Embed Size (px)
Citation preview
Basic principles of nuclear magnetic resonance
NMR spectroscopy in biology and medicine
Andrea Dóczy-Bodnár
Topics discussed in the lecture:• Origin of the magnetic moment of atomic nuclei;
• The phenomenon of Nuclear Magnetic Resonance: formation and detection using 1H nucleus as an example
• Basic principles of NMR spectroscopy, applications in biology/biochemistry
• Basic principles and applications of in vivo Magnetic Resonance Spectroscopy
Aim:• Understanding the principles of NMR phenomenon;
• Understanding the principles behind the medical and spectroscopical applications
of NMR;
• To get introduction to NMR spectroscopy and in vivo MR spectroscopy.
Overwiev
2
Relevant page numbers in the textbook:
- X/4.1 Physical principles of NMR (pages 596-602, ESR is not included)
Interconnections with previous Biophysics and other studies
• Composition of the atomic nucleus, properties of nucleons, shell model of the
nucleus;
• Electron spin, spin quantum number, magnetic spin quantum number;
• Behavior of a magnetic dipole in a static magnetic field.
3
Origin of the magnetic moment of atomic nuclei I.
• proton, neutron intrinsic angular momentum (spin) (gyroscope
model); I=1/2 (similar to electrons)
• overall spin of an atomic nucleus depends on the composition (see next slide)
• charge (or electric dipole) and spin magnetic moment(uneven distribution of quarks neutrons are electric dipoles magnetic moment)
• spin, magnetic moment – both are vector quantities
LN: nuclear spinMN: nuclear magnetic momentI: spin quantum number N: nuclear magnetongN: nuclear g-factorγN: gyromagnetic ratiogN and γN depend on the type of the nucleus
2h
!
Supplementary information
1 (1) NL I( I ) (2)N N NM L
2 (4)N pe m (3)N N NN
M g
L
A
Deutérium atommagja (https://chem.libretexts.org/)
B
no unpaired nucleon
1 unpaired nucleon(proton or neutron)
2 unpaired nucleons(1 proton + 1 neutron)
2H (deuterium)I=1
S=1/2
4He (helium)I=0S=0
Origin of the magnetic moment of atomic nuclei II.!
• Shell model of the nucleus: protons and neutrons fill their energy levels independently, in a pairwise fashion
• For a pair of protons or neutrons: spins have opposite directions they cancel out each other• Unpaired proton + unpaired neutron spins are parallel, they do not cancel each other!• At least one unpaired nucleon the net nuclear spin is different from zero nuclear magnetic moment
Some NMR compatible nuclei used in biology and medicine
• 1 proton, I=1/2• high gyromagnetic ratio• abundance in living organisms, organic compounds
!
mI= -1/2; β
mI= +1/2; α
mI=+1/2; α
mI=-1/2;
f0
f0
Larmor precession
Behavior of a ½-spin nucleus (e.g. 1H) in a magnetic field (B0) I.(simplified explanation: classical mechanics spiced with a drizzle of quantum mechanics)
• alignment (mI=±1/2) + precession (Larmor precession)• 2 possible alignments relative to B0 (in general: 2I+1)
• the two spin states have different Epot (Zeeman-effect)
0
1( ) (2a)
2pot N NE g B
0
1( ) (2b)
2pot N NE g B
N S
0 0 cos (1)pot N NE M B M B
M
Equations on this page are not required for the exam!
!
A B
C
mI= -1/2; β
mI= +1/2; α
mI=+1/2; α
mI=-1/2;
f0
f0
quantized excitation→ resonance absorption transition
Behavior of a ½-spin nucleus (e.g. 1H) in a magnetic field (B0) II.
electromagnetic field (oscillating magnetic field component!)
radiofrequency!
!
(1)
(2)
NE B
E hf
0
0
0 0 (3)2
Nf B
resonance frequency/Larmorfrequency
C. Boesch, Molecular aspects of medicine. 1999. 20: 185-318.
NMR works in the radiofrequency range → non-ionising radiation with high penetration depth! !
f depends on:• type of the nucleus (γN), external magnetic field
• for a certain type of nucleus (e.g. 1H) determined exclusively by the observed field
• factors influencing the magnetic field field the observed local magnetic field (Blocal)differs from B0 different resonance frequency information!
What can modulate the magnetic field observed by the nucleus?• chemical environment (structure of the molecule) → NMR spectroscopy• introducing spatial variations (applying magnetic field gradients) → MR imaging
Area under the line ~ concentration of nuclear spins
NMR spectral band
absorption
2 N
localf B
f
A B
Primary information in methods based on NMR phenomenon: resonance frequency + (relative) amount of nuclei with NMR spectrum
The NMR spectrum !
Behavior of a ½-spin nucleus (e.g. 1H) in a magnetic field (B0) III.
Population of spins:
But! Spins can be found in both states even without excitation – see next slide
What do we expect?
B0
!
mI=1/2; α
mI=-1/2;
E
kTN
eN
B0
M0
• thermal equilibrium• nonstop flips between the 2 levels (molecular motions oscillating magnetic fields micro-NMR transitions)
• slightly more spins at the lower level ( Boltzmann-distribution)
• population difference (Boltzmann-excess)
NMR signal – „extra” transitions due to excitation (emerges from the noise)
macroscopic magnetization (M0) along the z-axis (direction of B0) (longitudinal magnetization; MZ is
maximal)
random distribution of the xy components of magnetic moments no net magnetization in the xy plane (transversal magnetization ; MXY= 0)
The size of MZ depends on:• occupancy of the 2 spin states (B0; T)• amount/concentration of nuclei (spins)
Behavior of a ½-spin nucleus (e.g. 1H) in a magnetic field (B0) IV.
A B C
!
• disturbance of the equilibrium relaxation processes when the disturbance is over information about structure, dynamics (molecular motions) of the system
C. Boesch, Molecular aspects of medicine. 1999. 20: 185-318.
The stronger the external magnetic field the larger the energy difference (E) the larger theBoltzmann-excess
• greater signal-to-noise ratio greater sensitivity• larger M0
Behavior of a ½-spin nucleus (e.g. 1H) in a magnetic field (B0) V.
!
„Continous wave” NMR experiments
• constant magnetic field – frequency is varied• constant frequency – magnetic field is swept
absorption (→NMR signal) – where the resonance condition is fulfilled
Fourier transform or pulse NMR
How can we detect the resonance frequency?
!• the signal is detected after a short and intense RF pulse (not during excitation!)
• simultaneous excitation of all frequencies (bandwidth
of the pulse!)
• behavior of the macroscopic magnetization is examined
excitation – disturbance of the equilibriumdetection – during relaxation
• in addition to the usual spectral parameters (frequency, amount of absorbing nuclei) other information can also be gained relaxation parameters dynamic properties of the spin system)• importance of 90-degree pulse – formation of maximal transverse magnetization the signal is provided by the transverse magnetization!
Effect of the Rf pulse on the macroscopic magnetization I.
Rf pulse
magnetic component (B1) oscillates in the xy plane
90-degree Rf pulse
Excitation with the Rf pulse macroscopic magnetization changes as well: due to the magnetic component of the Rf field (B1) oscillating in the xy-plane it is “bounced off” of the equilibrium position (about B1,
toward the xy-plane)
• extent of „tipping out” depends on the strength and duration of the Rf pulse (e.g. 90-degree, 180-degree pulses)
• 90-degree pulse formation of maximum size transverse magnetization
5*
!
Excitation with the Rf pulse macroscopic magnetization changes as well: due to the magnetic component of the Rf field (B1) oscillating in the xy-plane it is “bounced off” of the equilibrium position (about B1,
toward the xy-plane)
• extent of „tipping out” depends on the strength and duration of the Rf pulse (e.g. 90-degree, 180-degree pulses)
• 90-degree pulse formation of maximum size transverse magnetization
How can we explain it?
extra transitions occupancy of the energy levels is modulated magnitude of MZ (longitudinal
magnetization) changes
fraction of spins will be “in phase” in the xy-plane (due to B1) formation of MXY (transverse magnetization, originally it was zero)
e.g. for the 90-degree pulse: phase coherence + equal occupancy of the two levels MZ = 0, MXY is maximal
M0 is stationary ( its direction is identical
with the axis of precession, i.e. B0)
direction of net magnetization is different from B0
precession of macroscopic magnetization
about B0 should be taken into account
this precession creates a fluctuating magnetic
field induces alternating voltage in a standing
detector coil NMR signal (the receiver and the
transmitter coil is the same)
0M
0B
x
y
z
RF impulzus
x
zM
0B
y
z
1B
precession of individual spins about B0 (Larmor precession) in theory the net magnetization
should also precess about B0 at the same frequency
With appropriate methods, the effect of B1 and the precession about
B0 can be separated (rotating reference frame – not discussed here)
the effect of pulse can be examined separately
!
16
Supplementary material
Effect of the Rf pulse on the macroscopic magnetization II.
Consequences of the 90-degree pulse
90º-degree Rf pulse (special importance!) –oscillating magnetic field in the XY plane macroscopic magnetization is rotated to the xy-plane: longitudinal magnetization disappears, transversal magnetization is formed
Equilibrium macroscopic magnetization:
macroscopic magnetization (M0) in the direction of B0 (z-axis, longitudinal magnetization)xy components of the individual magnetic moments are randomly aligned (no magnetic field in this plane) no macroscopic magnetization in the xy plane (transversal magnetization; MXY=0)
MXY produced by the 90-degree pulse precesses (spins precess in phase, at least for a while – see next slide) this precession creates an alternating magnetic field which can induce electric signal in a receiver coil NMR signal
90-degree pulse z z
yy
Consequences of the 90-degree pulse: MZ=0 ( equal occupancy of the two states)
MXY becomes nonzero (← phase coherence of spins)
What happens after the 90-degree pulse: relaxation processes, signal detection I.
C. Boesch, Molecular aspects of medicine. 1999. 20: 185-318.
Spin-lattice relaxation (T1): recovery of MZ
spin-spin relaxation (T2):decay of MXY
The systems tends to recover the equilibrium after the pulse is switched off relaxation
T1 (spin-lattice) relaxation: excited spins release their excess energy in the form of heat to the environment (other spins or „lattice”), recovery of longitudinal magnetization (exponential growth)
T2 (spin-spin) relaxation: decay of MXY („dephasing” of spins), the transient phase coherence produced by the pulse is gradually lost (exponential decay)
The two processes are parallelT1≥ T2
In biological tissues: T1>>T2
(the two processes can be separated in time)
!
5*
Relaxation processes, signal detection II.
precession of MXY about B0 induced voltage in the receiver coil free induction decay (FID) – NMR signal spectral information (frequency, intensity) can be derived by Fourier transformation (FT) (computer-assisted process)decay of the signal depends on T2
Supplementary information: due to magnetic field inhomogeneity the signal loss can be faster, T2*<T2
(methods are available to compensate for the effect of field inhomogeneity)
FT
!
FT
FID signal with T2 time constant
receiver
coil
time
Significance of relaxation processes
• width of NMR signal 1/T2
• scheduling NMR and MRI experiments
detection (T2, T2*) timing of detection and repetition
signal amplitude
repetition of sequences (T1)
• relaxation times depend on molecular motions (fluctuating magnetic fields)
dynamic properties of the spin system
e.g. tissue type-specific relaxation times in MRI
!
• pulse is short (tpulse) compared to the signal (10µs)• usually complex pulse sequences are applied• sequences are repeated improving signal-to-noise ratio• NMR signal is generated by the precession of MXY a pulse causing the appearance of MXY
should be involved (90-degree pulse)• relaxation times adjustment of repetition time, timing of detection
90o pulse
FID
Homogenous magnetic field
Practical aspects of NMR investigations
!
14.1 Tesla, 600 MHz(high resolution, analytical NMR)
1.5 Tesla, 64 MHz(medical MRI equipment)
C. Boesch, Molecular aspects of medicine. 1999. 20: 185-318.
NMR spectroscopy
Nuclear shielding (σ): caused by the magnetic field generated
by the circulating electrons at the place of the nucleus
depends on the chemical environment; only slight differences
different local magnetic field different resonance frequency (chemical shift)
Spin-spin coupling → fine structure of spectraMagnetic fields of nearby spins can also modulate the magnetic field observed by the nucleus, therefore the respective resonance frequency; the effect is lower than the shielding effect of electrons
0 (1 ) (1)effB B
!
610 (ppm) (2)ref
ref
f f
f
Determination of the chemical shift (δ)Absolute value of frequency, and so that of the chemical shift, depends on the applied external field in practice it is standardized using a reference material Chemical shift determined this way is independent of the applied field spectra recorded in different fields can be compared
f: frequency detected for the sample, fref – frequency of the reference material
23
1H-NMR spectrum of ethanol
1.5 Tesla
0.7 Tesla (Arnold et al., 1951)
CH3
CH2
OH
C. Boesch, Molecular aspects of medicine. 1999. 20: 185-318.
!
For molecules with more complicated structure the NMR spectrum will be also more
complex.
What is NMR spectroscopy good for?
• molecular structure analysis: composition, configuration, conformation, complexation;• analysis of molecular dynamics: intramolecular mobility, diffusion, exchange processes;• molecular interactions, binding processes;
„The end justifies the means.” Specialized pulse sequences and methodologies depending on the purpose of the investigation.Target nucleus (1H or other), pulse sequence (type, number and timing of the applied Rf. pulses) and otheracquisition parameters (e.g. solvent) depend on the desired information.
• quantitative NMR: analyte concentration, purity, composition of mixtures, etc.
Instant coffee (1H-NMR spectrum) NMR in Biology
Supplementary material
NMR spectroscopy in biomolecular research
• high-resolution structures of proteins (and other macromolecules) can be derived in solutioncomplementary to crystallography;
• dynamic processes can be followed on a time scale ranging from picoseconds to seconds• mapping interactions (e.g. protein/ligand interactions, etc.)• high resolution information on partially or wholly intrinsically unstructured proteins• 1H is the major target, but other NMR compatible isotopes (13C, 15N, 31P, etc.) are also examined –
isotope enrichment may be required!• complex pulse sequences, advanced techniques (e.g. multi-dimensional spectra – correlated
measurements of different NMR parameters)
Limitations:• low inherent sensitivity and high complexity of NMR data• size limit in structure determination: 35-50 kDa• limitations are (at least partially) alleviated by
developments in spectrometer technology, methodology and data processiondevelopments in biochemical methods (isotope labeling, recombinant technology, etc.)
Supplementary material
NMR spectra of proteins: 1D vs. multidimensional NMR
• 1D 1H-NMR protein spectra are rather complex (signal overlap)
• multidimensional (2, 3 or 4D) experimentsadditional spectral dimension(s)2 (or more) parameters are plot in correlationwith each other
• homo- and heteronuclear experiments• different combinations of chemical shifts and other NMR
parameters
Supplementary material
Example for the application of ex vivo metabolom analysis by NMR spectroscopy
Monitoring of Exogenous γ-Hydroxybutyric Acid in Body Fluids by NMR Spectroscopy. (Anal. Chem., 2017, 89 (16), pp 8343–8350.) - a future method?
Supplementary material
Magnetic resonance spectroscopy in living systems I. - in vivo MRS
• In vivo analytical technique: detection of different substances (mostly metabolites) on the basis of their characteristic NMR spectral peak „fingerprint” spectra
• function, damage of brain, muscles, etc.• biochemical information, non-invasive• 1H, 31P, 13C …• different techniques: e.g. single-voxel MRS, MRS imaging (simultaneous examination of multiple
voxels) , functional MRS …
• In general an anatomical MR image is recorded at first to determine the location of MRS examination• Complements information derived from MR images
e.g. location of a tumor (MRI) vs. aggressivity
• suppression of water signal is necessary! (relative amount of water is higher than that of the metabolites)
• higher magnetic field, higher detection sensitivity is required than for MRI:in case of 1H MRS the same MR equipment can be used as for MR imaging, but in the case ofother nuclei special equipments are required (different frequency, sensitivity)
!
Metabolite ppm Role Anomaly
myoInositol 3,6 Glial marker ↑ : gliomas, MS reactional gliosis↓ : herpetic encephalitis
Choline 3,2 Cell membrane metabolism marker ↑ : tumors, demyelinization
CreatinePhosphocreatine
3,0 Energy metabolism marker, serves as reference peak as it is ~ constant
GABA, GlutamateGlutamine
2,1-2,5 Intracellular neurotransmitter marker
↑ : hepatic encephalopathy
N-Acetyl-Aspartate
2,0 Healthy neuron marker ↑ : Canavan's disease↓ : neuronal distress
Succinate 2,4
Dis
ease
s
Pyogenic abscess
Acetate 1,9 Abscess
Alanine 1,5 (doublet)
Meningioma, Abscess
Lactate 1,3(doublet)
Ischemia, convulsions, tumors, mitochondrial cytopathies
↑ : anaerobic metabolism
Free lipids 0,91,4
Necrotic tumor (high grade)
Aminoacids 0,97 Pyogenic abscess
Principal metabolites in 1H-MRS
Supplementary material
In vivo MRS imaging (MRSI)
OligodendrogliomaMapping choline/NAA ratio gained from MRS spectra highest intensity at the position of the tumor
GlioblastomaEnrichment of contrast material (MRI) – defective blood-brain barrierDifferent MRS spectra tumor heterogeneity
MRI MRS
living
necrotic
MRI MRS
MRS – in a single voxel Choline/NAA ratio
Eur Biophys J (2010) 39:527–540
5*
1H NMR spectra (360 MHz) of HeLa cells suspended in PBS/D2O before treatment and at several time points following treatment with etoposide
Nature (2001) 8: 219-224
Magnetic resonance spectroscopy in living systems II.
Supplementary material
Ask yourself:- What property makes atomic nuclei suitable for NMR investigations? - What makes the 1H nucleus the most important target nucleus in biological and medical
applications of NMR? - What does the NMR resonance frequency depend on?- What kind of qualitative and quantitative information are carried by NMR spectra?
As a medical doctor:- What can be the advantage of in vivo MRS examinations for the patients compared to
other analytical techniques?- What are the disadvantages of in vivo MRS investigations?
Conclusion
