Introduction to NMR �

Ravinder Reddy�

Brief History of NMR �•  First detection of NMR �•  MSNMR �•  Polarization transfer�•  FT NMR �•  2D NMR �•  3D-NMR and protein structure�•  Development of MRI �•  Hyperpolarization �•  Ultrahigh Feilds�

Outline�•  Concept of SPIN �

–  Spin angular momentum�•  Spin quantum # of various spins�

–  Boltzman factor and sensitivity�–  Interaction of magnetic moment and Bo �–  CW NMR experiment, field or frequency sweep �–  Status of the magnetization in laboratory frame�–  Larmor precession �

•  Rotating frame�

History of NMR �

•  1926 Pauli’s prediction of nuclear spin �•  Detection of spin magnetic moment by

Stern and Gerlach- �– Passing a beam of Ag atoms through

magnetic field �•  1936 First theoretical prediction of

NMR by Gorter �•  attempt to detect the first NMR did not work (LiF &K[Al(SO4)2]12H2O) at low temp. �

History of NMR �

•  1945 First NMR of solution �•  Bloch et al for H2O and �•  Purcell et al for paraffin �•  1949 Discovery of chemical shifts�•  1952 Nobel prize in Physics to Bloch

and Purcell�

First NMR spectrum observed by Bloch�

First NMR spectrum�

•  1H NMR of �•  paraffin obtained �•  by Purcell� �•  EtOH obtained �•  by Bloch, �

High resolution NMR �

The Nobel Prize in Physics 1952 "for their development of new methods for nuclear magnetic precision measurements and discoveries in connection

therewith"

•  Felix Boch�–  Stanford University�–  1905-1983�

• Edward M. Purcell�– Harvard University �– 1912-1997�

"Dr Bloch and Dr Purcell! You have opened the road to new insight into the micro-world of nuclear physics. Each atom is like a subtle and refined instrument, playing its own faint, magnetic melody, inaudible to human ears. By your methods, this music has been made perceptible, and the characteristic melody of an atom can be used as an identification signal. This is not only anachievement of high intellectual beauty - it also places an analytic method of the highest value in the hands of scientists." From Les Prix Nobel en 1952, Editor Göran Liljestrand, [Nobel Foundation], Stockholm, 1953

Hahn Spin echoes�

History of NMR �• 1953 Polarization transfer from electron, Overhauser �

• 1964 First pulse FT NMR by Ernst and Anderson at Varian �

• 1971 Jeener’s proposal of 2 PULSE 2D EXPERIMENT�

• 1974 First demonstration of 2D NMR by Ernst (COSY)�

• 1979 2D 1H/1H NOESY; correlation with through- �• space transfer useful for structural determination �

1972 Lauterbur’s MRI EXPERIMENT�

• 1958 High resolution Solid-state NMR by Magic-angle spinning �

Experiment on Li7 �

Overhauser effect �NOESY - Spectroscopy based on the Nuclear Overhauser Effect; �HOESY - Heterogeneous Nuclear Overhauser Effect Spectroscopy; �ROESY - Rotational Frame Nuclear Overhauser Effect Spectroscopy; �TRNOE -Transferred Nuclear Overhauser Effect.�DNP- Dynamic Nuclear Polarization �

History of NMR �

• Richard R. Ernst • "for his contributions to the development of the methodology of high resolution nuclear magnetic resonance (NMR) spectroscopy” • Full Nobel prize in Chemistry 1991

• 1980 NMR protein structure by Wuthrich�• 1990 3D and 1H/15N/13C Triple resonance �• NMR of protein (MW 30K)�

• 1992 Nobel Prize in Chemistry to Ernst �• 1997 Ultra high field (~800 MHz) & TROSY(MW 100K)�

History of NMR �

•  2002 Nobel Prize in Chemistry to Wuthrich�

•  2002 Structural determination of protein in solids� • Kurt Wuthrich

• for his development of nuclear magnetic resonance spectroscopy for determining the three-dimensional structure of biological macromolecules in solution” • 1/2 Nobel prize in Chemistry 2002

First MRI �

•  Lauterbur, �•  Nature, 2424, 1973�

The Nobel Prize in Physiology or Medicine 2003 for their discoveries concerning Magnetic Resonance

Imaging

Paul C Lauterbur Peter Mansfield

Fourier Imaging �

Image�

•  Two  capillary  tubes  (1  mm  inner  diameter)  with  water  are  oriented  along  Y-­‐axis.  

•  The  image  shows  the  projection  image  in  zx  plane  

Phase  Contrast  MRA  

3T  

NMR/MRI  •  High  resolution  NMR  

–  Chemical  shifts,  Spin-­‐spin  and  dipolar  coupling  •  Through  bond  and  through  space  connectivity  •  Molecular  structure  

•  Magnetic  resonance  imaging  –  External  magnetic  field  gradients    

•  Ascribe  spatial  coordinates  of  spins  •  Create  spatial  distribution  of  spins  -­‐-­‐-­‐>  an  Image  •  Spin  density,  relaxation  rates,  diffusion,  exchange    •  Probe  tissue  structure,  function  and  physiology    

BOLD Effect (1989-90)�

•  Effect of deoxyhemoglobin on �

•  Proton T2 relaxation �•  Used this as a basis for�•  Blood oxygenation level

(BOLD) dependent contrast �

•  Neuronal function �•  Functional MRI (fMRI)��

•  Ogawa, S., Lee, T. M., Nayak, A. & Glynn, P. (1990) Magn.Reson. Med. 14,68-78.�

•  Ogawa,S.&Lee,T.M.(1990) Magn.Reson.Med.16,9-18. �•  Rosen,B.R.,Belliveau,J.W.,Vevea,J.M.&Brady,T.J. �

"(1990) Magn. Reson. Med. 14,249-265.��

History of NMR �

•  Diagnostic imaging �

•  Functional Imaging �

Proton MR image of human lung at 1.5T�

Susceptibility differences between air and tissue

A B C

D E F

G H I

Hyperpolarization of 3He�

(A) (A)(A)(B)(B)

Overhauser effect �NOESY - Spectroscopy based on the Nuclear Overhauser Effect; �HOESY - Heterogeneous Nuclear Overhauser Effect Spectroscopy; �ROESY - Rotational Frame Nuclear Overhauser Effect Spectroscopy; �TRNOE -Transferred Nuclear Overhauser Effect.�DNP- Dynamic Nuclear Polarization �

Hyperpolarization of 13C via DNP�

Fig. 4. (A) 13C spectrum of urea (natural abundance 13C) hyperpolarized by the DNP-NMR method. The concentration of urea was 59.6mM,and the polarization was 20%. (B) Thermal equilibrium spectrum of the same sample at 9.4 T and room temperature. This spectrum is acquired under Ernst-angle conditions (pulse angle of 13.5° and repetition time of 1 s based on a T1 of 60 s) with full 1H decoupling. The signal is averaged during 65 h (232,128 transients).

Hyperpolarized 13C images�13C coronal projection images of a rat. The image acquisitions were started immediately (a) and (2) seconds after completing the injection of the contrast agent(urea solution) . The scan time of each image was 0.24s. �

1H coronal image of a rat �• 2D 1H coronal image obtained from a rat. The total scan time was 1.7s.�

Metabolic Imaging by Hyperpolarized 13C Magnetic Resonance Imaging for In vivo

Tumor Diagnosis�Klaes Golman, René in't Zandt, Mathilde Lerche, Rikard Pehrson, and Jan Henrik Ardenkjaer-Larsen�

Overview of the major energetic metabolic pathway of the cell.

Golman K et al. Cancer Res 2006;66:10855-10860

©2006 by American Association for Cancer Research

Location of the image slab in the rat and the corresponding transversal 1H-NMR image.

Golman K et al. Cancer Res 2006;66:10855-10860

©2006 by American Association for Cancer Research

Ultra high field MRI �

•  1.5T clinical scanner�•  Evolved to 3T and

7T�•  Multiple RF coil

arrays has been introduced for acceleration image acquisition �

7T  whole  body  MRI  scanner  

MPRAGE Axial�3T 7T 3T CE

FLAIR Axial�3T 7T

Phase  Contrast  MRA  

3T   7T  

SNR  Map  of  23Na  Head  Images  at  7T  with    12  Channel  -­‐RF  Coil  

4x4x12 mm TE: 550 µs, TR: 25 ms 30 averages Spoiled gradient half-echo with acquisition-weighted half-Fourier readout

SNR

Sodium MRI and AD 3T�

[ROI located in the hippocampus. This 19% increase [Na] may be due to: 1.  An increase in extra-cellular volume of sodium. 2.  AD-related pathology resulting in an increase in [Na].

[Na] was 99.6mM and 83.6mM in the AD and control brains, respectively

Mellon et al, AJNR, 2009

Spin �•  Spin of a particle is its intrinsic angular momentum�•  The total angular momentum spin I �

•  For spin ½ , the magnitude is= 0.866 h�•  It is purely quantum mechanical phenomena�•  Spin angular momentum is quantized�•  It can only have values –I to I �•  For Spin ½, it can only have -1/2 and 1/2�•  Unpaired electrons, neutrons, and protons

each possess a spin of 1/2�

�

I(I +1)

Properties of particles�Particle� Rest mass

(kg)�Charge� Spin �

Electron � 9.109 10-30� -e� 1/2�

Neutron � 1.675 10-26�

�0� 1/2�

Proton � 1.673 10-26�

�+e� 1/2�

Photon � 0� 0� 1 �

Nuclear Spin �

•  Shell model for the nucleons�•  Like electrons, nucleons fill orbitals. �•  Spin can pair up when the orbitals fill and

cancel out.�•  Every element in the periodic table has an

isotope with a non zero nuclear spin.�

Spin properties�•  Nuclear spin may be related to the nucleon composition of a

nucleus: �•  Fermions: Odd mass nuclei �

–  (i.e. those having an odd number of nucleons) have fractional spins. Examples are I = 1/2 ( 1H, 13C, 19F ), I = 3/2 ( 11B ) & I = 5/2 ( 17O ).�

•  Bosons: Even mass nuclei �–  composed of odd numbers of protons and neutrons have integral spins.

Examples are I = 1 ( 2H, 14N ).       �•  Even mass nuclei composed of even numbers of protons and

neutrons have zero spin ( I = 0 ). �–  Examples are 12C, and 16O.�

Nuclear spins�Nuclei�(mass #)�

Unpaired protons�

Unpaired Neutrons�

Net Spin �

γ(MHz/T)�

1H � 1 � 0� 1/2� 42.58�2H � 1 � 1 � 1 � 6.54�31P� 1 � 0� 1/2� 17.25�23Na � 1 � 2� 3/2� 11.27�14N � 1 � 1 � 1 � 3.08�13C�(6p+7n)�

0� 1 � 1/2� 10.7�

19F� 1 � 0� 1/2� 40.08�

Nuclear Spin �•  Spin 1/2 nuclei have a spherical charge distribution,

and their nmr behavior is the easiest to understand. �

•  Nuclei with nonspherical charge distributions may be analyzed as prolate or oblate spinning bodies.�

•  All nuclei with non-zero spins have magnetic moments (µ), but the nonspherical nuclei also have an electric quadrupole moment (eQ). �

Prolate and oblate�

Prolate Oblate

Sphere

http://en.wikipedia.org/wiki/Spheroid

Resonance�•  Two spin states in the

magnetic field�•  Energy needed to

cause a transition E=ħγBo �

•  When the energy of the photon matches the energy difference between the two spin states an absorption of energy occurs (Resonance!)�

E=ħγBo �

http://www.cis.rit.edu/htbooks/nmr/inside.htm

Spin in a magnetic field�•  In a magnetic field of

Bo, a particle with net spin can absorb a photon of frequency ν ν=(γBo)/2π

E=hν�For hydrogen, � γ=42.58 MHz/T�

http://www.cis.rit.edu/htbooks/nmr/inside.htm

CW experiment �

•  Field sweep �

http://www.cis.rit.edu/htbooks/nmr/inside.htm

CW experiment �

•  Frequency sweep �

http://www.cis.rit.edu/htbooks/nmr/inside.htm

What is the size of nuclear magnetic resonance signal?�

•  What is the net magnetization from a collection of nuclear spins or from a sample?�

Boltzman Distribution �•  Magnetic field due to each

spin in each spin pocket is represented by a magnetization vector�

•  At room temperature, the number of spins in the lower energy level, N+, slightly more than that in upper level N-. �

•  N-/N+=exp(-ΔE/kT) �•  =1-(ΔE/kT)�

�

http://www.cis.rit.edu/htbooks/nmr/inside.htm

Boltzman factor�•  Boltzman factor�•  b=(N+-N-)/N=ΔE/2kT �•  K=1.3805x10-23 J/Kelvin �

•  T=300 k �•  ΔE= hν=6.626x10-34 Js x100 MHz �•  b= 7.99 x10-6�

•  How is the Boltzman factor changes with Bo and or T?�

Larmor Precession: �Spinning top�

•  Rapidly spinning top will precess in a direction determined by the torque exerted by its weight �

•  The torque. �

Nuclear magnetic dipole moment �•  Associated with each rotating

object there will be a angular momentum�

•  Each nuclear spin possesses a magnetic moment arising from the angular momentum of the nucleus�

•  The magnetic moment is a vector perpendicular to the current loop �

•  In a magnetic field (B) the magnetic moment will behave like magnetic dipole�

Larmor frequency�•  When a magnetic moment

directed at some angle w.rt. Bo direction, the field will exert a torque on the magnetic moment. This causes it to precess about the magnetic field direction.�

•  Torque is the rate of change of the nuclear spin angular momentum I �

Larmor precession �

�

τ =ΔIΔt

=I sinθΔφ

Δt

�

τ = µBsinθ =e2me

IBsinθ

�

ωLarmor =dφdt

=e2me

B

�

ωLarmor = γB0

Larmor precession �

http://www.quantum-physics.polytechnique.fr/en/

larmor.html��

Larmor Precession �

•  Precession of the magnetization vector around the z-axis of the magnetic field �

Rotating frame of reference�•  In the laboratory frame

the magnetization vector precess at the Larmor frequecny.�

•  To probe the changes induced in the frequency it is convenient to work in a rotating frame of reference�

•  In the rotating frame the magnetization vector, at equilibrium appears stationery.�

http://www.cis.rit.edu/htbooks/nmr/inside.htm

Magnetization vector�

•  Bo is along z-axis �•  Equilibrium

magnetization Mo is along z-axis�

•  Mx and My =0�

http://www.cis.rit.edu/htbooks/nmr/inside.htm

Rotating frame �

•  In the rotating frame the magnetization appear stationery.�

•  It can only change in the magnitude in response to perturbations�

http://www.cis.rit.edu/htbooks/nmr/inside.htm

Rotating frame vs Laboratory frame�•  Magnetization trajectory following RF field in �

•  Rotating frame�Laboratory frame�

http://www.cis.rit.edu/htbooks/nmr/inside.htm

Bloch’s NMR probe�

MRI: Magnet and Coils �

300-900 MHz 8.5-300 MHz

MRI: Magnet and Coils�

5-10 ml 50-4000 ml

MRI scanner�

MRI �

Water Fat

Bulk Spatial Water

Lipid

MRS�

MRS at 7T�

GABA GABA

GABA Modulation at 7T

Glu

Elevation of Glu in MS�•  A. 8 ml SVS

surrounding an acute enhancing lesion �

•  Chronic lesion �•  Total time for

one voxel is ~10 minutes�

•  Srinivasan, Barin, 128, 1016(2005) �

2D COSY of human brain �

Figure 1: Localized correlation spectrum in a 68-year-old patient with GBM. Spectroscopy was performed at 3.0 T by using a 32-channel head coil and a voxel size (shown in inset) of 25 3 25 3 20 mm 3 , increment size of 0.8 msec, 64 increments, eight averages per increment, repetition time of 1.25 seconds, total experimental time of 11 minutes, acquired vector of 1024 points, acquisition time of 512 msec, spectral width in F2 of 2000 Hz, and spectral width in F1 of 1250 Hz. In this case, the tumor fi lled the entire voxel; hence, the contribution from normal brain tissue is minimal. A summary of assignments and volumes of diagonal resonances and cross peaks is shown in the Table. Cr = creatine, Fuc = fucose, Glx = glutamate and glutamine, GPC = glycerophosphocholine, Icit = isocitrate, Lac = lactate, Lys = lysine/polyamine, PC = phosphocholine, Tau = taurine

Ramadan et al, Radiology: Volume 259: Number 2—May 2011

Current challenges�

•  Imaging single cell, and single molecule�

•  Protein misfolding �•  Prolonging spin relaxation �•  Limits on polarization �

•  Higher resolution �•  Real time functional mapping �

Course�•  Details on the spin-choreography in

different settings�– Theory�

• Bloch equations, FT, Relaxation, MRI, chemical exchange, PT, Density Matrix, Multispin-systems, Solidstate, Mutidimensional�

• Multiple quantum, Quadrupolar nuclei etc.�– Practicals�– Protein structure�– Structure and function of human organs�–  applications in biomedicine/clinical�