l . 2  biological d i f f u s i o n ,  between  lineshapes, times,  footnote  spectra  For  for  f  s u r f a c e - c o i l  relaxation  receiver,  resolution  and  number  peaks. for  the  diffusion  6,  p.85.  81  c o e f f i c i e n t s error  was  to  ±  lineshape  quartic  obtained  estimated  correspond to  were  two  data  a  y  is  the  the  deviations.  For  data  =  data  reduction  the  The  slopes  curve  and  f i t t i n g  routine  for  used. times  using  A{l-[1+W(1-e  T  is  t  RESULTS  U  GRADIENT  AND  Normal the  a  were  three  calculated  parameter  from  fit  to  the  -R/T  value,  ) }  e  -x/  T  [2.92]  }  W accounts  s p i n - l a t t i c e  for  relaxation  the  i n i t i a l  time  and  k  delay. were  performed  at  room  temperature.  in  an  NMR  tube,  9 0 ° - p u l s e  in  the  presence  DISCUSSION  MAGNITUDES NMR  spectra  application  gradient,  obtained  the  measurements  B.  static  standard  relaxation  relaxation  A l l  after  in  equilibrium  magnetization, is  squares.  (88)  function  A  least  uncertainty  was  inversion-recovery  linear  the  Nicolet  polynomials  S p i n - l a t t i c e  where  from  by  using  are the  x  for  of  a  water  shown  in  and  shim  y  F i g .  2.15.  c o i l s  of  The  recorded of  gradients  the  a were  superconducting  magnet. The  magnitude  calculated G  = 1 . 1 1  from mTm  -  1  the ,  is  of  the  gradient  linewidth consistent  at  produced  by  the  shim  c o i l  half-height,  with  values  calculated  from  a  82  3  Fig.  2.15  Spectra  and  position (B)  and  graphs  for x  the  shim  x  c o i l  transmitter-receiver (D)  shows  pulsed ms,  8  the  20-200  Larmor  frequency  shim  c o i l  (A),  (C)  with  a  (6  mm  attenuation  of  the  diffusion ms).  y  vs  shim  c o i l  smaller  c o i l  gradient =  of  diameter). spin  experiment  echo (A  =  in 280  83  graph  of  (Fig.  2.15(A))  with  Larmor  pulsed  and  2.5  f i r s t larger the  zeroes  methods  nonlinearities calculation In  an  obtained  (Fig.  that  cause.  The  smooth  curve  1.08 by  used,  were  in  of  mTm" , x  of  of  the  The  the  Larmor  shim,  is  and  produced  for  G  y  y  linear  in  component  c o i l s .  c o i l  was of  supposition and  not  power  to  the  was  a  of  that  1.2  an  was  coordinate  gradient  of  rt)  independent  our  magnitude  that  optimally  radiofrequency  a  from  J,(G  shim  shim  y  When  the  gradient  vs  the  suggesting  the  was  value,  obtained  not  confirming  to  *  large.  by  the  The  from  from  was  frequency  similar  a  of  asymmetry  of  2.2).  too  values  effective  the  agreement  magnet  probe,  for  experiment  average  values  spectrum  corresponding which  1  the  which  echo  (Table  much  the  position  spin  the  excellent  gradients  the  a  of  values  was the  distribution  graph  via  taking  a f f e c t i n g  in  nonlinearity  function  water  rt)  2.15(B)).  inhomogeneous  of  were  asymmetric  orientation  a  known  by  J,(G  weak  experiment an  of  were  for  shimmed,  the  obtained  1  gradients  four  using  c o e f f i c i e n t  mTm" ,  five  as  c a l i b r a t i o n  gradient  s e l f - d i f f u s i o n =  frequency  produced  mTm" .  The  2  Ay* other  methods  component observed  of in  magnet  is  either  the  shown Fig.  in  only the  the  gradient  the  2.15(C)  or  y  the  2  is - y  gradient  spectrum are  x  due  and to  the  estimation  (Table  gradients  shimmed; x  allowed  an  2  to the  2.2).  dependent shim be  can  of  The on be  linear  nonlinearity how  well  adjusted  nonlinear.  discontinuity  inhomogeneous  the  The in  the to  cause  distortion the  graph  distribution  of  of  84  Method of  x-shim  y-shim  x-gradient  1.08 ± 0.02  2.43 ± 0.03  calculation  Linewidth  1.11 ± 0.02  Lineshape**  1.12 t 0.04  1.10 ± 0.06  1.11 ± 0.05  1.04 + 0.09  2.39 + 0.11  2.47 ± 0.3  2.79 + 0.3  2.45 ± 0.3  Calibration*  1  J (&rt) x  a  C  2.51 ± 0.09  Uncertainties are ± 2 a ^From graphs of frequency vs. position fr'(o) - 1.2 ± 0.2 mTm" y ^By a pulsed f i e l d gradient d i f f u s i o n experiment. C  2  Table  2.2  Gradient J,(Grt)  magnitudes and  by  c a l i b r a t i o n  linewidths, by  lineshapes,  d i f f u s i o n .  85  radiofrequency (diameter A number about  6  38  c o i l  gauge  G  2.43  2.  a  A  diffusion  OF  beginning  radiofrequency information  d i s t o r t i o n . deadtime,  by  the  with  (-sin  u t i l i z i n g  a  signal  can  be  the  turns  current the  of  of  of  64  mA,  linewidth,  that  obtained  1  of  when  decay is  loss  large  set  the  to  allow  equal  to  of  the  a  a  a  delay  base  the  in  line  during of  have  the the been  spin-echo  produces effect  longer  of  rapidly  problems  the  domain  reduction  of  are  and  convolution  echo  much  a  zero  feature  without is  to  Those  natural  time  intensity of  large  gradients  of  part  leads  is  with  breakthrough  in  i n i t i a l  x)/x.  time  lineshapes  c h a r a c t e r i s t i c  acquired  echo  8  mTm" .  avoid  spectrum  formation  provided  a  signal  the  time  to  acquired,  experiments: which  fast  the  and  a  of  gradient  with  2.39  arise  The  resulting  spectrum  surmounted  not  =  a  from  procedure  (55).  ratio  With the  the  acquisition  is  noise  G  w i l l  when  with  agreement  analysis  Normal  content  signal  to  c o i l  TIME  the as  pulse  produce  calculated  DEAD  with  2.16).  to  experiment  good  with  associated  before  ideal  in  dispersion,  (Fig.  signal  an  RECEIVER  signal  decaying  transmitter  15 mm c o n s i s t i n g  experiment,  d i f f i c u l t y  is  smaller  found  gradient was  1  frequency used,  of  was  In  1  mTm" ,  EFFECT  a  radius  wire  1  magnitude  from  of  mTm" A" .  the =  from  mm).  Golay 27  power  than  a  secondary  from the  dead dwell  86  Time (ms)  Fig.  2.16  The of 0.3  spin a  echo  signal  y-gradient ms.  of  76  is  acquired  mTm"  1  and  in  the  lasts  for  presence about  87  time*. The  gradient  acquired  after  presence  of  times  100  and by  (D)  show  the  the  static  the  over  dwell  and  3.  time,  EFFECT As  OF  region  maximize  direction be  v a l i d  shorter  of  the  signal  for  F i g .  the  and  y  in  and  1  while  echo  (C)  were the  with  Figs.  2.17(B)  spectra,  of  the  much  better  F i g .  2.17(C)  dwell  obtained  spectra signal  to  shows  because  shows noise  some  of  reduced  a  further  time.  INHOMOGENEITY (C)  of  F i g .  2.15,  stems  from  Consideration  wherein  and  inhomogeneous. x  mTm"  2.17(A)  transmitter  that  21  measurements  probes  and  90° pulse  spin  in  dead  strength  shows is  of  give  spectrum  NMR  a  Comparison  inhomogeneity.  for  variations,  of  lineshape  radiofrequency  the  .  RADIOFREQUENCY  in  arrangement  5  spectrum  in  2.17(A)  MS r e s p e c t i v e l y  spectra  that  observed  d i f f i c u l t y  50  The  improvement  of  corresponding  echo  lineshapes.  Figs.  y-gradient  c a l c u l a t i o n  spin  in  application  MS and  magnitude  that and  of  a  spectra  c o i l  the  gradients  standard  extends  2.11(A)),  of  B,  order  that  it  required  is  the  beyond  to  s u s c e p t i b i l i t y  distribution In  sample  (Fig.  minimize  of  along  the  lineshape that  z  analysis B,(x)  and  * Dwell t i m e : The time i n t e r v a l between s u c c e s s i v e samples o f t h e t i m e d o m a i n NMR s i g n a l b y t h e d i g i t i z e r . For q u a d r a t u r e d e t e c t i o n the width of the observed spectrum or sweep w i d t h , is given b y ± (2 x d w e l l time)" . Usually the dead time i s a u t o m a t i c a l l y set equal to the dwell time. Magnitude c a l c u l a t i o n : The r e a l and imaginary p a r t s of the spectrum S are combined to give S = (ReS + I m S ) ' . 1  5  2  2  1  2  88  2  1  1  2  0 - 2  0  f 2  KHz  C  2 0-2 Fig.  2.17  (A) of  & a  Spectra  90° pulse  with (B)  (C)  dwell &  (D)  obtained times  The by  100  lengths  of  after the  21  13  MS and  90° pulse  180° p u l s e . 40  100  ms ms  The  after and  the  of MS  spin  application  a  gradient respectively.  echo  calculation  with 27  then  with  90° and  dwell  These 180°  a  pulse delay  y-gradient  the  spectra  pulse  MS r e s p e c t i v e l y ;  y-gradient  1  50  the  MS r e s p e c t i v e l y .  acquired  mTm" ,  the  again was  corresponding  50  after  presence MS and  magnitude  were  ms,  the 100  MS and  -2 KHz  0  recorded  in  times  spectra  10  2  relaxation  immediately of  was  180° pulse.  a  40  ms  before  switched The  delay  echo  was  6  on time s.  89  B,(y) the  be  uniform.  distribution A  B,(z)  consists of  evolution presence  OJ,  of  a  center  which  The  of The  with  i n t e n s i t i e s  is  the  of  to  lineshapes  for  in  length.  by  tube of  high  us  gradient the  a  CJ, ,  away  but  in  from  the  o f CJ,  of of  the 12.7  by  can  be  not  for  a through  peaks,  19.7  jus,  good  in  measuring  spectra.  the  uniformity  s l i c e  across  transmitter-receiver  y-gradient  the  better  given  radiation  magnitudes  In  indicates  obtained  non-uniform  2.18).  transmitter-receiver  center  resolution  the  frequencies,  sample.  much  length  in  (Fig.  y-distribution  over  the  signal  of  the  and  the  period  of  peaks  the  mapping  B^x)  for  greater  shows  the  at  13  of  and  90° pulse  the  the  the  or  The  exists  value  and  cm  extent  width  a  across  radiofrequency  direction  Consequently,  the  NMR  of  detection  0.5  to  normal  produced y  at  by  with  incremented  z - d i s t r i b u t i o n  frequency  the  of  distribution  the  mapping  distribution  direction  that  corresponds  agreement  in  the  2.19(B)).  sample.  that  1 cm  the  v e r i f i e d  sequence  acquisition  the  observed  across  distribution  KHz,  one  for  pulse  pulse  for  shows  were  sample.  experiment  the  showing  is  the  spin-echo  and  corresponds  extends  the  a  map  non-uniformity  (Fig.  across  gradient  along  2.19(A)  c o i l  B,  conditions  excitation  period  7B,,  Fig.  of  the  resulting =  of  two-dimensional  duration  The  These  Thus the  c o i l  is  the sample uniform  z - d i r e c t i o n . determined the  from  z-gradient.  90  27  R  {  T  T  I i \ ECHO • 1  Fig.  2.18  Pulse the  sequence  distribution  sample. the d,  for  The  of  the  one  the  excitation  delay  T and  detection  a delay  finally  period  a  rf  field  pulse  evolution period. A f o l l o w e d by  dimensional  P^  a  180°  gradient  produces  an  across  pulse pulse,  pulse  echo at  of  the  i s incremented  gradient T,  mapping  of  for  duration  a  further  during 2(d+T).  the  9 OA  Fig.  2.19  The co,  one for  spectra  dimensional the  z  were 2.13  (A)  Fig  ms  respectively,  960  MS i n  and  y  recorded  in  excitation  maps  with  d  (B)  and  T  the  P^,  increments  of  27  of  15  24  mTm"  y-gradient  was  25  mTm" .  1  MS.  and  1  c o i l  for  The was  5  MS  saddle  and  20  and  from  (B)  11.5  sequence  of  For  of  The  pulse  incremented  was  transmitter-receiver  distribution  intervals  180° pulse  pulse,  the  directions.  using  z-gradient  diameter.  for  (A)  15 the  the  in  to  fixed  fixed  shaped mm  MS  92  4.  STATIC For  GRADIENT comparison  gradients  of  1.1  with  gradients  F i g .  2.20.  gradient produce The  c o i l  of  75  lineshape  position  from  experiment  Eq. of  for  gradients  without  lineshape the  echo  a  increased.  slope  the  line  the  diffusion  a  2.19  difference  measured only  The  sample  of  10"  about  in  m s"  1  2  2  no  o>,  >>  the  value  (CJ -W)  for  a l l  0  of  of  the of of  was  for the  large  e f f e c t s  6  the  and  1  9  m  the  as  at from  value 2  s "  1  ,  for  was  literature 23  °C  error  temperature,  sample  in  apply.  10"  sources  include the  use  decreases  temperature  Possible  since  the  absolute  with  a  A  linewidth  x  vs  diffusion  130 m T m "  2.23  agreement a  2.21(A)  complicate  an  the  frequency  offset  the  is  water,  coefficient  longer  From  to  with  shown.  spectra  2.21(B),  for  %.  imprecision  condition may  9  of  was  approximately  thermostated,  6  x  the  is  the  2.20(A)).  of  F i g .  allow  further  gradient  Fig.  c o e f f i c i e n t  diffusion  known  in  In  resonance  of  (Fig.  graph  by  shimmed  agreement  c a p i l l a r y  would  in  produced  gradient  would  spectra  shown  be  tube  static  this  intensity  the  of  a  glass  effective  value  NMR  2.20(D)).  from  which  value  an  s t i l l  the  since  is  can  by  (Fig.  are  1  with  2.15),  gradients  indicated  significant  2r,  This  for  mTm"  good  the  obtained.  151  (Fig.  1  in  half-height, of  and  magnet  Hz  in  The  (89).  mTm*  experiments  is  2.47  pulses  time,  4  as  chosen  rf  2.4  2.20(C)  water  was  the  the  spectra  c a p i l l a r y  - 1  previous  background  of  F i g .  expected  plot  mTm  system,  in  MEASUREMENT  the  and  - 1  the  linewidths  stacked  with  mTm  Despite  spectrum  during  DIFFUSION  (11), in  the  which  is  not radius  spins  in  of the  the  92A  F i g .  2.20  (A)  Normal  tube; (B)  the  Spin  lengths 151  the  linewidth echo  of  mTm"  pulse,  90° pulse  13  delay  and  2  1.5  sequence  as  75  mTm"  and  duration  of  4 ms.  The  echo  time  u  x  time (D)  1  (B)  but  with  was  7 ms  same  with  y-gradient followed 10  ms  of 90°  after  the  the  was  NMR  pulse  the  and  with  1 ms  a  pulse  before  echo  time  180°  following  immediately  spectrum  in  ms  in  Hz.  y-gradient  The  16 M S .  water  90° and  acquisition  dwell  echo  4  with  MS,  for  and  on.  Spin  27  ms  y-gradient  (C)  about  duration  180° pulse  time  is  spectrum  and  1  spectrum  and  the  pulse pulse  by  and  of  a  delay  the  dwell  33 M S . Graph  gradient slope.  of of  vs  74.6  for  mTm"  1  data was  from  (C);  calculated  a from  the  93  Frequency (KHz)  93A  Fig.  2.21  (A)  Spectra  experiment radius, from 1  From 129  for  0.610  the  g/ml)  in  a  mm,  pulse  of  of  glass  c a p i l l a r y .  capillary  was  water  (assuming  a  / ,  the  of  the  tube  effective acquired  sequence  with  the  to  25  echo ms  in  time 20  the  water  interval  was  negligible  was  needed.  Room  (B)  Plot  Ln(A/A )  over  and  no  vs  T  3  this  2  for  is  a  23  the  Hahn  applied  incremented of  1 ms.  The  time  correction  was  of  (V=irr /).  using  increments  signal  density  gradient  was  The  estimated  y-gradient  (2T)  temperature Q  diffusion  the  of  (A).  a  were  The  of  gradient  data  throughout. 5 ms  in  length,  The  1  decay  static  linewidth  mTm" .  from  a  water  volume  the  echo  from  for  °C. spectra  in  T  2  X  (*10 s 6  3  )  95  c a p i l l a r y  tube  5.  GRADIENT  PULSED The  to  be  2.7).  Pulsed times of  pulsed  applied  (Fig.  f i e l d after  reduction to  effect  pulse.  presence  of  or  a  for  the  the  echo  180° and  and  In  the  after  and  a  and  is  2  to  2  obtained  a  normal  applied  from  for  23  shown of  Using  of  F i g .  43.5 a  ms  lineshape  [2.68], delay  less  2.22. than  or  in  This  .The  25  ms  t r a i l i n g  180° pulse  result  graph  an  in  would  cases,  the  effect  most  fashion. the  a  is  the  delays. pulsed  plot the  analysis,  The  the of  longer  same  the  echo severe  than  is  25  of  the  and  the  spin  diffusion  pulses  pulses  Ln(A/A )  of  3  were  vs  0  magnitude  diffusion  ms  small,  before  decay  gradient  the  between  pulse  gradient  Gradient  between  is  overlap  gradient  2.23.  for  The  the  cause of  delays  of  unequal  amplitude  at  is  the  the  linear  values  Eq.  varying  Fig.  the  gradient  in  in  spins.  pulse  in  those  °C,  in  produce  of  by  pulses  corresponding  currents  However  " t a i l "  at  the  the  gradient  180°  with  times  would  these  the  given  shown  decrease  delays.  the  separation  y G S (A-6/3). 2  a  is  and  eddy  of  requires  after  delay  these  of  in  are  for  tube.  acquired  pulse  time  of  either  water  s u f f i c i e n t  echo  the  application  180° pulse  experiment  of  either  s h i f t ,  effective  from  and  rephasing  decays  the  echo  The  shortest  pulse  of  either  time  both.  before  intensity  the  MEASUREMENTS  spectra  delay  of  experiment  gradient  vs  gradient  either  decay  gradient  in  dephasing  DIFFUSION  equally  the  the  misalignment  gradient  The  intensity  due  and  ms  96  F i g .  2.22  (A)  Pulsed  water. in  f i e l d  gradient  Y-gradient  duration  were  the  gradient  20,  25,  was  triggered  (B)  Graph  30,  of  pulses used.  pulses 35,  40,  at peak  spin of  The  echo  25.2  mTm"  delay,  d,  varied  from  45  50  time  and  spectra  1,  ms.  2,  vs  time  and  10  d.  ms  following 4,  10,  Acquisition  2T.  height  1  for  15,  97  I 0  1  1  0-5  1  yGY(A-S/3)  Fig.  2.23  Decay  of  the  gradient were to  time  echo  diffusion  3 ms  83.1  spin  in  between  temperature  1  in the  was  19  from  and  °C.  in  The  varied  increments  gradient 23  water  experiment.  duration  mTm"  (xio'm-'s)  of  pulses  pulsed  gradient  from  2.13  4.26 was  pulses mTm"  mTm" .  43.5  1  ms.  1  The Room  98  c o e f f i c i e n t  of  10-  the  a  m  9  s "  2  1  ;  difference  due  at  these  least would  water  value  of  3.7  larger  in  part  gradient  pulse,  decrease  further  possible  source  these  use  gradient both  a  t r a i l i n g Similar  c o i l s F i g .  2.24,  20  ms  of  from  c i r c l e ,  copper  which from  from  c i r c l e .  magnitude  7  and  with  from  The  the  unwanted  the  2.1  26.5  bore  of  is  pulses  in  cm  radiofrequency  allowing  eddy the  larger  the  and  In  pulse  are  magnet  gradient  y-gradient  signal  removed,  by  in  using  values  for  1/16 and  radiation.  straight  in  acts  wall as  duration  indicated  shield  the  was  obtained  the  by  for  gradient  water  with  to  currents.  gradient  7  f i e l d  effective  Data  decay  o.d.  the  pulsed  s h i e l d  With  preferrable  shown.  shown  the  in  is  copper  heights  and  the  Another  pulsed  thereby  which  with s,  in  of  to  measurements.  from  - 1  the  is  case.  s t i l l  with  c o i l  1.04  of  the  mind,  determining  mTm  expected  Table  cylinder,  lines  it  water,  of  peak  in  since  duration echo  (11), probably  above  the  x  1  is  thermostatted.  observed  8  integration  be  experiment,  for  time  cause  s -  not  surface  to  described  2  was  attenuation  1.1  echo  a  open  for  value  effective  to  m  9  variation  for  were  10"  2.27  the  gradient  experiments  by  an  the  x  was  in  experiments  echo  normally  triangle,  sample  slope  2.19  otherwise  l i e s  standard  the  observed  the  uncertainties  effects  and  closed  would  error  is  e f f e c t s  tending  particular  the  incremented  the  increase  the  constructed  diffusion  of  of  the  for  to  than  since  as  The  thereby  diffusion  water  %.  to  experimental  gradient  from  literature  serve  temperature  calculated  an  by  open  place,  by  gradient  l i n e .  In  thickness, shielding  99  0  4  8  (xlO'Vm ) 1  YG*b'(*-5/3) Fig.  2.24  Decay  of  the  spin  echo  diffusion  experiments  1.0  1.1  s  and  duration were  20  by  measurement  of  the  signal  The  by  Data  with of  for  pulsed water  indicated  the peak  copper  behaviour  (A  with is  echo  pulses by  (O)  shield  heights  respectively.  gradient with  y-gradient  integration,  predicted  l i n e .  1  ms.  obtained  obtained  mTm" ,  in  and )  the  shown  time  of and  in  place,  integration  indicates shield by  (•)  the  data  removed. straight  100  a l l  cases  the  behaviour for  as  the  shield with  shield  result  not  in  F i g .  of  a  the  echo  to  the  gradient obtain  the  shown  in  diffusion gradient  were  spin s  in  F i g .  the  the  Data  from with  (A)  and  echo  of  is  the  s  in  26  FID  decay  which  echo heights each  which  experiment  the  are  shown  application starting  (B).  and  of  the  magnet  times  spins  the  peak of  sequence  0.63  time  with  another the  of  values  echo  after  pulse  compared  measurements  phase  spin  acquired  exponential  The  FID  less also  is  at  intense shows  observed  with  time.  by  varying  the  and  echo  the  attenuation  on  from  echo  For  last  amplitude  presence  relative  in  pulses  place  compared  provided  refocussing the  Data  experiments  data  shorter  pulses,  behaviour.  seen  in  the  lower  expected  echo  e f f e c t s .  variation  c o i l s  0.13  echo  echo  the  that  the  gradient  shield  integration  be  gradient  However,  copper  place,  from  The  from  longer  the  eddy  can  improper  deviation  relative  exponentially.  time, at  reduced  current  gradient  2.25.  observed due  This  pulsed  The  significant  decay  the  from  the in  from  effects  shows  0  lineshape.  deviated  removed,  (A/A )  from  decay  that  s.  with  enhances  amplitude  using  0.5  shield  the  does  as  obtained  0  with  indicating  long  (A/A )  observed  obtained water,  2.26.  c o e f f i c i e n t magnitudes  data  of  from  time, which  from  using  The  duration  expected 2.19  it  x  x  was  show  pulsed  the  and  and  linewidths,  9  of  possible  to  more  gradient z  m s" 2  is  linear spin  gradient  behaviour 10~  amplitude  1  for at  also  echo  c o i l s ,  water 23  °C  shown.  are  with and  a  100A  Fig.  2.25  Spin  echo,  diffusion  FID  signals  experiment  s u r f a c e - c o i l  for  apparatus,  x-gradient  pulses  times  and  0.13  from  of  0.63  respectively.  r  a  water with  duration s  in  pulsed  (A)  gradient  using  1.0  mTm"  15 m s , and  the  (B)  1  and  echo  A  x26  < I  0  200  400  Acquisition Time (ms)  B -3  CL  £ < r  0  T 200  400  Acquisition Time (ms)  102  0  1  2  3  4  rttf(A-5/3) («10"*s/rn) f  Fig.  2.26  Decay  of  the  diffusion c o i l The  spin  experiments  apparatus predicted  l i n e .  Data  z-gradient duration x - c o i l ,  for  with  16 the  ms  in  and  2.1  echo  x-gradient  pulse  time  ms.  duration  and  is  z - c o i l  gradient  water,  ( • )  behaviour the  pulsed  for  x  increment  gradient 225  echo  using z  (O)  shown were  by  0.19  increment was  the  12  dashed with  gradient  1  ms  surface  gradients.  obtained  mTm" , time  the  s. was and  For 0.65 the  pulse the mTm" , 1  echo  103  The of  1.6  the  observed  and  for  x-gradient  than  the  that  of  z  for  a  1.26  x  F i g .  m  9  are  2  x  10~  Thus, performed delay the on  surface  improved a  later  wider  DIFFUSION  Fig.  OF  of  was  to  used the  By  data  of  2  s  _  pulse  10~  1  data  in m s~  0  2  and  NMR  the are  shown  of  the  F i g .  2.27,  for  1  apparatus,  could  method was  long with  than  the  high  c o i l  be  provided  but  enough less  the to  allow  precision  resolution  measurements  extending  the  was  measurement  attenuation.  BY  MQ  gradient  ECHOES  spin  the  resonances the  y  obtained  down,  by  than  x  to  respectively.  1  surface  III)  allowing  x  values  gradient  determine  proton  from  that  of  noise  similar  values  measurements  ACRYLONITRILE  2.9  system.  m  0  echo  pulsed  The  the  apparatus  modified  spin  1  currents  the  factors  Pulsing  was  indicate  resolution  settle  The  a c r y l o n i t r i l e AMX  1 0 "  (chapter  range  with high  precision  y - c o i l  diffusion  8.0  by  acoustical  ethanol.  and  gradient  to  c o i l  The  and  water  pulsed  each  f i e l d  c o i l  diffusion  the  the  eddy  obtained  x  louder  observations  water  7.04  expected,  respectively.  a  of  stronger  the  accurate  c o i l s  surface  for  using  following  the  of  1  x  than  produced  These  agreement  using  apparatus.  6.  _  faster  behaviour  2.27,  and  8  magnetic  over  s  in  independently 1.19  also  coeficients  10"  ethanol  z  induce  mixture  diffusion  and  x - c o i l .  In  4:1  the  The  pulses  c o i l .  is  c o i l  c o i l .  the  gradient z  12  decay  echo  sequence  diffusion of  which  selective  of  c o e f f i c i e n t constitute  detection  of  of an  104  0  2  A  6  * GY(A-S/3)  (*1Cf ,s/m ) 8  2  Fig.  2.27  Data and  for  the  ethanol  pulsed  ms,  of  and  c a l i b r a t i o n  of  ( O ) ,4:1  gradient  increment 12  diffusion  echo  mTm" , 1  time  using  mixture  (v/v),  method  1.6  a  with  water  are  of  obtained effective  gradient  0.112  2  s.  The  pulse  water using  the  z-gradient duration,  data  indicated  (•)  for by  "x".  105  multiple means  quantum  for  optimizing  experiments. preparation quantum  due  T  Spectra of  obtained Figure There  2.30  shows  recent  least  spin  shown  in  squares  energy  for  the  second  c o e f f i c i e n t s method  w i l l  also  into  the  be  higher  for  of  is  d i l u t e .  double  lines  an  the  spectra.  third  orders  of  of  The  larger  coherence  2.3. complex  slower the  system.  calculated  use  diffusion of  measurements.  conversion and  this  quantum  The  of  AMX  of  Table  studies  were  [2.72].  quantum  the  d i f f i c u l t y In  The  double  in  the  three  the  for  coherences, some  and  for  Eq.  quantum  inefficiency  t,,  s i g n a l .  preclude  single  o s c i l l a t o r y  maximum  d i f f u s i o n .  in  t r i p l e  preparation  2.29.  measurement  present  system  publication  useful  order  may  to  and  The  time  to  with  scheme  in  and  MQ  magnetization  the  summarized  the  enough  the  F i g .  six  in  The  echoes  fit  limitations  relative  times  are  for  technical large  and  sensitivity  of  level  slopes  greater  2.28.  give  the  observed  the  and  are  to  are  when  short  of  double  evolution  optimized  alternative  amplitude  coherence.  a l l  and  echo  the  and  mixtures,  long  precession  quantum  the  echo  Fig.  t r i p l e  This  quantum  in  an  parameters  single,  one  d i f f u s i o n  However,  the  be  the  gradients  in  from  to  decay  linear  transitions  rates  rise  offer  excitation  shown  the  were  and  should  shows  to  coherences by  negative  is  multiple  period  orders  the  arising  giving  the  T,  gradients  variation  time  is  components  delay  The  coherences,  behaviour  time  echoes,  when  of  single  relatively  context,  images  of  the we  human  T  2  note  is the  forearm  106  Fig.  2.28  The  variation  in  (A),  double  (B)  with  preparation  the and  amplitude t r i p l e  time,  r.  (C)  of  the  quantum  single echoes  106A  Fig.  2.29  Spectra double  and and  decay t r i p l e  a c r y l o n i t r i l e . obtained quantum  0.8  ms  pulse  The and  quantum  ms  and  pulse  The 256  of  a  3.8  was of  5  of  0.54  mTm"  and  t r i p l e  1  were  quantum 3  s  were  d  1  MQ  25.2  10 m s , of  used  30  ms  and  time  r  21  ms,  time  was  used.  the  of  1 1 0 ms  mTm" , 1  the  respectively. for  T  of  1.67  diffusion  with  0.77  single,  of  t r i p l e  evolution For  T  was  The of  ms,  and  for  allowed  of  1 ms  1.61  echoes  two  of  A  d  a  8  with 1  were  of  used.  mTm" , MQ  r  was  double  of  evolution were  of  The  with  mTm" ,  single,  spectrum  projection  acquired  increments  and  quantum  acquired  increments  x-gradient  of  set  incremental  experiments,  delays  the  for  coherences  increments  spectrum  ms.  is  echoes  90° pulse.  incremental 256  y-gradient 100  data  spin  single  normal  spectrum  y-gradient ms.  a  the  quantum  The  with  dimensional  300  of  mTm"  1  double Relaxation  e q u i l i b r a t i o n .  107  SQC  |«<Xot>-  Fig.  2.30  Schematic spin  diagram  system  double  as  quantum  indicated  is  of  found  the in  energy  a c r y l o n i t r i l e .  transitions  one  t r i p l e  levels  are  quantum  l a b e l l e d  for  an  The  six  D.  Not  t r a n s i t i o n .  AMX  109  TABLE coherence  Table  2.3  2-3  D UloVs"' )  single  4-2 ± 0 4  double  4-3 ± 0 2  triple  4-1 ± 0-2  Diffusion single, The from  coefficient  double  and  uncertainties least  squares  of  t r i p l e are fit  98 to  a c r y l o n i t r i l e quantum  spin  % confidence the  data  in  from echoes. intervals F i g .  2.29.  110  (90).  7.  IMAGING In  tubes  F i g .  2.31,  i.d.  um  15 a n d  28  projection the  GLASS  containing  140-220 of  OF  CAPILLARIES two  dimensional  water, in  1.2  (B)  are  the  c a p i l l a r i e s ,  proton  The  corresponding c o i l ,  e l l i p s o i d a l  the  d i f f e r i n g 0.47 (B)  and is  shape  f i e l d 1.01  mm,  for  c o i l  a  these  echo  are  effects  measurement  gradient,  the  w i l l  a  have  there the  were  echo  much  were of  weaker  smaller no  in  of  2.8  less  ms  in  2.22.  In  gradients effect  the  a  on  the  applied. middle  of  with  of  the  pulsed  the  The  and  30  gradient  eddy  of  the  and  a  ms.  of  in  thickness,  which  by  since  of  demanding  s l i c e  for  to  Eccles  more  presence  shape  due  using  5.8  time  Also,  by  2.31(A),  produced  is  resolution  size  the  the  of  directions,  smaller time  a  the  (A)  obtained  but  F i g .  in  y  to  ratio  The  in  similar mm,  than  observed  gradient  occurs  20  and  image  relaxation  F i g .  xy-plane.  transverse  an  noise  of  The  including  images,  extent  x  of  to  mm l e n g t h  the  radius  spin-spin  11  along  c a p i l l a r i e s of  an  ACETONE  c a p i l l a r y  correspond  images  that  parameters  2.31(B),  current  to  rf  and  views  the  of  signal  along the  AND  and  c a p i l l a r y  respectively.  for  experimental  Fig.  cm  (59)  solenoidal  times  of  comparable  Callaghan  1.5  of  into  (A)  with  to  WATER  images  in  images  density  transmitter-receiver  NMR  mm i . d . shown,  respectively.  of  CONTAINING  a  echo ms  in  eddy spin large  currents echo  the  acquisition  than  formation period,  if of the  110A  Fig.  2.31  Two  dimensional  containing (A)  Top  photograph. tubes  shown  in  phase  encoding  applied the  Fig  NMR  2.2  that  gradient  after The  MS,  y-gradient  of  9.3  mTm" ,  0.5  180° pulse  mTm" , 1  1.01  4  Bottom  with  140  pulse with  -  a  0.38 pulse each  of cm  4  y  of  ms,  were  acquired  in  The  image  - 1  ,  s.  length  (A).  167  x was  MS,  mTm" ,  f i e l d  and 28  with  0.47  y MS  T  of  a  of  and  c a p i l l a r i e s using  was  of  of of  28  15 m s ,  were  respectively. and  4  scans  fixed  increment  MS a n d  views  the  acquired  x-gradient  1  180° pulse The  instead  respectively.  and  38.9  was  relaxation  Mm i . d .  of  r  increment  MS a n d views  the  fixed  220  time  and  acquired  image  along  image.  f i e l d  and  was  10  28  sequence  90°-pulse  x-gradient  of  i.d.  duration  NMR  of  mTm  of  mm  d=T  photograph.  dwell  0.6  delay  x  T  of  the  1  The  sequence  y-gradient of  s.  cm a l o n g  (B)  tubes  pulse  T=0,  image  250  1.2  the  pulse  of  of  c a p i l l a r y  of  with  except  immediately  time  delay  glass  image  acquired  l 8 0 ° - p u l s e .  dwell  of  water.  c a p i l l a r y  of  images  relaxation 0.26  and  The  180°  were  used  for  111  1 12  echo  may  form  a  of  the  intensity may  overlap  Thus  the  echo  (13)  ms, of  as  in  gradient  and  images  to  a  were  (A)  is  2.19  (B), x  x  4.18  x  in  the  9  9  in  1 0 -  9  at  1  the  gradient  formation  with  echo  shown  (B).  the  pulse of  the  which  comparing  the  sequence signals has  a  the  in  larger  F i g . (B)  d i f f u s i o n  with  gradient  diffusion  measurement  m  pulsed 2  s-  1  (Fig.  2.33).  compared  in  water  agreement  a  The  2.8.  c o e f f i c i e n t  (A) to  of  be the  shown  diffusion  in  This  to  of  image  the  intensities  c o e f f i c i e n t  2.69,  of  in  is  .  7  is  on  m  1  of  normal  Eq.  _  the  acetone,  is  a  using  s  of  times  c a l c u l a t e d , 2  pulse.  containing image  2.32,  pulse  water  left  F i g .  180°  containing  diffusion °C,  echo  the  the  one  acetone  23  Thus  and  In  contrasted  the  spin  2r  IV.  intensity  taking 2  f i r s t  obtained  By  than  change.  be  the  water.  m s"  not  later  s t a b i l i z e  using  for  than  was 10"  on  or  to  chapter  other  greater  10"  obtained  in  can  diffusion  and  acetone 4.10  serves  acquired  c o e f f i c i e n t  the  c a p i l l a r i e s ,  the  and  w i l l  of  images  decrease  and  t a i l  mm i . d .  (A)  The  the  and  earlier  signal  described  1.2  right  l i t t l e  value of  be  112A  F i g .  2.32  (A)  NMR  image  (on  the  right)  image Fig.  2.8  and of 3  was  and 1.3  ms  of  and  a  dwell mTm" T  of  20  180° pulses  The  f i e l d  of  directions  (B) 45.8 a  ms.  the  Same  as  mTm"  1  diffusion  of  with  6  27  =  The  sequence of  75.6  x-gradient  and  water  l e f t ) .  of  MS  acquisitions  mTm"  1  d,  of  the  90°  respectively.  cm a l o n g was  in  increment  time,  durations  0.62  4  were (A)  a  z-gradient  of  in  pulse  encoding  13  was  the  pulse  MS,  The  were  averaging  increments  the  phase  view  and  50  containing  (on  y-gradient  with  1  with  time  and  Signal  acetone  acquired with  and  c a p i l l a r i e s  the  not  x  and  y  applied.  and  128  used.  except  a  z-gradient  5 ms  was  applied  contrasted  image.  to  pulse  of  produce  X-coordinate (cm)  acetone  water  ~ 1 — i — i — i — r ~ -8  2.33  A  -4 0 U Frequency (kHz) stacked  plot  containing pulse with  water  sequence the  of  spectra and  and  from  acetone,  parameters  x-gradient  incremented  for  3.8  turned mTm"  1  off to  8  c a p i l l a r i e s acquired of  Fig.  and 145  with 2.32  the  the except  z-gradient  mTm" . 1  III.  A.  has  become  translational  technique  to  only  achieved; The quite  on  many  possesses  liquids  limited  an  5  by  in  x  a  large,  of  with  in  solution  hydrogen  in  metals  (107-109)  . of  the  a-  0-  H 0  and  The  diffusion  was  determined  concentrat  measurements in  of  also  linked  of  by  dextran,  glucose  c o e f f i c i e n t  and  of  Tm" .  extrapolation  from  2  and  be  is  already  systems  on  (104),  surfaces solution  determination  by  c o e f f i c i e n t s  of  methyl-D-glucoside  at  is  1  work  the  a  C to  describes  pulsed  characterize  human  forearm;  a  the  in  polysaccharide units,  in  i n f i n i t e  D 0. 2  dilution  measurements  gradient motion  surface  1 15  1  (24,95-99),  monomeric  glucose  9  1.5  diffusion  D-glucose  I0" m s"  can  aqueous  reports the  1 x  biological  molecules  of  The  polymers,  c o l l o i d s  in  of  performing  that  published  and  study  of  various  ions.  Section  in-vivo,  and  1-6  in  reach  in  of  from  dissolved  water  the  samples.  gradient  in  chapter  method  anomers  of  of  of  range,  may  (100-103),  this  gradient  consisting  of  gradients  (105,106)  pulsed  2  for  1  molecules  the  D 0,  2  studies  polymers  B  dynamic  m s~  for  capability  types  application  dissolved  Section  1 3  technique  the  magnitude  (91-94),  in  wide  I0~  the  with  different  practice  range  and  important  d i f f u s i o n ,  measurements  2  MEASUREMENT  INTRODUCTION NMR  for  DIFFUSION  spin of  c o i l  echo  water was  and  used  to  l i p i d ,  116  provide  B.  l o c a l i z a t i o n  DIFFUSION The  played  study  a  matter.  role  the  of in  diffusion  irregular  of  was  able  to  due  liquids the  to  once  (1905-1912)  molecular  make  obtained  suspended  motion  in  establishing  c o e f f i c i e n t  size  signals.  LIQUIDS  Einstein  diffusion and  IN  of  by  theory  a  connection  a  macroscopic  p a r t i c l e s  c o l l i s i o n s  in  a  with  of  between  l i q u i d  the  measurement, undergoing  molecules  of  the  l i q u i d  where  f  is  p a r t i c l e  the  of  continuous  f r i c t i o n  radius f l u i d  r,  of  [3-1]  kT  D=  f  c o e f f i c i e n t .  moving  viscosity  with  a  uniform f  n,  For  0  is  spherical velocity  given  in  a  by  [3-2]  f = 6TTVjr e  From  this,  Avogadro's  number  found  to  be  in  agreement  other  types  of  phenomena  Today  this s t i l l  diffusion  measurements  themselves  a  provides  more  (111,112).  the  be  determined  results  of  known  as  the  studies  was of  Stokes-Einstein  a  very  useful  means  and  much  effort  has  rigorous The  and  (110).  relation,  equation,  establishing  with  could  connection  equation  is  for  valid  of  been the  interpreting given  to  molecules  s t r i c t l y  in  the  117 limit  that  molecules the in  the of  equation  d i f f u s i n g  the  surrounding  seems  (113).  radius  to  be  are  often  shape  the  solute  and  thesis  we  is  much  medium.  valid  Deviations  equation of  p a r t i c l e  for  As  than  discussed  by  molecules  from  the  in  terms  discussed  larger  as  the Edward,  small  as  5  A  Stokes-Einstein  interactions  of  the  with  variation  the  of  solvent  molecules. In measure and  this the  methyl  diffusion  b i o l o g i c a l  "fuels"  conformation  affects sugar  and  the  as  have  the  a  which  has  of  diffusion  correlation  of  between  of  of  the  the  molecule  was  found  for  determining  on  blocks"  for  in  carbohydrates  interest.  of  (115).  providing NMR  that  the  equatorial  solution, of  been  groups  structure.  values  c o e f f i c i e n t s  of  in  has  and  (114)  equatorial By  It  hydroxyl  number  aqueous  as  hydration,  of  water  l i m i t i n g  diffusion  widely  The  to  D-glucose  occur  molecules  larger  of  method  solution.  equatorial  the  number  studies.  aqueous  some  sugar  sugars  the  such  been  gradient  /3 a n o m e r s  glucose,  effect  and  in  in  interaction  has  stronger  and  c e l l u l o s e .  of  c o e f f i c i e n t s  useful  a  pulsed  "building  number  hydration  molecule  as  solute  solutions that  and  such  groups the  the  p a r t i c u l a r l y  polysaccharides  suggested  of  the  D-glucopyranoside  Carbohydrates,  aqueous  apply  In  a  study  a  diffusion hydroxyl an  groups  accurate  could  prove  in  means  118  1.  EXPERIMENTAL Experiments  previously  in  magnitudes  for  determined  by  c o e f f i c i e n t  2.  RESULTS Fig.  spectra give The  spectrum the a  signal time,  can 0.38  diffusion  observed error,  the  of  reduced in  these  to  same  p a r t i a l l y  of  5.8 of  The  a  4.6  PPM  water of  glucose  in  and  chemical  for  a to  each  are  diffusion  within  2  %.  and  are  (1.0 by by  the  we  diffusion D 0  29  %.  This  2  is  leads  long  echo  the  water  Thus  isomers  of  The  and  that 0  any  isomers  c o e f f i c i e n t . than  reduction in  the  experimental  slower  difference  to  determined  of  a  H  with  the  conclude  between  in  be  for  limits  M)  the  can  1  that  summarized.  this  hydration  This  relaxation.  data  the  From  alter  for  allow  isomer  so  2  normal  exchange  molecules. T ,  anomers  0  respectively.  the  s u f f i c i e n t l y  using  spectra,  to  and  gradient  by  concentration accounted  the  pulsed  time,  be  glucose  at  of  water.  D-glycoside  shape  s u f f i c i e n t  in  because  3 . 1 ,  methyl  in  were  diffusion  relaxation  c o e f f i c i e n t s Table  M  plot  protons  reduced  differences  diffusion  stacked  to  protons  estimated  not  due  been  and  the  described  gradient  known  peaks  In  The  with  d i s t i n c t  s  differences are  a  spin-spin  separately. D-glucose  shows  be  II.  measurements  1.0  hydroxyl  chapter  apparatus  gradient  D-glucose,  has  the  DISCUSSION  signal  shortened  pulsed  of  with  water.  AND  to  large  a l l  B.1,  calibration  3.1  rise  performed  section  of  for  were  can  the  in  The H 0  only  2  be  viscosity  at  119  Chemical  Fig.  3.1  A  stacked  glucose,  plot 0.5  M  Shift ( P P M )  of  pulsed  gradient  in  water.  The  5.8  PPM a r e  assigned  the  0  anomers  and  a  to of  the  1  H  doublets anomeric  D-glucose  spectra at  4.6  protons  for and of  respectively.  120  TABLE  3-1  D-glucose 1 - 0 M in D 0 <x -anomer -anomer  2-95  D-glucose 1 0 M in H 0 anomer (3 -anomer  4-19  2  x10" mV 9  1  2-97  2  methylglycoside 0-1M"in <x- anomer (9- anomer  Table  3.1  4-16 D 0 2  Diffusion  c o e f f i c i e n t s  D-glucose  and  4-84 4-88  of  the  a  D-methylglycoside.  and  /3 a n o m e r s  of  121  of  D  2  0 which  is  1.23 times  greater  than  that  of  H  2  0  at  25° C  (116) . In  F i g .  (Pharmacia in  an  151  experiment be  diffusion  plot  0.05 x  of  agreement obtained x  with from  1 0 "  1  0  the m  2  Such  2  s '  6.3  x  1  m  method.  1  at  In  data  literature  by  of  the  D  was ,  1 0 "  0 ,  2  determined  1  m s"  1  2  in  up  to  agreement  (102).  1  aqueous  was m e a s u r e d  gives  using  the  3 . 3 , extrapolation a  value  d i l u t i o n . of  for  This  6.75 x  interference Northrop  was  reasonable  glucose  value  Dextran  incremented  in  F i g .  i n f i n i t e  shift 1  of  1  concentrations  D  of  is  I 0  fringes  McBain  that  1.  INTRODUCTION  6.17 x  equation  is  smaller  PROTON  is  medicine. peaks  of  an  IN-VIVO  There  value  deviation  C.  show  s "  predicted  suggested  and  s "  the  Stokes-Einstein value.  2  in  of  r  m  2  s "  1  and  (117)  porous  6.70  in °  1  of  of  disk  (118).  technique The  m  0  1  of  s e l f - d i f f u s i o n 1  %(w/v)  c o e f f i c i e n t  gradient  1 0 "  c o e f f i c i e n t  gradient  1 0 "  value  various  f i e l d  4.3  the  6.24 x  The  pulsed  6.78  where  literature  of  diffusion  9000)  w  the  solutions  ±  to  1  the  the  T - 1 0 , M  mTm" ,  with  3 . 2 ,  already  empirical  in  the  example,  attributed  to  1  known  3  1  P  OF  m  0  than  correction  SPECTROSCOPY  interest For  is  10"  HUMAN  ADP, ATP,  s "  the  and be  1  from  the  experimental  it  has  made  been  (113).  FOREARM  application spectra  2  of  from  NMR t o human  phosphocreatine  biology  forearm and  121A  Fig.  3.2  (A)  Stacked  spectra The  of  increments gradient The  spectra  from of  graph  coefficient  pulsed  4.3  were  15 ms  (A). is  3.98  7.97  mTm  - 1  mTm" .  was  of  f i e l d  (T10),  pulses  pulses  in  of  dextran  gradient  incremented  (B)  plot  115  vs  0  6.24  the x  (w/v) in  to  in  D 0. 2  duration  151 time  mTm  - 1  and  in  19  between  ms.  Ln(A/A ) From  %  The  1  gradient  y G 6 (A-6/3) 2  2  slope  10"  1  1  m  2  the 2  s  _  1  .  for  diffusion  5  4  3  Chemical Shift (PPM)  0  1 KVo (A-S/3) x  2  3 ("Itf.s/rrf)  123  Concentration of Glucose  Fig.  3.3  The  variation  D-glucose The  room  with  of  the  diffusion  concentration  temperature  was  23  in °C.  (M)  c o e f f i c i e n t aqueous  of  solution.  124  inorganic  intensities transport  reflect  processes  complex.  divided region  into from  extract  is  spin  also,  values  by  by  to  at  360  phosphocreatine, In  this  characterize in  human  the  forearm  longitudinal that  work  that  time  offers is  apply  a  echo  to  in  of  with  for  normal have  T  It 2  the  to  In the  obtained  protons  of  (120).  of  were  shorter  been  motion  measurements  spins.  proton  translational  direction  the  eliminating  gradient  gradient  quantity  decay.  pulsed  The  and  the  the  muscle.  to  contribution  by  attributed  anserine  the  simplifying  causing  spectra  peaks  of  the  spins  means  observed  and  way  times  and  be  spectra.  II,  magnetization  (proximodistal)  diffusion  against  may  second,  composition  determined  relaxation  showing  taurine  be  potentially  localize  and,  one  chapter  echo  spin  we  obtained  resultant  this  MHz  spatially  provides  metabolic  spectroscopist  the  transverse  from  to  and  the  are  vivo  from  the  the  spectra  chemical  discriminate  Recently,  and  the  w i l l  composition  Considering  in  is  in  relative  body  about  spin-spin  spectra. rat  F i r s t ,  signal  signal  signal  such  the  discussed  systems,  water  of  spectroscopy  the  corresponding  large  forearm  goal  increasing  biological  the  the  echo  possible  of  within,  the  the  subject.  which  As  in  the  parts.  echo  in  of  two  spectra.  the  and  The  properties  Spin  to  out  information  transport  such  nature  carried  Changes  differences  properties  heterogeneous  quite  (119).  phosphate  was  the  technique  water  applied  along  effectively  the  and in  to fat  the  forearm  so  one-dimensional  125  in  that  of  the  d i r e c t i o n . forearm  surface The  c o i l ,  region  muscle,  is  c h i e f l y  like  in  which few  this  10%  about  several  system  in  composition  and  relaxation  times  denotes  a  general  magnetization the  i  t  h  M(t)  phase)  be  n of  is  shown  more  the  of  to  the  scale.  than  half  subcutaneous  greater  part  may  of  but  Muscle  system  middle  and  remainder  (122).  blood  with  the  something  fibres,  reside,  dimensions,  different degrees exchange  motion  at  but  in  are  up  a  to  exchanging water  the  given  phases  present time  slow  (T^  chemical  of  motion  with  surfaces  correspondingly  relaxation for  also  The  chemical  be  position  i n t r a c e l l u l a r ,  d i f f e r i n g  w ill  fraction  skin.  the  (123).  restricted  of  the  of  is  through  r a d i a l i s  transverse  long  have  consisting the  in  in  including  molecules,  denotes  water  environments  w i l l  interactions  and  The  somewhat  carpi  should  the  microns  skin,  and  flowing  centimetres  Water  system  flexor  view  3.4.  probably  tissue  be  F i g .  the  muscles,  half  of  in  on  is  the  should  tens  shown  sampled  connective  water  cross-sectional  placed  b r a c h i o - r a d i a l i s fat,  A  due  dissolved  (124).  affected.  (125), the  or  T ),  the  case  (T^<<  exchange  i  Spin For  a  if  in  2  to  f c  ^  phase,  T^  lifetime  by  71  M(t)=  I  Be  [33]  125A  Fig.  3.4  Cross-section  through  the middle  (A) and t h e s u p e r f i c i a l the  forearm  (121)). diameter  muscles  of the forearm on t h e f r o n t of  (B) ( f r o m G r a n t ' s A t l a s o f Anatomy  The a p p r o x i m a t e surface  coil  l o c a t i o n o f t h e 2.7 cm  i s shown.  127  relaxes  independently  situation  would  with  pertain,  compartmentalization, from  diffusion For  the  of  for  where  between  case  time  the  constant  instance, the  rapid  in  water  various  T\.  is  Such  the  a  presence  physically  of  barred  regions.  exchange  (T\  >>  lifetime  in  the  phase),  M (t) = e it, In  this  regime,  c h a r a c t e r i s t i c  the time  whole T  system  given  relaxes  with  a  single  by  [3-5]  1/T=jr IJ/Tj.  In  the  forearm,  compartmentalization  with is  relaxation  rates.  shown  that  spin-spin  to  multiexponential  be  spin  l a t t i c e L i p i d s  The  1  occur  t r i a c y l g l y c e r o l s  e f f i c i e n t  expected  Previous  b i o l o g i c a l  in  and  the  0  lead of  rates about  body  in  a  ( t r i g l y c e r i d e s , " f u e l s " .  of to  tissue, multiexponential  b i o l o g i c a l of  water  f i f t y  tissue  indeed  times  have tend  faster  than  (126,127).  rates  Lipids are constituents are insoluble in water but organic solvents. 1  are  types  to  studies  relaxation  relaxation 0  different  The  wide  variety  (I))  serve  phospholipids  of  forms.  primarily (II)  as  are  of a n i m a l or p l a n t tissue that c a n be d i s s o l v e d a n d e x t r a c t e d  by  128  essential  components  0 II R,—C  of  membranes.  0 II R—C—0—CH  0  0  0  (I)  2  0  R-c 0 II R -C  CH  (II)  R - C - O - C H  CH —0  0  3  0 II P—0 —R_  2  OH The to  latter broad  form  NMR  lines  dipole-dipole  (128). high  oriented  Consequently,  NMR),  a  microseconds  of  site  In the 5  of  adipose  glands,  for  the  1  and  to  of  not  form  diameter  (129).  fat  storage,  these  occupying  cavity,  these  generally  averaging shift  under  (as  d i s t i n c t  w i l l  be  the  decay  detected.  t r i a c y l g l y c e r o l s  (adipocytes)  in  diameter,  chemical  signal  w i l l  w i l l  p a r t i a l  measured  associated  c e l l s 1  and  and  spectroscopy  abdominal  many  only  when  storage  c e l l s  c y t o s o l  jum  the  NMR  state  major  to  interaction  resolution  few  due  phases  which and  under  insoluble  large, In  occur  adipocytes,  droplets  v i r t u a l l y  can  the  of  conditions from  In  be  as  entire  of  s o l i d  rapidly,  within  mammals,  the  in  muscle,  the  cytoplasm mammary  skin.  droplets the  the  is  the  rise  anisotropy  triglycerides  anhydrous  give  coalesce from  c e l l s large  0.2  in to  specialized as  80  jum  in  cytosol.  A l l intermediary metabolism takes place in the cytoplasm, most of it in the c y t o s o l . The c y t o s o l generally represents a b o u t 55% o f the t o t a l c e l l volume and c o n t a i n s thousands of enzymes that catalyze the r e a c t i o n s of g l y c o l y s i s and gluconeogenesis, as well as the b i o s y n t h e s i s of sugars, fatty acids, n u c l e o t i d e s and amino a c i d s (129). 1  1  129  The  release  involves  their  produced  this  are  normal  way  m i l l i l i t e r about  69000)  THE  EFFECT  side  by  from  2.5  (Table  flows more  2  for  of  the  each  segment  only  1 to  blood  about  2/3  the  free  which  a  albumin  they  and  after  plasma  serum  acids  where  a  milligram  Whole is  tissue  fatty  blood,  serum  about  fat.  3 and  heart  cross  aorta  to  area.  of  cm  in  the  are  per  meal,  per  contains  albumin  flowing The  randomly  is  in  the  of  it  is  small in  If  a l l  cm  of  inversely  length  the  of  c a p i l l a r i e s oriented.  are Only  c a p i l l a r i e s venous  c a p i l l a r i e s in  aorta  However,  in  at  system,  put  each to  conditions,  the  0.3 the  in  the about  since  the 1 mm,  c a p i l l a r i e s than  few  any  its  and  mm t o  less a  and  range  proportional  only  remains  an  were  would  the  flow  resting in  into  a r t e r i o l e s  area  for  2  blood  second  aorta  vessels  sectional  under  blood  the  a r t e r i e s ,  c a p i l l a r i e s .  typical  seconds.  is  Thus,  33  a  of  2500  velocity  c i r c u l a t i o n  have  through  system  total  The  second  c a p i l l a r i e s  the  The  Immediately  c a p i l l a r i e s .  the  averages  mm p e r  diameter  of  (131)).  3.2  the  divided  their  c r o s s - s e c t i o n a l  0.3  adipose  FLOW  from  network  cm  velocity  contain  55% o f  to  protein  tissues.  may  BLOOD  side,  segment  l i p a s e s .  t r i a c y l g l y c e r o l  OF  increasingly .a  the  from  (130).  Blood  f i n a l l y  by  % protein,  (MW  by  transferred  various  plasma  of  7-8  are  bound  to  human  t r i a c y l g l y c e r o l s  hydrolysis  reversibly  transported  of  10  percent  instant, which  flow  for  urn of but is  in  130  TABLE  3-2 cm  Table  3.2  2  Aorta  2-5  Small arteries  20  Arterioles  40  Capillaries  2500  Venules  250  Small veins  80  Venae cavae  8  Cross- sectional  areas  of  blood  vessels  (131).  131  slow, of  and  3 mms"  supply. could  pooling may  1  and  exist  in  S u f f i c i e n t l y  mimic  back-eddies a  large  fraction  randomized  diffusion  on  the  common,  in  time  so of  that the  direction., scale  of  a  v e l o c i t i e s blood  this  flow  spin-echo  experiment.  2.  EXPERIMENTAL Experiments  described  in  using  a  times  were  were in  chapter  surface  gradient  were  made  long  enough  were  from  gradient by  at  RESULTS  AND  Normal subjects'* and  3.5(B)  proton M & F,  composition PPM  in  of F i g .  subject M was ( 1 . 5 m, 47 kg). 1  2  that  and using  of  on  water.  were the  effects  The  measured  skin  of  peak  c o e f f i c i e n t s of  magnitudes  known  A l l  experiments  value  23-26  °C.  of  the  right  of  the  flexor  echo  slow  heights  the  temperature,  and  from  diffusion  gradient  spectroscopy in  relative  r e f l e c t s  placed  previously  lines  were  for  the  were  DISCUSSION  b r a c h i - r a d i a l i s  increased  5.3  ambient  so  apparatus  signals  variation  calibration  performed  NMR  was  spectra  c o e f f i c i e n t  the  minimized.  the  diffusion  3.  B.2.  which  determined  determined  II,  using  c o i l  response  pulsed  done  an the  the  region  muscles  are  intensity obvious two  of  the  are  a  (1.6  also m,  the seen  52  in  kg)  in  the  in  whereas  two  The F i g .  body  peaks  Hahn  of  r a d i a l i s  3.5.  peak  l i p i d in  carpi  F i g .  l i p i d  difference  subjects;  3.5(B) male  shown  forearms  at  spin F  1.7  and  echo  was  a  female  132  A  B  i  i  1  5 0 Chemical Shift (PPM)  Fig.  3.5  Normal  proton  subjects 47  kg).  (M:  1 —  5 0 Chemical Shift (PPM)  spectra male,  1.6  of m,  the 52  right kg;  F:  forearms female,  of 1.5  two m,  133  spectra were  for  measured  Changes  in  spin-spin PPM  subject  are  with  the  comparison  l i p i d with  peaks  in  shorter  spin  times,  determined  by  The  shorter  compared pulse  to  that  sequence  latter  spectral 80  of  is  T  224  Williams  et  due  However,  experiment  are  360  ms.  is  to  in  ms,  at. to  of  this of  F i g .  the  for  comes the  3.6(C)  in  Table  ms)  in  because be  3.3. protons  by  a  CPMG  the  relaxation  to  of  l i p i d  (292  diffusion  were  graph  the  (120)  l i k e l y  1.7  water  3.6(B),  to  expected  and  spin-spin  F i g .  f i t  ms. the  1.3  intensity  summarized  88  600  the  in  3.6(B)  that  at  that  The  longer  also  MHz  show  F i g .  show  spectra  are &  400  peaks  relative  and  in  confirmation  squares  probably  at  also  ,86  2  l i p i d  spectra  3.7)  f i e l d .  density  time,  from  clearly  gradient  the  of  the  large  least  (Fig.  values  inhomogeneous the  echo for  of  Further  pulsed  linear  vs 2T  0  the  spectra  ranging  spectra  slowly.  the  relaxation  Ln(A/A )  times  with  echo  intensities  The  more  spin  times  relative  relaxation  much  The  echo  different.  relaxes from  M.  times  for  the  smaller  than  at  MHz. The  with  that  method). major ranged  T  2  value  of The  i n t r a c e l l u l a r barnacle signal  Williams latter  component, from  2.7  the  the et  water, al.  value  to  100  w i l l  ms.  have  (126,127).  740ms,  (120)  intracellular  water  muscle  from  for  be  (28.8  For  intracellular  long  ms,  by  characteristic  water,  Similar  been  is  T  since  2  values  obtained echo  from  times  component  of  w i l l  the  compared the of echo  CPMG the times  for studies 200 be  ms  on  giant  the  attenuated  134  Fig.  3.6  Normal echo  proton  spectra  spectra for  respectively. with  echo  view  of  the  subject  Pulsed  time 4-6  and  of  M  stacked in  gradient  224  PPM  a  ms  in  region  (A) spin  (C) in  plot  and  (D).  Hahn  (B)  echo  with  of  an  spectra enlarged  D 0  04  0-5  Echo time Plot (B-D)  of  0-6  0-4  (2T,s)  Ln(A/A )  from  -t  0  Hahn  0-5  0-6  (2Z,s)  Echo time vs  echo  r  for  water  spectra  of  (A)  and  subject  l i p i d M.  136  TABLE 33 EXPERIMENTAL VALUES Chemical Shift T2 D/D (PPM) (ms) Lipid 120 0-20,0.23,0.26,0-17 1-3 Lipid 88 1-7 0  Water Unsaturated lipid  4- 8  740  070,0.64, —,1-11  5- 3  86  022,021,0-21,0-17  LITERATURE VALUES T (ms)  Assignment Intracellular water  2  Extracellular water Fat Table  3.3  Chemical times for 2  *:  and  28-8  Williams et al.  400  Foster et al.  292  Williams et al.  spin-spin  relative and  (T )  diffusion  in-vivo;  fat  relaxation  2  D  rates 0  =  (D/D ) 0  3.05  x  10"  1  The  data  experiments a,b  Foster et al.  s h i f t s ,  water  m s"  35  and  c,  (a,b,c,d)  correspond  with  times  and  echo  400  ms  for  d.  of  to  224  ms  for  9  137  by  about  PPM  in  three  F i g .  orders  3.6(B)  is  previous  study  barnacle  muscle  was  attributed  also  of  of  probably  the  gave  magnitude. due  spin-spin a  to  the  with  extracellular  signal  at  extracellular  relaxation  component  to  Thus  a  T  2  water.  of  water  of  400  water  4.8  in  ms  (Foster  A  which  et  al.  ,  (127)). Further from  evidence  diffusion were  90°  180° pulses  Spectra an  3.6(D). is  due  measured  obtained  enlarged  view  The to  decrease  in  the  signal  at  4.5  higher  mobility.  signals in  points  in  are  of  A l l  the  of  to  T  spin  The  flow  motions  Diffusion  more  are  with  the  gradient.  F i g .  shown  3.6(C)  in  majority  of  the  water.  signals  as  the  gradient  d i f f u s i o n .  quickly the of  and  of  the  water  and  400  lines  are  the  best  Except  for  the  f i r s t  for  water  the  l i n e s . would  at  echo  There  cause  time is  400  no  The is  the  ms  straight  signal  water  r e f l e c t s  decay 224  The  and  F i g .  l i p i d  times  ms  and are  fit  by  few  ms,  a l l  of  apparent  o s c i l l a t o r y  behaviour.  d i f f u s i v e .  c o e f f i c i e n t s  three  is  between  the in  echo  the  showing  which  shown  spin  of  of  analysis.  on  gradient  obtained  intensity  the  effect  was  separation  region  the  of  echo  3.8(C),  nearly  PPM  of  2  the  squares  bulk  experiments,  4-6  f i e l d  the  M are  relative  Graphs  3.8.  F i g .  effect  the  assignment  incrementing  subject  PPM d e c a y s  F i g .  least  data  due  for  linear  the  of  A,  and  amplitude  is  shown  from  shorter  increased  fat  fixed  the  Pulsed  keeping  increased  the  support  measurements.  spectra and  to  echo  from time  repetitions 224  ms  and  of one  these at  400  ms,  137A  Fig.  3.8  (A)  Decay  of  the  gradient  spin  gradient  pulse  time  0.224  z-gradient (B)  Decay  from of  spectra  Data and  are x)  increment of  signal  duration,  (0  in-vivo,  human  echo  s.  experiments  water  water  (x)  pulsed  forearm  and  of  human  duration,  forearm 6,  Calibration effective  pulsed  of data  gradient  (0  1  ms  and 0)  (0)  signals  the  same  in  (A).  gradient  acquired 20  mTm" .  with  and  echo  separate  echo  water  from  and  spin  (C)  (•)  ms  effective  gradient  acquired  with  two  l i p i d  as  signals  for  1.84  parameters  of  12  the  experimental Decay  of  shown  is  pulsed  acquired  6,  and  from  l i p i d spin  spectra  (0  0)  echo  spectra  with  gradient  pulse  echo  time  s.  using  increment  of  water 0.53  0.4  gave  an  mTm" . 1  139  are  summarized  echo  time  subject  224  M.  diffusion smaller 3.05 may  X  ms  The  Table was  than 9  2  s  _  compared  i n t r a c e l l u l a r  (132-134),  of  in  that in  with  c o e f f i c i e n t  for  increase  diffusion  be  in  randomized  Eq.  [2.81],  5.5  x  1 0 "  1  estimated  0  would  0.33  mms  part  of  -  1  the  randomized  normal  0.1-0.2  rate  From  is  the  m s"  1  2  and  for  to  the  expected  but  would  motion  to  the  The  a  blood  the  and  0.7. the  3.5  to  x  contribution  flow  of  suggests  extracellular  0.2 that water  is  of  the  m  9  s "  2  that  1  .  The  there and  0.14  may  using  d i f f u s i o n  is  mms" .  The  1  velocity  is  less  c a p i l l a r i e s , major water  to  is  due  normal  compared at  reduction  From  3.3,  is  in  the  due  is  diffusion  10"  normal  that  of  0.6-0.66  (92).  Table  flow  which  1  diffusion  indication in  were  gave  This  larger  extracellular  reduction  2  with  °C,  root-mean-squared  indicate  of  a  randomized  for  ms  m s"  9  0.5-0.6  data due  224  muscle,  ms,  an  37  for  obtained,  contribution  water  s,  was  remainder  10"  of  frog  400  the  flow.  corresponds of  flow.  be ,  time,  water  value  than  echo  at  muscle  the  x  factor  excised  measurements  time  2.2  observed  barnacle  measurement  and  water a  the  echo  about  by  of F  at  normal  with  water  and  of  (11),  1  One  subject  measurements  that m  3.3.  of  c o e f f i c i e n t s  10"  be  in  echo  to  to  diffusion  the  times  diffusion  of  undergoing  restricted  d i f f u s i o n . The for  the  plasma  l i p i d s  giving  following is  small  rise  reasons. (Table  3.4,  to The  NMR  signals  quantity  (135,136)),  of and  are fat  i n t r a c e l l u l a r in  the  since  the  blood T  2  of  140  TABLE  3-4  Water content  ref.  Skeletal muscle  79-2  K-Diem  1970  Epidermis  64-5  K-Diem  1970  Blood plasma  93  P-L Altman 1973  Table  3.4  Normal  tissue  expressed tissue  as  from  water a  content  percentage  Diem  (135)  and  in  per  adult kilo  Altman  humans  of  fat-free  (136).  141  the  l i p i d s  is  contribution under the  the  from  were  of  randomized  as  the  echo  decreased  der  is  9.05  A.  globules, used  987  A  Since the  as  a  10"  is  100  might  2  s  be  _  1  motion  slight  decrease  increased,  on  to  1  2  times  the  m  s  2  -  1  the  and These  of as  motion  urn  The  der  °C,  the  NMR echo  50  diffusion  value  would  experiment. time  the  c e l l .  distances  are  x  observed times of  the  The  is  inside  echo  6.57  produce  3.16  for  of  d i f f u s i v i t y  Eq.  the  (137),  cp  of  for  radius  cytoplasmic This  the  value  l i q u i d  increased of  a  using  Waals  forms  30  as  acid  (113).  observed  The  be  estimated  The  prediction  23  is  calculated  globules.  to  increase  Taking  the  fat  scale  effect  to  oleic  van  at  the  um  respectively.  .  o i l  effects  coefficient s  volume  the  displacement  0.4  three  to  time  the  can  equation.  cytoplasm  larger.  restricted  17  l i p i d s  increments  and  root-mean-squared is  the  with  olive  d i f f u s i v i t y  contrary  due  of  the  of  plasma,  if  d i f f u s i v i t y  corresponding in  detectable  Furthermore  d i f f u s i v i t y the  any  motion.  ester  a  not  blood  the  group  fat  1 0 "  in  would  Instead  estimate  entraining  random  be  molecular  and  attributable  streaming  probably  the  viscosity  x  fat  the  cause  the  the  rough  water,  Stokes-Einstein  with  3  5  m  in  restricted  atomic  is  0  fat  extracellular  experiments.  c o e f f i c i e n t  the  c o e f f i c i e n t 1  to  increased.  attached,  Waals  obtained  is  time  these  t r i g l y c e r i d e ,  molecules  of  of  should  diffusion  typical  of  due  flow  using  that  extracellular  indicating  estimated  van  than  conditions  signals  The  less  is The  diffusion  of  0.224  same  and  order  of  142  the  size  of  The  effective  Measurements values in  the  globules  would  root-mean-squared of  cytoplasmic  of  about  70  ams~  animal  c e l l s  is  rarely  experiments  that  w i l l  be  1  in  faster to  found  velocity  streaming  (137)  required  be  a  in  few  than  5  confirm  is  in 66  plants cases, urns- . 1  these  adipocytes. /zms- . 1  have but  given  streaming  Further observations.  IV.  A.  NMR  IMAGING  INTRODUCTION Two-  imaging (1~4)  and  is  of  coming  soft  a  whole  5  mm  1  mm i n - p l a n e  a  current mm  for  plants,  into  in  studies  interest  of  or  to  applications  (59,139)  of  10 in  smaller  studies  txm o r  developmental  substructures  of  term  "spatial  resolution"  from  10  Mm i n  the  distribution  been  in  provide  potentially  0.2  of  is  the  such  are  the  II.  While  it  and  information,  chemical  shift  useful.  143  best  better  than  For  is  considerable say  transport range  to  0.1  in  of  images  Here,  the  Numbers  showing  that  system  exceeds  the  should.  T  use  sizes,  2  and  The  mapping  gradients  much  effort  diffusion  (1-4), are  of  as  contrasted  parameters  and  we  quantity.  applying  these  mm.  at  from  identifiable  pixel  T,  be  Recent  this  as  by  manipulating as  wider  computer  data,  as  resolution, water  show  mean  achieved  substantial at  to  of  a  2  resolution  (3)  there  mm d i m e n s i o n s .  (59,139)  chapter  directed  parameters  -  capability  resolution  described can  20  display  spatial the  to  0.1  ago  biology.  samples  diagnosis  about  as  for  medical  sometimes  spatial such  resonance  Spatial  samples,  better  biological  can  magnetic  in  years  thickness  improving  physiological  use  man.  two  today  s l i c e  in  in  quoted  basis, a  proton  increasing  defects  scanner,  volume  biological  dimensional  tissue  body  on  3  three-  imaging has other also  1 44  In  this  techniques in  pupae  (section  chapter,  for  imaging  the  Douglas  B)  and  in  cone  reproductive  map  proton  (section  of  the  and  distributions  Barbara  moth, caps  apparatus  colfaxiana  marine  alga,  C).  INTRODUCTION  pharate  suited than  to  (140)^ . 3  of  the  Douglas-fir  NMR  separate and  The  f l u i d  responded  orientations  with  as  and  "head-up"  allowed  it  for was  any  cone  studies  of  as  'H-NMR  the  in-vivo  the  f i r s t  found  to  to  that the  insect  are  particularly  because  well  they  imaging  to  the  the  colfaxiana  two  gravity,  In  opposing  hereafter  more  fluids  l i p i d  observation  B.  have  aqueous as  time.  species,  Barbara  moth,  containing  fluids)  differently respect  study  Olethreutidae),  compartments  bodies  experiments  to  1  moulting  has  used  ( H~NMR)  application  animals  discrete  adults  be  proton  (haemolymph  these  can  (Lepidoptera:  two  these  NMR  adults  colfaxiana  reserves study of  of  these  course  of  pharate principal referred  to  "head-down".  The term " p h a r a t e " insect development in the pupal c u t i c l e and 3  to  described  COLFAXIANA  Although  1  used  f i r  mediterranea  B . BARBARA  previously  are  of  Acetabularia  1.  the  adult is used to describe the which the developing adult is separated from it by m o u l t i n g  stage of within f l u i d .  Used i n t e r c h a n g e a b l y in this paper are the terms "pharate adult", "pupae", "insect" and " a n i m a l " , they are used to describe this same d e v e l o p m e n t a l s t a g e . "Pupae" i s used most often as t h i s term i s the most d e s c r i p t i v e of the external c h a r a c t e r i s t i c s .  1 45  Barbara  colfaxi  damages  Pseudotsuga  Douglas-fir, natural  ana  stands  and  diapause  that  spans  diapause  occurs  menziesii  seed  in  two,  pharate  c h a r a c t e r i s t i c s  are  this  study  contained  near  Keremeos,  by  Dr.  John  (Canadian  2.  were  adult  a  the  Service,  insect  P a c i f i c  the  The  used  cones  in  collected  kindly  provided  Forestry  V i c t o r i a ,  a  external  Insects  were  both  (141-144).  but  Douglas-fir They  in  exhibits  winters  (140).  of  Franco,  stage,  pupa  inside  of  This more  Columbia.  Manville  Forestry  of  seeds  Centre  B.C.)  EXPERIMENTAL Cones  were  stored  not  eclose  next  (will spring)  pupae  during  the  preferred  were  degrees  cones from  communication). pupae  were  hardware and  as  eight  ambient  run  glass  of  is  head  H-NMR  using  position  of  and 6.3  in  Chapter  were  used. ° C ) .  inside  a  were  pupae  NMR T  2.  held  at  The  body  at  and  of  +15  to  individual imaging  9 0 ° - p u l s e  pupae  the  A l l  personal  magnet  5 mm NMR  examined  1985.  images  The  next  inside  the  Experiments The  and  pupae.  with  light  emerge  A p r i l ,  Manv.ille,  (21-24  pupae  and  these  both  cones  individual  (J.  same  until  (will  their  1984  spectra  the  dark  from  on  sheds  uppermost  horizontal 1  and  November,  described  The  spring)  orientation  temperature  tube.  unheated  extracted  transients  v e r t i c a l  in  performed  natural  Douglas-fir 20  were  months  experiments  a  those  B r i t i s h  F.  or  and  (Mirb.),  orchards.  one, the  cones  tube  were  were  18  done  at  us  maintained  using  center  was  of  a  3 mm  the  rf  in i.d.  c o i l  1 46  by  small  pieces  NMR  tube.  and  the  The  of  pupae  head-down  were  obtained  Fig.  2.5.  A l l  sensing  The  The and  AND  water  pupae  in  water  spectra pupae two  —  years;  50  for  pupa  (Fig.  the  4.2).  experiment showed  of  the  head-up  Proton  were 7  about  mm)  was  shown  well  of  of  the (H/U)  distribution  conducted  which  with  two  and  light  in  the and  decay echo  of  shown  in on  whole  within  the  incomplete  d i s t i n c t  also  is  for  F i g . 4.8  Spectra  animal  head-up  4 . 1 .  The  PPM d u e  obtained  show  more  the  an  to  l i p i d  with  the  increased  pronounced  for  the  in  the  were  consistent  for  from  two  collected  dark,  s i t e s ,  male  and  relaxation  head-up l i p i d  times  in  differences  and  the  pupae,  1 PPM a n d  s p i n - l a t t i c e  water  The  are  orientation  multi-exponential  presence  both  sequence  two  respectively.  both  from  for  of  individuals  The  s  bottom  a r t i f a c t s  orientational  individuals.  0.4  at  reversible,  another  by  c o i l ;  s p l i t t i n g  The  over  (3  spectra  head-up  were  pulse  studies  orientations  and  peak.  the  precluded.  NMR  protons  dispersion  the  NMR  rf  signals  the  in  in  DISCUSSION  proton  show  placed  orientations.  animal  the  thus  head-down  spectra and  of  were  RESULTS  vivo  paper  examined  using  entire  f i e l d  exposure  3.  in  were  (H/D)  maps  insects.  tissue  protons water  ranging  behaviour water  a l l  viable over  female  times  orientation  proton  determined  were  1.2  and  respectively  signal from  in  2 ms  (Fig.  components  a  Hahn  to  4.3) with  120  echo ms,  suggesting spin-spin  the  A  B  T—I—I—  i—i—r  10  10  5  0  5  0  Chemical shift (PPM) 4.1  Normal  proton  colfaxiana or i e n t a t  for ions.  spectra the  of  pupae  head-up  and  of  Barbara  head-down  147A  Fig.  4.2  Proton  spectra  recovery  time  (A) for  and  graphs  water  inversion-recovery  spectra  colfaxiana.  The  recovery  12,  17,  22,  32,  42,  and  402  ms,  1.0,  Using  three  1.2±0.1 respect  and  52,  1.4,  0.4±0.04  s  and of  times 77,  1.8,  parameter  ively.  (B)  of  peak l i p i d  height (C)  vi  from  Barbara varied  102, 2.2,  f i t s ,  the  for  water  152, 2.6 T,  from  7,  202,  252  and  3.0  values  and  fat  s.  were  148  Recovery  time  (s)  148A  Fig.  4.3  Proton  spectra  echo  time  echo  spectra  times  for  varied  36,  44,  52,  The  decay  73  % and  l i p i d  of  signal  plot  (B)  from  2,  70,  the  % of gave  of  and  Barbara  times,  27  and  water  60,  of  relaxation  (A)  l i p i d  8,  80,  12,  90,  100,  water  signal  21  55  a  and  i n i t i a l T  2  (C)  of  19  echo 24,  and  two  Hahn  30,  120  and  ms.  spin-spin  corresponding  signal ms.  20,  110  give  ms,  from  The  16,  VJ  height  colfaxiana.  4,  the  peak  the  to  1  1  1 1—  10 5 0 -5 Chemical shift (PPM)  B  3 < c  0  005  0-1  Echo Time (2t,s)  0  005 Echo  time  150  relaxation 27  % of  l i p i d  times  the  280  was  Hz  for  are  much  measured  spin-spin This  inhomogeneity  is  The  NMR  line  observed  is  further  in-vivo  is  due  the  pulse  head-down the  distributions in  the  abdomen  fluids  in  the  upper  well  separated  proposed  maps  and  of  shows  the  of  the  redistribution pupae. protons  The  of  to  resonance  vary  at  half  be  in  for  expected  15 H z  F i g .  that  and  and  l i p i d from 17  the  Hz  f i e l d the  the  lineshape  taken  4.4.  The  from  a  narrow  broadening  fluids  in  pupa,  the F i g .  of  the  head-up  of  the  T  the  between  the  with  associated  of  The pupa  spectra  between  are  of  located  aqueous are  two  the  quite  components  d i s t r i b u t i o n  produced  with  the  water  upper  by  the  the  different  the  and  data.  2  spectra  in  to  using  Comparison  reserves  correspond the  the  obtained  4.5.  l i p i d  parts  frequencies  continuously  along  orientations.  lower  are  l i p i d  for  the  both  changes  the  linewidths  healthy  shown  proton  pupae,  the  haemolymph  and  a  explain  the  of  T  determining  of  2.5,  probably  Comparison that  of  that  in  and  previously  inversion  water  is  shows  mainly  2  The  magnetic  shown  F i g .  orientations  73  inhomogeneity.  of  of  that  evidence  direction  sequence  to  235 Hz  times,  factor  is  to  distribution  and  would  spectrum  micropipet  anteroposterior  than  suggests  using  The  protons  major  corresponding  observed  relaxation  the  and  respectively.  The  water  pupa  lines  a  ms,  signal  larger  respectively.  linewidth.  55  19 m s .  protons,  and  and  observed  protons  height,  21  parts and  and  of  the  l i p i d  lower  parts  151  1  ~~1  10  1  5  0  Chemical Shift (PPM)  Fig.  4.4  Normal  proton  from  pupa  a  of  spectrum  Barbara  of  colfaxi  trimethylsilylpropionate) reference.  haemolymph  was  ana. added  extracted  TSP as  (Sodium a  3  -  151A  Fig.  4.5  Normal along  proton the  Barbara  colfaxiana  the  pupa  pulse  time  2 ms,  echo  1  The  of  f i e l d  displayed.  four  time, of  was  16  view  There  acquisitions  experiment  1.2  about  distribution  direction in  sequence  increment  were  proton  orientations.  z-gradient  s.  and  anteroposterior  "head-down" using  spectra  the The  of  ms  maps  - 1  2.5  and  and  were  acquired  encoding  relaxation cm  were  128  gradient  17  and  phase  1.0  the  live  with  was  and  a  "head-up"  F i g .  mTm  of  total  minutes.  of  maps  which  time  delay, 0.86  cm  increments for  the  Up  Down "T"  15  10  0  T  T"  •5  15  Chemical shift (PPM)  ~T~  10  T"  5  0  -5  Chemical shift (PPM)  153  of  the  pupa.  affected  in  Since the  corresponding more  clearly  obtained several proton also  same  seen  in  spectrum  for  and  proton  pupa, the  was  in  unusual  degree  of  corresponding  feature  at  cm a n d  proton  similar  feature  also  map.  A  observed  orientation protons  in  in  the  (Fig. the  4.6  0.5  3.5  4.6  (B))  (Fig.  v a r i a b i l i t y  compared  4.5  spatial  (B)).  4.7  NMR  pupa  spectra  in  immediately  with  (B)  (B),  in  that  (A),  haemolymph  (C)  in  with  partly  The  resonance  also  the  that  a  observed  of  stage  or  that  of  live  f i r s t  are  then l i q u i d  and  pair  is  frequencies  the  in  the  F i g . the  the  twenty  same  nitrogen.  inversion that  of the  determined  the  pupa  the  previous  map  increased due  to  a  be  pupae  are  shown  (A),  (C)  is  The  pupa's  a  in  two  the  smaller of  a  taken  after  change  dead.  show  individual,  The  the  of  may  distribution by  degree  responses.  minutes  of  pupa  spectra,  orientational of  the  head-up  larger  dead  of  a  intensity  4.6  pupa  The  in  in  the  cone  head-down  for  show  a  4.6)  observed  an  indicating is  less  for  region  is  suggest  (C)  and  with  map  cm  typical  and  inmersion  spectra  The  but  and  PPM  is  (Fig.  from  to  orientation  differences  spectra  (A)-(D).  healthy  in  These  developmental  Proton  minute  to  heterogeneity  different  Fig.  (A)).  to  orientation  (Fig.  proton  s p l i t t i n g 5  This  performed.  head-up  are  attributed  maps  removed  was  the  an  0.4  be  distribution  which  pupa  may  resonances  s u s c e p t i b i l i t y .  experiment  this  l i p i d  variation  magnetic  the  before  water  the  in  another  weeks  the  way,  changes  from  shows  both  than  the  heart.  The  in  153A  Fig.  4.6  Normal p r o t o n along  and p r o t o n d i s t r i b u t i o n  the a n t e r o - p o s t e r i o r  colfaxiana in  spectra  pupa,  several  direction  weeks a f t e r  of a  maps  Barbara  harvesting,  t h e "head-up" a n d "head-down" o r i e n t a t i o n s . The  map was a c q u i r e d w i t h t h e p u l s e sequence o f Fig.  2.5 w i t h a z - g r a d i e n t i n c r e m e n t  w i t h phase e n c o d i n g 24 ms. The f i e l d  time  o f view  0.68  cm a r e shown. F o u r  each  o f t h e 128 g r a d i e n t  time  f o r the experiment  of 1.2  o f 2 ms, a n d echo  mTm"  1  time  was 0.96 cm o f w h i c h acquistions  were u s e d f o r  i n c r e m e n t s and t h e t o t a l was a b o u t  17 m i n u t e s .  155  T  1  1—  T  1  r  10  5  0  10  5  0  Chemical  1  1  10  5  shift  1  I I I  0  10 5 0  Chemical Fig.  4.7  Normal pupa  (PPM)  proton  before  liquid Spectra fungal  shift spectra  (A)  and  nitrogen, in  (D)  ( PPM)  infection.  of  Barbara  a  after  and  are  of  immersion  twenty a  pupa  minutes which  colfaxiana (B)  in  later died  (C). of  156  fourth  pair  fungal  infection,  indicates not  of  a  loss  observed  used  spectra, and of  for  conclusion,  to  map  body  are  of  reduced f l u i d s ;  a  pupa  signal  chemical  shift  anteroposterior  direction  B.  colfaxiana  These  that  haemolymph,  orientation resonance  of  C.  1.  the  an  aqueous  pupae of  ACETABULARIA  of  when  was  changed.  the  protons  in  and  of  a  ratio  changes  l i p i d  were  has  along  been  the  adults.  consisting  the  mostly  v e r t i c a l  Variations probably  magnetic  spatial  imaging  pharate  f l u i d s ,  redistributed  indicator  in  due  the  to  s u s c e p t i b i l i t y  heterogeneity.  MEDITERRANEA  INTRODUCTION  s i n g l e - c e l l e d , develops,  its  of  differences  Acetabularia  to  the  frequencies  corresponding provided  were  noise  resolved  water  of  to  died  individual.  of  show  that  orientational  distribution  maps  the  the  this  In  (D),  4  cm  and  vegetative  40-70  a  rays.  400  the  is  and  f u l l y  ray  tip  in  um  the  cap, is  alga.  growth,  c e l l  about  formed, with  an  into  the  8  400 rays  many  several a  At  mm i n ym  large months  c y l i n d r i c a l the  produces  40  to  unusually  Over  diameter.  about  broadens  cytoplasm  is  green  growth,  Each  stem,  continuous  by  discoid  central cap  marine  largely  long  extremity  mediterranea  at  its  where  um  at  the  at  f i r s t  chloroplasts.  c e l l  culmination  up of  upper  diameter  wide  it  and it  with  leaves  periphery. contain The  single  the  When  157  nucleus, and  at  the  numerous  these,  in  nuclei  a  with  divide  material  aqueous  d i f f e r  from  parameters  to  which  govern  resonance  spectroscopy.  different  water  types,  NMR  imaging;  object  for  Caps  vary  needs  or  less  no  It  is  f l a t ,  s l i c e  in  in  ways  as  Without  would  it  has  no  in  and  to in  can  no  discrimination,  signal  resolution with  an  into  can  be  ordinary  the  xy  plane  plane.  estimated  by  photograph,  the arrays  there  is  l i k e l y  to  affect  the  proton  magnetic  a  of  various  sensitivity  very  low  of  contrast  from  cup-shaped  many  work.  which  to  are  Imaging  then  achieved  the by  The  disc  (xy  plane)  projecting effective  comparison  taken  is  are  regions.  this  of  wall.  A l l  outside,  select  be  in  water  the  done  dry  shape,  possible was  be  of  becomes  crowded  d i f f e r e n t i a l  cap  Each  daughters  cysts  in  the  selection  spatial  the  which  two-dimensionally z-axis  rather  s e n s i t i v i t y  rays.  gametes.  cysts;  divides  c e l l u l o s i c  ultimate  the  the  cap  heavy  inside  substantially  umbrella-shaped. more  into  Water  outside  the  then  cytoplasm,  b i f l a g e l l a t e  bundled  solution.  a  c e l l , the  and  with  and  form  the  populate  cyst  structures  that  of  chloroplasts  further,  is  multimembranous only  nuclei  spherical  membrane-enclosed l i v i n g  extremity  daughter  together  encysted The  lower  in  the  of  the  with total  spatial the  NMR  image  dissecting  microscope. The  c e l l s  o r i g i n a l l y culture  for  used  c o l l e c t e d many  in in  this the  work Bay  generations,  are of  f i r s t  from  Naples, in  specimens and  Europe,  maintained then  in  the  in  158  laboratory  of  Dr.  the  laboratory  are  kept  medium)  in  of  20  °C  ft-candles  on  a  cut  off  several  2.  EXPERIMENTAL  for  T,  (Fig  be  2.8)  T  this  For  heals.  outside  the  For on  was  end  magnet. imaged  at  UBC).  in  They  (Shepard's  300-500  For  imaging,  Shepard's  caps  medium  they  of  a  for  up  Data  were  of in  c i r c l e  Mounting  The  of  end  of  the  sample  acquisition  in  took  kept  in  17  very  the  pulse z  imaging. severed centre of  cap,  with,  and  the  c l e a r l y ,  from  probably  the  placed  but  the medium. mounted  in  the  sample as  is  a  4.12(A).  magnet mins  using  medium  with  used  gradient  Shepard's  then  F i g .  the  in  tube  and  the  two  180°  contact  the  was  this  4.10(B)  5 mm O . D . ,  in  from  which  at  was  the  were  envelope  d i r e c t l y  tube  the  wound  were  the  which  outer  removed  Figs.  of  the  caps  after  in  increasing  method  conveniently  caps  by  requires  and  d i r e c t l y  the  then  glass  before  on  caps,  is  obtained  contrasting  used  inside  medium.  f a i n t l y  minutes.  currently  /called  inversion-recovery  done  mature  Contact  complete  in  were  achieved  not  were  Water  imaging, the  l i t  cycle.  kept  equally  was  cysts,  surrounding  the  applied  which  stalk.  never  light:dark  Diffusion  Experiments the  and  (Chemistry,  chambers  and  UBC)  (145,146)  contrasting  2  whilst  and  gradient,  growth  stalks  with  time  to  Harrison  sea-water  12:12  contrast.  pulses  L.G.  (Botany,  days.  Images echo  Dr.  in  the  to  the  Green  a r t i f i c i a l  at  were  B.R.  for  took 128  only x  128  a  few points  159  in  the  images  averaging delay. often was  of  shown four  Specimens returned  lost the  and  the  removal  seen  by  response  made  specimen 4.10); used  with  did  but  D 0.  not  the  several  from  the  to  brief  exchange  image  times  and  of  a  the  used  condition  Water  2  with  during  medium  repeated  medium  4.10-4.12,  repeats  water  with  their  Figs.  complete  to  incomplete  in  of  signal  a  relaxation  2  again.  the  This  immersion the  cysts  with  the  D 0  in  in  2  which  almost  recovery  most  clearly  Shepard's a  5  were  deteriorated was  of  and  The  caps  medium.  specimen  s  experiment  in  vanished  using  healthy  minutes  had  (Fig.  previously  completely  after  been  this  treatment. The  stacked  demonstrated mm;  the  count  v i s i b l e images  in  a  in  more  the  4.8.  of  computer count  values  linewidths  of  for  one  the  time of  no  better  several  and  rays  the  as  time than  fewer  sample.  mature  for  The best  the  caps  These  KHz the  are  and (T,)  were  values  i n t r a c e l l u l a r  1.8  from  immature  s p i n - l a t t i c e  4.9).  about  expected  for The  (Fig.  literature  be  usually  computer  and 0.3-0.4  than  those  color-coded contrasted  photomicrograph.  DISCUSSION  times  respectively  would  was  same  spectra  F i g .  relaxation  rays  l i t t l e  resolution  photomicrograph  AND  Proton shown  of  gave  RESULTS  required  effective  required  examples  3.  an  plots  value,  17  mature  and  spin-spin  about are  water  about  two  100 Hz  0.58  s  caps  and  are (T ) 2  19 ms  consistent  with  (126,127).  The  times  from  T . 2  greater This  than  160  i  i  1  1  -A  -2  0  2  r  A  Frequency ( K H z )  B  T—r i—r - 6 -A - 2 0 2 4 6  Frequency ( K H z )  i  i — r  r  6 -A -2 0  2  A 6  Frequency ( K H z ) Fig.  4.8  Normal (B)  and  proton (C)  relaxation  spectra  two delay  for:  mature 2  s  (A)  caps,  and  4  an  immature  acquired  complete  cap;  with repeats.  160A  Fig.  4.9  Proton  spectra  recovery  time  in in  NMR  experiment  and  180° pulses  and  the  50,  100,  1.5,  2  and  to  the  three  echo  plot  of  is  from  80,  90,  18.7  ms.  ,T,  13  cap.  med.  27  MS  The  from  1,  750  ms  then  from  and  relaxation 0.58  delay s  90°  respectively,  varied  was  vs  inversion-recovery  A.  and  intensity  was  in  (C)  attenuation 2,  an  of  ±  10,  was  0.05  s  25,  1, 10  s  by  a  f i t .  spectra  echo  to  The  calculated  Hahn  70,  mature  time  parameter  varied  a  were  s.  graph  from  500,  2.5  and  (B)  on  recovery 250,  (A)  4,  100,  and vs  the echo  corresponding time  (D) 40,  which  8,  12,  16,  20,  30,  50,  and  110  ms.  The  calculated  60, T  2  161  162  indicates  that  governing  the  sample  another.  to  differences sample  holder.  The  probable  that  numbered  seen  The  spurious  is  or  image  (Fig.  4  ms  the  long,  produce  in  both  "normal" Fig.  4.13.  poorly  in  resolution  s i g n i f i c a n t l y  the  of  image at  about  due  factor  from  one  of  positioning  the  on  the  inhomogeneity  are  to  differences  pair  are  may  of  into  in  them.  31  rays  ms  at  the  rays  are  clearly  to  256  the  the  as  x  256  cap.  drying  The of  4.11),  16  mTm  and  - 1  correspondence; which  is  two  uneven the  of  contrasted  have  low-signal  in  can with  bundles  points  resolved  it  (Fig.  diffusion-contrasted  with  of  some  the  spatial  the  of  in  confused  of  o'clock",  v i s i b l e  cap  remainder  pulses  in  towards  diffusion  showed  "9  c l e a r l y and  due  A  are  shown  are  present  contrast  2  by  l i n e s " ,  become  "ridges"  a  be  T  as  taper  mm l e v e l  image,  s e r i a l l y  "dotted  "dots"  and  cap  were  cysts  z-gradient  time  of  of  T,  between  echo  mature  i d e n t i f i e d  0.1  the  a  cysts  be  the  with  with  of  up  the  whether  "normal"  the  could  that  images  cysts,  The  clumps  ray  of  2  break  4.12)  image  D 0,  and  with  the  main  spaces  defective  to  major  deuterium-contrasted  cap  In  the  in  a  bundles  clear  cysts  the  consequence  also  interfaces  the  noise  not  a  cause  As  the  resolution. it  47  every  the  in  and  and  immersion  and  of  was  is  s u s c e p t i b i l i t y .  pictures.  centre be  at  photomicrograph  4.10.  both  exist  varied  latter  samples  5 minute  Fig.  The  broadening  which  the  diamagnetic  the  lineshape  in  gradients  A  inhomogeneous  cap  f a i l e d  regions  image. shown  A  in  sections  and  intensity  and  during  the  162A  Fig.  4.10  (A) A.  Top  photograph: reproductive  med.  bundles living (B)  of  cysts  of  after  5 min  the  medium  made  with  a  fixed  time  22  with  phase  MS,  data  of  a  mature  patches  essentially  white  magnetic  in  same  in  with  The  D 0. 2  y-gradient  an  are  a l l  the  of  2  amplitude;  The  image  and  is  v e r t i c a l black  10.1  s.  to  line  and  orientation, sea  water  was  acquired  mTm"  1  of  with  0.111  echo  time  dwell mTm"  7  Colour-coding: is  high  comprised  lines  photomicrograph  ms,  light  interpolated  The  image  2  resonance  a r t i f i c i a l  increment  time  delay  the  of  x-gradient  points  the  dark  Proton  immersion  signal  display.  cap,  encoding  amplitude.  The  same  relaxation low  The  containing  photograph:  image  is  cap.  of  material.  Bottom  and  Photomicrograph  256 is  mark the  of  x  an  x  128  a r t i f a c t .  same  image  dark  for  image  the  ms  signal  128  256  1  feature  resptively.  163A  F i g .  4.11  (A)  T,-contrasted  using time  an of  image  inversion 0.3  s.  pulse  Imaging  y-gradient  of  x-gradient  increment  encoding  relaxation (B)  T  2  17.7  time  of  delay  of  2  cap  x-gradient  increment time  151  5 ms, 2  cm  the  and  both  x  of  1  0.48  s.  1  6  a  fixed  time  14 M S ,  with  phase  ms  and  Acetabularia  mature  with  a  fixed  dwell  mTm" time  The y  a  and  echo  delay  recovery  s.  mTm"  relaxation in  mTm"  acquired  of  encoding  0.124  obtained  a  were  dwell  time  cap  by  with  echo  image  y-gradient  mature  followed  1  of  ms,  a  parameters  mTm"  2  contrasted  mediterranea  of  1  32  f i e l d  time  and ms of  directions.  16  MS,  phase and view  was  0.97  X-coordinate (cm)  164A  Fig.  4.12  (A) of  Image  of  signal  a  intensity  (horizontal), ( v e r t i c a l ) .  The  sequence  10.1  mTm"  increment of  delay (B)  (C)  1.5  of  2  cap  ms,  the  fixed  (A)  same  a  time  24  with  phase  and  fixed MS,  apart, 180°  mTm" and  of  25  JUS,  spin  x-gradient  phase  encoding  and  relaxation  time  7  copy  of  photomicrograph  and  a  (C),  ms  with  encoding  4  applied  pulses.  of  ms  2  scale of  10.1  s.  4  ms, The  long,  mTm" of  echo  1  the  mm. cap  acquired with  0.063 time  z-gradient  after  of  same  were  spaced  immediately  of  the  data  increment  time  delay  were  1  The  y-gradient x-gradient  a  image  orientation.  relaxation 16  y-gradient  a  echo  Diffusion-contrasted the  using  with  1  plots  y-direction  acquired  time  mTm"  128  s.  as  with  of  0.126  in  as  x-coordinate  were  dwell  Xerographic  same  in  of  displayed  versus  data  with  and  1  cap  stacked  echo  time  mature  15.1 the  dwell mTm"  31  1  ms  pulses ms 90°  and  165  165A  Fig.  4.13  Normal  image  acquired fixed 16  MS,  using  time  along  delay points  the  x  and  151  2  ms,  of  2  mTm  and y  echo s.  the  mediterranea  sequence  increment  of  256  pulse  of  x-gradient  relaxation x  the  y-gradient  encoding  256  Acelabularia  of  and  - 1  of  directions.  8  image  f i e l d  of  F i g .  dwell  1.2  time  The  of  cap  1  and  phase  and  consists view  with  time  mTm" ms  2.3  was  of 0.97  cm  166  167  experiment  which  variations  are  extent  because  noise  ratio  about  25.  lasted  34  minutes.  observed  in  the  the  in  Ultimately, translational encoding  those  intervals.  motion  during  i n i t i a l pulse  the  motion  phase  and  Acetabularia  in  4.2  caps  the  of  2.2 4  during  frequency  in  ms  and  is  2.2  be  is  also  to  was  the for  between  gradient and  only the  ignored.  The  intervals  and  these  have  achieved.  for  signal  intervals  minimized been  lesser  4.13,  important can  a  The  and  the  encoding  period F i g .  less.  to  resolution  encoding,  displacement  for  The  water  over  that  NMR  images  of  interval  um.  In  conclusion,  of  Acetabularia  corresponding  to  resolution  0.1  of  limiting  image  from  variation  the  a i r - c a p  spins  F i g .  root-mean-squared is  of  the  is  but  4.12(A)  limiting  pulse  times  Figs.  intensity  images  time  factor  detection  y-gradient sequence  images,  frequency  For  the  other  experimental  normal  Similar  two  the  medit erranea  show  distribution  of  mm.  quality  interface.  in  dimensional  Besides is  signal  inhomogeneous  diamagnetic  features  cysts to  mature  with  noise,  spatial a  feature  broadening  susceptibility  at  arising the  CONCLUSIONS  The  determination  linewidths obtained  gave  by  of  values  water.  forearm,  attributed  gradient which  c a l i b r a t i o n  c o e f f i c i e n t human  of  to  a  of  the  observed  with  root-mean-square  Chemical  is  water  shift  d i s t r i b u t i o n  of  direction  pupae  These upon  of  maps the  the  to  with  water.  resonance  for  of  proton  T  of  2  with the  about  0.8  Measurements that  a  flow  of  major in  proton  maps  showing  in  the  of  between  the  of  s  was  the  part  of  the  the  anteroposterior have of  the  pupa.  different  frequencies  of  1  colfaxiana  d i s t r i b u t i o n  diffusion  c a p i l l a r i e s  mms" .  l i p i d  and  those  spectra  0.15  orientation  varied  lineshapes  of  Barbara the  values  suggests  velocity  from  agreement  randomized  and  of  that  v e r t i c a l  study  resolved  water  show  s u s c e p t i b i l i t y causing  due  in  known  signal  motion a  the  i n t e r c e l l u l a r  " d i f f u s i v i t y "  were  using  In  water  magnitudes  been water  The  parts  the  obtained. depended  magnetic of  protons  the  pupa  to  vary  correspondingly. Images  Acetabularia  of  resembling  the  radial  specimens.  The  spatial  0.1  mm.  For  T,  and  T  2  features  in  the  image  the  caps  or  the  spaces  the  best  resolution  the  image  are  in  probably  medi t er r anea  structure  of  resolution  was  contrasting, arise  from  between which due  to  the  them.  the the  168  caps  is  not  groups D  2  features  from  estimated  it  the  showed  mature to  be  clear of  whether  cysts  0-contrasting  features cysts.  within gave  "highlighted"  in  SUGGESTIONS  1.  IN-VIVO  PULSED  In-vivo  diffusion  were  complicated  echo  times  The  use  because  were  the  allow  echo for  the  compartments  (91).  appears  to  suppress look  be  the  T  2  .  small  randomly  involve  the  The  at  blood  existing water  this  flow  Further  in  by  using  the  H  2  0  data  be  due  over of  sample  a  the  range  diffusion  in  region,  169  that  B,  has  the  echo  blood  to  short  T  water,  and  2  and  with  d i f f u s i v i t y time  due  these  of  echo with  it  it  of was  undergoing  of  after  muscle  times,  which  be  required  section  echo  with  in be  motion  arm, or  vibration.  measurements  would  with to  of  less  5 0 ms w o u l d  III,  data.  pulses,  extracellular  showed  instead  produce  as  long  r e l i a b l e  diffusion  signal  increased  and  gradient  30 t o  long  and other  system  and a c o u s t i c a l  chapter  investigations  direction  w i l l  anisotropic in  currents  diffusion of  80 MHz  obtain  1 0 urn (24),  might  measurements  muscle  as  the  eddy  restricted  i n t r a c e l l u l a r  oriented  transverse  of  feasible,  that  d i f f u s i o n .  times  described  extracellular  suggested  of  As  primarily  longer  currents  accurate  on  square  eddy  Echo  of  of  WORK  MEASUREMENTS  to  change  study  measurements  c e l l s  the  as  order  instead  more  times.  in  of  abrupt  and reduce  adequate  for  less  ECHO  effects  required  of  SPIN  measurements  the  sinusoidal  should  shorter  by  of  coupling, This  GRADIENT  FOR FUTURE  to  effects times,  a  rest  genuine  large and  may  in  the  proportion after  1 70  vigorous  exercise.  measured  such  signal;  2.  then  the  over  a  the  flow  would  test 0.1  caps  "microscopic" mm l e v e l , it  without  serious  prominent be  could  be  the  vein  less  1)  work  Spatial  arm to  may  also  maximize  be  blood  random.  it  is  the  can  determined  by  be  same  highest  compatible  the  size.  sample  contrasting  have  investigated. parts  of  the  between  them,  further  work  If  the  A l l  c o i l the  not,  sample, are  with  the  is  bundles  highlighted  should  be  NMR  biology,  done  by  on  imaging  other  sample. much, the  is,  for  this  size  dwell  time  of  made of  yet  small  l i n e s :  been  not  and  improved  p o s s i b i l i t i e s  it  environment  2  with  be  yet  H 0  at  and  factors  the  cannot  however,  E s p e c i a l l y ,  microscopic  developmental  rf  used  geometry,  this  be  object  imaging  Acetabularia  of  not  NMR  the  three  kind  gradient  and  on  suitable  of  from  instrumental  c o i l ,  very  size  work  probably  the  and  its  along  because  d i g i t i z e r ,  a  b r i e f l y  equipment the  be  resolution  Future  could  resolution  of  removed  with  to  spatial  damage.  samples  Further  proved  because  b i o l o g i c a l  2)  of  IMAGING  because  as  regions  as  Acetabularia to  Other  so  far  present of the  smaller  because  various  kinds  of  of  exhaustively quite  of  cysts  T,  and  T  or 2  certain the  which  spaces  contrasting,  and  this.  is  especially  to  achieve  for  a p p l i c a b i l i t y  animals,  it  is  going  in  171  to  be  necessary  to  environment.  NMR  suitable  this  shift  for  to  be  chemical achieved  external  water;  into  c e l l  the  useful the  methods  water the  main  v e l o c i t i e s  3)  The  the a)  by of  to  spatial  w i l l  successful,  this and 100  to  so  do  of  how  the  Nit el I a,  also  in  in  which  of  and  the  serve  as  a  eliminate any  c e l l s  very  the  may  medium  If  could  c e l l s  diffuse  to  healthy  as  is  This  not  could  streaming and  chemical  the  contribution  that  not  problem  the  environment.  properties  plant,  The  negligible.  which  studies  are  upon  outside  Acetabularia  aqueous  such  be  the  agents  used.  the  and  nulling  transverse  species  reduce  cytoplasmic  Chara  up  be  then  stalk  (stoneworts)  to  preliminary  prove  transport  inside  paramagnetic  from  in-vivo,  studied  water  paramagnetic  interference  these  component.  desired  aqueous  rely  the  differences  for  these  to  should  sample  since  in  solvent  prepare  contrasting  2  for  selectively  adding  T  immersed  to  shift  applying  samples  sequences  between  by  at  application  due  distinguish  and  pulse  differences  magnetization  look  of can  be  rapid  be  studied  in  charophytes  streaming  reaches  Mms" . 1  resolution  may  be  improved  by  implementing  following: The  factor which  sensitivity (ratio was  samples. c o i l  of  about This  may sample  0.1  could  preferrably  for be  be  improved  volume  B.  colfaxiana  achieved  following  to  a  by  by  increasing  volume  of  and  the  A.  constructing  solenoidal  design;  the rf  f i l l i n g c o i l )  mediterranea a  smaller  the  probe  rf  1 72  would from b)  then the  have  of  in  image  c)  a  A  of  at  512  x  are  of  sample.  particular, from  Biological  could  of  has  extended  seastars),  one  of  samples  to  such  which  are  suppression  problems  of  increasing  the  number  of  number color  for  the  of  points  levels  in  be  microns.  and  a  the  to  should  and  the  attainable  to  and  of  built.  spatial  of  the  partitioning  of  the  another. could  the  wide  stages.  studied  include  immature  cap  animal  stage  reported Many  by  and  and  of  the  (139)  sea  embryo  and  embryos  (e.g.  objects  solved  set  be  characteristics  about present  smaller  mm,  study  been  for  1  8-10  quantity  suitable be  mTm"  magnitudes  echinoderms  can  400  existing  l i k e l y  s i n g l e - c e l l  widely  the  are  lacking  later as  size,  effects  sample  already  could  tens  the  the  b i o l o g i s t s ,  to  by  achieving  above,  upon  systems  Imaging  invertebrates,  the  about  the  specimens  laevis be  of  depend  vary  of  current  radius  w i l l  Xenopus  insertion  increment,  1 mm i n  gradient  resolution  embryos.  allow  achieved  and  capable  Eddy  such  Acetabularia  512  objects  implementation  w i l l  be  gradient  of  c o i l s ,  In  may  per  current.  gradient  water  to  image.  c o i l s  problem  The  to  imaging  gradient 10  scans  displayed For  modified  improvement  number  the  be  side.  Further  the  to  of  of  this marine  urchins  and  developmental if  the  water  resolution  improved  GLOSSARY  OF  TERMS  B i f l a g e l l a t e gametes: Mature haploid reproductive or c e l l s w h i c h a r e m o t i l e a n d p o s s e s s two f l a g e l l a (slender, whiplike p r o c e s s e s of a c e l l ) .  sex  Chloroplast: A type of c e l l p l a s t i d occurring in the green parts of p l a n t s , containing chlorophyll pigments, and functioning in photosynthesis and protein synthesis. Cuticle: A noncellular, hardened an e p i t h e l i a l sheet, such as arthropods. Cytoplasm:  The  living  contents  of  or membranous s e c r e t i o n the exoskeleton of  a  c e l l  excluding  of  the  plasma membrane, v a c u o l e s and n u c l e u s . It is a viscous fluid s u r r o u n d e d by t h e p l a s m a membrane a n d contains organelles such as mitochondria, Golgi apparatus, ribosomes. Diapause: A period development in snails. Eclosion:  Emergence  Haemolymph: The circulatory Magneti by pro int  of spontaneously certain insects,  of  the  circulatory system.  adult f l u i d  suspended growth or mites, crustanceans  from of  the  pupa  animals  and  case.  with  an  open  c s u s c e p t i b i l i t y : Magnetic susceptibility is measured the r a t i o of the intensity of the magnetization duced in a susbstance to the magnetizing force or ensity of f i e l d to which it is subjected.  Moulting f l u i d s : A f l u i d the c u t i c l e prior to  which softens moulting.  the  lower  layer  of  Pharate instar: A stage in the development of an insect during which the c u t i c l e has become s e p a r a t e d from the hypodermis but has not yet been ruptured or c a s t o f f . A pharate adult is w i t h i n but free from the pupal integument. Pupa: A the  n o n - f e e d i n g and r e l a t i v e l y inactive stage between larva and the adult in Holometabolous insects.  173  BIBLIOGRAPHY  1.  P.  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